NAMIC Wiki - User contributions [en]

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T14:44:54Z

Cpoynton: /* Key Investigators */

__NOTOC__

{|
|[[File:PD susc est ppm1.png|thumb|200 px|Susceptibility Map 1]]
|[[File:PD susc est ppm2.png|thumb|200 px|Susceptibility Map 2]]
|}

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells
* UCLA: Andrei Irimia

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>

* Algorithm: Improved background field correction, resulting in improved mean susceptibility values:

Thalamus ( -0.06 ppm )
Caudate (0.02 ppm)
Putamen (0.05 ppm)
Globus Pallidus (0.11 ppm)

* Applications: Obtained 3 TBI cases from DBP 3, which we are currently analyzing

</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T14:27:40Z

Cpoynton: /* Key Investigators */

__NOTOC__

{|
|[[File:PD susc est ppm1.png|thumb|200 px|Susceptibility Map 1]]
|[[File:PD susc est ppm2.png|thumb|200 px|Susceptibility Map 2]]
|}

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>

* Algorithm: Improved background field correction, resulting in improved mean susceptibility values:

Thalamus ( -0.06 ppm )
Caudate (0.02 ppm)
Putamen (0.05 ppm)
Globus Pallidus (0.11 ppm)

* Applications: Obtained 3 TBI cases from DBP 3, which we are currently analyzing

</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T14:27:12Z

Cpoynton: /* Key Investigators */

__NOTOC__

{|
|[[File:PD susc est ppm1.png|thumb|200 px|Susceptibility Map 1]]
|[[File:PD susc est ppm2.png|thumb|200 px|Susceptibility Map 2]]
|}

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>

* Algorithm: Improved background field correction

resulting in improved mean susceptibility values:
Thalamus ( -0.06 ppm )
Caudate (0.02 ppm)
Putamen (0.05 ppm)
Globus Pallidus (0.11 ppm)

* Applications: Obtained 3 TBI cases from DBP 3, which we are currently analyzing

</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T14:26:29Z

Cpoynton: /* Key Investigators */

__NOTOC__

{|
|[[File:PD susc est ppm1.png|thumb|200 px|Susceptibility Map 1]]
|[[File:PD susc est ppm2.png|thumb|200 px|Susceptibility Map 2]]
|}

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>

* Algorithm: Improved background field correction

* resulting in improved mean susceptibility values in Thalamus ( -0.06 ppm ), Caudate (0.02 ppm), Putamen (0.05 ppm), Globus Pallidus (0.11 ppm)

* Applications: Obtained 3 TBI cases from DBP 3, which we are currently analyzing

</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T14:26:08Z

Cpoynton: /* Key Investigators */

__NOTOC__

{|
|[[File:PD susc est ppm1.png|thumb|200 px|Susceptibility Map 1]]
|[[File:PD susc est ppm2.png|thumb|200 px|Susceptibility Map 2]]
|}

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>

* Algorithm: Improved background field correction

resulting in improved mean susceptibility values in Thalamus ( -0.06 ppm ), Caudate (0.02 ppm), Putamen (0.05 ppm), Globus Pallidus (0.11 ppm)

* Applications: Obtained 3 TBI cases from DBP 3, which we are currently analyzing

</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T14:25:51Z

Cpoynton: /* Key Investigators */

__NOTOC__

{|
|[[File:PD susc est ppm1.png|thumb|200 px|Susceptibility Map 1]]
|[[File:PD susc est ppm2.png|thumb|200 px|Susceptibility Map 2]]
|}

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>

* Algorithm: Improved background field correction

resulting in improved mean susceptibility values in Thalamus ( -0.06 ppm ), Caudate (0.02 ppm), Putamen (0.05 ppm), Globus Pallidus (0.11 ppm)
* Applications: Obtained 3 TBI cases from DBP 3, which we are currently analyzing

</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T14:25:28Z

Cpoynton: /* Key Investigators */

__NOTOC__

{|
|[[File:PD susc est ppm1.png|thumb|200 px|Susceptibility Map 1]]
|[[File:PD susc est ppm2.png|thumb|200 px|Susceptibility Map 2]]
|}

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>

* Algorithm: Improved background field correction
- resulting in improved mean susceptibility values in Thalamus ( -0.06 ppm ), Caudate (0.02 ppm), Putamen (0.05 ppm), Globus Pallidus (0.11 ppm)
* Applications: Obtained 3 TBI cases from DBP 3, which we are currently analyzing

</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T14:05:58Z

Cpoynton:

__NOTOC__

{|
|[[File:PD susc est ppm1.png|thumb|200 px|Susceptibility Map 1]]
|[[File:PD susc est ppm2.png|thumb|200 px|Susceptibility Map 2]]
|}

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>

* Algorithm: Improved background field correction
* Applications: Obtained 3 TBI cases from DBP 3, which we are currently analyzing

</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T14:00:18Z

Cpoynton:

__NOTOC__

{|
|[[File:PD susc est ppm1.png|thumb|200 px|Susceptibility Map 1]]
|[[File:PD susc est ppm2.png|thumb|200 px|Susceptibility Map 2]]
|}

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>



</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T13:59:10Z

Cpoynton:

__NOTOC__

{|
|[[File:PD susc est ppm1.png|thumb|200 px|Susceptibility Map]]
|[[File:PD susc est ppm2.png|thumb|200 px|Susceptibility Map 2]]
|}

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>



</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

File:PD susc est ppm2.png

2011-06-24T13:58:30Z

Cpoynton:

File:PD susc est ppm1.png

2011-06-24T13:58:20Z

Cpoynton:

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T13:35:36Z

Cpoynton:

__NOTOC__

{|
|[[File:Namic pic.bmp|thumb|200 px|Susceptibility Map]]
|[[File:PD susc est mask2 fixed snap2.png|thumb|200 px|Susceptibility Map 2]]
|}

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>



</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T13:34:47Z

Cpoynton:

__NOTOC__

{|
|[[File:Namic pic.bmp|200 px|Susceptibility Map]]
|[[File:PD susc est mask2 fixed snap2.png|200 px|Susceptibility Map 2]]
|}

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>



</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T13:34:17Z

Cpoynton:

__NOTOC__

{|
|[[File:Namic pic.bmp|thumb|Susceptibility Map]]
|[[File:PD susc est mask2 fixed snap2.png|thumb|Susceptibility Map]]
|}

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>



</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

File:PD susc est mask2 fixed snap2.png

2011-06-24T13:33:20Z

Cpoynton:

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T13:33:04Z

Cpoynton:

__NOTOC__

{|
|[[File:Namic pic.bmp|thumb|Susceptibility Map]]

|}

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>



</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T13:31:42Z

Cpoynton:

__NOTOC__

{|
|[[File:Namic pic.bmp|thumb|Susceptibility Map]]
|[[File:PD susc est mask2 fixed snap2.png|thumb|Susceptibility Map 2]]
|}

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>



</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

File:PD susc est mask3 fixed snap2.png

2011-06-24T13:31:24Z

Cpoynton:

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T13:27:58Z

Cpoynton:

__NOTOC__

{|
|[[File:Namic pic.bmp|thumb|Susceptibility Map]]
|[[File:PD susc est mask2 fixed.png|thumb|Susceptibility Map 2]]
|}

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>



</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T13:27:18Z

Cpoynton:

__NOTOC__

{|
|[[File:Namic pic.bmp|thumb|Susceptibility Map]]
|[[File:PD susc est mask2 fixed.png|thumb|Susceptibility Map - Improved background field correction]]
|}

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>



</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T13:25:40Z

Cpoynton:

__NOTOC__
<gallery>
{|
|[[File:Namic pic.bmp|thumb|Susceptibility Map]]
|[[File:PD susc est mask2 fixed.png|thumb|Susceptibility Map - Improved background field correction]]
|}
</gallery>

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>



</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T13:25:25Z

Cpoynton:

__NOTOC__
<gallery>
{|
|File:Namic pic.bmp|thumb|Susceptibility Map]]
|File:PD susc est mask2 fixed.png|thumb|Susceptibility Map - Improved background field correction]]
|}
</gallery>

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>



</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T13:25:06Z

Cpoynton:

__NOTOC__
<gallery>
{|
|Image:Namic pic.bmp|thumb|Susceptibility Map]]
|Image:PD susc est mask2 fixed.png|thumb|Susceptibility Map - Improved background field correction]]
|}
</gallery>

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>



</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-24T13:24:20Z

Cpoynton:

__NOTOC__
<gallery>
{|
|Image:Namic pic.bmp|[[2011_Summer_Project_Week#Projects|Susceptibility Map]]
|Image:PD susc est mask2 fixed.png|[[2011_Summer_Project_Week#Projects|Susceptibility Map - Improved background field correction]]
|}
</gallery>

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>



</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

File:PD susc est mask2 fixed.png

2011-06-24T13:21:48Z

Cpoynton:

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-20T17:47:11Z

Cpoynton: /* Key Investigators */

__NOTOC__
<gallery>
Image:Namic pic.bmp|[[2011_Summer_Project_Week#Projects|Susceptibility Map]]
</gallery>

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show improved correlation with postmortem iron concentrations relative to competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>



</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-20T17:37:51Z

Cpoynton:

__NOTOC__
<gallery>
Image:Namic pic.bmp|[[2011_Summer_Project_Week#Projects|Susceptibility Map]]
</gallery>

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show qualitative improvement over two methods commonly used to infer underlying susceptibility values,
and quantitative susceptibility estimates show better correlation with postmortem iron concentrations than competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>



</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-20T17:37:25Z

Cpoynton:

__NOTOC__
<gallery>
Image:Namic pic.bmp|[[2011_Summer_Project_Week#Projects|Projects List]]
</gallery>

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show qualitative improvement over two methods commonly used to infer underlying susceptibility values,
and quantitative susceptibility estimates show better correlation with postmortem iron concentrations than competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>



</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

File:Namic pic.bmp

2011-06-20T17:36:29Z

Cpoynton:

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-20T17:33:00Z

Cpoynton: /* Key Investigators */

__NOTOC__
<gallery>
Image:PW-MIT2011.png|[[2011_Summer_Project_Week#Projects|Projects List]]
</gallery>

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfields through application of the Laplacian.

Results show qualitative improvement over two methods commonly used to infer underlying susceptibility values,
and quantitative susceptibility estimates show better correlation with postmortem iron concentrations than competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>



</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

2011 Summer Project Week Quantitative Magnetic Susceptibility Mapping

2011-06-20T17:32:13Z

Cpoynton:

__NOTOC__
<gallery>
Image:PW-MIT2011.png|[[2011_Summer_Project_Week#Projects|Projects List]]
</gallery>

'''Full Title of Project'''

Quantitative Magnetic Susceptibility Mapping

==Key Investigators==
* MIT: Clare Poynton
* BWH: Sandy Wells

<div style="margin: 20px;">
<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Objective</h3>

Quantifying magnetic susceptibility in the brain from the phase of the MR signal provides a non-invasive means for measuring the
accumulation of iron believed to occur with aging and neurodegenerative disease.

We describe a variational approach to susceptibility estimation that incorporates a tissue-air atlas to resolve ambiguity
in the susceptibility estimates, while eliminating additional biasfi�elds through application of the Laplacian.

Results show qualitative improvement over two methods commonly used to infer underlying susceptibility values,
and quantitative susceptibility estimates show better correlation with postmortem iron concentrations than competing methods.

The goal for this week is to apply this method to evaluate magnetic susceptibility of lesions associated with TBI.

</div>

<div style="width: 27%; float: left; padding-right: 3%;">

<h3>Approach, Plan</h3>
Our plan for the project week:
* Discuss applications with collaborators and try to refine the algorithm

</div>

<div style="width: 40%; float: left;">

<h3>Progress</h3>



</div>
</div>

<div style="width: 97%; float: left;">

==References==

</div>

Projects:QuantitativeSusceptibilityMapping

2011-03-27T22:40:27Z

Cpoynton: /* Forward Model (Eq. 1) */

= Introduction =

There is increasing evidence that excessive iron deposition in specific regions
of the brain is associated with neurodegenerative disorders such as Alzheimer's
and Parkinson's disease [1]. The role of iron in the pathogenesis of these diseases
remains unknown and is difficult to determine without a non-invasive method
to quantify its concentration in-vivo. Since iron is a ferromagnetic substance,
changes in iron concentration result in local changes in the magnetic susceptibility of tissue.
In magnetic resonance imaging (MRI) experiments, differences
in magnetic susceptibility cause perturbations in the local magnetic field, which
can be computed from the phase of the MR signal (in a gradient echo sequence, the observed field is proportional to the MR phase).

= Description =

In MRI, magnetic susceptibility differences cause measurable perturbations in the local magnetic field that can be modeled as the convolution of a dipole-like kernel with the spatial susceptibility distribution. In the Fourier domain, the kernel exhibits zeros at the magic angle, preventing direct inversion of the field map; also, limited observations make the problem ill-posed. The observed data is also corrupted by confounding fields (ie. those from tissue/air interfaces, mis-set shims, and other non-local sources). Previous work has shown that MR images can be successfully reconstructed from under-sampled observations by exploiting the sparsity of in-vivo data under various transforms using methods from compressed sensing [2]. In susceptibility estimation, the forward model results in under-sampling of the data in the Fourier domain, but accurate estimates can be obtained using the Laplacian and L1 norm, which promote sparse solutions while removing external field artifacts. Our variational method for susceptibility estimation is described in Figs. 1-2.

{|
|[[File:Namic wiki fig1.png|thumb|400px|Fig 1. Relevant notation]]
|}

{|
|[[File:Latex pdf zoomed to paint equations.PNG|thumb|400px|Fig 2. Applying the Laplacian to the forward model in [1] eliminates non-local phase artifacts to give [2]. The first term in [3] provides regularization, penalizing large differences in spatial frequency relative to Magnitude data, while the second penalizes departures from [2], enforcing agreement of high frequency phase effects.]]
|}

== Forward Model (Eq. 1) ==

The forward model relates the perturbing field to the unknown susceptibility through a local term and convolution of the second z-derivative of the Green’s function of the Laplacian with the unknown susceptibility map [3].

== Bias Field Elimination (Eq. 2) ==

Applying the Laplacian removes non-local phase effects such as shim fields, which are a solution to the Laplace equation.

== Objective Function (Eq. 3) ==

The first term provides regularization, penalizing solutions with large differences in spatial frequency structure relative to the magnitude image.
The second term penalizes departures from Eq. 2, by enforcing agreement of high frequency phase effects while eliminating low order bias fields.

== Data Acquisition ==

Cylindrical and rectangular phantoms were made using Magnevist (gadopentetate dimeglumine) solutions of 0.5, 1.0, 2.0, and 3.0 mM corresponding to susceptibility values of 0.15, 0.31, 0.62, and 0.94 ppm [4,5]. Field maps were obtained using a 3D multi-echo GRE sequence on a 3T Siemens Trio MRI.

= Results =

Application of the Laplacian removes substantial inhomogeniety in the field map in both phantoms as shown in Fig. 3 (Rectangular phantom) and Fig. 4 (Cylindrical phantom). Rectangular phantom: mean estimated susceptibility values for water and Magnevist were -9.049 and 0.6273 ppm, with true values of -9.050 and 0.6270 ppm. Cylindrical phantom: the estimated susceptibility map allowed different concentrations of Magnevist to be clearly identified and reasonable estimates were obtained in the presence of significant noise and bias due to external field effects.

{|
|[[File:Box mag.jpg|thumb|300|Fig 3a. Magnitude Image]]
|[[File:Box fmap.png|thumb|300|Fig 3b. Field map]]
|[[File:Box fmap lp.png|thumb|300|Fig 3c. Laplacian of the Field]]
|[[File:Box susc.png|thumb|300|Fig 3d. Estimated Susceptibility (ppm)]]
|}

{|
|[[File:Cyl mag.png|thumb|300|Fig 4a. Magnitude Image]]
|[[File:Cyl fmap.png|thumb|300|Fig 4b. Field map]]
|[[File:Cyl fmap lp.png|thumb|300|Fig 4c. Laplacian of the Field]]
|[[File:Cyl susc.png|thumb|300|Fig 4d. Estimated Susceptibility (ppm)]]
|[[File:Susc plot2.png|thumb|100|Fig 4e. Estimated vs. True mean susceptibility values for each tube (ppm)]]
|}

= Future Directions =

Future work will focus on quantifying magnetic susceptibility and iron content in the brain. Further development of the method described above has generated the preliminary results shown below in Fig 5.

{|
|[[File:Miccai fig1 crop.png|thumb|600px|Fig 5. The field map (left), laplacian of the field (center) and estimated susceptibility map (right) for a young healthy subject is shown. Taking the Laplacian of the fieldmap successfully eliminates the substantial biasfields in the observed field. The estimated susceptibility map shares similar high frequency structure with the Laplacian of the observed field while low frequency structure is preserved by additional modeling constraints.]]
|}

= References =

1. Zecca L, et al. Nat Rev Neurosci, 5:863{73, Nov 2004.

2. Lustig M,et al. MRM. 2007. 58(6):1182.

3. Jenkinson M, et al. MRM. 2004. 52(3):471.

4. de Rochefort L, et al. MRM.2010. 63(1):194.

5. Weisskoff RM, et al. MRM. 1992. 24(2):375.

= Key Investigators =

* MIT: Clare Poynton, Elfar Adalsteinsson
* Harvard/BWH: William Wells
* Stanford: Adolf Pfefferbaum, Edith Sullivan

Projects:QuantitativeSusceptibilityMapping

2011-03-27T21:40:21Z

Cpoynton: /* Key Investigators */

= Introduction =

There is increasing evidence that excessive iron deposition in specific regions
of the brain is associated with neurodegenerative disorders such as Alzheimer's
and Parkinson's disease [1]. The role of iron in the pathogenesis of these diseases
remains unknown and is difficult to determine without a non-invasive method
to quantify its concentration in-vivo. Since iron is a ferromagnetic substance,
changes in iron concentration result in local changes in the magnetic susceptibility of tissue.
In magnetic resonance imaging (MRI) experiments, differences
in magnetic susceptibility cause perturbations in the local magnetic field, which
can be computed from the phase of the MR signal (in a gradient echo sequence, the observed field is proportional to the MR phase).

