Longitudinal biomedical studies monitor individuals over time to capture dynamics in brain development, disease progression, and treatment effects. However, estimating trajectories of brain biomarkers is challenging due to biological variability, inconsistencies in measurement protocols (e.g., differences in MRI scanners) as well as scarcity and irregularity in longitudinal measurements. Herein, we introduce a novel personalized deep kernel regression framework for forecasting brain biomarkers, with application to regional volumetric measurements. Our approach integrates two key components: a population model that captures brain trajectories from a large and diverse cohort, and a subject-specific model that captures individual trajectories. To optimally combine these, we propose Adaptive Shrinkage Estimation, which effectively balances population and subject-specific models. We assess our model’s performance through predictive accuracy metrics, uncertainty quantification, and validation against external clinical studies. Benchmarking against state-of-the-art statistical and machine learning models—including linear mixed effects models, generalized additive models, and deep learning methods—demonstrates the superior predictive performance of our approach. Additionally, we apply our method to predict trajectories of composite neuroimaging biomarkers, which highlights the versatility of our approach in modeling the progression of longitudinal neuroimaging biomarkers. Furthermore, validation on three external neuroimaging studies confirms the robustness of our method across different clinical contexts. We make the code available at https://github.com/vatass/AdaptiveShrinkageDKGP.

Spatial location and molecular interactions have long been linked to the connectivity patterns of neural circuits. Yet, at the macroscale of human brain networks, the interplay between spatial position, gene expression, and connectivity remains incompletely understood. Recent efforts to map the human transcriptome and connectome have yielded spatially resolved brain atlases, however modeling the relationship between high-dimensional transcriptomic data and connectivity while accounting for inherent spatial confounds presents a significant challenge. In this paper, we present the first deep learning approaches for predicting whole-brain functional connectivity from gene expression and regional spatial coordinates, including our proposed Spatiomolecular Transformer (SMT). SMT explicitly models biological context by tokenizing genes based on their transcription start site (TSS) order to capture multi-scale genomic organization, and incorporating regional 3D spatial location via a dedicated context [CLS] token within its multi-head self-attention mechanism. We rigorously benchmark context-aware neural networks, including SMT and a single-gene resolution Multilayer-Perceptron (MLP), to established rules-based and bilinear methods. Crucially, to ensure that learned relationships in any model are not mere artifacts of spatial proximity, we introduce novel spatiomolecular null maps preserving key transcriptomic autocorrelation structure. Context-aware neural networks outperform linear methods, significantly exceed our stringent null map estimates, and generalize across diverse connectomic datasets and parcellation resolutions. Together, these findings demonstrate a strong, predictable link between the spatial distributions of gene expression and functional brain network architecture, and establish a rigorously validated deep learning framework for decoding this relationship. Code to reproduce our results is available at: github.com/neuroinfolab/GeneEx2Conn.

We introduce a novel conformal prediction framework for constructing conformal prediction bands with high probability around biomarker trajectories observed at subject-specific, randomly-timed follow-up visits. Existing conformal methods typically assume fixed time grids, limiting their applicability in longitudinal clinical studies. Our approach addresses this limitation by defining a time-varying nonconformity score that normalizes prediction errors using model-derived uncertainty estimates, enabling conformal inference at arbitrary time points. We evaluate our method on two well-established brain biomarkers—hippocampal and ventricular volume—using a range of standard and state-of-the-art predictors. Across models, our conformalized predictors consistently achieve nominal coverage with tighter prediction intervals compared to baseline uncertainty estimates. To further account for population heterogeneity, we develop group-conditional conformal bands with formal coverage guarantees across clinically relevant and high-risk subgroups. Finally, we demonstrate the clinical utility of our approach in identifying subjects at risk of progression to Alzheimer’s disease. We introduce an uncertainty-aware progression metric based on the lower conformal bound and show that it enables the identification of 17.5\% more high-risk subjects compared to standard slope-based methods, highlighting the value of uncertainty calibration in real-world clinical decision making. We make the code available at \href{https://github.com/vatass/ConformalBiomarkerTrajectories}{\texttt{github.com/vatass/ConformalBiomarkerTrajectories}}.

