HistoEM: A Pathologist-Guided and Explainable Workflow Using Histogram Embedding for Gland Classification.

Pathologists have, over several decades, developed criteria for diagnosing and grading prostate cancer. However, this knowledge has not, so far, been included in the design of convolutional neural networks (CNN) for prostate cancer detection and grading. Further, it is not known whether the features learned by machine-learning algorithms coincide with diagnostic features used by pathologists. We propose a framework that enforces algorithms to learn the cellular and subcellular differences between benign and cancerous prostate glands in digital slides from hematoxylin and eosin-stained tissue sections. After accurate gland segmentation and exclusion of the stroma, the central component of the pipeline, named HistoEM, utilizes a histogram embedding of features from the latent space of the CNN encoder. Each gland is represented by 128 feature-wise histograms that provide the input into a second network for benign vs cancer classification of the whole gland. Cancer glands are further processed by a U-Net structured network to separate low-grade from high-grade cancer. Our model demonstrates similar performance compared with other state-of-the-art prostate cancer grading models with gland-level resolution. To understand the features learned by HistoEM, we first rank features based on the distance between benign and cancer histograms and visualize the tissue origins of the 2 most important features. A heatmap of pixel activation by each feature is generated using Grad-CAM and overlaid on nuclear segmentation outlines. We conclude that HistoEM, similar to pathologists, uses nuclear features for the detection of prostate cancer. Altogether, this novel approach can be broadly deployed to visualize computer-learned features in histopathology images.

Using Convolutional Neural Networks to Derive Neighborhood Built Environments from Google Street View Images and Examine Their Associations with Health Outcomes.

Built environment neighborhood characteristics are difficult to measure and assess on a large scale. Consequently, there is a lack of sufficient data that can help us investigate neighborhood characteristics as structural determinants of health on a national level. The objective of this study is to utilize publicly available Google Street View images as a data source for characterizing built environments and to examine the influence of built environments on chronic diseases and health behaviors in the United States. Data were collected by processing 164 million Google Street View images from November 2019 across the United States. Convolutional Neural Networks, a class of multi-layer deep neural networks, were used to extract features of the built environment. Validation analyses found accuracies of 82% or higher across neighborhood characteristics. In regression analyses controlling for census tract sociodemographics, we find that single-lane roads (an indicator of lower urban development) were linked with chronic conditions and worse mental health. Walkability and urbanicity indicators such as crosswalks, sidewalks, and two or more cars were associated with better health, including reduction in depression, obesity, high blood pressure, and high cholesterol. Street signs and streetlights were also found to be associated with decreased chronic conditions. Chain link fence (physical disorder indicator) was generally associated with poorer mental health. Living in neighborhoods with a built environment that supports social interaction and physical activity can lead to positive health outcomes. Computer vision models using manually annotated Google Street View images as a training dataset were able to accurately identify neighborhood built environment characteristics. These methods increases the feasibility, scale, and efficiency of neighborhood studies on health.

A Nonparametric Approach for Estimating Three-Dimensional Fiber Orientation Distribution Functions (ODFs) in Fibrous Materials.

Many biological tissues contain an underlying fibrous microstructure that is optimized to suit a physiological function. The fiber architecture dictates physical characteristics such as stiffness, diffusivity, and electrical conduction. Abnormal deviations of fiber architecture are often associated with disease. Thus, it is useful to characterize fiber network organization from image data in order to better understand pathological mechanisms. We devised a method to quantify distributions of fiber orientations based on the Fourier transform and the Qball algorithm from diffusion MRI. The Fourier transform was used to decompose images into directional components, while the Qball algorithm efficiently converted the directional data from the frequency domain to the orientation domain. The representation in the orientation domain does not require any particular functional representation, and thus the method is nonparametric. The algorithm was verified to demonstrate its reliability and used on datasets from microscopy to show its applicability. This method increases the ability to extract information of microstructural fiber organization from experimental data that will enhance our understanding of structure-function relationships and enable accurate representation of material anisotropy in biological tissues.