= Description =

In MRI, magnetic susceptibility differences cause measurable perturbations in the local magnetic field that can be modeled as the convolution of a dipole-like kernel with the spatial susceptibility distribution. In the Fourier domain, the kernel exhibits zeros at the magic angle, preventing direct inversion of the field map; also, limited observations make the problem ill-posed. The observed data is also corrupted by confounding fields (ie. those from tissue/air interfaces, mis-set shims, and other non-local sources). Previous work has shown that MR images can be successfully reconstructed from under-sampled observations by exploiting the sparsity of in-vivo data under various transforms using methods from compressed sensing [2]. In susceptibility estimation, the forward model results in under-sampling of the data in the Fourier domain, but accurate estimates can be obtained using the Laplacian and L1 norm, which promote sparse solutions while removing external field artifacts. Our variational method for susceptibility estimation is described in Figs. 1-2.

{|
|[[File:Namic wiki fig1.png|thumb|400px|Fig 1. Relevant notation]]
|}

{|
|[[File:Latex pdf zoomed to paint equations.PNG|thumb|400px|Fig 2. Applying the Laplacian to the forward model in [1] eliminates non-local phase artifacts to give [2]. The first term in [3] provides regularization, penalizing large differences in spatial frequency relative to Magnitude data, while the second penalizes departures from [2], enforcing agreement of high frequency phase effects.]]
|}

== Forward Model (Eq. 1) ==

The forward model relates the perturbing field to the unknown susceptibility through a local term and convolution of the second z-derivative of the Green’s function of the Laplacian [3].

== Bias Field Elimination (Eq. 2) ==

Applying the Laplacian removes non-local phase effects such as shim fields, which are a solution to the Laplace equation.

== Objective Function (Eq. 3) ==

The first term provides regularization, penalizing solutions with large differences in spatial frequency structure relative to the magnitude image.
The second term penalizes departures from Eq. 2, by enforcing agreement of high frequency phase effects while eliminating low order bias fields.

== Data Acquisition ==

Cylindrical and rectangular phantoms were made using Magnevist (gadopentetate dimeglumine) solutions of 0.5, 1.0, 2.0, and 3.0 mM corresponding to susceptibility values of 0.15, 0.31, 0.62, and 0.94 ppm [4,5]. Field maps were obtained using a 3D multi-echo GRE sequence on a 3T Siemens Trio MRI.

= Results =

Application of the Laplacian removes substantial inhomogeniety in the field map in both phantoms as shown in Fig. 3 (Rectangular phantom) and Fig. 4 (Cylindrical phantom). Rectangular phantom: mean estimated susceptibility values for water and Magnevist were -9.049 and 0.6273 ppm, with true values of -9.050 and 0.6270 ppm. Cylindrical phantom: the estimated susceptibility map allowed different concentrations of Magnevist to be clearly identified and reasonable estimates were obtained in the presence of significant noise and bias due to external field effects.

{|
|[[File:Box mag.jpg|thumb|300|Fig 3a. Magnitude Image]]
|[[File:Box fmap.png|thumb|300|Fig 3b. Field map]]
|[[File:Box fmap lp.png|thumb|300|Fig 3c. Laplacian of the Field]]
|[[File:Box susc.png|thumb|300|Fig 3d. Estimated Susceptibility (ppm)]]
|}

{|
|[[File:Cyl mag.png|thumb|300|Fig 4a. Magnitude Image]]
|[[File:Cyl fmap.png|thumb|300|Fig 4b. Field map]]
|[[File:Cyl fmap lp.png|thumb|300|Fig 4c. Laplacian of the Field]]
|[[File:Cyl susc.png|thumb|300|Fig 4d. Estimated Susceptibility (ppm)]]
|[[File:Susc plot2.png|thumb|100|Fig 4e. Estimated vs. True mean susceptibility values for each tube (ppm)]]
|}

= Future Directions =

Future work will focus on quantifying magnetic susceptibility and iron content in the brain. Further development of the method described above has generated the preliminary results shown below in Fig 5.

{|
|[[File:Miccai fig1 crop.png|thumb|600px|Fig 5. The field map (left), laplacian of the field (center) and estimated susceptibility map (right) for a young healthy subject is shown. Taking the Laplacian of the fieldmap successfully eliminates the substantial biasfields in the observed field. The estimated susceptibility map shares similar high frequency structure with the Laplacian of the observed field while low frequency structure is preserved by additional modeling constraints.]]
|}

= References =

1. Zecca L, et al. Nat Rev Neurosci, 5:863{73, Nov 2004.

2. Lustig M,et al. MRM. 2007. 58(6):1182.

3. Jenkinson M, et al. MRM. 2004. 52(3):471.

4. de Rochefort L, et al. MRM.2010. 63(1):194.

5. Weisskoff RM, et al. MRM. 1992. 24(2):375.

= Key Investigators =

* MIT: Clare Poynton, Elfar Adalsteinsson
* Harvard/BWH: William Wells
* Stanford: Adolf Pfefferbaum, Edith Sullivan

Projects:QuantitativeSusceptibilityMapping

2011-03-27T21:40:06Z

Cpoynton:

= Introduction =

There is increasing evidence that excessive iron deposition in specific regions
of the brain is associated with neurodegenerative disorders such as Alzheimer's
and Parkinson's disease [1]. The role of iron in the pathogenesis of these diseases
remains unknown and is difficult to determine without a non-invasive method
to quantify its concentration in-vivo. Since iron is a ferromagnetic substance,
changes in iron concentration result in local changes in the magnetic susceptibility of tissue.
In magnetic resonance imaging (MRI) experiments, differences
in magnetic susceptibility cause perturbations in the local magnetic field, which
can be computed from the phase of the MR signal (in a gradient echo sequence, the observed field is proportional to the MR phase).

= Description =

In MRI, magnetic susceptibility differences cause measurable perturbations in the local magnetic field that can be modeled as the convolution of a dipole-like kernel with the spatial susceptibility distribution. In the Fourier domain, the kernel exhibits zeros at the magic angle, preventing direct inversion of the field map; also, limited observations make the problem ill-posed. The observed data is also corrupted by confounding fields (ie. those from tissue/air interfaces, mis-set shims, and other non-local sources). Previous work has shown that MR images can be successfully reconstructed from under-sampled observations by exploiting the sparsity of in-vivo data under various transforms using methods from compressed sensing [2]. In susceptibility estimation, the forward model results in under-sampling of the data in the Fourier domain, but accurate estimates can be obtained using the Laplacian and L1 norm, which promote sparse solutions while removing external field artifacts. Our variational method for susceptibility estimation is described in Figs. 1-2.

{|
|[[File:Namic wiki fig1.png|thumb|400px|Fig 1. Relevant notation]]
|}

{|
|[[File:Latex pdf zoomed to paint equations.PNG|thumb|400px|Fig 2. Applying the Laplacian to the forward model in [1] eliminates non-local phase artifacts to give [2]. The first term in [3] provides regularization, penalizing large differences in spatial frequency relative to Magnitude data, while the second penalizes departures from [2], enforcing agreement of high frequency phase effects.]]
|}

== Forward Model (Eq. 1) ==

The forward model relates the perturbing field to the unknown susceptibility through a local term and convolution of the second z-derivative of the Green’s function of the Laplacian [3].

== Bias Field Elimination (Eq. 2) ==

Applying the Laplacian removes non-local phase effects such as shim fields, which are a solution to the Laplace equation.

== Objective Function (Eq. 3) ==

The first term provides regularization, penalizing solutions with large differences in spatial frequency structure relative to the magnitude image.
The second term penalizes departures from Eq. 2, by enforcing agreement of high frequency phase effects while eliminating low order bias fields.

== Data Acquisition ==

Cylindrical and rectangular phantoms were made using Magnevist (gadopentetate dimeglumine) solutions of 0.5, 1.0, 2.0, and 3.0 mM corresponding to susceptibility values of 0.15, 0.31, 0.62, and 0.94 ppm [4,5]. Field maps were obtained using a 3D multi-echo GRE sequence on a 3T Siemens Trio MRI.

= Results =

Application of the Laplacian removes substantial inhomogeniety in the field map in both phantoms as shown in Fig. 3 (Rectangular phantom) and Fig. 4 (Cylindrical phantom). Rectangular phantom: mean estimated susceptibility values for water and Magnevist were -9.049 and 0.6273 ppm, with true values of -9.050 and 0.6270 ppm. Cylindrical phantom: the estimated susceptibility map allowed different concentrations of Magnevist to be clearly identified and reasonable estimates were obtained in the presence of significant noise and bias due to external field effects.

{|
|[[File:Box mag.jpg|thumb|300|Fig 3a. Magnitude Image]]
|[[File:Box fmap.png|thumb|300|Fig 3b. Field map]]
|[[File:Box fmap lp.png|thumb|300|Fig 3c. Laplacian of the Field]]
|[[File:Box susc.png|thumb|300|Fig 3d. Estimated Susceptibility (ppm)]]
|}

{|
|[[File:Cyl mag.png|thumb|300|Fig 4a. Magnitude Image]]
|[[File:Cyl fmap.png|thumb|300|Fig 4b. Field map]]
|[[File:Cyl fmap lp.png|thumb|300|Fig 4c. Laplacian of the Field]]
|[[File:Cyl susc.png|thumb|300|Fig 4d. Estimated Susceptibility (ppm)]]
|[[File:Susc plot2.png|thumb|100|Fig 4e. Estimated vs. True mean susceptibility values for each tube (ppm)]]
|}

= Future Directions =

Future work will focus on quantifying magnetic susceptibility and iron content in the brain. Further development of the method described above has generated the preliminary results shown below in Fig 5.

{|
|[[File:Miccai fig1 crop.png|thumb|600px|Fig 5. The field map (left), laplacian of the field (center) and estimated susceptibility map (right) for a young healthy subject is shown. Taking the Laplacian of the fieldmap successfully eliminates the substantial biasfields in the observed field. The estimated susceptibility map shares similar high frequency structure with the Laplacian of the observed field while low frequency structure is preserved by additional modeling constraints.]]
|}

= References =

1. Zecca L, et al. Nat Rev Neurosci, 5:863{73, Nov 2004.

2. Lustig M,et al. MRM. 2007. 58(6):1182.

3. Jenkinson M, et al. MRM. 2004. 52(3):471.

4. de Rochefort L, et al. MRM.2010. 63(1):194.

5. Weisskoff RM, et al. MRM. 1992. 24(2):375.

= Key Investigators =

* MIT: Clare Poynton, Elfar Adalsteinsson, Polina Golland
* Harvard/BWH: William Wells
* Stanford: Adolf Pfefferbaum, Edith Sullivan

Algorithm:MIT

2011-03-27T21:36:24Z

Cpoynton: /* Quantitative Susceptibility Mapping */

Back to [[Algorithm:Main|NA-MIC Algorithms]]
__NOTOC__
= Overview of MIT Algorithms (PI: Polina Golland) =

Our group seeks to model statistical variability of anatomy and function across subjects and between populations and to utilize computational models of such variability to improve predictions for individual subjects, as well as characterize populations. Our long-term goal is to develop methods for joint modeling of anatomy and function and to apply them in clinical and scientific studies. We work primarily with anatomical, DTI and fMRI images. We actively contribute implementations of our algorithms to the NAMIC-kit.

= MIT Projects =

{| cellpadding="10" style="text-align:left;"
|| [[Image:Segmentation_example2.png|250px]]
||

== [[Projects:NonparametricSegmentation| Nonparametric Models for Supervised Image Segmentation]] ==

We propose a non-parametric, probabilistic model for the automatic segmentation of medical images,
given a training set of images and corresponding label maps. The resulting inference algorithms we
develop rely on pairwise registrations between the test image and individual training images. The
training labels are then transferred to the test image and fused to compute a final segmentation of
the test subject. [[Projects:NonparametricSegmentation|More...]]

<font color="red">'''New: '''</font> M.R. Sabuncu, B.T.T Yeo, K. Van Leemput, B. Fischl, and P. Golland. A Generative Model for Image Segmentation Based on Label Fusion. IEEE Transactions on Medical Imaging, 29(10):1714-1729, 2010.

|-

| | [[Image:TGIt.gif|center| 150px]]
| |

== [[Projects:LatentAtlasSegmentation|Joint Segmentation of Image Ensembles via Latent Atlases]] ==

Spatial priors, such as probabilistic atlases, play an important role in MRI segmentation. The atlases are typically generated by averaging manual labels of aligned brain regions across different subjects. However, the availability of comprehensive, reliable and suitable manual segmentations is limited. We therefore propose a joint segmentation of corresponding, aligned structures in the entire population that does not require a probability atlas.
[[Projects:LatentAtlasSegmentation|More...]]

<font color="red">'''New: '''</font> T. Riklin Raviv, K. Van-Leemput, B.M. Menze, W.M. Wells III, and P. Golland. Joint Segmentation of Image Ensembles via Latent Atlases, Special Issue of Medical Image Analysis (MedIA), 14(5):654-665, 2010.

|-

|| [[Image:Mdepa_MDE_scar_seg_3D.png| 250px]]
||

== [[Projects:AblationScarSegmentation | Cardiac Ablation Scar Segmentation]] ==

Catheter radio-frequency (RF) ablation is a technique used to treat atrial fibrillation, a very common heart condition. The objective of this project is to automatically segment the scar created by RF ablation in delayed enhancement MR images acquired after the procedure. This will then provide surgeons with a visualization which will help them to rapidly evaluate the success of the procedure.
[[Projects:AblationScarSegmentation|More...]]

<font color="red">'''New: '''</font> M. Depa, M.R. Sabuncu, G. Holmvang, R. Nezafat, E.J. Schmidt, and P. Golland. Robust Atlas-Based Segmentation of Highly Variable Anatomy: Left Atrium Segmentation. In Proc. of MICCAI Workshop on Statistical Atlases and Computational Models of the Heart: Mapping Structure and Function, LNCS 6364:85-94, 2010.

|-

| | [[Image:Tumor_model.jpg‎|center|150px]]
| |

== [[Projects:TumorModeling|Brain Tumor Segmentation and Modeling]] ==

We are interested in developing computational methods for the assimilation of magnetic resonance image data into physiological models of glioma - the most frequent primary brain tumor - for a patient-adaptive modeling of tumor growth. [[Projects:TumorModeling|More...]]

<font color="red">'''New: '''</font> Menze BH, Van Leemput K, Honkela A, Konukoglu E, Weber MA, Ayache N and Golland P. A generative approach for image-based modeling of tumor growth. Proc IPMI 2011. LNCS. 12p

|-

{| cellpadding="10" style="text-align:left;"
|| [[Image:lh.pm14686.BA2.gif|250px]]
||

== [[Projects:LearningRegistrationCostFunctions| Learning Task-Optimal Registration Cost Functions]] ==

We present a framework for learning the parameters of registration cost functions. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. We propose a principled approach to learn these parameters with respect to particular applications. [[Projects:LearningRegistrationCostFunctions|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, M.R. Sabuncu, T. Vercauteren, D. Holt, K. Amunts, K. Zilles, P. Golland, and B. Fischl. Learning Task-Optimal Registration Cost Functions for Localizing Cytoarchitecture and Function in the Cerebral Cortex. IEEE Transactions on Medical Imaging, 29(7):1424-1441, 2010.

|-

| | [[Image:CoordinateChart.png|250px]]
| |

== [[Projects:SphericalDemons|Spherical Demons: Fast Surface Registration]] ==

We present the fast Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizers for the modified demons objective function can be efficiently approximated on the sphere using convolution. Based on the one parameter subgroups of diffeomorphisms, [[Projects:SphericalDemons|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, M.R. Sabuncu, T. Vercauteren, N. Ayache, B. Fischl and P. Golland. Spherical Demons: Fast Diffeomorphic Landmark-Free Surface Registration. IEEE Transactions on Medical Imaging, 29(3):650-668, 2010.

|-

| | [[Image:epi_correction_small.jpg|200px]]
| |

== [[Projects:FieldmapFreeDistortionCorrection|Fieldmap-Free EPI Distortion Correction]] ==

In this project we aim to improve the EPI distortion correction algorithms. [[Projects:FieldmapFreeDistortionCorrection|More...]]

<font color="red">'''New: '''</font> Poynton C., Jenkinson M., Wells III W. Atlas-Based Improved Prediction of Magnetic Field Inhomogeneity for Distortion Correction of EPI Data. In Proc. MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, LNCS 5761:951-959, 2009.

|-

| | [[Image:Namic wiki.png|200px]]
| |

== [[Projects:QuantitativeSusceptibilityMapping| Quantitative Susceptibility Mapping ]] ==

There is increasing evidence that excessive iron deposition in specific regions
of the brain is associated with neurodegenerative disorders such as Alzheimer's
and Parkinson's disease. The role of iron in the pathogenesis of these diseases
remains unknown and is difficult to determine without a non-invasive method
to quantify its concentration in-vivo. Since iron is a ferromagnetic substance,
changes in iron concentration result in local changes in the magnetic susceptibility of tissue.
In magnetic resonance imaging (MRI) experiments, differences
in magnetic susceptibility cause perturbations in the local magnetic field, which
can be computed from the phase of the MR signal.[[Projects:QuantitativeSusceptibilityMapping|More...]]

<font color="red">'''New: '''</font> Poynton C., Wells W. A Variational Approach to Susceptibility Estimation that is insensitive to B0 Inhomogeneity. In Proc. ISMRM: Int. Soc. of Magnetic Resonance in Medicine, 2011 (in press).

|-

| | [[Image:mit_fmri_clustering_parcellation2_xsub.png|200px]]
| |

== [[Projects:fMRIClustering|Improving fMRI Analysis using Supervised and Unsupervised Learning]] ==

One of the major goals in the analysis of fMRI data is the detection of networks in the brain with similar functional behavior. A wide variety of methods including hypothesis-driven statistical tests, supervised, and unsupervised learning methods have been employed to find these networks. In this project, we develop novel learning algorithms that enable more efficient inferences from fMRI measurements. [[Projects:fMRIClustering|More...]]

<font color="red">'''New: '''</font> G. Langs, Y. Tie, L. Rigolo, A.J. Golby, and P. Golland. Functional Geometry Alignment for Localization of Brain Areas. To appear in Proc. NIPS: Neural Information Processing Systems, 2010.

<font color="red">'''New: '''</font> A. Venkataraman, Y. Rathi, M. Kubicki, C-F. Westin and P. Golland. Joint Generative Model for fMRI/DWI and its Application to Population Studies. In Proc. MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, LNCS 6361:191-199, 2010.

<font color="red">'''New: '''</font> D. Lashkari, E. Vul, N.G. Kanwisher, and P. Golland. Discovering structure in the space of fMRI selectivity profiles. NeuroImage, 3(15):1085-1098, 2010.

<font color="red">'''New: '''</font> A. Venkataraman, M. Kubicki, C.-F. Westin, and P. Golland. Robust Feature Selection in Resting-State fMRI Connectivity Based on Population Studies. In Proc. MMBIA: IEEE Computer Society Workshop on Mathematical Methods in Biomedical Image Analysis, 2010.