We propose a method for extracting physics-based biomarkers from a single multiparametric Magnetic Resonance Imaging (mpMRI) scan bearing a glioma tumor. We account for mass effect, the deformation of brain parenchyma due to the growing tumor, which on its own is an important radiographic feature but its automatic quantification remains an open problem. In particular, we calibrate a partial differential equation (PDE) tumor growth model that captures mass effect, parameterized by a single scalar parameter, tumor proliferation, migration, while localizing the tumor initiation site. The single-scan calibration problem is severely ill-posed because the precancerous, healthy, brain anatomy is unknown. To address the ill-posedness, we introduce an ensemble inversion scheme that uses a number of normal subject brain templates as proxies for the healthy precancer subject anatomy. We verify our solver on a synthetic dataset and perform a retrospective analysis on a clinical dataset of 216 glioblastoma (GBM) patients. We analyze the reconstructions using our calibrated biophysical model and demonstrate that our solver provides both global and local quantitative measures of tumor biophysics and mass effect. We further highlight the improved performance in model calibration through the inclusion of mass effect in tumor growth models-including mass effect in the model leads to 10% increase in average dice coefficients for patients with significant mass effect. We further evaluate our model by introducing novel biophysics-based features and using them for survival analysis. Our preliminary analysis suggests that including such features can improve patient stratification and survival prediction.

Investigating the relationship between genetic variation and phenotypic traits is a key issue in quantitative genetics. Specifically for Alzheimer's disease, the association between genetic markers and quantitative traits remains vague while, once identified, will provide valuable guidance for the study and development of genetic-based treatment approaches. Currently, to analyze the association of two modalities, sparse canonical correlation analysis (SCCA) is commonly used to compute one sparse linear combination of the variable features for each modality, giving a pair of linear combination vectors in total that maximizes the cross-correlation between the analyzed modalities. One drawback of the plain SCCA model is that the existing findings and knowledge cannot be integrated into the model as priors to help extract interesting correlation as well as identify biologically meaningful genetic and phenotypic markers. To bridge this gap, we introduce preference matrix guided SCCA (PM-SCCA) that not only takes priors encoded as a preference matrix but also maintains computational simplicity. A simulation study and a real-data experiment are conducted to investigate the effectiveness of the model. Both experiments demonstrate that the proposed PM-SCCA model can capture not only genotype-phenotype correlation but also relevant features effectively.

Multi-site fMRI studies face the challenge that the pooling introduces systematic non-biological site-specific variance due to hardware, software, and environment. In this paper, we propose to reduce site-specific variance in the estimation of hierarchical Sparsity Connectivity Patterns (hSCPs) in fMRI data via a simple yet effective matrix factorization while preserving biologically relevant variations. Our method leverages unsupervised adversarial learning to improve the reproducibility of the components. Experiments on simulated datasets display that the proposed method can estimate components with higher accuracy and reproducibility, while preserving age-related variation on a multi-center clinical data set.

Since its renaissance, deep learning has been widely used in various medical imaging tasks and has achieved remarkable success in many medical imaging applications, thereby propelling us into the so-called artificial intelligence (AI) era. It is known that the success of AI is mostly attributed to the availability of big data with annotations for a single task and the advances in high performance computing. However, medical imaging presents unique challenges that confront deep learning approaches. In this survey paper, we first present traits of medical imaging, highlight both clinical needs and technical challenges in medical imaging, and describe how emerging trends in deep learning are addressing these issues. We cover the topics of network architecture, sparse and noisy labels, federating learning, interpretability, uncertainty quantification, etc. Then, we present several case studies that are commonly found in clinical practice, including digital pathology and chest, brain, cardiovascular, and abdominal imaging. Rather than presenting an exhaustive literature survey, we instead describe some prominent research highlights related to these case study applications. We conclude with a discussion and presentation of promising future directions.