Prediction of femoral head coverage from articulated statistical shape models of patients with developmental dysplasia of the hip.

Developmental dysplasia of the hip (DDH) is commonly described as reduced femoral head coverage due to anterolateral acetabular deficiency. Although reduced coverage is the defining trait of DDH, more subtle and localized anatomic features of the joint are also thought to contribute to symptom development and degeneration. These features are challenging to identify using conventional approaches. Herein, we assessed the morphology of the full femur and hemi-pelvis using an articulated statistical shape model (SSM). The model determined the morphological and pose-based variations associated with DDH in a population of Japanese females and established which of these variations predict coverage. Computed tomography (CT) images of 83 hips from 47 patients were segmented for input into a correspondence-based SSM. The dominant modes of variation in the model initially represented scale and pose. After removal of these factors through individual bone alignment, femoral version and neck-shaft angle, pelvic curvature, and acetabular version dominated the observed variation. Femoral head oblateness and prominence of the acetabular rim and various muscle attachment sites of the femur and hemi-pelvis were found to predict 3D CT-based coverage measurements (R2 = 0.5-0.7 for the full bones, R2 = 0.9 for the joint). Statement of Clinical Significance: Currently, clinical measurements of DDH only consider the morphology of the acetabulum. However, the results of this study demonstrated that variability in femoral head shape and several muscle attachment sites were predictive of femoral head coverage. These morphological differences may provide insight into improved clinical diagnosis and surgical planning based on functional adaptations of patients with DDH.

Community-Based Measurements Reveal Unseen Differences during Air Pollution Episodes.

Short-term exposure to fine particulate matter (PM2.5) pollution is linked to numerous adverse health effects. Pollution episodes, such as wildfires, can lead to substantial increases in PM2.5 levels. However, sparse regulatory measurements provide an incomplete understanding of pollution gradients. Here, we demonstrate an infrastructure that integrates community-based measurements from a network of low-cost PM2.5 sensors with rigorous calibration and a Gaussian process model to understand neighborhood-scale PM2.5 concentrations during three pollution episodes (July 4, 2018, fireworks; July 5 and 6, 2018, wildfire; Jan 3-7, 2019, persistent cold air pool, PCAP). The firework/wildfire events included 118 sensors in 84 locations, while the PCAP event included 218 sensors in 138 locations. The model results accurately predict reference measurements during the fireworks (n: 16, hourly root-mean-square error, RMSE, 12.3-21.5 µg/m3, n(normalized)RMSE: 14.9-24%), the wildfire (n: 46, RMSE: 2.6-4.0 µg/m3; nRMSE: 13.1-22.9%), and the PCAP (n: 96, RMSE: 4.9-5.7 µg/m3; nRMSE: 20.2-21.3%). They also revealed dramatic geospatial differences in PM2.5 concentrations that are not apparent when only considering government measurements or viewing the US Environmental Protection Agency's AirNow visualizations. Complementing the PM2.5 estimates and visualizations are highly resolved uncertainty maps. Together, these results illustrate the potential for low-cost sensor networks that combined with a data-fusion algorithm and appropriate calibration and training can dynamically and with improved accuracy estimate PM2.5 concentrations during pollution episodes. These highly resolved uncertainty estimates can provide a much-needed strategy to communicate uncertainty to end users.

An Optimal, Generative Model for Estimating Multi-Label Probabilistic Maps.

Multi-label probabilistic maps, a.k.a. probabilistic segmentations, parameterize a population of intimately co-existing anatomical shapes and are useful for various medical imaging applications, such as segmentation, anatomical atlases, shape analysis, and consensus generation. Existing methods to estimate probabilistic segmentations rely on ad hoc intermediate representations (e.g., average of Gaussian-smoothed label maps and smoothed signed distance maps) that do not necessarily conform to the underlying generative process. Generative modeling of such maps could help discover as well as aide in the statistical analysis of sub-groups in a population via clustering and mixture modeling techniques. In this paper, we propose an estimation of multi-label probabilistic maps and showcase their favorable performance for modeling anatomical shapes such as the left atrium of the human heart and brain structures. The proposed formulation relies on a constrained optimization in the natural parameter space of the exponential family form of categorical distributions. A smoothness prior provides generalizability in the model and helps achieve greater performance in modeling tasks for unseen samples. We demonstrate and compare the effectiveness of the proposed method for Bayesian image segmentation, multi-atlas segmentation, and shape-based clustering.