<font color="red">'''New: '''</font> D. Lashkari, R. Sridharan, E. Vul, P.-J. Hsieh, N. Kanwisher, and P. Golland. Nonparametric Hierarchical Bayesian Model for Functional Brain Parcellation. In Proc. MMBIA: IEEE Computer Society Workshop on Mathematical Methods in Biomedical Image Analysis, 2010.

|-

{| cellpadding="10" style="text-align:left;"
|| [[Image:TetrahedralAtlasWarp.gif‎ |250px]]
||

== [[Projects:BayesianMRSegmentation| Bayesian Segmentation of MRI Images]] ==

The aim of this project is to develop, implement, and validate a generic method for segmenting MRI images that automatically adapts to different acquisition sequences. [[Projects:BayesianMRSegmentation|More...]]

<font color="red">'''New: '''</font> K. Van Leemput, A. Bakkour, T. Benner, G. Wiggins, L.L. Wald, J. Augustinack, B.C. Dickerson, P. Golland, and B. Fischl. Automated Segmentation of Hippocampal Subfields from Ultra-High Resolution In Vivo MRI. Hippocampus, 19:549-557, 2009.

<font color="red">'''New: '''</font> K. Van Leemput. Encoding Probabilistic Atlases Using Bayesian Inference. IEEE Transactions on Medical Imaging, 28(6):822-837, 2009.

|-

| | [[Image:ICluster_templates.gif|250px]]
| |

== [[Projects:MultimodalAtlas|Multimodal Atlas]] ==

In this work, we propose and investigate an algorithm that jointly co-registers a collection of images while computing multiple templates. The algorithm, called '''iCluster''', is used to compute multiple atlases for a given population.
[[Projects:MultimodalAtlas|More...]]

<font color="red">'''New: '''</font> Image-driven Population Analysis through Mixture-Modeling, M.R. Sabuncu, S.K. Balci, M.E. Shenton and P. Golland. IEEE Transactions on Medical Imaging, 28(9):1473 - 1487, 2009.

|-

| | [[Image:GroupwiseSummary.PNG|200px]]
| |

== [[Projects:GroupwiseRegistration|Groupwise Registration]] ==

We extend a previously demonstrated entropy based groupwise registration method to include a free-form deformation model based on B-splines. We provide an efficient implementation using stochastic gradient descents in a multi-resolution setting. We demonstrate the method in application to a set of 50 MRI brain scans and compare the results to a pairwise approach using segmentation labels to evaluate the quality of alignment.

In a related project, we develop a method that reconciles the practical advantages of symmetric registration with the asymmetric nature of image-template registration by adding a simple correction factor to the symmetric cost function. We instantiate our model within a log-domain diffeomorphic registration framework. Our experiments show exploiting the asymmetry in image-template registration improves alignment in the image coordinates. [[Projects:GroupwiseRegistration|More...]]

<font color="red">'''New: '''</font> Asymmetric Image-Template Registration, M.R. Sabuncu, B.T. Thomas Yeo, T. Vercauteren, K. Van Leemput, P. Golland. In Proc. MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, LNCS 5761:565-573, 2009.

|-

| | [[Image:JointRegSeg.png|200px]]
| |

== [[Projects:RegistrationRegularization|Optimal Atlas Regularization in Image Segmentation]] ==

We propose a unified framework for computing atlases from manually labeled data sets at various degrees of “sharpness” and the joint registration and segmentation of a new brain with these atlases. Using this framework, we investigate the tradeoff between warp regularization and image ﬁdelity, i.e. the smoothness of the new subject warp and the sharpness of the atlas in a segmentation application.
[[Projects:RegistrationRegularization|More...]]

|-

| | [[Image:FoldingSpeedDetection.png|150px|]]
| |

== [[Projects:ShapeAnalysisWithOvercompleteWavelets|Shape Analysis With Overcomplete Wavelets]] ==

In this work, we extend the Euclidean wavelets to the sphere. The resulting over-complete spherical wavelets are invariant to the rotation of the spherical image parameterization. We apply the over-complete spherical wavelet to cortical folding development [[Projects:ShapeAnalysisWithOvercompleteWavelets|More...]]

|-

| | [[Image:Models.jpg|200px]]
| |

== [[Projects:DTIModeling|Fiber Tract Modeling, Clustering, and Quantitative Analysis]] ==

The goal of this work is to model the shape of the fiber bundles and use this model description in clustering and statistical analysis of fiber tracts. [[Projects:DTIModeling|More...]]

|-

| | [[Image:Progress_Registration_Segmentation_Shape.jpg|180px]]
| |

== [[Projects:ShapeBasedSegmentationAndRegistration|Shape Based Segmentation and Registration]] ==

This type of algorithm assigns a tissue type to each voxel in the volume. Incorporating prior shape information biases the label assignment towards contiguous regions that are consistent with the shape model. [[Projects:ShapeBasedSegmentationAndRegistration|More...]]

|-

| | [[Image:MIT_DTI_JointSegReg_atlas3D.jpg|200px]]
| |

== [[Projects:DTIFiberRegistration|Joint Registration and Segmentation of DWI Fiber Tractography]] ==

The goal of this work is to jointly register and cluster DWI fiber tracts obtained from a group of subjects. [[Projects:DTIFiberRegistration|More...]]

|-

| | [[Image:brain.png|200px]]
| |

== [[Projects:DTIClustering|DTI Fiber Clustering and Fiber-Based Analysis]] ==

The goal of this project is to provide structural description of the white matter architecture as a partition into coherent fiber bundles and clusters, and to use these bundles for quantitative measurement. [[Projects:DTIClustering|More...]]

|-

| | [[Image:FMRIEvaluationchart.jpg|200px]]
| |

== [[Projects:fMRIDetection|fMRI Detection and Analysis]] ==

We are exploring algorithms for improved fMRI detection and interpretation by incorporting spatial priors and anatomical information to guide the detection. [[Projects:fMRIDetection|More...]]

<font color="red">'''New: '''</font> W. Ou, W.M. Wells III, and P. Golland. Combining Spatial Priors and Anatomical Information for fMRI Detection. Medical Image Analysis, 14(3):318-331, 2010.

|-

| | [[Image:Thalamus_algo_outline.png|200px]]
| |

== [[Projects:DTISegmentation|DTI-based Segmentation]] ==

Unlike conventional MRI, DTI provides adequate contrast to segment the thalamic nuclei, which are gray matter structures. [[Projects:DTISegmentation|More...]]

|-

| | [[Image:ConnectivityMap.png|200px]]
| |

== [[Projects:DTIStochasticTractography|Stochastic Tractography]] ==

This work calculates posterior distributions of white matter fiber tract parameters given diffusion observations in a DWI volume. [[Projects:DTIStochasticTractography|More...]]

|-

| | [[Image:HippocampalShapeDifferences.gif|200px]]
| |

== [[Projects:ShapeAnalysis|Population Analysis of Anatomical Variability]] ==

Our goal is to develop mathematical approaches to modeling anatomical variability within and across populations using tools like local shape descriptors of specific regions of interest and global constellation descriptors of multiple ROI's. [[Projects:ShapeAnalysis|More...]]

|}

Algorithm:MIT

2011-03-27T21:35:52Z

Cpoynton: /* Quantitative Susceptibility Mapping */

Back to [[Algorithm:Main|NA-MIC Algorithms]]
__NOTOC__
= Overview of MIT Algorithms (PI: Polina Golland) =

Our group seeks to model statistical variability of anatomy and function across subjects and between populations and to utilize computational models of such variability to improve predictions for individual subjects, as well as characterize populations. Our long-term goal is to develop methods for joint modeling of anatomy and function and to apply them in clinical and scientific studies. We work primarily with anatomical, DTI and fMRI images. We actively contribute implementations of our algorithms to the NAMIC-kit.

= MIT Projects =

{| cellpadding="10" style="text-align:left;"
|| [[Image:Segmentation_example2.png|250px]]
||

== [[Projects:NonparametricSegmentation| Nonparametric Models for Supervised Image Segmentation]] ==

We propose a non-parametric, probabilistic model for the automatic segmentation of medical images,
given a training set of images and corresponding label maps. The resulting inference algorithms we
develop rely on pairwise registrations between the test image and individual training images. The
training labels are then transferred to the test image and fused to compute a final segmentation of
the test subject. [[Projects:NonparametricSegmentation|More...]]

<font color="red">'''New: '''</font> M.R. Sabuncu, B.T.T Yeo, K. Van Leemput, B. Fischl, and P. Golland. A Generative Model for Image Segmentation Based on Label Fusion. IEEE Transactions on Medical Imaging, 29(10):1714-1729, 2010.

|-

| | [[Image:TGIt.gif|center| 150px]]
| |

== [[Projects:LatentAtlasSegmentation|Joint Segmentation of Image Ensembles via Latent Atlases]] ==

Spatial priors, such as probabilistic atlases, play an important role in MRI segmentation. The atlases are typically generated by averaging manual labels of aligned brain regions across different subjects. However, the availability of comprehensive, reliable and suitable manual segmentations is limited. We therefore propose a joint segmentation of corresponding, aligned structures in the entire population that does not require a probability atlas.
[[Projects:LatentAtlasSegmentation|More...]]

<font color="red">'''New: '''</font> T. Riklin Raviv, K. Van-Leemput, B.M. Menze, W.M. Wells III, and P. Golland. Joint Segmentation of Image Ensembles via Latent Atlases, Special Issue of Medical Image Analysis (MedIA), 14(5):654-665, 2010.

|-

|| [[Image:Mdepa_MDE_scar_seg_3D.png| 250px]]
||

== [[Projects:AblationScarSegmentation | Cardiac Ablation Scar Segmentation]] ==

Catheter radio-frequency (RF) ablation is a technique used to treat atrial fibrillation, a very common heart condition. The objective of this project is to automatically segment the scar created by RF ablation in delayed enhancement MR images acquired after the procedure. This will then provide surgeons with a visualization which will help them to rapidly evaluate the success of the procedure.
[[Projects:AblationScarSegmentation|More...]]

<font color="red">'''New: '''</font> M. Depa, M.R. Sabuncu, G. Holmvang, R. Nezafat, E.J. Schmidt, and P. Golland. Robust Atlas-Based Segmentation of Highly Variable Anatomy: Left Atrium Segmentation. In Proc. of MICCAI Workshop on Statistical Atlases and Computational Models of the Heart: Mapping Structure and Function, LNCS 6364:85-94, 2010.

|-

| | [[Image:Tumor_model.jpg‎|center|150px]]
| |

== [[Projects:TumorModeling|Brain Tumor Segmentation and Modeling]] ==

We are interested in developing computational methods for the assimilation of magnetic resonance image data into physiological models of glioma - the most frequent primary brain tumor - for a patient-adaptive modeling of tumor growth. [[Projects:TumorModeling|More...]]

<font color="red">'''New: '''</font> Menze BH, Van Leemput K, Honkela A, Konukoglu E, Weber MA, Ayache N and Golland P. A generative approach for image-based modeling of tumor growth. Proc IPMI 2011. LNCS. 12p

|-

{| cellpadding="10" style="text-align:left;"
|| [[Image:lh.pm14686.BA2.gif|250px]]
||

== [[Projects:LearningRegistrationCostFunctions| Learning Task-Optimal Registration Cost Functions]] ==

We present a framework for learning the parameters of registration cost functions. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. We propose a principled approach to learn these parameters with respect to particular applications. [[Projects:LearningRegistrationCostFunctions|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, M.R. Sabuncu, T. Vercauteren, D. Holt, K. Amunts, K. Zilles, P. Golland, and B. Fischl. Learning Task-Optimal Registration Cost Functions for Localizing Cytoarchitecture and Function in the Cerebral Cortex. IEEE Transactions on Medical Imaging, 29(7):1424-1441, 2010.

|-

| | [[Image:CoordinateChart.png|250px]]
| |

== [[Projects:SphericalDemons|Spherical Demons: Fast Surface Registration]] ==

We present the fast Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizers for the modified demons objective function can be efficiently approximated on the sphere using convolution. Based on the one parameter subgroups of diffeomorphisms, [[Projects:SphericalDemons|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, M.R. Sabuncu, T. Vercauteren, N. Ayache, B. Fischl and P. Golland. Spherical Demons: Fast Diffeomorphic Landmark-Free Surface Registration. IEEE Transactions on Medical Imaging, 29(3):650-668, 2010.

|-

| | [[Image:epi_correction_small.jpg|200px]]
| |

== [[Projects:FieldmapFreeDistortionCorrection|Fieldmap-Free EPI Distortion Correction]] ==

In this project we aim to improve the EPI distortion correction algorithms. [[Projects:FieldmapFreeDistortionCorrection|More...]]

<font color="red">'''New: '''</font> Poynton C., Jenkinson M., Wells III W. Atlas-Based Improved Prediction of Magnetic Field Inhomogeneity for Distortion Correction of EPI Data. In Proc. MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, LNCS 5761:951-959, 2009.

|-

| | [[Image:Namic wiki.png|200px]]
| |

== [[Projects:QuantitativeSusceptibilityMapping| Quantitative Susceptibility Mapping ]] ==

There is increasing evidence that excessive iron deposition in specific regions
of the brain is associated with neurodegenerative disorders such as Alzheimer's
and Parkinson's disease. The role of iron in the pathogenesis of these diseases
remains unknown and is difficult to determine without a non-invasive method
to quantify its concentration in-vivo. Since iron is a ferromagnetic substance,
changes in iron concentration result in local changes in the magnetic susceptibility of tissue.
In magnetic resonance imaging (MRI) experiments, differences
in magnetic susceptibility cause perturbations in the local magnetic field, which
can be computed from the phase of the MR signal (in a gradient echo sequence, the observed field is proportional to the MR phase).[[Projects:QuantitativeSusceptibilityMapping|More...]]

<font color="red">'''New: '''</font> Poynton C., Wells W. A Variational Approach to Susceptibility Estimation that is insensitive to B0 Inhomogeneity. In Proc. ISMRM: Int. Soc. of Magnetic Resonance in Medicine, 2011 (in press).

|-

| | [[Image:mit_fmri_clustering_parcellation2_xsub.png|200px]]
| |

== [[Projects:fMRIClustering|Improving fMRI Analysis using Supervised and Unsupervised Learning]] ==

One of the major goals in the analysis of fMRI data is the detection of networks in the brain with similar functional behavior. A wide variety of methods including hypothesis-driven statistical tests, supervised, and unsupervised learning methods have been employed to find these networks. In this project, we develop novel learning algorithms that enable more efficient inferences from fMRI measurements. [[Projects:fMRIClustering|More...]]

<font color="red">'''New: '''</font> G. Langs, Y. Tie, L. Rigolo, A.J. Golby, and P. Golland. Functional Geometry Alignment for Localization of Brain Areas. To appear in Proc. NIPS: Neural Information Processing Systems, 2010.

<font color="red">'''New: '''</font> A. Venkataraman, Y. Rathi, M. Kubicki, C-F. Westin and P. Golland. Joint Generative Model for fMRI/DWI and its Application to Population Studies. In Proc. MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, LNCS 6361:191-199, 2010.

<font color="red">'''New: '''</font> D. Lashkari, E. Vul, N.G. Kanwisher, and P. Golland. Discovering structure in the space of fMRI selectivity profiles. NeuroImage, 3(15):1085-1098, 2010.

<font color="red">'''New: '''</font> A. Venkataraman, M. Kubicki, C.-F. Westin, and P. Golland. Robust Feature Selection in Resting-State fMRI Connectivity Based on Population Studies. In Proc. MMBIA: IEEE Computer Society Workshop on Mathematical Methods in Biomedical Image Analysis, 2010.

<font color="red">'''New: '''</font> D. Lashkari, R. Sridharan, E. Vul, P.-J. Hsieh, N. Kanwisher, and P. Golland. Nonparametric Hierarchical Bayesian Model for Functional Brain Parcellation. In Proc. MMBIA: IEEE Computer Society Workshop on Mathematical Methods in Biomedical Image Analysis, 2010.

|-

{| cellpadding="10" style="text-align:left;"
|| [[Image:TetrahedralAtlasWarp.gif‎ |250px]]
||

== [[Projects:BayesianMRSegmentation| Bayesian Segmentation of MRI Images]] ==

The aim of this project is to develop, implement, and validate a generic method for segmenting MRI images that automatically adapts to different acquisition sequences. [[Projects:BayesianMRSegmentation|More...]]

<font color="red">'''New: '''</font> K. Van Leemput, A. Bakkour, T. Benner, G. Wiggins, L.L. Wald, J. Augustinack, B.C. Dickerson, P. Golland, and B. Fischl. Automated Segmentation of Hippocampal Subfields from Ultra-High Resolution In Vivo MRI. Hippocampus, 19:549-557, 2009.

<font color="red">'''New: '''</font> K. Van Leemput. Encoding Probabilistic Atlases Using Bayesian Inference. IEEE Transactions on Medical Imaging, 28(6):822-837, 2009.

|-

| | [[Image:ICluster_templates.gif|250px]]
| |

== [[Projects:MultimodalAtlas|Multimodal Atlas]] ==

In this work, we propose and investigate an algorithm that jointly co-registers a collection of images while computing multiple templates. The algorithm, called '''iCluster''', is used to compute multiple atlases for a given population.
[[Projects:MultimodalAtlas|More...]]

<font color="red">'''New: '''</font> Image-driven Population Analysis through Mixture-Modeling, M.R. Sabuncu, S.K. Balci, M.E. Shenton and P. Golland. IEEE Transactions on Medical Imaging, 28(9):1473 - 1487, 2009.

|-

| | [[Image:GroupwiseSummary.PNG|200px]]
| |

== [[Projects:GroupwiseRegistration|Groupwise Registration]] ==

We extend a previously demonstrated entropy based groupwise registration method to include a free-form deformation model based on B-splines. We provide an efficient implementation using stochastic gradient descents in a multi-resolution setting. We demonstrate the method in application to a set of 50 MRI brain scans and compare the results to a pairwise approach using segmentation labels to evaluate the quality of alignment.

In a related project, we develop a method that reconciles the practical advantages of symmetric registration with the asymmetric nature of image-template registration by adding a simple correction factor to the symmetric cost function. We instantiate our model within a log-domain diffeomorphic registration framework. Our experiments show exploiting the asymmetry in image-template registration improves alignment in the image coordinates. [[Projects:GroupwiseRegistration|More...]]