The study of functional networks of the human brain has been of significant interest in cognitive neuroscience for over two decades, albeit they are typically extracted at a single scale using various methods, including decompositions like ICA. However, since numerous studies have suggested that the functional organization of the brain is hierarchical, analogous decompositions might better capture functional connectivity patterns. Moreover, hierarchical decompositions can efficiently reduce the very high dimensionality of functional connectivity data. This paper provides a novel method for the extraction of hierarchical connectivity components in the human brain using resting-state fMRI. The method builds upon prior work of Sparse Connectivity Patterns (SCPs) by introducing a hierarchy of sparse, potentially overlapping patterns. The components are estimated by cascaded factorization of correlation matrices generated from fMRI. The goal of the paper is to extract sparse interpretable hierarchically-organized patterns using correlation matrices where a low rank decomposition is formed by a linear combination of a higher rank decomposition. We formulate the decomposition as a non-convex optimization problem and solve it using gradient descent algorithms with adaptive step size. Along with the hierarchy, our method aims to capture the heterogeneity of the set of common patterns across individuals. We first validate our model through simulated experiments. We then demonstrate the effectiveness of the developed method on two different real-world datasets by showing that multi-scale hierarchical SCPs are reproducible between sub-samples and are more reproducible as compared to single scale patterns. We also compare our method with an existing hierarchical community detection approach.

Functional brain network analysis has been a powerful tool for measuring brain function in normal and pathologic states based on resting state fMRI (rsfMRI) data. Recent advances in pattern recognition and sparse modeling have enabled us to characterize subject-specific functional brain networks and derive clinically useful biomarkers. In this paper, we briefly introduce our recent work in the development of functional brain network analytic techniques, including functional brain network modeling, pattern recognition of functional brain networks, as well as modeling heterogeneous patterns of functional connectivity. Finally, we discuss some current challenges that have received and are likely to receive more attention in the near future.

We present SIBIA (Scalable Integrated Biophysics-based Image Analysis), a framework for coupling biophysical models with medical image analysis. It provides solvers for an image-driven inverse brain tumor growth model and an image registration problem, the combination of which can eventually help in diagnosis and prognosis of brain tumors. The two main computational kernels of SIBIA are a Fast Fourier Transformation (FFT) implemented in the library AccFFT to discretize differential operators, and a cubic interpolation kernel for semi-Lagrangian based advection. We present efficiency and scalability results for the computational kernels, the inverse tumor solver and image registration on two x86 systems, Lonestar 5 at the Texas Advanced Computing Center and Hazel Hen at the Stuttgart High Performance Computing Center. We showcase results that demonstrate that our solver can be used to solve registration problems of unprecedented scale, 40963 resulting in ∼ 200 billion unknowns---a problem size that is 64X larger than the state-of-the-art. For problem sizes of clinical interest, SIBIA is about 8X faster than the state-of-the-art.

Many brain disorders and diseases exhibit heterogeneous symptoms and imaging characteristics. This heterogeneity is typically not captured by commonly adopted neuroimaging analyses that seek only a main imaging pattern when two groups need to be differentiated (e.g., patients and controls, or clinical progressors and non-progressors). We propose a novel probabilistic clustering approach, CHIMERA, modeling the pathological process by a combination of multiple regularized transformations from normal/control population to the patient population, thereby seeking to identify multiple imaging patterns that relate to disease effects and to better characterize disease heterogeneity. In our framework, normal and patient populations are considered as point distributions that are matched by a variant of the coherent point drift algorithm. We explain how the posterior probabilities produced during the MAP optimization of CHIMERA can be used for clustering the patients into groups and identifying disease subtypes. CHIMERA was first validated on a synthetic dataset and then on a clinical dataset mixing 317 control subjects and patients suffering from Alzheimer's Disease (AD) and Parkison's Disease (PD). CHIMERA produced better clustering results compared to two standard clustering approaches. We further analyzed 390 T1 MRI scans from Alzheimer's patients. We discovered two main and reproducible AD subtypes displaying significant differences in cognitive performance.