Self-Supervised Discovery of Anatomical Shape Landmarks.

Statistical shape analysis is a very useful tool in a wide range of medical and biological applications. However, it typically relies on the ability to produce a relatively small number of features that can capture the relevant variability in a population. State-of-the-art methods for obtaining such anatomical features rely on either extensive preprocessing or segmentation and/or significant tuning and post-processing. These shortcomings limit the widespread use of shape statistics. We propose that effective shape representations should provide sufficient information to align/register images. Using this assumption we propose a self-supervised, neural network approach for automatically positioning and detecting landmarks in images that can be used for subsequent analysis. The network discovers the landmarks corresponding to anatomical shape features that promote good image registration in the context of a particular class of transformations. In addition, we also propose a regularization for the proposed network which allows for a uniform distribution of these discovered landmarks. In this paper, we present a complete framework, which only takes a set of input images and produces landmarks that are immediately usable for statistical shape analysis. We evaluate the performance on a phantom dataset as well as 2D and 3D images.

Combined Estimation of Shape and Pose for Statistical Analysis of Articulating Joints.

Quantifying shape variations in articulated joints is of utmost interest to understand the underlying joint biomechanics and associated clinical symptoms. For joint comparisons and analysis, the relative positions of the bones can confound subsequent analysis. Clinicians design specific image acquisition protocols to neutralize the individual pose variations. However, recent studies have shown that even specific acquisition protocols fail to achieve consistent pose. The individual pose variations are largely attributed to the day-to-day functioning of the patient, such as gait during walk, as well as interactions between specific morphologies and joint alignment. This paper presents a novel two-step method to neutralize such patient-specific variations while simultaneously preserving the inherent relationship of the articulated joint. The resulting shape models are then used to discover clinically relevant shape variations in a population of hip joints.

Which Two-dimensional Radiographic Measurements of Cam Femoroacetabular Impingement Best Describe the Three-dimensional Shape of the Proximal Femur?