<font color="red">'''New: '''</font> Asymmetric Image-Template Registration, M.R. Sabuncu, B.T. Thomas Yeo, T. Vercauteren, K. Van Leemput, P. Golland. In Proc. MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, LNCS 5761:565-573, 2009.

|-

| | [[Image:JointRegSeg.png|200px]]
| |

== [[Projects:RegistrationRegularization|Optimal Atlas Regularization in Image Segmentation]] ==

We propose a unified framework for computing atlases from manually labeled data sets at various degrees of “sharpness” and the joint registration and segmentation of a new brain with these atlases. Using this framework, we investigate the tradeoff between warp regularization and image ﬁdelity, i.e. the smoothness of the new subject warp and the sharpness of the atlas in a segmentation application.
[[Projects:RegistrationRegularization|More...]]

|-

| | [[Image:FoldingSpeedDetection.png|150px|]]
| |

== [[Projects:ShapeAnalysisWithOvercompleteWavelets|Shape Analysis With Overcomplete Wavelets]] ==

In this work, we extend the Euclidean wavelets to the sphere. The resulting over-complete spherical wavelets are invariant to the rotation of the spherical image parameterization. We apply the over-complete spherical wavelet to cortical folding development [[Projects:ShapeAnalysisWithOvercompleteWavelets|More...]]

|-

| | [[Image:Models.jpg|200px]]
| |

== [[Projects:DTIModeling|Fiber Tract Modeling, Clustering, and Quantitative Analysis]] ==

The goal of this work is to model the shape of the fiber bundles and use this model description in clustering and statistical analysis of fiber tracts. [[Projects:DTIModeling|More...]]

|-

| | [[Image:Progress_Registration_Segmentation_Shape.jpg|180px]]
| |

== [[Projects:ShapeBasedSegmentationAndRegistration|Shape Based Segmentation and Registration]] ==

This type of algorithm assigns a tissue type to each voxel in the volume. Incorporating prior shape information biases the label assignment towards contiguous regions that are consistent with the shape model. [[Projects:ShapeBasedSegmentationAndRegistration|More...]]

|-

| | [[Image:MIT_DTI_JointSegReg_atlas3D.jpg|200px]]
| |

== [[Projects:DTIFiberRegistration|Joint Registration and Segmentation of DWI Fiber Tractography]] ==

The goal of this work is to jointly register and cluster DWI fiber tracts obtained from a group of subjects. [[Projects:DTIFiberRegistration|More...]]

|-

| | [[Image:brain.png|200px]]
| |

== [[Projects:DTIClustering|DTI Fiber Clustering and Fiber-Based Analysis]] ==

The goal of this project is to provide structural description of the white matter architecture as a partition into coherent fiber bundles and clusters, and to use these bundles for quantitative measurement. [[Projects:DTIClustering|More...]]

|-

| | [[Image:FMRIEvaluationchart.jpg|200px]]
| |

== [[Projects:fMRIDetection|fMRI Detection and Analysis]] ==

We are exploring algorithms for improved fMRI detection and interpretation by incorporting spatial priors and anatomical information to guide the detection. [[Projects:fMRIDetection|More...]]

<font color="red">'''New: '''</font> W. Ou, W.M. Wells III, and P. Golland. Combining Spatial Priors and Anatomical Information for fMRI Detection. Medical Image Analysis, 14(3):318-331, 2010.

|-

| | [[Image:Thalamus_algo_outline.png|200px]]
| |

== [[Projects:DTISegmentation|DTI-based Segmentation]] ==

Unlike conventional MRI, DTI provides adequate contrast to segment the thalamic nuclei, which are gray matter structures. [[Projects:DTISegmentation|More...]]

|-

| | [[Image:ConnectivityMap.png|200px]]
| |

== [[Projects:DTIStochasticTractography|Stochastic Tractography]] ==

This work calculates posterior distributions of white matter fiber tract parameters given diffusion observations in a DWI volume. [[Projects:DTIStochasticTractography|More...]]

|-

| | [[Image:HippocampalShapeDifferences.gif|200px]]
| |

== [[Projects:ShapeAnalysis|Population Analysis of Anatomical Variability]] ==

Our goal is to develop mathematical approaches to modeling anatomical variability within and across populations using tools like local shape descriptors of specific regions of interest and global constellation descriptors of multiple ROI's. [[Projects:ShapeAnalysis|More...]]

|}

Algorithm:MIT

2011-03-27T21:35:35Z

Cpoynton: /* Quantitative Susceptibility Mapping */

Back to [[Algorithm:Main|NA-MIC Algorithms]]
__NOTOC__
= Overview of MIT Algorithms (PI: Polina Golland) =

Our group seeks to model statistical variability of anatomy and function across subjects and between populations and to utilize computational models of such variability to improve predictions for individual subjects, as well as characterize populations. Our long-term goal is to develop methods for joint modeling of anatomy and function and to apply them in clinical and scientific studies. We work primarily with anatomical, DTI and fMRI images. We actively contribute implementations of our algorithms to the NAMIC-kit.

= MIT Projects =

{| cellpadding="10" style="text-align:left;"
|| [[Image:Segmentation_example2.png|250px]]
||

== [[Projects:NonparametricSegmentation| Nonparametric Models for Supervised Image Segmentation]] ==

We propose a non-parametric, probabilistic model for the automatic segmentation of medical images,
given a training set of images and corresponding label maps. The resulting inference algorithms we
develop rely on pairwise registrations between the test image and individual training images. The
training labels are then transferred to the test image and fused to compute a final segmentation of
the test subject. [[Projects:NonparametricSegmentation|More...]]

<font color="red">'''New: '''</font> M.R. Sabuncu, B.T.T Yeo, K. Van Leemput, B. Fischl, and P. Golland. A Generative Model for Image Segmentation Based on Label Fusion. IEEE Transactions on Medical Imaging, 29(10):1714-1729, 2010.

|-

| | [[Image:TGIt.gif|center| 150px]]
| |

== [[Projects:LatentAtlasSegmentation|Joint Segmentation of Image Ensembles via Latent Atlases]] ==

Spatial priors, such as probabilistic atlases, play an important role in MRI segmentation. The atlases are typically generated by averaging manual labels of aligned brain regions across different subjects. However, the availability of comprehensive, reliable and suitable manual segmentations is limited. We therefore propose a joint segmentation of corresponding, aligned structures in the entire population that does not require a probability atlas.
[[Projects:LatentAtlasSegmentation|More...]]

<font color="red">'''New: '''</font> T. Riklin Raviv, K. Van-Leemput, B.M. Menze, W.M. Wells III, and P. Golland. Joint Segmentation of Image Ensembles via Latent Atlases, Special Issue of Medical Image Analysis (MedIA), 14(5):654-665, 2010.

|-

|| [[Image:Mdepa_MDE_scar_seg_3D.png| 250px]]
||

== [[Projects:AblationScarSegmentation | Cardiac Ablation Scar Segmentation]] ==

Catheter radio-frequency (RF) ablation is a technique used to treat atrial fibrillation, a very common heart condition. The objective of this project is to automatically segment the scar created by RF ablation in delayed enhancement MR images acquired after the procedure. This will then provide surgeons with a visualization which will help them to rapidly evaluate the success of the procedure.
[[Projects:AblationScarSegmentation|More...]]

<font color="red">'''New: '''</font> M. Depa, M.R. Sabuncu, G. Holmvang, R. Nezafat, E.J. Schmidt, and P. Golland. Robust Atlas-Based Segmentation of Highly Variable Anatomy: Left Atrium Segmentation. In Proc. of MICCAI Workshop on Statistical Atlases and Computational Models of the Heart: Mapping Structure and Function, LNCS 6364:85-94, 2010.

|-

| | [[Image:Tumor_model.jpg‎|center|150px]]
| |

== [[Projects:TumorModeling|Brain Tumor Segmentation and Modeling]] ==

We are interested in developing computational methods for the assimilation of magnetic resonance image data into physiological models of glioma - the most frequent primary brain tumor - for a patient-adaptive modeling of tumor growth. [[Projects:TumorModeling|More...]]

<font color="red">'''New: '''</font> Menze BH, Van Leemput K, Honkela A, Konukoglu E, Weber MA, Ayache N and Golland P. A generative approach for image-based modeling of tumor growth. Proc IPMI 2011. LNCS. 12p

|-

{| cellpadding="10" style="text-align:left;"
|| [[Image:lh.pm14686.BA2.gif|250px]]
||

== [[Projects:LearningRegistrationCostFunctions| Learning Task-Optimal Registration Cost Functions]] ==

We present a framework for learning the parameters of registration cost functions. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. We propose a principled approach to learn these parameters with respect to particular applications. [[Projects:LearningRegistrationCostFunctions|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, M.R. Sabuncu, T. Vercauteren, D. Holt, K. Amunts, K. Zilles, P. Golland, and B. Fischl. Learning Task-Optimal Registration Cost Functions for Localizing Cytoarchitecture and Function in the Cerebral Cortex. IEEE Transactions on Medical Imaging, 29(7):1424-1441, 2010.

|-

| | [[Image:CoordinateChart.png|250px]]
| |

== [[Projects:SphericalDemons|Spherical Demons: Fast Surface Registration]] ==

We present the fast Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizers for the modified demons objective function can be efficiently approximated on the sphere using convolution. Based on the one parameter subgroups of diffeomorphisms, [[Projects:SphericalDemons|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, M.R. Sabuncu, T. Vercauteren, N. Ayache, B. Fischl and P. Golland. Spherical Demons: Fast Diffeomorphic Landmark-Free Surface Registration. IEEE Transactions on Medical Imaging, 29(3):650-668, 2010.

|-

| | [[Image:epi_correction_small.jpg|200px]]
| |

== [[Projects:FieldmapFreeDistortionCorrection|Fieldmap-Free EPI Distortion Correction]] ==

In this project we aim to improve the EPI distortion correction algorithms. [[Projects:FieldmapFreeDistortionCorrection|More...]]

<font color="red">'''New: '''</font> Poynton C., Jenkinson M., Wells III W. Atlas-Based Improved Prediction of Magnetic Field Inhomogeneity for Distortion Correction of EPI Data. In Proc. MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, LNCS 5761:951-959, 2009.

|-

| | [[Image:Namic wiki.png|200px]]
| |

== [[Projects:QuantitativeSusceptibilityMapping| Quantitative Susceptibility Mapping ]] ==

There is increasing evidence that excessive iron deposition in specific regions
of the brain is associated with neurodegenerative disorders such as Alzheimer's
and Parkinson's disease [1]. The role of iron in the pathogenesis of these diseases
remains unknown and is difficult to determine without a non-invasive method
to quantify its concentration in-vivo. Since iron is a ferromagnetic substance,
changes in iron concentration result in local changes in the magnetic susceptibility of tissue.
In magnetic resonance imaging (MRI) experiments, differences
in magnetic susceptibility cause perturbations in the local magnetic field, which
can be computed from the phase of the MR signal (in a gradient echo sequence, the observed field is proportional to the MR phase).[[Projects:QuantitativeSusceptibilityMapping|More...]]

<font color="red">'''New: '''</font> Poynton C., Wells W. A Variational Approach to Susceptibility Estimation that is insensitive to B0 Inhomogeneity. In Proc. ISMRM: Int. Soc. of Magnetic Resonance in Medicine, 2011 (in press).

|-

| | [[Image:mit_fmri_clustering_parcellation2_xsub.png|200px]]
| |

== [[Projects:fMRIClustering|Improving fMRI Analysis using Supervised and Unsupervised Learning]] ==

One of the major goals in the analysis of fMRI data is the detection of networks in the brain with similar functional behavior. A wide variety of methods including hypothesis-driven statistical tests, supervised, and unsupervised learning methods have been employed to find these networks. In this project, we develop novel learning algorithms that enable more efficient inferences from fMRI measurements. [[Projects:fMRIClustering|More...]]

<font color="red">'''New: '''</font> G. Langs, Y. Tie, L. Rigolo, A.J. Golby, and P. Golland. Functional Geometry Alignment for Localization of Brain Areas. To appear in Proc. NIPS: Neural Information Processing Systems, 2010.

<font color="red">'''New: '''</font> A. Venkataraman, Y. Rathi, M. Kubicki, C-F. Westin and P. Golland. Joint Generative Model for fMRI/DWI and its Application to Population Studies. In Proc. MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, LNCS 6361:191-199, 2010.

<font color="red">'''New: '''</font> D. Lashkari, E. Vul, N.G. Kanwisher, and P. Golland. Discovering structure in the space of fMRI selectivity profiles. NeuroImage, 3(15):1085-1098, 2010.

<font color="red">'''New: '''</font> A. Venkataraman, M. Kubicki, C.-F. Westin, and P. Golland. Robust Feature Selection in Resting-State fMRI Connectivity Based on Population Studies. In Proc. MMBIA: IEEE Computer Society Workshop on Mathematical Methods in Biomedical Image Analysis, 2010.

<font color="red">'''New: '''</font> D. Lashkari, R. Sridharan, E. Vul, P.-J. Hsieh, N. Kanwisher, and P. Golland. Nonparametric Hierarchical Bayesian Model for Functional Brain Parcellation. In Proc. MMBIA: IEEE Computer Society Workshop on Mathematical Methods in Biomedical Image Analysis, 2010.

|-

{| cellpadding="10" style="text-align:left;"
|| [[Image:TetrahedralAtlasWarp.gif‎ |250px]]
||

== [[Projects:BayesianMRSegmentation| Bayesian Segmentation of MRI Images]] ==

The aim of this project is to develop, implement, and validate a generic method for segmenting MRI images that automatically adapts to different acquisition sequences. [[Projects:BayesianMRSegmentation|More...]]

<font color="red">'''New: '''</font> K. Van Leemput, A. Bakkour, T. Benner, G. Wiggins, L.L. Wald, J. Augustinack, B.C. Dickerson, P. Golland, and B. Fischl. Automated Segmentation of Hippocampal Subfields from Ultra-High Resolution In Vivo MRI. Hippocampus, 19:549-557, 2009.

<font color="red">'''New: '''</font> K. Van Leemput. Encoding Probabilistic Atlases Using Bayesian Inference. IEEE Transactions on Medical Imaging, 28(6):822-837, 2009.

|-

| | [[Image:ICluster_templates.gif|250px]]
| |

== [[Projects:MultimodalAtlas|Multimodal Atlas]] ==

In this work, we propose and investigate an algorithm that jointly co-registers a collection of images while computing multiple templates. The algorithm, called '''iCluster''', is used to compute multiple atlases for a given population.
[[Projects:MultimodalAtlas|More...]]

<font color="red">'''New: '''</font> Image-driven Population Analysis through Mixture-Modeling, M.R. Sabuncu, S.K. Balci, M.E. Shenton and P. Golland. IEEE Transactions on Medical Imaging, 28(9):1473 - 1487, 2009.

|-

| | [[Image:GroupwiseSummary.PNG|200px]]
| |

== [[Projects:GroupwiseRegistration|Groupwise Registration]] ==

We extend a previously demonstrated entropy based groupwise registration method to include a free-form deformation model based on B-splines. We provide an efficient implementation using stochastic gradient descents in a multi-resolution setting. We demonstrate the method in application to a set of 50 MRI brain scans and compare the results to a pairwise approach using segmentation labels to evaluate the quality of alignment.

In a related project, we develop a method that reconciles the practical advantages of symmetric registration with the asymmetric nature of image-template registration by adding a simple correction factor to the symmetric cost function. We instantiate our model within a log-domain diffeomorphic registration framework. Our experiments show exploiting the asymmetry in image-template registration improves alignment in the image coordinates. [[Projects:GroupwiseRegistration|More...]]

<font color="red">'''New: '''</font> Asymmetric Image-Template Registration, M.R. Sabuncu, B.T. Thomas Yeo, T. Vercauteren, K. Van Leemput, P. Golland. In Proc. MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, LNCS 5761:565-573, 2009.

|-

| | [[Image:JointRegSeg.png|200px]]
| |

== [[Projects:RegistrationRegularization|Optimal Atlas Regularization in Image Segmentation]] ==

We propose a unified framework for computing atlases from manually labeled data sets at various degrees of “sharpness” and the joint registration and segmentation of a new brain with these atlases. Using this framework, we investigate the tradeoff between warp regularization and image ﬁdelity, i.e. the smoothness of the new subject warp and the sharpness of the atlas in a segmentation application.
[[Projects:RegistrationRegularization|More...]]

|-

| | [[Image:FoldingSpeedDetection.png|150px|]]
| |

== [[Projects:ShapeAnalysisWithOvercompleteWavelets|Shape Analysis With Overcomplete Wavelets]] ==

In this work, we extend the Euclidean wavelets to the sphere. The resulting over-complete spherical wavelets are invariant to the rotation of the spherical image parameterization. We apply the over-complete spherical wavelet to cortical folding development [[Projects:ShapeAnalysisWithOvercompleteWavelets|More...]]

|-

| | [[Image:Models.jpg|200px]]
| |

== [[Projects:DTIModeling|Fiber Tract Modeling, Clustering, and Quantitative Analysis]] ==

The goal of this work is to model the shape of the fiber bundles and use this model description in clustering and statistical analysis of fiber tracts. [[Projects:DTIModeling|More...]]

|-

| | [[Image:Progress_Registration_Segmentation_Shape.jpg|180px]]
| |

== [[Projects:ShapeBasedSegmentationAndRegistration|Shape Based Segmentation and Registration]] ==

This type of algorithm assigns a tissue type to each voxel in the volume. Incorporating prior shape information biases the label assignment towards contiguous regions that are consistent with the shape model. [[Projects:ShapeBasedSegmentationAndRegistration|More...]]

|-

| | [[Image:MIT_DTI_JointSegReg_atlas3D.jpg|200px]]
| |

== [[Projects:DTIFiberRegistration|Joint Registration and Segmentation of DWI Fiber Tractography]] ==

The goal of this work is to jointly register and cluster DWI fiber tracts obtained from a group of subjects. [[Projects:DTIFiberRegistration|More...]]

|-

| | [[Image:brain.png|200px]]
| |

== [[Projects:DTIClustering|DTI Fiber Clustering and Fiber-Based Analysis]] ==

The goal of this project is to provide structural description of the white matter architecture as a partition into coherent fiber bundles and clusters, and to use these bundles for quantitative measurement. [[Projects:DTIClustering|More...]]

|-

| | [[Image:FMRIEvaluationchart.jpg|200px]]
| |

== [[Projects:fMRIDetection|fMRI Detection and Analysis]] ==

We are exploring algorithms for improved fMRI detection and interpretation by incorporting spatial priors and anatomical information to guide the detection. [[Projects:fMRIDetection|More...]]