We present a generic method for automatic detection of abnormal regions in medical images as deviations from a normative data base. The algorithm decomposes an image, or more broadly a function defined on the image grid, into the superposition of a normal part and a residual term. A statistical model is constructed with regional sparse learning to represent normative anatomical variations among a reference population (e.g., healthy controls), in conjunction with a Markov random field regularization that ensures mutual consistency of the regional learning among partially overlapping image blocks. The decomposition is performed in a principled way so that the normal part fits well with the learned normative model, while the residual term absorbs pathological patterns, which may then be detected through a statistical significance test. The decomposition is applied to multiple image features from an individual scan, detecting abnormalities using both intensity and shape information. We form an iterative scheme that interleaves abnormality detection with deformable registration, gradually improving robustness of the spatial normalization and precision of the detection. The algorithm is evaluated with simulated images and clinical data of brain lesions, and is shown to achieve robust deformable registration and localize pathological regions simultaneously. The algorithm is also applied on images from Alzheimer's disease patients to demonstrate the generality of the method.

Groupwise registration of point sets is the fundamental step in creating statistical shape models (SSMs). When the number of points on the sets varies across the population, each point set is often regarded as a spatially transformed Gaussian mixture model (GMM) sample, and the registration problem is formulated as the estimation of the underlying GMM from the training samples. Thus, each Gaussian in the mixture specifies a landmark (or model point), which is probabilistically corresponded to a training point. The Gaussian components, transformations, and probabilistic matches are often computed by an expectation-maximization (EM) algorithm. To avoid over- and under-fitting errors, the SSM should be optimized by tuning the required number of components. In this paper, rather than manually setting the number of components before training, we start from a maximal model and prune out the negligible points during the registration by a sparsity criterion. We show that by searching over the continuous space for optimal sparsity level, we can reduce the fitting errors (generalization and specificities), and thereby help the search process for a discrete number of model points. We propose an EM framework, adopting a symmetric Dirichlet distribution as a prior, to enforce sparsity on the mixture weights of Gaussians. The negligible model points are pruned by a quadratic programming technique during EM iterations. The proposed EM framework also iteratively updates the estimates of the rigid registration parameters of the point sets to the mean model. Next, we apply the principal component analysis to the registered and equal-length training point sets and construct the SSMs. This method is evaluated by learning of sparse SSMs from 15 manually segmented caudate nuclei, 24 hippocampal, and 20 prostate data sets. The generalization, specificity, and compactness of the proposed model favorably compare to a traditional EM based model.

We propose a new method for deformable registration of pre-operative and post-recurrence brain MR scans of glioma patients. Performing this type of intra-subject registration is challenging as tumor, resection, recurrence, and edema cause large deformations, missing correspondences, and inconsistent intensity profiles between the scans. To address this challenging task, our method, called PORTR, explicitly accounts for pathological information. It segments tumor, resection cavity, and recurrence based on models specific to each scan. PORTR then uses the resulting maps to exclude pathological regions from the image-based correspondence term while simultaneously measuring the overlap between the aligned tumor and resection cavity. Embedded into a symmetric registration framework, we determine the optimal solution by taking advantage of both discrete and continuous search methods. We apply our method to scans of 24 glioma patients. Both quantitative and qualitative analysis of the results clearly show that our method is superior to other state-of-the-art approaches.