BACKGROUND: Many two-dimensional (2-D) radiographic views are used to help diagnose cam femoroacetabular impingement (FAI), but there is little consensus as to which view or combination of views is most effective at visualizing the magnitude and extent of the cam lesion (ie, severity). Previous studies have used a single image from a sequence of CT or MR images to serve as a reference standard with which to evaluate the ability of 2-D radiographic views and associated measurements to describe the severity of the cam lesion. However, single images from CT or MRI data may fail to capture the apex of the cam lesion. Thus, it may be more appropriate to use measurements of three-dimensional (3-D) surface reconstructions from CT or MRI data to serve as an anatomic reference standard when evaluating radiographic views and associated measurements used in the diagnosis of cam FAI. QUESTIONS/PURPOSES: The purpose of this study was to use digitally reconstructed radiographs and 3-D statistical shape modeling to (1) determine the correlation between 2-D radiographic measurements of cam FAI and 3-D metrics of proximal femoral shape; and 2) identify the combination of radiographic measurements from plain film projections that were most effective at predicting the 3-D shape of the proximal femur. METHODS: This study leveraged previously acquired CT images of the femur from a convenience sample of 37 patients (34 males; mean age, 27 years, range, 16-47 years; mean body mass index [BMI], 24.6 kg/m, range, 19.0-30.2 kg/m) diagnosed with cam FAI imaged between February 2005 and January 2016. Patients were diagnosed with cam FAI based on a culmination of clinical examinations, history of hip pain, and imaging findings. The control group consisted of 59 morphologically normal control participants (36 males; mean age, 29 years, range, 15-55 years; mean BMI, 24.4 kg/m, range, 16.3-38.6 kg/m) imaged between April 2008 and September 2014. Of these controls, 30 were cadaveric femurs and 29 were living participants. All controls were screened for evidence of femoral deformities using radiographs. In addition, living control participants had no history of hip pain or previous surgery to the hip or lower limbs. CT images were acquired for each participant and the surface of the proximal femur was segmented and reconstructed. Surfaces were input to our statistical shape modeling pipeline, which objectively calculated 3-D shape scores that described the overall shape of the entire proximal femur and of the region of the femur where the cam lesion is typically located. Digital reconstructions for eight plain film views (AP, Meyer lateral, 45° Dunn, modified 45° Dunn, frog-leg lateral, Espié frog-leg, 90° Dunn, and cross-table lateral) were generated from CT data. For each view, measurements of the α angle and head-neck offset were obtained by two researchers (intraobserver correlation coefficients of 0.80-0.94 for the α angle and 0.42-0.80 for the head-neck offset measurements). The relationships between radiographic measurements from each view and the 3-D shape scores (for the entire proximal femur and for the region specific to the cam lesion) were assessed with linear correlation. Additionally, partial least squares regression was used to determine which combination of views and measurements was the most effective at predicting 3-D shape scores. RESULTS: Three-dimensional shape scores were most strongly correlated with α angle on the cross-table view when considering the entire proximal femur (r = -0.568; p < 0.001) and on the Meyer lateral view when considering the region of the cam lesion (r = -0.669; p < 0.001). Partial least squares regression demonstrated that measurements from the Meyer lateral and 90° Dunn radiographs produced the optimized regression model for predicting shape scores for the proximal femur (R = 0.405, root mean squared error of prediction [RMSEP] = 1.549) and the region of the cam lesion (R = 0.525, RMSEP = 1.150). Interestingly, views with larger differences in the α angle and head-neck offset between control and cam FAI groups did not have the strongest correlations with 3-D shape. CONCLUSIONS: Considered together, radiographic measurements from the Meyer lateral and 90° Dunn views provided the most effective predictions of 3-D shape of the proximal femur and the region of the cam lesion as determined using shape modeling metrics. CLINICAL RELEVANCE: Our results suggest that clinicians should consider using the Meyer lateral and 90° Dunn views to evaluate patients in whom cam FAI is suspected. However, the α angle and head-neck offset measurements from these and other plain film views could describe no more than half of the overall variation in the shape of the proximal femur and cam lesion. Thus, caution should be exercised when evaluating femoral head anatomy using the α angle and head-neck offset measurements from plain film radiographs. Given these findings, we believe there is merit in pursuing research that aims to develop the framework necessary to integrate statistical shape modeling into clinical evaluation, because this could aid in the diagnosis of cam FAI.

A Cooperative Autoencoder for Population-Based Regularization of CNN Image Registration.

Spatial transformations are enablers in a variety of medical image analysis applications that entail aligning images to a common coordinate systems. Population analysis of such transformations is expected to capture the underlying image and shape variations, and hence these transformations are required to produce anatomically feasible correspondences. This is usually enforced through some smoothness-based generic metric or regularization of the deformation field. Alternatively, population-based regularization has been shown to produce anatomically accurate correspondences in cases where anatomically unaware (i.e., data independent) regularization fail. Recently, deep networks have been used to generate spatial transformations in an unsupervised manner, and, once trained, these networks are computationally faster and as accurate as conventional, optimization-based registration methods. However, the deformation fields produced by these networks require smoothness penalties, just as the conventional registration methods, and ignores population-level statistics of the transformations. Here, we propose a novel neural network architecture that simultaneously learns and uses the population-level statistics of the spatial transformations to regularize the neural networks for unsupervised image registration. This regularization is in the form of a bottleneck autoencoder, which learns and adapts to the population of transformations required to align input images by encoding the transformations to a low dimensional manifold. The proposed architecture produces deformation fields that describe the population-level features and associated correspondences in an anatomically relevant manner and are statistically compact relative to the state-of-the-art approaches while maintaining computational efficiency. We demonstrate the efficacy of the proposed architecture on synthetic data sets, as well as 2D and 3D medical data.