<font color="red">'''New: '''</font> W. Ou, W.M. Wells III, and P. Golland. Combining Spatial Priors and Anatomical Information for fMRI Detection. Medical Image Analysis, 14(3):318-331, 2010.

|-

| | [[Image:Thalamus_algo_outline.png|200px]]
| |

== [[Projects:DTISegmentation|DTI-based Segmentation]] ==

Unlike conventional MRI, DTI provides adequate contrast to segment the thalamic nuclei, which are gray matter structures. [[Projects:DTISegmentation|More...]]

|-

| | [[Image:ConnectivityMap.png|200px]]
| |

== [[Projects:DTIStochasticTractography|Stochastic Tractography]] ==

This work calculates posterior distributions of white matter fiber tract parameters given diffusion observations in a DWI volume. [[Projects:DTIStochasticTractography|More...]]

|-

| | [[Image:HippocampalShapeDifferences.gif|200px]]
| |

== [[Projects:ShapeAnalysis|Population Analysis of Anatomical Variability]] ==

Our goal is to develop mathematical approaches to modeling anatomical variability within and across populations using tools like local shape descriptors of specific regions of interest and global constellation descriptors of multiple ROI's. [[Projects:ShapeAnalysis|More...]]

|}

Algorithm:MIT

2011-03-27T21:33:25Z

Cpoynton: /* Quantitative Susceptibility Mapping */

Back to [[Algorithm:Main|NA-MIC Algorithms]]
__NOTOC__
= Overview of MIT Algorithms (PI: Polina Golland) =

Our group seeks to model statistical variability of anatomy and function across subjects and between populations and to utilize computational models of such variability to improve predictions for individual subjects, as well as characterize populations. Our long-term goal is to develop methods for joint modeling of anatomy and function and to apply them in clinical and scientific studies. We work primarily with anatomical, DTI and fMRI images. We actively contribute implementations of our algorithms to the NAMIC-kit.

= MIT Projects =

{| cellpadding="10" style="text-align:left;"
|| [[Image:Segmentation_example2.png|250px]]
||

== [[Projects:NonparametricSegmentation| Nonparametric Models for Supervised Image Segmentation]] ==

We propose a non-parametric, probabilistic model for the automatic segmentation of medical images,
given a training set of images and corresponding label maps. The resulting inference algorithms we
develop rely on pairwise registrations between the test image and individual training images. The
training labels are then transferred to the test image and fused to compute a final segmentation of
the test subject. [[Projects:NonparametricSegmentation|More...]]

<font color="red">'''New: '''</font> M.R. Sabuncu, B.T.T Yeo, K. Van Leemput, B. Fischl, and P. Golland. A Generative Model for Image Segmentation Based on Label Fusion. IEEE Transactions on Medical Imaging, 29(10):1714-1729, 2010.

|-

| | [[Image:TGIt.gif|center| 150px]]
| |

== [[Projects:LatentAtlasSegmentation|Joint Segmentation of Image Ensembles via Latent Atlases]] ==

Spatial priors, such as probabilistic atlases, play an important role in MRI segmentation. The atlases are typically generated by averaging manual labels of aligned brain regions across different subjects. However, the availability of comprehensive, reliable and suitable manual segmentations is limited. We therefore propose a joint segmentation of corresponding, aligned structures in the entire population that does not require a probability atlas.
[[Projects:LatentAtlasSegmentation|More...]]

<font color="red">'''New: '''</font> T. Riklin Raviv, K. Van-Leemput, B.M. Menze, W.M. Wells III, and P. Golland. Joint Segmentation of Image Ensembles via Latent Atlases, Special Issue of Medical Image Analysis (MedIA), 14(5):654-665, 2010.

|-

|| [[Image:Mdepa_MDE_scar_seg_3D.png| 250px]]
||

== [[Projects:AblationScarSegmentation | Cardiac Ablation Scar Segmentation]] ==

Catheter radio-frequency (RF) ablation is a technique used to treat atrial fibrillation, a very common heart condition. The objective of this project is to automatically segment the scar created by RF ablation in delayed enhancement MR images acquired after the procedure. This will then provide surgeons with a visualization which will help them to rapidly evaluate the success of the procedure.
[[Projects:AblationScarSegmentation|More...]]

<font color="red">'''New: '''</font> M. Depa, M.R. Sabuncu, G. Holmvang, R. Nezafat, E.J. Schmidt, and P. Golland. Robust Atlas-Based Segmentation of Highly Variable Anatomy: Left Atrium Segmentation. In Proc. of MICCAI Workshop on Statistical Atlases and Computational Models of the Heart: Mapping Structure and Function, LNCS 6364:85-94, 2010.

|-

| | [[Image:Tumor_model.jpg‎|center|150px]]
| |

== [[Projects:TumorModeling|Brain Tumor Segmentation and Modeling]] ==

We are interested in developing computational methods for the assimilation of magnetic resonance image data into physiological models of glioma - the most frequent primary brain tumor - for a patient-adaptive modeling of tumor growth. [[Projects:TumorModeling|More...]]

<font color="red">'''New: '''</font> Menze BH, Van Leemput K, Honkela A, Konukoglu E, Weber MA, Ayache N and Golland P. A generative approach for image-based modeling of tumor growth. Proc IPMI 2011. LNCS. 12p

|-

{| cellpadding="10" style="text-align:left;"
|| [[Image:lh.pm14686.BA2.gif|250px]]
||

== [[Projects:LearningRegistrationCostFunctions| Learning Task-Optimal Registration Cost Functions]] ==

We present a framework for learning the parameters of registration cost functions. The parameters of the registration cost function -- for example, the tradeoff between the image similarity and regularization terms -- are typically determined manually through inspection of the image alignment and then fixed for all applications. We propose a principled approach to learn these parameters with respect to particular applications. [[Projects:LearningRegistrationCostFunctions|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, M.R. Sabuncu, T. Vercauteren, D. Holt, K. Amunts, K. Zilles, P. Golland, and B. Fischl. Learning Task-Optimal Registration Cost Functions for Localizing Cytoarchitecture and Function in the Cerebral Cortex. IEEE Transactions on Medical Imaging, 29(7):1424-1441, 2010.

|-

| | [[Image:CoordinateChart.png|250px]]
| |

== [[Projects:SphericalDemons|Spherical Demons: Fast Surface Registration]] ==

We present the fast Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizers for the modified demons objective function can be efficiently approximated on the sphere using convolution. Based on the one parameter subgroups of diffeomorphisms, [[Projects:SphericalDemons|More...]]

<font color="red">'''New: '''</font> B.T.T. Yeo, M.R. Sabuncu, T. Vercauteren, N. Ayache, B. Fischl and P. Golland. Spherical Demons: Fast Diffeomorphic Landmark-Free Surface Registration. IEEE Transactions on Medical Imaging, 29(3):650-668, 2010.

|-

| | [[Image:epi_correction_small.jpg|200px]]
| |

== [[Projects:FieldmapFreeDistortionCorrection|Fieldmap-Free EPI Distortion Correction]] ==

In this project we aim to improve the EPI distortion correction algorithms. [[Projects:FieldmapFreeDistortionCorrection|More...]]

<font color="red">'''New: '''</font> Poynton C., Jenkinson M., Wells III W. Atlas-Based Improved Prediction of Magnetic Field Inhomogeneity for Distortion Correction of EPI Data. In Proc. MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, LNCS 5761:951-959, 2009.

|-

| | [[Image:Namic wiki.png|200px]]
| |

== [[Projects:QuantitativeSusceptibilityMapping| Quantitative Susceptibility Mapping ]] ==

In MRI, magnetic susceptibility differences cause perturbations in the local magnetic field that can be modeled as the convolution of a dipole-like kernel with the spatial susceptibility distribution. In the Fourier domain, the kernel exhibits zeros at the magic angle, preventing direct inversion of the field map. The observed data is also corrupted by confounding bias fields (ie. those from tissue/air interfaces, mis-set shims, and other non-local sources) [1]. We describe a variational method for susceptibility estimation that is based on the Laplacian operator. Using the Laplacian of the field and the L1 norm, confounding field artifacts are effectively eliminated and sparse solutions that agree well with true susceptibility values are obtained. [[Projects:QuantitativeSusceptibilityMapping|More...]]

<font color="red">'''New: '''</font> Poynton C., Wells W. A Variational Approach to Susceptibility Estimation that is insensitive to B0 Inhomogeneity. In Proc. ISMRM: Int. Soc. of Magnetic Resonance in Medicine, 2011 (in press).

|-

| | [[Image:mit_fmri_clustering_parcellation2_xsub.png|200px]]
| |

== [[Projects:fMRIClustering|Improving fMRI Analysis using Supervised and Unsupervised Learning]] ==

One of the major goals in the analysis of fMRI data is the detection of networks in the brain with similar functional behavior. A wide variety of methods including hypothesis-driven statistical tests, supervised, and unsupervised learning methods have been employed to find these networks. In this project, we develop novel learning algorithms that enable more efficient inferences from fMRI measurements. [[Projects:fMRIClustering|More...]]

<font color="red">'''New: '''</font> G. Langs, Y. Tie, L. Rigolo, A.J. Golby, and P. Golland. Functional Geometry Alignment for Localization of Brain Areas. To appear in Proc. NIPS: Neural Information Processing Systems, 2010.

<font color="red">'''New: '''</font> A. Venkataraman, Y. Rathi, M. Kubicki, C-F. Westin and P. Golland. Joint Generative Model for fMRI/DWI and its Application to Population Studies. In Proc. MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, LNCS 6361:191-199, 2010.

<font color="red">'''New: '''</font> D. Lashkari, E. Vul, N.G. Kanwisher, and P. Golland. Discovering structure in the space of fMRI selectivity profiles. NeuroImage, 3(15):1085-1098, 2010.

<font color="red">'''New: '''</font> A. Venkataraman, M. Kubicki, C.-F. Westin, and P. Golland. Robust Feature Selection in Resting-State fMRI Connectivity Based on Population Studies. In Proc. MMBIA: IEEE Computer Society Workshop on Mathematical Methods in Biomedical Image Analysis, 2010.

<font color="red">'''New: '''</font> D. Lashkari, R. Sridharan, E. Vul, P.-J. Hsieh, N. Kanwisher, and P. Golland. Nonparametric Hierarchical Bayesian Model for Functional Brain Parcellation. In Proc. MMBIA: IEEE Computer Society Workshop on Mathematical Methods in Biomedical Image Analysis, 2010.

|-

{| cellpadding="10" style="text-align:left;"
|| [[Image:TetrahedralAtlasWarp.gif‎ |250px]]
||

== [[Projects:BayesianMRSegmentation| Bayesian Segmentation of MRI Images]] ==

The aim of this project is to develop, implement, and validate a generic method for segmenting MRI images that automatically adapts to different acquisition sequences. [[Projects:BayesianMRSegmentation|More...]]

<font color="red">'''New: '''</font> K. Van Leemput, A. Bakkour, T. Benner, G. Wiggins, L.L. Wald, J. Augustinack, B.C. Dickerson, P. Golland, and B. Fischl. Automated Segmentation of Hippocampal Subfields from Ultra-High Resolution In Vivo MRI. Hippocampus, 19:549-557, 2009.

<font color="red">'''New: '''</font> K. Van Leemput. Encoding Probabilistic Atlases Using Bayesian Inference. IEEE Transactions on Medical Imaging, 28(6):822-837, 2009.

|-

| | [[Image:ICluster_templates.gif|250px]]
| |

== [[Projects:MultimodalAtlas|Multimodal Atlas]] ==

In this work, we propose and investigate an algorithm that jointly co-registers a collection of images while computing multiple templates. The algorithm, called '''iCluster''', is used to compute multiple atlases for a given population.
[[Projects:MultimodalAtlas|More...]]

<font color="red">'''New: '''</font> Image-driven Population Analysis through Mixture-Modeling, M.R. Sabuncu, S.K. Balci, M.E. Shenton and P. Golland. IEEE Transactions on Medical Imaging, 28(9):1473 - 1487, 2009.

|-

| | [[Image:GroupwiseSummary.PNG|200px]]
| |

== [[Projects:GroupwiseRegistration|Groupwise Registration]] ==

We extend a previously demonstrated entropy based groupwise registration method to include a free-form deformation model based on B-splines. We provide an efficient implementation using stochastic gradient descents in a multi-resolution setting. We demonstrate the method in application to a set of 50 MRI brain scans and compare the results to a pairwise approach using segmentation labels to evaluate the quality of alignment.

In a related project, we develop a method that reconciles the practical advantages of symmetric registration with the asymmetric nature of image-template registration by adding a simple correction factor to the symmetric cost function. We instantiate our model within a log-domain diffeomorphic registration framework. Our experiments show exploiting the asymmetry in image-template registration improves alignment in the image coordinates. [[Projects:GroupwiseRegistration|More...]]

<font color="red">'''New: '''</font> Asymmetric Image-Template Registration, M.R. Sabuncu, B.T. Thomas Yeo, T. Vercauteren, K. Van Leemput, P. Golland. In Proc. MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, LNCS 5761:565-573, 2009.

|-

| | [[Image:JointRegSeg.png|200px]]
| |

== [[Projects:RegistrationRegularization|Optimal Atlas Regularization in Image Segmentation]] ==

We propose a unified framework for computing atlases from manually labeled data sets at various degrees of “sharpness” and the joint registration and segmentation of a new brain with these atlases. Using this framework, we investigate the tradeoff between warp regularization and image ﬁdelity, i.e. the smoothness of the new subject warp and the sharpness of the atlas in a segmentation application.
[[Projects:RegistrationRegularization|More...]]

|-

| | [[Image:FoldingSpeedDetection.png|150px|]]
| |

== [[Projects:ShapeAnalysisWithOvercompleteWavelets|Shape Analysis With Overcomplete Wavelets]] ==

In this work, we extend the Euclidean wavelets to the sphere. The resulting over-complete spherical wavelets are invariant to the rotation of the spherical image parameterization. We apply the over-complete spherical wavelet to cortical folding development [[Projects:ShapeAnalysisWithOvercompleteWavelets|More...]]

|-

| | [[Image:Models.jpg|200px]]
| |

== [[Projects:DTIModeling|Fiber Tract Modeling, Clustering, and Quantitative Analysis]] ==

The goal of this work is to model the shape of the fiber bundles and use this model description in clustering and statistical analysis of fiber tracts. [[Projects:DTIModeling|More...]]

|-

| | [[Image:Progress_Registration_Segmentation_Shape.jpg|180px]]
| |

== [[Projects:ShapeBasedSegmentationAndRegistration|Shape Based Segmentation and Registration]] ==

This type of algorithm assigns a tissue type to each voxel in the volume. Incorporating prior shape information biases the label assignment towards contiguous regions that are consistent with the shape model. [[Projects:ShapeBasedSegmentationAndRegistration|More...]]

|-

| | [[Image:MIT_DTI_JointSegReg_atlas3D.jpg|200px]]
| |

== [[Projects:DTIFiberRegistration|Joint Registration and Segmentation of DWI Fiber Tractography]] ==

The goal of this work is to jointly register and cluster DWI fiber tracts obtained from a group of subjects. [[Projects:DTIFiberRegistration|More...]]

|-

| | [[Image:brain.png|200px]]
| |

== [[Projects:DTIClustering|DTI Fiber Clustering and Fiber-Based Analysis]] ==

The goal of this project is to provide structural description of the white matter architecture as a partition into coherent fiber bundles and clusters, and to use these bundles for quantitative measurement. [[Projects:DTIClustering|More...]]

|-

| | [[Image:FMRIEvaluationchart.jpg|200px]]
| |

== [[Projects:fMRIDetection|fMRI Detection and Analysis]] ==

We are exploring algorithms for improved fMRI detection and interpretation by incorporting spatial priors and anatomical information to guide the detection. [[Projects:fMRIDetection|More...]]

<font color="red">'''New: '''</font> W. Ou, W.M. Wells III, and P. Golland. Combining Spatial Priors and Anatomical Information for fMRI Detection. Medical Image Analysis, 14(3):318-331, 2010.

|-

| | [[Image:Thalamus_algo_outline.png|200px]]
| |

== [[Projects:DTISegmentation|DTI-based Segmentation]] ==

Unlike conventional MRI, DTI provides adequate contrast to segment the thalamic nuclei, which are gray matter structures. [[Projects:DTISegmentation|More...]]

|-

| | [[Image:ConnectivityMap.png|200px]]
| |

== [[Projects:DTIStochasticTractography|Stochastic Tractography]] ==

This work calculates posterior distributions of white matter fiber tract parameters given diffusion observations in a DWI volume. [[Projects:DTIStochasticTractography|More...]]

|-

| | [[Image:HippocampalShapeDifferences.gif|200px]]
| |

== [[Projects:ShapeAnalysis|Population Analysis of Anatomical Variability]] ==

Our goal is to develop mathematical approaches to modeling anatomical variability within and across populations using tools like local shape descriptors of specific regions of interest and global constellation descriptors of multiple ROI's. [[Projects:ShapeAnalysis|More...]]

|}

Projects:QuantitativeSusceptibilityMapping

2011-03-27T21:27:42Z

Cpoynton: /* References */

= Introduction =

There is increasing evidence that excessive iron deposition in specific regions
of the brain is associated with neurodegenerative disorders such as Alzheimer's
and Parkinson's disease [1]. The role of iron in the pathogenesis of these diseases
remains unknown and is difficult to determine without a non-invasive method
to quantify its concentration in-vivo. Since iron is a ferromagnetic substance,
changes in iron concentration result in local changes in the magnetic susceptibility of tissue.
In magnetic resonance imaging (MRI) experiments, differences
in magnetic susceptibility cause perturbations in the local magnetic field, which
can be computed from the phase of the MR signal (in a gradient echo sequence, the observed field is proportional to the MR phase).

= Description =

In MRI, magnetic susceptibility differences cause measurable perturbations in the local magnetic field that can be modeled as the convolution of a dipole-like kernel with the spatial susceptibility distribution. In the Fourier domain, the kernel exhibits zeros at the magic angle, preventing direct inversion of the field map; also, limited observations make the problem ill-posed. The observed data is also corrupted by confounding fields (ie. those from tissue/air interfaces, mis-set shims, and other non-local sources). Previous work has shown that MR images can be successfully reconstructed from under-sampled observations by exploiting the sparsity of in-vivo data under various transforms using methods from compressed sensing [2]. In susceptibility estimation, the forward model results in under-sampling of the data in the Fourier domain, but accurate estimates can be obtained using the Laplacian and L1 norm, which promote sparse solutions while removing external field artifacts. Our variational method for susceptibility estimation is described in Figs. 1-2.