Evaluating various algorithms for the inter-subject registration of brain magnetic resonance images (MRI) is a necessary topic receiving growing attention. Existing studies evaluated image registration algorithms in specific tasks or using specific databases (e.g., only for skull-stripped images, only for single-site images, etc.). Consequently, the choice of registration algorithms seems task- and usage/parameter-dependent. Nevertheless, recent large-scale, often multi-institutional imaging-related studies create the need and raise the question whether some registration algorithms can 1) generally apply to various tasks/databases posing various challenges; 2) perform consistently well, and while doing so, 3) require minimal or ideally no parameter tuning. In seeking answers to this question, we evaluated 12 general-purpose registration algorithms, for their generality, accuracy and robustness. We fixed their parameters at values suggested by algorithm developers as reported in the literature. We tested them in 7 databases/tasks, which present one or more of 4 commonly-encountered challenges: 1) inter-subject anatomical variability in skull-stripped images; 2) intensity homogeneity, noise and large structural differences in raw images; 3) imaging protocol and field-of-view (FOV) differences in multi-site data; and 4) missing correspondences in pathology-bearing images. Totally 7,562 registrations were performed. Registration accuracies were measured by (multi-)expert-annotated landmarks or regions of interest (ROIs). To ensure reproducibility, we used public software tools, public databases (whenever possible), and we fully disclose the parameter settings. We show evaluation results, and discuss the performances in light of algorithms' similarity metrics, transformation models and optimization strategies. We also discuss future directions for the algorithm development and evaluations.

Deformable image registration is a fundamental task in medical image processing. Among its most important applications, one may cite: 1) multi-modality fusion, where information acquired by different imaging devices or protocols is fused to facilitate diagnosis and treatment planning; 2) longitudinal studies, where temporal structural or anatomical changes are investigated; and 3) population modeling and statistical atlases used to study normal anatomical variability. In this paper, we attempt to give an overview of deformable registration methods, putting emphasis on the most recent advances in the domain. Additional emphasis has been given to techniques applied to medical images. In order to study image registration methods in depth, their main components are identified and studied independently. The most recent techniques are presented in a systematic fashion. The contribution of this paper is to provide an extensive account of registration techniques in a systematic manner.

This paper presents a novel dimensionality reduction method for classification in medical imaging. The goal is to transform very high-dimensional input (typically, millions of voxels) to a low-dimensional representation (small number of constructed features) that preserves discriminative signal and is clinically interpretable. We formulate the task as a constrained optimization problem that combines generative and discriminative objectives and show how to extend it to the semi-supervised learning (SSL) setting. We propose a novel large-scale algorithm to solve the resulting optimization problem. In the fully supervised case, we demonstrate accuracy rates that are better than or comparable to state-of-the-art algorithms on several datasets while producing a representation of the group difference that is consistent with prior clinical reports. Effectiveness of the proposed algorithm for SSL is evaluated with both benchmark and medical imaging datasets. In the benchmark datasets, the results are better than or comparable to the state-of-the-art methods for SSL. For evaluation of the SSL setting in medical datasets, we use images of subjects with mild cognitive impairment (MCI), which is believed to be a precursor to Alzheimer's disease (AD), as unlabeled data. AD subjects and normal control (NC) subjects are used as labeled data, and we try to predict conversion from MCI to AD on follow-up. The semi-supervised extension of this method not only improves the generalization accuracy for the labeled data (AD/NC) slightly but is also able to predict subjects which are likely to converge to AD.

A number of conditions are characterized by pathologies that form continuous or nearly-continuous spectra spanning from the absence of pathology to very pronounced pathological changes (e.g., normal aging, mild cognitive impairment, Alzheimer's). Moreover, diseases are often highly heterogeneous with a number of diagnostic subcategories or subconditions lying within the spectra (e.g., autism spectrum disorder, schizophrenia). Discovering coherent subpopulations of subjects within the spectrum of pathological changes may further our understanding of diseases, and potentially identify subconditions that require alternative or modified treatment options. In this paper, we propose an approach that aims at identifying coherent subpopulations with respect to the underlying MRI in the scenario where the condition is heterogeneous and pathological changes form a continuous spectrum. We describe a joint maximum-margin classification and clustering (JointMMCC) approach that jointly detects the pathologic population via semi-supervised classification, as well as disentangles heterogeneity of the pathological cohort by solving a clustering subproblem. We propose an efficient solution to the nonconvex optimization problem associated with JointMMCC. We apply our proposed approach to an medical resonance imaging study of aging, and identify coherent subpopulations (i.e., clusters) of cognitively less stable adults.