DeepSSM: A Deep Learning Framework for Statistical Shape Modeling from Raw Images.

Statistical shape modeling is an important tool to characterize variation in anatomical morphology. Typical shapes of interest are measured using 3D imaging and a subsequent pipeline of registration, segmentation, and some extraction of shape features or projections onto some lower-dimensional shape space, which facilitates subsequent statistical analysis. Many methods for constructing compact shape representations have been proposed, but are often impractical due to the sequence of image preprocessing operations, which involve significant parameter tuning, manual delineation, and/or quality control by the users. We propose DeepSSM: a deep learning approach to extract a low-dimensional shape representation directly from 3D images, requiring virtually no parameter tuning or user assistance. DeepSSM uses a convolutional neural network (CNN) that simultaneously localizes the biological structure of interest, establishes correspondences, and projects these points onto a low-dimensional shape representation in the form of PCA loadings within a point distribution model. To overcome the challenge of the limited availability of training images with dense correspondences, we present a novel data augmentation procedure that uses existing correspondences on a relatively small set of processed images with shape statistics to create plausible training samples with known shape parameters. In this way, we leverage the limited CT/MRI scans (40-50) into thousands of images needed to train a deep neural net. After the training, the CNN automatically produces accurate low-dimensional shape representations for unseen images. We validate DeepSSM for three different applications pertaining to modeling pediatric cranial CT for characterization of metopic craniosynostosis, femur CT scans identifying morphologic deformities of the hip due to femoroacetabular impingement, and left atrium MRI scans for atrial fibrillation recurrence prediction.

Shape analysis of the basioccipital bone in Pax7-deficient mice.

We compared the cranial base of newborn Pax7-deficient and wildtype mice using a computational shape modeling technology called particle-based modeling (PBM). We found systematic differences in the morphology of the basiooccipital bone, including a broadening of the basioccipital bone and an antero-inferior inflection of its posterior edge in the Pax7-deficient mice. We show that the Pax7 cell lineage contributes to the basioccipital bone and that the location of the Pax7 lineage correlates with the morphology most effected by Pax7 deficiency. Our results suggest that the Pax7-deficient mouse may be a suitable model for investigating the genetic control of the location and orientation of the foramen magnum, and changes in the breadth of the basioccipital.

ShapeCut: Bayesian surface estimation using shape-driven graph.

A variety of medical image segmentation problems present significant technical challenges, including heterogeneous pixel intensities, noisy/ill-defined boundaries and irregular shapes with high variability. The strategy of estimating optimal segmentations within a statistical framework that combines image data with priors on anatomical structures promises to address some of these technical challenges. However, methods that rely on local optimization techniques and/or local shape penalties (e.g., smoothness) have been proven to be inadequate for many difficult segmentation problems. These challenging segmentation problems can benefit from the inclusion of global shape priors within a maximum-a-posteriori estimation framework, which biases solutions toward an object class of interest. In this paper, we propose a maximum-a-posteriori formulation that relies on a generative image model by incorporating both local and global shape priors. The proposed method relies on graph cuts as well as a new shape parameters estimation that provides a global updates-based optimization strategy. We demonstrate our approach on synthetic datasets as well as on the left atrial wall segmentation from late-gadolinium enhancement MRI, which has been shown to be effective for identifying myocardial fibrosis in the diagnosis of atrial fibrillation. Experimental results prove the effectiveness of the proposed approach in terms of the average surface distance between extracted surfaces and the corresponding ground-truth, as well as the clinical efficacy of the method in the identification of fibrosis and scars in the atrial wall.

Does Removal of Subchondral Cortical Bone Provide Sufficient Resection Depth for Treatment of Cam Femoroacetabular Impingement?