{|
|[[File:Namic wiki fig1.png|thumb|400px|Fig 1. Relevant notation]]
|}

{|
|[[File:Latex pdf zoomed to paint equations.PNG|thumb|400px|Fig 2. Applying the Laplacian to the forward model in [1] eliminates non-local phase artifacts to give [2]. The first term in [3] provides regularization, penalizing large differences in spatial frequency relative to Magnitude data, while the second penalizes departures from [2], enforcing agreement of high frequency phase effects.]]
|}

== Forward Model (Eq. 1) ==

The forward model relates the perturbing field to the unknown susceptibility through a local term and convolution of the second z-derivative of the Green’s function of the Laplacian [3].

== Bias Field Elimination (Eq. 2) ==

Applying the Laplacian removes non-local phase effects such as shim fields, which are a solution to the Laplace equation.

== Objective Function (Eq. 3) ==

The first term provides regularization, penalizing solutions with large differences in spatial frequency structure relative to the magnitude image.
The second term penalizes departures from Eq. 2, by enforcing agreement of high frequency phase effects while eliminating low order bias fields.

== Data Acquisition ==

Cylindrical and rectangular phantoms were made using Magnevist (gadopentetate dimeglumine) solutions of 0.5, 1.0, 2.0, and 3.0 mM corresponding to susceptibility values of 0.15, 0.31, 0.62, and 0.94 ppm [4,5]. Field maps were obtained using a 3D multi-echo GRE sequence on a 3T Siemens Trio MRI.

= Results =

Application of the Laplacian removes substantial inhomogeniety in the field map in both phantoms as shown in Fig. 3 (Rectangular phantom) and Fig. 4 (Cylindrical phantom). Rectangular phantom: mean estimated susceptibility values for water and Magnevist were -9.049 and 0.6273 ppm, with true values of -9.050 and 0.6270 ppm. Cylindrical phantom: the estimated susceptibility map allowed different concentrations of Magnevist to be clearly identified and reasonable estimates were obtained in the presence of significant noise and bias due to external field effects.

{|
|[[File:Box mag.jpg|thumb|300|Fig 3a. Magnitude Image]]
|[[File:Box fmap.png|thumb|300|Fig 3b. Field map]]
|[[File:Box fmap lp.png|thumb|300|Fig 3c. Laplacian of the Field]]
|[[File:Box susc.png|thumb|300|Fig 3d. Estimated Susceptibility (ppm)]]
|}

{|
|[[File:Cyl mag.png|thumb|300|Fig 4a. Magnitude Image]]
|[[File:Cyl fmap.png|thumb|300|Fig 4b. Field map]]
|[[File:Cyl fmap lp.png|thumb|300|Fig 4c. Laplacian of the Field]]
|[[File:Cyl susc.png|thumb|300|Fig 4d. Estimated Susceptibility (ppm)]]
|[[File:Susc plot2.png|thumb|100|Fig 4e. Estimated vs. True mean susceptibility values for each tube (ppm)]]
|}

= Future Directions =

Future work will focus on quantifying magnetic susceptibility and iron content in the brain. Further development of the method described above has generated the preliminary results shown below in Fig 5.

{|
|[[File:Miccai fig1 crop.png|thumb|600px|Fig 5. The field map (left), laplacian of the field (center) and estimated susceptibility map (right) for a young healthy subject is shown. Taking the Laplacian of the fieldmap successfully eliminates the substantial biasfields in the observed field. The estimated susceptibility map shares similar high frequency structure with the Laplacian of the observed field while low frequency structure is preserved by additional modeling constraints.]]
|}

= References =
1. Zecca L, et al. Nat Rev Neurosci, 5:863{73, Nov 2004.

2. Lustig M,et al. MRM. 2007. 58(6):1182.

3. Jenkinson M, et al. MRM. 2004. 52(3):471.

4. de Rochefort L, et al. MRM.2010. 63(1):194.

5. Weisskoff RM, et al. MRM. 1992. 24(2):375.

Projects:QuantitativeSusceptibilityMapping

2011-03-27T21:27:29Z

Cpoynton:

= Introduction =

There is increasing evidence that excessive iron deposition in specific regions
of the brain is associated with neurodegenerative disorders such as Alzheimer's
and Parkinson's disease [1]. The role of iron in the pathogenesis of these diseases
remains unknown and is difficult to determine without a non-invasive method
to quantify its concentration in-vivo. Since iron is a ferromagnetic substance,
changes in iron concentration result in local changes in the magnetic susceptibility of tissue.
In magnetic resonance imaging (MRI) experiments, differences
in magnetic susceptibility cause perturbations in the local magnetic field, which
can be computed from the phase of the MR signal (in a gradient echo sequence, the observed field is proportional to the MR phase).

= Description =

In MRI, magnetic susceptibility differences cause measurable perturbations in the local magnetic field that can be modeled as the convolution of a dipole-like kernel with the spatial susceptibility distribution. In the Fourier domain, the kernel exhibits zeros at the magic angle, preventing direct inversion of the field map; also, limited observations make the problem ill-posed. The observed data is also corrupted by confounding fields (ie. those from tissue/air interfaces, mis-set shims, and other non-local sources). Previous work has shown that MR images can be successfully reconstructed from under-sampled observations by exploiting the sparsity of in-vivo data under various transforms using methods from compressed sensing [2]. In susceptibility estimation, the forward model results in under-sampling of the data in the Fourier domain, but accurate estimates can be obtained using the Laplacian and L1 norm, which promote sparse solutions while removing external field artifacts. Our variational method for susceptibility estimation is described in Figs. 1-2.

{|
|[[File:Namic wiki fig1.png|thumb|400px|Fig 1. Relevant notation]]
|}

{|
|[[File:Latex pdf zoomed to paint equations.PNG|thumb|400px|Fig 2. Applying the Laplacian to the forward model in [1] eliminates non-local phase artifacts to give [2]. The first term in [3] provides regularization, penalizing large differences in spatial frequency relative to Magnitude data, while the second penalizes departures from [2], enforcing agreement of high frequency phase effects.]]
|}

== Forward Model (Eq. 1) ==

The forward model relates the perturbing field to the unknown susceptibility through a local term and convolution of the second z-derivative of the Green’s function of the Laplacian [3].

== Bias Field Elimination (Eq. 2) ==

Applying the Laplacian removes non-local phase effects such as shim fields, which are a solution to the Laplace equation.

== Objective Function (Eq. 3) ==

The first term provides regularization, penalizing solutions with large differences in spatial frequency structure relative to the magnitude image.
The second term penalizes departures from Eq. 2, by enforcing agreement of high frequency phase effects while eliminating low order bias fields.

== Data Acquisition ==

Cylindrical and rectangular phantoms were made using Magnevist (gadopentetate dimeglumine) solutions of 0.5, 1.0, 2.0, and 3.0 mM corresponding to susceptibility values of 0.15, 0.31, 0.62, and 0.94 ppm [4,5]. Field maps were obtained using a 3D multi-echo GRE sequence on a 3T Siemens Trio MRI.

= Results =

Application of the Laplacian removes substantial inhomogeniety in the field map in both phantoms as shown in Fig. 3 (Rectangular phantom) and Fig. 4 (Cylindrical phantom). Rectangular phantom: mean estimated susceptibility values for water and Magnevist were -9.049 and 0.6273 ppm, with true values of -9.050 and 0.6270 ppm. Cylindrical phantom: the estimated susceptibility map allowed different concentrations of Magnevist to be clearly identified and reasonable estimates were obtained in the presence of significant noise and bias due to external field effects.

{|
|[[File:Box mag.jpg|thumb|300|Fig 3a. Magnitude Image]]
|[[File:Box fmap.png|thumb|300|Fig 3b. Field map]]
|[[File:Box fmap lp.png|thumb|300|Fig 3c. Laplacian of the Field]]
|[[File:Box susc.png|thumb|300|Fig 3d. Estimated Susceptibility (ppm)]]
|}

{|
|[[File:Cyl mag.png|thumb|300|Fig 4a. Magnitude Image]]
|[[File:Cyl fmap.png|thumb|300|Fig 4b. Field map]]
|[[File:Cyl fmap lp.png|thumb|300|Fig 4c. Laplacian of the Field]]
|[[File:Cyl susc.png|thumb|300|Fig 4d. Estimated Susceptibility (ppm)]]
|[[File:Susc plot2.png|thumb|100|Fig 4e. Estimated vs. True mean susceptibility values for each tube (ppm)]]
|}

= Future Directions =

Future work will focus on quantifying magnetic susceptibility and iron content in the brain. Further development of the method described above has generated the preliminary results shown below in Fig 5.

{|
|[[File:Miccai fig1 crop.png|thumb|600px|Fig 5. The field map (left), laplacian of the field (center) and estimated susceptibility map (right) for a young healthy subject is shown. Taking the Laplacian of the fieldmap successfully eliminates the substantial biasfields in the observed field. The estimated susceptibility map shares similar high frequency structure with the Laplacian of the observed field while low frequency structure is preserved by additional modeling constraints.]]
|}

= References =
1. Zecca L, et al. Nat Rev Neurosci, 5:863{73, Nov 2004.
2. Lustig M,et al. MRM. 2007. 58(6):1182.
3. Jenkinson M, et al. MRM. 2004. 52(3):471.
4. de Rochefort L, et al. MRM.2010. 63(1):194.
5. Weisskoff RM, et al. MRM. 1992. 24(2):375.

Projects:QuantitativeSusceptibilityMapping

2011-03-27T21:25:57Z

Cpoynton:

= Introduction =

There is increasing evidence that excessive iron deposition in specific regions
of the brain is associated with neurodegenerative disorders such as Alzheimer's
and Parkinson's disease [1]. The role of iron in the pathogenesis of these diseases
remains unknown and is difficult to determine without a non-invasive method
to quantify its concentration in-vivo. Since iron is a ferromagnetic substance,
changes in iron concentration result in local changes in the magnetic susceptibility of tissue.
In magnetic resonance imaging (MRI) experiments, differences
in magnetic susceptibility cause perturbations in the local magnetic field, which
can be computed from the phase of the MR signal (in a gradient echo sequence, the observed field is proportional to the MR phase).

= Description =

In MRI, magnetic susceptibility differences cause measurable perturbations in the local magnetic field that can be modeled as the convolution of a dipole-like kernel with the spatial susceptibility distribution. In the Fourier domain, the kernel exhibits zeros at the magic angle, preventing direct inversion of the field map; also, limited observations make the problem ill-posed. The observed data is also corrupted by confounding fields (ie. those from tissue/air interfaces, mis-set shims, and other non-local sources). Previous work has shown that MR images can be successfully reconstructed from under-sampled observations by exploiting the sparsity of in-vivo data under various transforms using methods from compressed sensing [1]. In susceptibility estimation, the forward model results in under-sampling of the data in the Fourier domain, but accurate estimates can be obtained using the Laplacian and L1 norm, which promote sparse solutions while removing external field artifacts. Our variational method for susceptibility estimation is described in Figs. 1-2.

{|
|[[File:Namic wiki fig1.png|thumb|400px|Fig 1. Relevant notation]]
|}

{|
|[[File:Latex pdf zoomed to paint equations.PNG|thumb|400px|Fig 2. Applying the Laplacian to the forward model in [1] eliminates non-local phase artifacts to give [2]. The first term in [3] provides regularization, penalizing large differences in spatial frequency relative to Magnitude data, while the second penalizes departures from [2], enforcing agreement of high frequency phase effects.]]
|}

== Forward Model (Eq. 1) ==

The forward model relates the perturbing field to the unknown susceptibility through a local term and convolution of the second z-derivative of the Green’s function of the Laplacian [2].

== Bias Field Elimination (Eq. 2) ==

Applying the Laplacian removes non-local phase effects such as shim fields, which are a solution to the Laplace equation.

== Objective Function (Eq. 3) ==

The first term provides regularization, penalizing solutions with large differences in spatial frequency structure relative to the magnitude image.
The second term penalizes departures from Eq. 2, by enforcing agreement of high frequency phase effects while eliminating low order bias fields.

== Data Acquisition ==

Cylindrical and rectangular phantoms were made using Magnevist (gadopentetate dimeglumine) solutions of 0.5, 1.0, 2.0, and 3.0 mM corresponding to susceptibility values of 0.15, 0.31, 0.62, and 0.94 ppm [3,4]. Field maps were obtained using a 3D multi-echo GRE sequence on a 3T Siemens Trio MRI.

= Results =

Application of the Laplacian removes substantial inhomogeniety in the field map in both phantoms as shown in Fig. 3 (Rectangular phantom) and Fig. 4 (Cylindrical phantom). Rectangular phantom: mean estimated susceptibility values for water and Magnevist were -9.049 and 0.6273 ppm, with true values of -9.050 and 0.6270 ppm. Cylindrical phantom: the estimated susceptibility map allowed different concentrations of Magnevist to be clearly identified and reasonable estimates were obtained in the presence of significant noise and bias due to external field effects.

{|
|[[File:Box mag.jpg|thumb|300|Fig 3a. Magnitude Image]]
|[[File:Box fmap.png|thumb|300|Fig 3b. Field map]]
|[[File:Box fmap lp.png|thumb|300|Fig 3c. Laplacian of the Field]]
|[[File:Box susc.png|thumb|300|Fig 3d. Estimated Susceptibility (ppm)]]
|}

{|
|[[File:Cyl mag.png|thumb|300|Fig 4a. Magnitude Image]]
|[[File:Cyl fmap.png|thumb|300|Fig 4b. Field map]]
|[[File:Cyl fmap lp.png|thumb|300|Fig 4c. Laplacian of the Field]]
|[[File:Cyl susc.png|thumb|300|Fig 4d. Estimated Susceptibility (ppm)]]
|[[File:Susc plot2.png|thumb|100|Fig 4e. Estimated vs. True mean susceptibility values for each tube (ppm)]]
|}

= Future Directions =

Future work will focus on quantifying magnetic susceptibility and iron content in the brain. Further development of the method described above has generated the preliminary results shown below in Fig 5.

{|
|[[File:Miccai fig1 crop.png|thumb|600px|Fig 5. The field map (left), laplacian of the field (center) and estimated susceptibility map (right) for a young healthy subject is shown. Taking the Laplacian of the fieldmap successfully eliminates the substantial biasfields in the observed field. The estimated susceptibility map shares similar high frequency structure with the Laplacian of the observed field while low frequency structure is preserved by additional modeling constraints.]]
|}

= References =

2. Lustig M,et al. MRM. 2007. 58(6):1182.
3. Jenkinson M, et al. MRM. 2004. 52(3):471.
4. de Rochefort L, et al. MRM.2010. 63(1):194.
5. Weisskoff RM, et al. MRM. 1992. 24(2):375.

Projects:QuantitativeSusceptibilityMapping

2011-03-27T21:25:16Z

Cpoynton:

= Introduction =

There is increasing evidence that excessive iron deposition in specific regions
of the brain is associated with neurodegenerative disorders such as Alzheimer's
and Parkinson's disease [1]. The role of iron in the pathogenesis of these diseases
remains unknown and is difficult to determine without a non-invasive method
to quantify its concentration in-vivo. Since iron is a ferromagnetic substance,
changes in iron concentration result in local changes in the magnetic susceptibility of tissue.
In magnetic resonance imaging (MRI) experiments, differences
in magnetic susceptibility cause perturbations in the local magnetic field, which
can be computed from the phase of the MR signal (in a gradient echo sequence, the observed field is proportional to the MR phase).

= Description =

In MRI, magnetic susceptibility differences cause measurable perturbations in the local magnetic field that can be modeled as the convolution of a dipole-like kernel with the spatial susceptibility distribution. In the Fourier domain, the kernel exhibits zeros at the magic angle, preventing direct inversion of the field map; also, limited observations make the problem ill-posed. The observed data is also corrupted by confounding fields (ie. those from tissue/air interfaces, mis-set shims, and other non-local sources). Previous work has shown that MR images can be successfully reconstructed from under-sampled observations by exploiting the sparsity of in-vivo data under various transforms using methods from compressed sensing [1]. In susceptibility estimation, the forward model results in under-sampling of the data in the Fourier domain, but accurate estimates can be obtained using the Laplacian and L1 norm, which promote sparse solutions while removing external field artifacts. Our variational method for susceptibility estimation is described in Figs. 1-2.

{|
|[[File:Namic wiki fig1.png|thumb|400px|Fig 1. Relevant notation]]
|}

{|
|[[File:Latex pdf zoomed to paint equations.PNG|thumb|400px|Fig 2. Applying the Laplacian to the forward model in [1] eliminates non-local phase artifacts to give [2]. The first term in [3] provides regularization, penalizing large differences in spatial frequency relative to Magnitude data, while the second penalizes departures from [2], enforcing agreement of high frequency phase effects.]]
|}

== Forward Model (Eq. 1) ==

The forward model relates the perturbing field to the unknown susceptibility through a local term and convolution of the second z-derivative of the Green’s function of the Laplacian [2].

== Bias Field Elimination (Eq. 2) ==

Applying the Laplacian removes non-local phase effects such as shim fields, which are a solution to the Laplace equation.

== Objective Function (Eq. 3) ==

The first term provides regularization, penalizing solutions with large differences in spatial frequency structure relative to the magnitude image.
The second term penalizes departures from Eq. 2, by enforcing agreement of high frequency phase effects while eliminating low order bias fields.

== Data Acquisition ==

Cylindrical and rectangular phantoms were made using Magnevist (gadopentetate dimeglumine) solutions of 0.5, 1.0, 2.0, and 3.0 mM corresponding to susceptibility values of 0.15, 0.31, 0.62, and 0.94 ppm [3,4]. Field maps were obtained using a 3D multi-echo GRE sequence on a 3T Siemens Trio MRI.

= Results =

Application of the Laplacian removes substantial inhomogeniety in the field map in both phantoms as shown in Fig. 3 (Rectangular phantom) and Fig. 4 (Cylindrical phantom). Rectangular phantom: mean estimated susceptibility values for water and Magnevist were -9.049 and 0.6273 ppm, with true values of -9.050 and 0.6270 ppm. Cylindrical phantom: the estimated susceptibility map allowed different concentrations of Magnevist to be clearly identified and reasonable estimates were obtained in the presence of significant noise and bias due to external field effects.