We present a generative approach for simultaneously registering a probabilistic atlas of a healthy population to brain magnetic resonance (MR) scans showing glioma and segmenting the scans into tumor as well as healthy tissue labels. The proposed method is based on the expectation maximization (EM) algorithm that incorporates a glioma growth model for atlas seeding, a process which modifies the original atlas into one with tumor and edema adapted to best match a given set of patient's images. The modified atlas is registered into the patient space and utilized for estimating the posterior probabilities of various tissue labels. EM iteratively refines the estimates of the posterior probabilities of tissue labels, the deformation field and the tumor growth model parameters. Hence, in addition to segmentation, the proposed method results in atlas registration and a low-dimensional description of the patient scans through estimation of tumor model parameters. We validate the method by automatically segmenting 10 MR scans and comparing the results to those produced by clinical experts and two state-of-the-art methods. The resulting segmentations of tumor and edema outperform the results of the reference methods, and achieve a similar accuracy from a second human rater. We additionally apply the method to 122 patients scans and report the estimated tumor model parameters and their relations with segmentation and registration results. Based on the results from this patient population, we construct a statistical atlas of the glioma by inverting the estimated deformation fields to warp the tumor segmentations of patients scans into a common space.

This paper investigates the problem of atlas registration of brain images with gliomas. Multiparametric imaging modalities (T1, T1-CE, T2, and FLAIR) are first utilized for segmentations of different tissues, and to compute the posterior probability map (PBM) of membership to each tissue class, using supervised learning. Similar maps are generated in the initially normal atlas, by modeling the tumor growth, using reaction-diffusion equation. Deformable registration using a demons-like algorithm is used to register the patient images with the tumor bearing atlas. Joint estimation of the simulated tumor parameters (e.g., location, mass effect and degree of infiltration), and the spatial transformation is achieved by maximization of the log-likelihood of observation. An expectation-maximization algorithm is used in registration process to estimate the spatial transformation and other parameters related to tumor simulation are optimized through asynchronous parallel pattern search (APPSPACK). The proposed method has been evaluated on five simulated data sets created by statistically simulated deformations (SSD), and fifteen real multichannel glioma data sets. The performance has been evaluated both quantitatively and qualitatively, and the results have been compared to ORBIT, an alternative method solving a similar problem. The results show that our method outperforms ORBIT, and the warped templates have better similarity to patient images.

Gaussian smoothing of images prior to applying voxel-based statistics is an important step in voxel-based analysis and statistical parametric mapping (VBA-SPM) and is used to account for registration errors, to Gaussianize the data and to integrate imaging signals from a region around each voxel. However, it has also become a limitation of VBA-SPM based methods, since it is often chosen empirically and lacks spatial adaptivity to the shape and spatial extent of the region of interest, such as a region of atrophy or functional activity. In this paper, we propose a new framework, named optimally-discriminative voxel-based analysis (ODVBA), for determining the optimal spatially adaptive smoothing of images, followed by applying voxel-based group analysis. In ODVBA, nonnegative discriminative projection is applied regionally to get the direction that best discriminates between two groups, e.g., patients and controls; this direction is equivalent to local filtering by an optimal kernel whose coefficients define the optimally discriminative direction. By considering all the neighborhoods that contain a given voxel, we then compose this information to produce the statistic for each voxel. Finally, permutation tests are used to obtain a statistical parametric map of group differences. ODVBA has been evaluated using simulated data in which the ground truth is known and with data from an Alzheimer's disease (AD) study. The experimental results have shown that the proposed ODVBA can precisely describe the shape and location of structural abnormality.

A deformable registration method is proposed for registering a normal brain atlas with images of brain tumor patients. The registration is facilitated by first simulating the tumor mass effect in the normal atlas in order to create an atlas image that is as similar as possible to the patient's image. An optimization framework is used to optimize the location of tumor seed as well as other parameters of the tumor growth model, based on the pattern of deformation around the tumor region. In particular, the optimization is implemented in a multiresolution and hierarchical scheme, and it is accelerated by using a principal component analysis (PCA)-based model of tumor growth and mass effect, trained on a computationally more expensive biomechanical model. Validation on simulated and real images shows that the proposed registration framework, referred to as ORBIT (optimization of tumor parameters and registration of brain images with tumors), outperforms other available registration methods particularly for the regions close to the tumor, and it has the potential to assist in constructing statistical atlases from tumor-diseased brain images.

