# Algorithms

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# Algorithms

The NA-MIC Algorithm scientists are responsible for pushing the boundaries of applied mathematical techniques in the context of the challenges of the Center's driving biological projects(DBPs). Their effort is currently focused on personalized medicine or patient-specific analysis of images. The goal is to address clinical problems that entail sequences of images from individuals with pathologies that deviate from normal population datasets. These applications are characterized by images that vary significantly from one patient to another, or from one time point to another, in ways that present distinct challenges to the current state-of-art algorithms used for image analysis. The clinical applications of the DBPs reflect this emphasis on individually distinct anatomy, pathology, and function. The importance of this new emphasis for the Algorithm effort is best understood in the context of the current technology for medical image analysis. Although image analysis tools are based on quite diverse methodologies, the most widely used methods rely on a large degree of anatomical similarity. For instance, tools for brain image analysis lean heavily upon the geometric regularity and stability of brain anatomy and function. Tools for image-guided therapy rely on carefully configured or engineered environments. This regularity or predictability allows prior knowledge, encoded as either a set of rules or population statistics, to constrain the problem and enable effective interpretation of images.

While these applications are important, much of medical practice has not benefited from the associated advances in medical image analysis. Indeed, most clinical practice is concerned with the treatment of patients who are either injured or exhibit a pathology that, when imaged, does not present itself in the highly predictable manner assumed by many analysis methods. The aim of the Algorithms team is to address a new set of technical challenges that represent opportunities to advance image analysis tools to impact a broader spectrum of applications in clinical practice. These include (1) Statistical models of anatomy and pathology, (2) Geometric correspondence, (3) User interactive tools for segmentation, and (4) Longitudinal and time-series analysis.

## Statistical models of anatomy and pathology

We are currently developing technologies for representing and applying statistical models to capture a wider range of anatomies and pathologies than is currently considered by state-of-art technologies in image analysis. Such statistical models play an important role in virtually all types of advanced algorithms in medical image analysis. However, these methods rely on relatively simple, parametric distributions. Unfortunately, traditional parametric models cannot capture large, inherently nonlinear anatomical variations in heterogeneous populations. For instance, the changes in the surrounding anatomy induced by a tumor or positions of organs in a highly deformable anatomy, such as the abdomen, cannot be represented as small, continuous deviations from a mean. More sophisticated statistical models are needed to adequately address problems in personalized medicine. Over the next several years our research in statistical modeling from images will be used to produce practical algorithms directly relevant to the clinical problems of the current DBPs. Specifically, we will develop models that can handle (1) changes in heart images that result from fibrosis and remodeling; (2) longitudinal change due to tissue degeneration in brain disorders such as Huntington's Disease; (3) differences in anatomical images induced by changes in the tumor and surrounding structures during radiation treatment; and (4) dramatic effects of traumatic brain injury, intensity and shape of brain structures, and the effects of lesions on white matter connectivity.

## Geometric correspondence

We are also developing tools for geometric correspondence between images, coordinate systems, shapes, and anatomies that are robust to anatomical and pathological variability. Establishing anatomical correspondences between pairs of patients, groups of patients, patients and templates, and individual patients over time is important for automatic and user-assisted image analysis. As with statistical models, state-of-art approaches typically rely on assumptions about geometric mappings or transformations, such as smoothness or invertibility, which make the analysis and computation more manageable. However, in applications that entail pathologies and thus more deformable anatomies, collections of anatomical objects can have very different shapes, topologies, and intensity boundary profiles. The ability to establish geometric correspondences, with and without expert guidance, in challenging clinical circumstances is essential for the DBPs. For example, in imaging patients with traumatic brain injuries, we propose to develop new methods to identify anatomy in the presence of large displacements and missing parts of organs and tissues, as well dramatic discrepancies in intensity or signal. For head and neck cancer imaging, the patient’s pose can dramatically affect the relative positions of tissues and organs, and for atrial fibrillation, physicians have requested comparisons of heart images taken before and after the process of remodeling. To address these problems, we will develop more flexible, general, and robust techniques for geometric correspondence.

## User interactive tools for segmentation

New tools are needed for user-guided segmentation of tissues, organs, and lesions to enable clinicians to process images in very general circumstances. We are currently developing methodologies for patient-specific image segmentation that can be used in settings where the heterogeneity and variability of anatomy, pathology, and/or injury impedes the construction of conventional high level statistical models, but where users can see the structures of interest by observing contrast, lines, shapes, textures, or other image attributes - a development important for all DBPs. Our work will address the challenges of formulating the problem to capture important image properties and incorporate user input quickly and effectively. Beyond the DBPs, experience tell us that the range of medical and biological applications is so diverse that a set of reliable, light-weight, easy-to-use tools is a critical need. Furthermore, even when more automated analyses are feasible, they require some level of bootstrapping, using examples from segmentations that are driven by user interaction and low-level image features. We will address these problems by developing new formulations that make better use of user input and image features, new optimization strategies that are fast and effective, and new computational algorithms that run very efficiently on state-of-art computer architectures.

## Longitudinal and time-series analysis

We are developing algorithms for statistical and geometric analysis that operate on multiple images of the same patient, or on collections of patients acquired over time. These algorithms are essential for patient-specific data analysis to assess how disease or injury progresses or responds to treatment. Current cross-sectional analysis of longitudinal data does not provide a model of growth or change that considers the inherent correlation of repeated images of individuals, nor does it tell us how an individual patient changes relative to a change over time of a comparable healthy or disease-specific population, which often defines the basis for treatment planning. Two aspects are of particular importance for this project. First, when the progression or time behavior of a condition is an important component of the differences between groups, the statistical power of comparisons benefit from subject-specific, time-dependent analysis. Second, the availability of longitudinal data presents an opportunity to leverage images at multiple time points for evaluations of shape and function. This adds a dynamic aspect to the process that can be useful in recognizing important aspects of disease or recovery. Longitudinal image analysis is important for all four DBPs in this project. The traumatic brain injury DBP, for instance, will monitor the progress of patients during recovery, and tools for systematically analyzing these changes will be essential. Likewise, the Head and Neck Cancer DBP, the Atrial Fibrillation DBP, and the Huntington’s Disease DBP all will require comparisons of patients across multiple time points, and the ability to consolidate these longitudinal models across collections of patients in comparison to healthy controls.