{|
|[[File:Box mag.jpg|thumb|300|Fig 3a. Magnitude Image]]
|[[File:Box fmap.png|thumb|300|Fig 3b. Field map]]
|[[File:Box fmap lp.png|thumb|300|Fig 3c. Laplacian of the Field]]
|[[File:Box susc.png|thumb|300|Fig 3d. Estimated Susceptibility (ppm)]]
|}

{|
|[[File:Cyl mag.png|thumb|300|Fig 4a. Magnitude Image]]
|[[File:Cyl fmap.png|thumb|300|Fig 4b. Field map]]
|[[File:Cyl fmap lp.png|thumb|300|Fig 4c. Laplacian of the Field]]
|[[File:Cyl susc.png|thumb|300|Fig 4d. Estimated Susceptibility (ppm)]]
|[[File:Susc plot2.png|thumb|100|Fig 4e. Estimated vs. True mean susceptibility values for each tube (ppm)]]
|}

= Future Directions =

Future work will focus on quantifying magnetic susceptibility and iron content in the brain. Further development of the method described above has generated the preliminary results shown below in Fig 5.

{|
|[[File:Miccai fig1 crop.png|thumb|600px|Fig 5. The field map (left), laplacian of the field (center) and estimated susceptibility map (right) for a young healthy subject is shown. Taking the Laplacian of the fieldmap successfully eliminates the substantial biasfields in the observed field. The estimated susceptibility map shares similar high frequency structure with the Laplacian of the observed field while low frequency structure is preserved by additional modeling constraints.]]
|}

= References =

1. Lustig M,et al. MRM. 2007. 58(6):1182.
2. Jenkinson M, et al. MRM. 2004. 52(3):471.
3. de Rochefort L, et al. MRM.2010. 63(1):194.
4. Weisskoff RM, et al. MRM. 1992. 24(2):375.
5. Cantillon-Murphy P, et al. NMR in Biomedicine, 2009. 22: 891.
6. http://www.fmrib.ox.ac.uk/fsl/.

Projects:QuantitativeSusceptibilityMapping

2011-03-27T21:23:09Z

Cpoynton: /* Future Directions */

= Introduction =

There is increasing evidence that excessive iron deposition in specific regions
of the brain is associated with neurodegenerative disorders such as Alzheimer's
and Parkinson's disease [1]. The role of iron in the pathogenesis of these diseases
remains unknown and is difficult to determine without a non-invasive method
to quantify its concentration in-vivo. Since iron is a ferromagnetic substance,
changes in iron concentration result in local changes in the magnetic susceptibility of tissue.
In magnetic resonance imaging (MRI) experiments, differences
in magnetic susceptibility cause perturbations in the local magnetic field, which
can be computed from the phase of the MR signal (in a gradient echo sequence, the observed field is proportional to the MR phase).

= Description =

In MRI, magnetic susceptibility differences cause measurable perturbations in the local magnetic field that can be modeled as the convolution of a dipole-like kernel with the spatial susceptibility distribution. In the Fourier domain, the kernel exhibits zeros at the magic angle, preventing direct inversion of the field map; also, limited observations make the problem ill-posed. The observed data is also corrupted by confounding fields (ie. those from tissue/air interfaces, mis-set shims, and other non-local sources). Previous work has shown that MR images can be successfully reconstructed from under-sampled observations by exploiting the sparsity of in-vivo data under various transforms using methods from compressed sensing [1]. In susceptibility estimation, the forward model results in under-sampling of the data in the Fourier domain, but accurate estimates can be obtained using the Laplacian and L1 norm, which promote sparse solutions while removing external field artifacts. Our variational method for susceptibility estimation is described in Figs. 1-2.

{|
|[[File:Namic wiki fig1.png|thumb|400px|Fig 1. Relevant notation]]
|}

{|
|[[File:Latex pdf zoomed to paint equations.PNG|thumb|400px|Fig 2. Applying the Laplacian to the forward model in [1] eliminates non-local phase artifacts to give [2]. The first term in [3] provides regularization, penalizing large differences in spatial frequency relative to Magnitude data, while the second penalizes departures from [2], enforcing agreement of high frequency phase effects.]]
|}

== Forward Model (Eq. 1) ==

The forward model relates the perturbing field to the unknown susceptibility through a local term and convolution of the second z-derivative of the Green’s function of the Laplacian [2].

== Bias Field Elimination (Eq. 2) ==

Applying the Laplacian removes non-local phase effects such as shim fields, which are a solution to the Laplace equation.

== Objective Function (Eq. 3) ==

The first term provides regularization, penalizing solutions with large differences in spatial frequency structure relative to the magnitude image.
The second term penalizes departures from Eq. 2, by enforcing agreement of high frequency phase effects while eliminating low order bias fields.

== Data Acquisition ==

Cylindrical and rectangular phantoms were made using Magnevist (gadopentetate dimeglumine) solutions of 0.5, 1.0, 2.0, and 3.0 mM corresponding to susceptibility values of 0.15, 0.31, 0.62, and 0.94 ppm [3,4]. Field maps were obtained using a 3D multi-echo GRE sequence on a 3T Siemens Trio MRI.

= Results =

Application of the Laplacian removes substantial inhomogeniety in the field map in both phantoms as shown in Fig. 3 (Rectangular phantom) and Fig. 4 (Cylindrical phantom). Rectangular phantom: mean estimated susceptibility values for water and Magnevist were -9.049 and 0.6273 ppm, with true values of -9.050 and 0.6270 ppm. Cylindrical phantom: the estimated susceptibility map allowed different concentrations of Magnevist to be clearly identified and reasonable estimates were obtained in the presence of significant noise and bias due to external field effects.

{|
|[[File:Box mag.jpg|thumb|300|Fig 3a. Magnitude Image]]
|[[File:Box fmap.png|thumb|300|Fig 3b. Field map]]
|[[File:Box fmap lp.png|thumb|300|Fig 3c. Laplacian of the Field]]
|[[File:Box susc.png|thumb|300|Fig 3d. Estimated Susceptibility (ppm)]]
|}

{|
|[[File:Cyl mag.png|thumb|300|Fig 4a. Magnitude Image]]
|[[File:Cyl fmap.png|thumb|300|Fig 4b. Field map]]
|[[File:Cyl fmap lp.png|thumb|300|Fig 4c. Laplacian of the Field]]
|[[File:Cyl susc.png|thumb|300|Fig 4d. Estimated Susceptibility (ppm)]]
|[[File:Susc plot2.png|thumb|100|Fig 4e. Estimated vs. True mean susceptibility values for each tube (ppm)]]
|}

= Future Directions =

Future work will focus on quantifying magnetic susceptibility and iron content in the brain. Further development of the method described above has generated the preliminary results shown below in Fig 5.

{|
|[[File:Miccai fig1 crop.png|thumb|600px|Fig 5. The field map (left), laplacian of the field (center) and estimated susceptibility map (right) for a young healthy subject is shown. Taking the Laplacian of the fieldmap successfully eliminates the substantial biasfields in the observed field. The estimated susceptibility map shares similar high frequency structure with the Laplacian of the observed field while low frequency structure is preserved by additional modeling constraints.]]
|}

Projects:QuantitativeSusceptibilityMapping

2011-03-27T21:18:49Z

Cpoynton: /* Future Directions */

= Introduction =

There is increasing evidence that excessive iron deposition in specific regions
of the brain is associated with neurodegenerative disorders such as Alzheimer's
and Parkinson's disease [1]. The role of iron in the pathogenesis of these diseases
remains unknown and is difficult to determine without a non-invasive method
to quantify its concentration in-vivo. Since iron is a ferromagnetic substance,
changes in iron concentration result in local changes in the magnetic susceptibility of tissue.
In magnetic resonance imaging (MRI) experiments, differences
in magnetic susceptibility cause perturbations in the local magnetic field, which
can be computed from the phase of the MR signal (in a gradient echo sequence, the observed field is proportional to the MR phase).

= Description =

In MRI, magnetic susceptibility differences cause measurable perturbations in the local magnetic field that can be modeled as the convolution of a dipole-like kernel with the spatial susceptibility distribution. In the Fourier domain, the kernel exhibits zeros at the magic angle, preventing direct inversion of the field map; also, limited observations make the problem ill-posed. The observed data is also corrupted by confounding fields (ie. those from tissue/air interfaces, mis-set shims, and other non-local sources). Previous work has shown that MR images can be successfully reconstructed from under-sampled observations by exploiting the sparsity of in-vivo data under various transforms using methods from compressed sensing [1]. In susceptibility estimation, the forward model results in under-sampling of the data in the Fourier domain, but accurate estimates can be obtained using the Laplacian and L1 norm, which promote sparse solutions while removing external field artifacts. Our variational method for susceptibility estimation is described in Figs. 1-2.

{|
|[[File:Namic wiki fig1.png|thumb|400px|Fig 1. Relevant notation]]
|}

{|
|[[File:Latex pdf zoomed to paint equations.PNG|thumb|400px|Fig 2. Applying the Laplacian to the forward model in [1] eliminates non-local phase artifacts to give [2]. The first term in [3] provides regularization, penalizing large differences in spatial frequency relative to Magnitude data, while the second penalizes departures from [2], enforcing agreement of high frequency phase effects.]]
|}

== Forward Model (Eq. 1) ==

The forward model relates the perturbing field to the unknown susceptibility through a local term and convolution of the second z-derivative of the Green’s function of the Laplacian [2].

== Bias Field Elimination (Eq. 2) ==

Applying the Laplacian removes non-local phase effects such as shim fields, which are a solution to the Laplace equation.

== Objective Function (Eq. 3) ==

The first term provides regularization, penalizing solutions with large differences in spatial frequency structure relative to the magnitude image.
The second term penalizes departures from Eq. 2, by enforcing agreement of high frequency phase effects while eliminating low order bias fields.

== Data Acquisition ==

Cylindrical and rectangular phantoms were made using Magnevist (gadopentetate dimeglumine) solutions of 0.5, 1.0, 2.0, and 3.0 mM corresponding to susceptibility values of 0.15, 0.31, 0.62, and 0.94 ppm [3,4]. Field maps were obtained using a 3D multi-echo GRE sequence on a 3T Siemens Trio MRI.

= Results =

Application of the Laplacian removes substantial inhomogeniety in the field map in both phantoms as shown in Fig. 3 (Rectangular phantom) and Fig. 4 (Cylindrical phantom). Rectangular phantom: mean estimated susceptibility values for water and Magnevist were -9.049 and 0.6273 ppm, with true values of -9.050 and 0.6270 ppm. Cylindrical phantom: the estimated susceptibility map allowed different concentrations of Magnevist to be clearly identified and reasonable estimates were obtained in the presence of significant noise and bias due to external field effects.

{|
|[[File:Box mag.jpg|thumb|300|Fig 3a. Magnitude Image]]
|[[File:Box fmap.png|thumb|300|Fig 3b. Field map]]
|[[File:Box fmap lp.png|thumb|300|Fig 3c. Laplacian of the Field]]
|[[File:Box susc.png|thumb|300|Fig 3d. Estimated Susceptibility (ppm)]]
|}

{|
|[[File:Cyl mag.png|thumb|300|Fig 4a. Magnitude Image]]
|[[File:Cyl fmap.png|thumb|300|Fig 4b. Field map]]
|[[File:Cyl fmap lp.png|thumb|300|Fig 4c. Laplacian of the Field]]
|[[File:Cyl susc.png|thumb|300|Fig 4d. Estimated Susceptibility (ppm)]]
|[[File:Susc plot2.png|thumb|100|Fig 4e. Estimated vs. True mean susceptibility values for each tube (ppm)]]
|}

= Future Directions =

Future work will focus on quantifying magnetic susceptibility and iron content in the brain. Further development of the method described above has generated the preliminary results shown below in Fig 5.

{|
|[[File:Miccai fig1 crop.png|thumb|800px|Fig 5. The field map (left), laplacian of the field (center) and estimated susceptibility map (right) for a young healthy subject is shown. Taking the Laplacian of the fieldmap successfully eliminates the substantial biasfields in the observed field. The estimated susceptibility map shares similar high frequency structure with the Laplacian of the observed field while low frequency structure is preserved by additional modeling constraints.]]
|}

Projects:QuantitativeSusceptibilityMapping

2011-03-27T21:18:10Z

Cpoynton: /* Future Directions */

= Introduction =

There is increasing evidence that excessive iron deposition in specific regions
of the brain is associated with neurodegenerative disorders such as Alzheimer's
and Parkinson's disease [1]. The role of iron in the pathogenesis of these diseases
remains unknown and is difficult to determine without a non-invasive method
to quantify its concentration in-vivo. Since iron is a ferromagnetic substance,
changes in iron concentration result in local changes in the magnetic susceptibility of tissue.
In magnetic resonance imaging (MRI) experiments, differences
in magnetic susceptibility cause perturbations in the local magnetic field, which
can be computed from the phase of the MR signal (in a gradient echo sequence, the observed field is proportional to the MR phase).

= Description =

In MRI, magnetic susceptibility differences cause measurable perturbations in the local magnetic field that can be modeled as the convolution of a dipole-like kernel with the spatial susceptibility distribution. In the Fourier domain, the kernel exhibits zeros at the magic angle, preventing direct inversion of the field map; also, limited observations make the problem ill-posed. The observed data is also corrupted by confounding fields (ie. those from tissue/air interfaces, mis-set shims, and other non-local sources). Previous work has shown that MR images can be successfully reconstructed from under-sampled observations by exploiting the sparsity of in-vivo data under various transforms using methods from compressed sensing [1]. In susceptibility estimation, the forward model results in under-sampling of the data in the Fourier domain, but accurate estimates can be obtained using the Laplacian and L1 norm, which promote sparse solutions while removing external field artifacts. Our variational method for susceptibility estimation is described in Figs. 1-2.

{|
|[[File:Namic wiki fig1.png|thumb|400px|Fig 1. Relevant notation]]
|}

{|
|[[File:Latex pdf zoomed to paint equations.PNG|thumb|400px|Fig 2. Applying the Laplacian to the forward model in [1] eliminates non-local phase artifacts to give [2]. The first term in [3] provides regularization, penalizing large differences in spatial frequency relative to Magnitude data, while the second penalizes departures from [2], enforcing agreement of high frequency phase effects.]]
|}

== Forward Model (Eq. 1) ==

The forward model relates the perturbing field to the unknown susceptibility through a local term and convolution of the second z-derivative of the Green’s function of the Laplacian [2].

== Bias Field Elimination (Eq. 2) ==

Applying the Laplacian removes non-local phase effects such as shim fields, which are a solution to the Laplace equation.

== Objective Function (Eq. 3) ==

The first term provides regularization, penalizing solutions with large differences in spatial frequency structure relative to the magnitude image.
The second term penalizes departures from Eq. 2, by enforcing agreement of high frequency phase effects while eliminating low order bias fields.

== Data Acquisition ==

Cylindrical and rectangular phantoms were made using Magnevist (gadopentetate dimeglumine) solutions of 0.5, 1.0, 2.0, and 3.0 mM corresponding to susceptibility values of 0.15, 0.31, 0.62, and 0.94 ppm [3,4]. Field maps were obtained using a 3D multi-echo GRE sequence on a 3T Siemens Trio MRI.

= Results =

Application of the Laplacian removes substantial inhomogeniety in the field map in both phantoms as shown in Fig. 3 (Rectangular phantom) and Fig. 4 (Cylindrical phantom). Rectangular phantom: mean estimated susceptibility values for water and Magnevist were -9.049 and 0.6273 ppm, with true values of -9.050 and 0.6270 ppm. Cylindrical phantom: the estimated susceptibility map allowed different concentrations of Magnevist to be clearly identified and reasonable estimates were obtained in the presence of significant noise and bias due to external field effects.

{|
|[[File:Box mag.jpg|thumb|300|Fig 3a. Magnitude Image]]
|[[File:Box fmap.png|thumb|300|Fig 3b. Field map]]
|[[File:Box fmap lp.png|thumb|300|Fig 3c. Laplacian of the Field]]
|[[File:Box susc.png|thumb|300|Fig 3d. Estimated Susceptibility (ppm)]]
|}

{|
|[[File:Cyl mag.png|thumb|300|Fig 4a. Magnitude Image]]
|[[File:Cyl fmap.png|thumb|300|Fig 4b. Field map]]
|[[File:Cyl fmap lp.png|thumb|300|Fig 4c. Laplacian of the Field]]
|[[File:Cyl susc.png|thumb|300|Fig 4d. Estimated Susceptibility (ppm)]]
|[[File:Susc plot2.png|thumb|100|Fig 4e. Estimated vs. True mean susceptibility values for each tube (ppm)]]
|}

= Future Directions =

Future work will focus on quantifying magnetic susceptibility and iron content in the brain. Further development of the method described above has generated the preliminary results shown below in Fig 5.

{|
|[[File:Miccai fig1 crop.png|thumb|800px|Fig 5. The field map (left), laplacian of the field (center) and estimated susceptibility map (right) for a young healthy subject is shown. Taking the Laplacian of the fieldmap successfully eliminates the substantial biasfields in the observed field map. The estimated susceptibility map shares similar high frequency structure with the Laplacian of the observed field while low frequency structure is preserved by additional modeling constraints.]]
|}

Projects:QuantitativeSusceptibilityMapping

2011-03-27T21:17:36Z

Cpoynton: /* Future Directions */

= Introduction =

There is increasing evidence that excessive iron deposition in specific regions
of the brain is associated with neurodegenerative disorders such as Alzheimer's
and Parkinson's disease [1]. The role of iron in the pathogenesis of these diseases
remains unknown and is difficult to determine without a non-invasive method
to quantify its concentration in-vivo. Since iron is a ferromagnetic substance,
changes in iron concentration result in local changes in the magnetic susceptibility of tissue.
In magnetic resonance imaging (MRI) experiments, differences
in magnetic susceptibility cause perturbations in the local magnetic field, which
can be computed from the phase of the MR signal (in a gradient echo sequence, the observed field is proportional to the MR phase).

= Description =

In MRI, magnetic susceptibility differences cause measurable perturbations in the local magnetic field that can be modeled as the convolution of a dipole-like kernel with the spatial susceptibility distribution. In the Fourier domain, the kernel exhibits zeros at the magic angle, preventing direct inversion of the field map; also, limited observations make the problem ill-posed. The observed data is also corrupted by confounding fields (ie. those from tissue/air interfaces, mis-set shims, and other non-local sources). Previous work has shown that MR images can be successfully reconstructed from under-sampled observations by exploiting the sparsity of in-vivo data under various transforms using methods from compressed sensing [1]. In susceptibility estimation, the forward model results in under-sampling of the data in the Fourier domain, but accurate estimates can be obtained using the Laplacian and L1 norm, which promote sparse solutions while removing external field artifacts. Our variational method for susceptibility estimation is described in Figs. 1-2.