BACKGROUND: Residual impingement resulting from insufficient resection of bone during the index femoroplasty is the most-common reason for revision surgery in patients with cam-type femoroacetabular impingement (FAI). Development of surgical resection guidelines therefore could reduce the number of patients with persistent pain and reduced ROM after femoroplasty. QUESTIONS/PURPOSES: We asked whether removal of subchondral cortical bone in the region of the lesion in patients with cam FAI could restore femoral anatomy to that of screened control subjects. To evaluate this, we analyzed shape models between: (1) native cam and screened control femurs to observe the location of the cam lesion and establish baseline shape differences between groups, and (2) cam femurs with simulated resections and screened control femurs to evaluate the sufficiency of subchondral cortical bone thickness to guide resection depth. METHODS: Three-dimensional (3-D) reconstructions of the inner and outer cortical bone boundaries of the proximal femur were generated by segmenting CT images from 45 control subjects (29 males; 15 living subjects, 30 cadavers) with normal radiographic findings and 28 nonconsecutive patients (26 males) with a diagnosis of cam FAI based on radiographic measurements and clinical examinations. Correspondence particles were placed on each femur and statistical shape modeling (SSM) was used to create mean shapes for each cohort. The geometric difference between the mean shape of the patients with cam FAI and that of the screened controls was used to define a consistent region representing the cam lesion. Subchondral cortical bone in this region was removed from the 3-D reconstructions of each cam femur to create a simulated resection. SSM was repeated to determine if the resection produced femoral anatomy that better resembled that of control subjects. Correspondence particle locations were used to generate mean femur shapes and evaluate shape differences using principal component analysis. RESULTS: In the region of the cam lesion, the median distance between the mean native cam and control femurs was 1.8 mm (range, 1.0-2.7 mm). This difference was reduced to 0.2 mm (range, -0.2 to 0.9 mm) after resection, with some areas of overresection anteriorly and underresection superiorly. In the region of resection for each subject, the distance from each correspondence particle to the mean control shape was greater for the cam femurs than the screened control femurs (1.8 mm, [range, 1.1-2.9 mm] and 0.0 mm [range, -0.2-0.1 mm], respectively; p < 0.031). After resection, the distance was not different between the resected cam and control femurs (0.3 mm; range, -0.2-1.0; p > 0.473). CONCLUSIONS: Removal of subchondral cortical bone in the region of resection reduced the deviation between the mean resected cam and control femurs to within a millimeter, which resulted in no difference in shape between patients with cam FAI and control subjects. Collectively, our results support the use of the subchondral cortical-cancellous bone margin as a visual intraoperative guide to limit resection depth in the correction of cam FAI. CLINICAL RELEVANCE: Use of the subchondral cortical-cancellous bone boundary may provide a method to guide the depth of resection during arthroscopic surgery, which can be observed intraoperatively without advanced tooling, or imaging.

Quantitative comparison of cortical bone thickness using correspondence-based shape modeling in patients with cam femoroacetabular impingement.

The proximal femur is abnormally shaped in patients with cam-type femoroacetabular impingement (FAI). Impingement may elicit bone remodeling at the proximal femur, causing increases in cortical bone thickness. We used correspondence-based shape modeling to quantify and compare cortical thickness between cam patients and controls for the location of the cam lesion and the proximal femur. Computed tomography images were segmented for 45 controls and 28 cam-type FAI patients. The segmentations were input to a correspondence-based shape model to identify the region of the cam lesion. Median cortical thickness data over the region of the cam lesion and the proximal femur were compared between mixed-gender and gender-specific groups. Median [interquartile range] thickness was significantly greater in FAI patients than controls in the cam lesion (1.47 [0.64] vs. 1.13 [0.22] mm, respectively; p < 0.001) and proximal femur (1.28 [0.30] vs. 0.97 [0.22] mm, respectively; p < 0.001). Maximum thickness in the region of the cam lesion was more anterior and less lateral (p < 0.001) in FAI patients. Male FAI patients had increased thickness compared to male controls in the cam lesion (1.47 [0.72] vs. 1.10 [0.19] mm, respectively; p < 0.001) and proximal femur (1.25 [0.29] vs. 0.94 [0.17] mm, respectively; p < 0.001). Thickness was not significantly different between male and female controls. CLINICAL SIGNIFICANCE: Studies of non-pathologic cadavers have provided guidelines regarding safe surgical resection depth for FAI patients. However, our results suggest impingement induces cortical thickening in cam patients, which may strengthen the proximal femur. Thus, these previously established guidelines may be too conservative. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:1743-1753, 2017.