{|
|[[File:Namic wiki fig1.png|thumb|400px|Fig 1. Relevant notation]]
|}

{|
|[[File:Latex pdf zoomed to paint equations.PNG|thumb|400px|Fig 2. Applying the Laplacian to the forward model in [1] eliminates non-local phase artifacts to give [2]. The first term in [3] provides regularization, penalizing large differences in spatial frequency relative to Magnitude data, while the second penalizes departures from [2], enforcing agreement of high frequency phase effects.]]
|}

== Forward Model (Eq. 1) ==

The forward model relates the perturbing field to the unknown susceptibility through a local term and convolution of the second z-derivative of the Green’s function of the Laplacian [2].

== Bias Field Elimination (Eq. 2) ==

Applying the Laplacian removes non-local phase effects such as shim fields, which are a solution to the Laplace equation.

== Objective Function (Eq. 3) ==

The first term provides regularization, penalizing solutions with large differences in spatial frequency structure relative to the magnitude image.
The second term penalizes departures from Eq. 2, by enforcing agreement of high frequency phase effects while eliminating low order bias fields.

== Data Acquisition ==

Cylindrical and rectangular phantoms were made using Magnevist (gadopentetate dimeglumine) solutions of 0.5, 1.0, 2.0, and 3.0 mM corresponding to susceptibility values of 0.15, 0.31, 0.62, and 0.94 ppm [3,4]. Field maps were obtained using a 3D multi-echo GRE sequence on a 3T Siemens Trio MRI.

= Results =

Application of the Laplacian removes substantial inhomogeniety in the field map in both phantoms as shown in Fig. 3 (Rectangular phantom) and Fig. 4 (Cylindrical phantom). Rectangular phantom: mean estimated susceptibility values for water and Magnevist were -9.049 and 0.6273 ppm, with true values of -9.050 and 0.6270 ppm. Cylindrical phantom: the estimated susceptibility map allowed different concentrations of Magnevist to be clearly identified and reasonable estimates were obtained in the presence of significant noise and bias due to external field effects.

{|
|[[File:Box mag.jpg|thumb|300|Fig 3a. Magnitude Image]]
|[[File:Box fmap.png|thumb|300|Fig 3b. Field map]]
|[[File:Box fmap lp.png|thumb|300|Fig 3c. Laplacian of the Field]]
|[[File:Box susc.png|thumb|300|Fig 3d. Estimated Susceptibility (ppm)]]
|}

{|
|[[File:Cyl mag.png|thumb|300|Fig 4a. Magnitude Image]]
|[[File:Cyl fmap.png|thumb|300|Fig 4b. Field map]]
|[[File:Cyl fmap lp.png|thumb|300|Fig 4c. Laplacian of the Field]]
|[[File:Cyl susc.png|thumb|300|Fig 4d. Estimated Susceptibility (ppm)]]
|[[File:Susc plot2.png|thumb|100|Fig 4e. Estimated vs. True mean susceptibility values for each tube (ppm)]]
|}

= Future Directions =

Future work will focus on quantifying magnetic susceptibility and iron content in the brain. Further development of the method described above has generated the preliminary results shown below in Fig 5.

{|
|[[File:Miccai fig1 crop.png|thumb|800px|Fig 5. The field map (left), laplacian of the field (center) and estimated susceptibility map (right) for a young healthy subject is shown above. Taking the Laplacian of the fieldmap successfully eliminates the substantial biasfields in the observed field map. The estimated susceptibility map shares similar high frequency structure with the Laplacian of the observed field while low frequency structure is preserved by additional modeling constraints.]]
|}

Projects:QuantitativeSusceptibilityMapping

2011-03-27T21:16:46Z

Cpoynton: /* Future Directions */

= Introduction =

There is increasing evidence that excessive iron deposition in specific regions
of the brain is associated with neurodegenerative disorders such as Alzheimer's
and Parkinson's disease [1]. The role of iron in the pathogenesis of these diseases
remains unknown and is difficult to determine without a non-invasive method
to quantify its concentration in-vivo. Since iron is a ferromagnetic substance,
changes in iron concentration result in local changes in the magnetic susceptibility of tissue.
In magnetic resonance imaging (MRI) experiments, differences
in magnetic susceptibility cause perturbations in the local magnetic field, which
can be computed from the phase of the MR signal (in a gradient echo sequence, the observed field is proportional to the MR phase).

= Description =

In MRI, magnetic susceptibility differences cause measurable perturbations in the local magnetic field that can be modeled as the convolution of a dipole-like kernel with the spatial susceptibility distribution. In the Fourier domain, the kernel exhibits zeros at the magic angle, preventing direct inversion of the field map; also, limited observations make the problem ill-posed. The observed data is also corrupted by confounding fields (ie. those from tissue/air interfaces, mis-set shims, and other non-local sources). Previous work has shown that MR images can be successfully reconstructed from under-sampled observations by exploiting the sparsity of in-vivo data under various transforms using methods from compressed sensing [1]. In susceptibility estimation, the forward model results in under-sampling of the data in the Fourier domain, but accurate estimates can be obtained using the Laplacian and L1 norm, which promote sparse solutions while removing external field artifacts. Our variational method for susceptibility estimation is described in Figs. 1-2.

{|
|[[File:Namic wiki fig1.png|thumb|400px|Fig 1. Relevant notation]]
|}

{|
|[[File:Latex pdf zoomed to paint equations.PNG|thumb|400px|Fig 2. Applying the Laplacian to the forward model in [1] eliminates non-local phase artifacts to give [2]. The first term in [3] provides regularization, penalizing large differences in spatial frequency relative to Magnitude data, while the second penalizes departures from [2], enforcing agreement of high frequency phase effects.]]
|}

== Forward Model (Eq. 1) ==

The forward model relates the perturbing field to the unknown susceptibility through a local term and convolution of the second z-derivative of the Green’s function of the Laplacian [2].

== Bias Field Elimination (Eq. 2) ==

Applying the Laplacian removes non-local phase effects such as shim fields, which are a solution to the Laplace equation.

== Objective Function (Eq. 3) ==

The first term provides regularization, penalizing solutions with large differences in spatial frequency structure relative to the magnitude image.
The second term penalizes departures from Eq. 2, by enforcing agreement of high frequency phase effects while eliminating low order bias fields.

== Data Acquisition ==

Cylindrical and rectangular phantoms were made using Magnevist (gadopentetate dimeglumine) solutions of 0.5, 1.0, 2.0, and 3.0 mM corresponding to susceptibility values of 0.15, 0.31, 0.62, and 0.94 ppm [3,4]. Field maps were obtained using a 3D multi-echo GRE sequence on a 3T Siemens Trio MRI.

= Results =

Application of the Laplacian removes substantial inhomogeniety in the field map in both phantoms as shown in Fig. 3 (Rectangular phantom) and Fig. 4 (Cylindrical phantom). Rectangular phantom: mean estimated susceptibility values for water and Magnevist were -9.049 and 0.6273 ppm, with true values of -9.050 and 0.6270 ppm. Cylindrical phantom: the estimated susceptibility map allowed different concentrations of Magnevist to be clearly identified and reasonable estimates were obtained in the presence of significant noise and bias due to external field effects.

{|
|[[File:Box mag.jpg|thumb|300|Fig 3a. Magnitude Image]]
|[[File:Box fmap.png|thumb|300|Fig 3b. Field map]]
|[[File:Box fmap lp.png|thumb|300|Fig 3c. Laplacian of the Field]]
|[[File:Box susc.png|thumb|300|Fig 3d. Estimated Susceptibility (ppm)]]
|}

{|
|[[File:Cyl mag.png|thumb|300|Fig 4a. Magnitude Image]]
|[[File:Cyl fmap.png|thumb|300|Fig 4b. Field map]]
|[[File:Cyl fmap lp.png|thumb|300|Fig 4c. Laplacian of the Field]]
|[[File:Cyl susc.png|thumb|300|Fig 4d. Estimated Susceptibility (ppm)]]
|[[File:Susc plot2.png|thumb|100|Fig 4e. Estimated vs. True mean susceptibility values for each tube (ppm)]]
|}

= Future Directions =

Future work will focus on quantifying magnetic susceptibility and iron content in the brain. Preliminary results based in part on the method described above are shown below in Fig 5.

{|
|[[File:Miccai fig1 crop.png|thumb|800px|Fig 5. The field map (left), laplacian of the field (center) and estimated susceptibility map (right) for a young healthy subject is shown above. Taking the Laplacian of the fieldmap successfully eliminates the substantial biasfields in the observed field map. The estimated susceptibility map shares similar high frequency structure with the Laplacian of the observed field while low frequency structure is preserved by additional modeling constraints.]]
|}

Projects:QuantitativeSusceptibilityMapping

2011-03-27T21:16:39Z

Cpoynton: /* Future Directions */

= Introduction =

There is increasing evidence that excessive iron deposition in specific regions
of the brain is associated with neurodegenerative disorders such as Alzheimer's
and Parkinson's disease [1]. The role of iron in the pathogenesis of these diseases
remains unknown and is difficult to determine without a non-invasive method
to quantify its concentration in-vivo. Since iron is a ferromagnetic substance,
changes in iron concentration result in local changes in the magnetic susceptibility of tissue.
In magnetic resonance imaging (MRI) experiments, differences
in magnetic susceptibility cause perturbations in the local magnetic field, which
can be computed from the phase of the MR signal (in a gradient echo sequence, the observed field is proportional to the MR phase).

= Description =

In MRI, magnetic susceptibility differences cause measurable perturbations in the local magnetic field that can be modeled as the convolution of a dipole-like kernel with the spatial susceptibility distribution. In the Fourier domain, the kernel exhibits zeros at the magic angle, preventing direct inversion of the field map; also, limited observations make the problem ill-posed. The observed data is also corrupted by confounding fields (ie. those from tissue/air interfaces, mis-set shims, and other non-local sources). Previous work has shown that MR images can be successfully reconstructed from under-sampled observations by exploiting the sparsity of in-vivo data under various transforms using methods from compressed sensing [1]. In susceptibility estimation, the forward model results in under-sampling of the data in the Fourier domain, but accurate estimates can be obtained using the Laplacian and L1 norm, which promote sparse solutions while removing external field artifacts. Our variational method for susceptibility estimation is described in Figs. 1-2.

{|
|[[File:Namic wiki fig1.png|thumb|400px|Fig 1. Relevant notation]]
|}

{|
|[[File:Latex pdf zoomed to paint equations.PNG|thumb|400px|Fig 2. Applying the Laplacian to the forward model in [1] eliminates non-local phase artifacts to give [2]. The first term in [3] provides regularization, penalizing large differences in spatial frequency relative to Magnitude data, while the second penalizes departures from [2], enforcing agreement of high frequency phase effects.]]
|}

== Forward Model (Eq. 1) ==

The forward model relates the perturbing field to the unknown susceptibility through a local term and convolution of the second z-derivative of the Green’s function of the Laplacian [2].

== Bias Field Elimination (Eq. 2) ==

Applying the Laplacian removes non-local phase effects such as shim fields, which are a solution to the Laplace equation.

== Objective Function (Eq. 3) ==

The first term provides regularization, penalizing solutions with large differences in spatial frequency structure relative to the magnitude image.
The second term penalizes departures from Eq. 2, by enforcing agreement of high frequency phase effects while eliminating low order bias fields.

== Data Acquisition ==

Cylindrical and rectangular phantoms were made using Magnevist (gadopentetate dimeglumine) solutions of 0.5, 1.0, 2.0, and 3.0 mM corresponding to susceptibility values of 0.15, 0.31, 0.62, and 0.94 ppm [3,4]. Field maps were obtained using a 3D multi-echo GRE sequence on a 3T Siemens Trio MRI.

= Results =

Application of the Laplacian removes substantial inhomogeniety in the field map in both phantoms as shown in Fig. 3 (Rectangular phantom) and Fig. 4 (Cylindrical phantom). Rectangular phantom: mean estimated susceptibility values for water and Magnevist were -9.049 and 0.6273 ppm, with true values of -9.050 and 0.6270 ppm. Cylindrical phantom: the estimated susceptibility map allowed different concentrations of Magnevist to be clearly identified and reasonable estimates were obtained in the presence of significant noise and bias due to external field effects.

{|
|[[File:Box mag.jpg|thumb|300|Fig 3a. Magnitude Image]]
|[[File:Box fmap.png|thumb|300|Fig 3b. Field map]]
|[[File:Box fmap lp.png|thumb|300|Fig 3c. Laplacian of the Field]]
|[[File:Box susc.png|thumb|300|Fig 3d. Estimated Susceptibility (ppm)]]
|}

{|
|[[File:Cyl mag.png|thumb|300|Fig 4a. Magnitude Image]]
|[[File:Cyl fmap.png|thumb|300|Fig 4b. Field map]]
|[[File:Cyl fmap lp.png|thumb|300|Fig 4c. Laplacian of the Field]]
|[[File:Cyl susc.png|thumb|300|Fig 4d. Estimated Susceptibility (ppm)]]
|[[File:Susc plot2.png|thumb|100|Fig 4e. Estimated vs. True mean susceptibility values for each tube (ppm)]]
|}

= Future Directions =

Future work will focus on quantifying magnetic susceptibility and iron content in the brain. Preliminary results based in part on the method described above are shown below in Fig 5.

{|
|[[File:Miccai fig1 crop.png|thumb|800|Fig 5. The field map (left), laplacian of the field (center) and estimated susceptibility map (right) for a young healthy subject is shown above. Taking the Laplacian of the fieldmap successfully eliminates the substantial biasfields in the observed field map. The estimated susceptibility map shares similar high frequency structure with the Laplacian of the observed field while low frequency structure is preserved by additional modeling constraints.]]
|}

Projects:QuantitativeSusceptibilityMapping

2011-03-27T21:16:10Z

Cpoynton: /* Future Directions */

= Introduction =

There is increasing evidence that excessive iron deposition in specific regions
of the brain is associated with neurodegenerative disorders such as Alzheimer's
and Parkinson's disease [1]. The role of iron in the pathogenesis of these diseases
remains unknown and is difficult to determine without a non-invasive method
to quantify its concentration in-vivo. Since iron is a ferromagnetic substance,
changes in iron concentration result in local changes in the magnetic susceptibility of tissue.
In magnetic resonance imaging (MRI) experiments, differences
in magnetic susceptibility cause perturbations in the local magnetic field, which
can be computed from the phase of the MR signal (in a gradient echo sequence, the observed field is proportional to the MR phase).

= Description =

In MRI, magnetic susceptibility differences cause measurable perturbations in the local magnetic field that can be modeled as the convolution of a dipole-like kernel with the spatial susceptibility distribution. In the Fourier domain, the kernel exhibits zeros at the magic angle, preventing direct inversion of the field map; also, limited observations make the problem ill-posed. The observed data is also corrupted by confounding fields (ie. those from tissue/air interfaces, mis-set shims, and other non-local sources). Previous work has shown that MR images can be successfully reconstructed from under-sampled observations by exploiting the sparsity of in-vivo data under various transforms using methods from compressed sensing [1]. In susceptibility estimation, the forward model results in under-sampling of the data in the Fourier domain, but accurate estimates can be obtained using the Laplacian and L1 norm, which promote sparse solutions while removing external field artifacts. Our variational method for susceptibility estimation is described in Figs. 1-2.

{|
|[[File:Namic wiki fig1.png|thumb|400px|Fig 1. Relevant notation]]
|}

{|
|[[File:Latex pdf zoomed to paint equations.PNG|thumb|400px|Fig 2. Applying the Laplacian to the forward model in [1] eliminates non-local phase artifacts to give [2]. The first term in [3] provides regularization, penalizing large differences in spatial frequency relative to Magnitude data, while the second penalizes departures from [2], enforcing agreement of high frequency phase effects.]]
|}

== Forward Model (Eq. 1) ==

The forward model relates the perturbing field to the unknown susceptibility through a local term and convolution of the second z-derivative of the Green’s function of the Laplacian [2].

== Bias Field Elimination (Eq. 2) ==

Applying the Laplacian removes non-local phase effects such as shim fields, which are a solution to the Laplace equation.

== Objective Function (Eq. 3) ==

The first term provides regularization, penalizing solutions with large differences in spatial frequency structure relative to the magnitude image.
The second term penalizes departures from Eq. 2, by enforcing agreement of high frequency phase effects while eliminating low order bias fields.

== Data Acquisition ==

Cylindrical and rectangular phantoms were made using Magnevist (gadopentetate dimeglumine) solutions of 0.5, 1.0, 2.0, and 3.0 mM corresponding to susceptibility values of 0.15, 0.31, 0.62, and 0.94 ppm [3,4]. Field maps were obtained using a 3D multi-echo GRE sequence on a 3T Siemens Trio MRI.

= Results =

Application of the Laplacian removes substantial inhomogeniety in the field map in both phantoms as shown in Fig. 3 (Rectangular phantom) and Fig. 4 (Cylindrical phantom). Rectangular phantom: mean estimated susceptibility values for water and Magnevist were -9.049 and 0.6273 ppm, with true values of -9.050 and 0.6270 ppm. Cylindrical phantom: the estimated susceptibility map allowed different concentrations of Magnevist to be clearly identified and reasonable estimates were obtained in the presence of significant noise and bias due to external field effects.

{|
|[[File:Box mag.jpg|thumb|300|Fig 3a. Magnitude Image]]
|[[File:Box fmap.png|thumb|300|Fig 3b. Field map]]
|[[File:Box fmap lp.png|thumb|300|Fig 3c. Laplacian of the Field]]
|[[File:Box susc.png|thumb|300|Fig 3d. Estimated Susceptibility (ppm)]]
|}

{|
|[[File:Cyl mag.png|thumb|300|Fig 4a. Magnitude Image]]
|[[File:Cyl fmap.png|thumb|300|Fig 4b. Field map]]
|[[File:Cyl fmap lp.png|thumb|300|Fig 4c. Laplacian of the Field]]
|[[File:Cyl susc.png|thumb|300|Fig 4d. Estimated Susceptibility (ppm)]]
|[[File:Susc plot2.png|thumb|100|Fig 4e. Estimated vs. True mean susceptibility values for each tube (ppm)]]
|}

= Future Directions =

Future work will focus on quantifying magnetic susceptibility and iron content in the brain. Preliminary results based in part on the method described above are shown below in Fig 5.

{|
|[[File:Miccai fig1 crop.png|800|Fig 5. The field map (left), laplacian of the field (center) and estimated susceptibility map (right) for a young healthy subject is shown above. Taking the Laplacian of the fieldmap successfully eliminates the substantial biasfields in the observed field map. The estimated susceptibility map shares similar high frequency structure with the Laplacian of the observed field while low frequency structure is preserved by additional modeling constraints.]]
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