OPTIMAL PARAMETER MAP ESTIMATION FOR SHAPE REPRESENTATION: A GENERATIVE APPROACH.

Probabilistic label maps are a useful tool for important medical image analysis tasks such as segmentation, shape analysis, and atlas building. Existing methods typically rely on blurred signed distance maps or smoothed label maps to model uncertainties and shape variabilities, which do not conform to any generative model or estimation process, and are therefore suboptimal. In this paper, we propose to learn probabilistic label maps using a generative model on given set of binary label maps. The proposed approach generalizes well on unseen data while simultaneously capturing the variability in the training samples. Efficiency of the proposed approach is demonstrated for consensus generation and shape-based clustering using synthetic datasets as well as left atrial segmentations from late-gadolinium enhancement MRI.

Evaluating Shape Alignment via Ensemble Visualization.

The visualization of variability in surfaces embedded in 3D, which is a type of ensemble uncertainty visualization, provides a means of understanding the underlying distribution of a collection or ensemble of surfaces. This work extends the contour boxplot technique to 3D and evaluates it against an enumeration-style visualization of the ensemble members and other conventional visualizations used by atlas builders. The authors demonstrate the efficacy of using the 3D contour boxplot ensemble visualization technique to analyze shape alignment and variability in atlas construction and analysis as a real-world application.

Architecting the Finite Element Method Pipeline for the GPU.

The finite element method (FEM) is a widely employed numerical technique for approximating the solution of partial differential equations (PDEs) in various science and engineering applications. Many of these applications benefit from fast execution of the FEM pipeline. One way to accelerate the FEM pipeline is by exploiting advances in modern computational hardware, such as the many-core streaming processors like the graphical processing unit (GPU). In this paper, we present the algorithms and data-structures necessary to move the entire FEM pipeline to the GPU. First we propose an efficient GPU-based algorithm to generate local element information and to assemble the global linear system associated with the FEM discretization of an elliptic PDE. To solve the corresponding linear system efficiently on the GPU, we implement a conjugate gradient method preconditioned with a geometry-informed algebraic multi-grid (AMG) method preconditioner. We propose a new fine-grained parallelism strategy, a corresponding multigrid cycling stage and efficient data mapping to the many-core architecture of GPU. Comparison of our on-GPU assembly versus a traditional serial implementation on the CPU achieves up to an 87 × speedup. Focusing on the linear system solver alone, we achieve a speedup of up to 51 × versus use of a comparable state-of-the-art serial CPU linear system solver. Furthermore, the method compares favorably with other GPU-based, sparse, linear solvers.

Multiatlas segmentation as nonparametric regression.

This paper proposes a novel theoretical framework to model and analyze the statistical characteristics of a wide range of segmentation methods that incorporate a database of label maps or atlases; such methods are termed as label fusion or multiatlas segmentation. We model these multiatlas segmentation problems as nonparametric regression problems in the high-dimensional space of image patches. We analyze the nonparametric estimator's convergence behavior that characterizes expected segmentation error as a function of the size of the multiatlas database. We show that this error has an analytic form involving several parameters that are fundamental to the specific segmentation problem (determined by the chosen anatomical structure, imaging modality, registration algorithm, and label-fusion algorithm). We describe how to estimate these parameters and show that several human anatomical structures exhibit the trends modeled analytically. We use these parameter estimates to optimize the regression estimator. We show that the expected error for large database sizes is well predicted by models learned on small databases. Thus, a few expert segmentations can help predict the database sizes required to keep the expected error below a specified tolerance level. Such cost-benefit analysis is crucial for deploying clinical multiatlas segmentation systems.