Diffusion tensor magnetic resonance imaging (DT-MRI) provides a comprehensive characterization of white matter (WM) in the brain and therefore, plays a crucial role in the investigation of diseases in which WM is suspected to be compromised such as multiple sclerosis and neuropsychiatric disorders like schizophrenia. However changes induced by pathology may be subtle and affected regions of the brain can only be revealed by a group-based analysis of patients in comparison with healthy controls. This in turn requires voxel-based statistical analysis of spatially normalized brain DT images, as in the case of conventional MR images. However this process is rendered extremely challenging in DT-MRI due to the high dimensionality of the data and its inherent non-linearity that causes linear component analysis methods to be inapplicable. We therefore propose a novel framework for the statistical analysis of DT-MRI data using manifold-based techniques such as isomap and kernel PCA that determine the underlying manifold structure of the data, embed it to a manifold and help perform high dimensional statistics on the manifold to determine regions of difference between the groups of patients and controls. The framework has been successfully applied to DT-MRI data from patients with schizophrenia, as well as to study developmental changes in small animals, both of which identify regional changes, indicating the need for manifold-based methods for the statistical analysis of DTI.

In this article we propose parallel algorithms for the construction of conforming finite-element discretization on linear octrees. Existing octree-based discretizations scale to billions of elements, but the complexity constants can be high. In our approach we use several techniques to minimize overhead: a novel bottom-up tree-construction and 2:1 balance constraint enforcement; a Golomb-Rice encoding for compression by representing the octree and element connectivity as an Uniquely Decodable Code (UDC); overlapping communication and computation; and byte alignment for cache efficiency. The cost of applying the Laplacian is comparable to that of applying it using a direct indexing regular grid discretization with the same number of elements. Our algorithm has scaled up to four billion octants on 4096 processors on a Cray XT3 at the Pittsburgh Supercomputing Center. The overall tree construction time is under a minute in contrast to previous implementations that required several minutes; the evaluation of the discretization of a variable-coefficient Laplacian takes only a few seconds.

This paper presents a method for classification of structural brain magnetic resonance (MR) images, by using a combination of deformation-based morphometry and machine learning methods. A morphological representation of the anatomy of interest is first obtained using a high-dimensional mass-preserving template warping method, which results in tissue density maps that constitute local tissue volumetric measurements. Regions that display strong correlations between tissue volume and classification (clinical) variables are extracted using a watershed segmentation algorithm, taking into account the regional smoothness of the correlation map which is estimated by a cross-validation strategy to achieve robustness to outliers. A volume increment algorithm is then applied to these regions to extract regional volumetric features, from which a feature selection technique using support vector machine (SVM)-based criteria is used to select the most discriminative features, according to their effect on the upper bound of the leave-one-out generalization error. Finally, SVM-based classification is applied using the best set of features, and it is tested using a leave-one-out cross-validation strategy. The results on MR brain images of healthy controls and schizophrenia patients demonstrate not only high classification accuracy (91.8% for female subjects and 90.8% for male subjects), but also good stability with respect to the number of features selected and the size of SVM kernel used.

Methods of computational anatomy are typically based on a spatial transformation that maps a template to an individual anatomy and vice versa. However, important morphological characteristics are frequently not captured by this transformation, thereby leading to lossy representations. We extend this formulation by incorporating residual anatomical information, i.e., information that is not captured by the shape transformation but is necessary in order to fully and exactly reconstruct the anatomy under measurement. We, therefore, arrive at a lossless morphological representation. By virtue of being lossless, this representation allows us to represent the same anatomy by an infinite number of pairs [transformation, residual], since different residuals correspond to different transformations. We treat these pairs as members of an anatomical equivalence class (AEC), which we approximate using principal component analysis. We show that projection onto the orthogonal to the AEC subspace produces measurements that allow us to better detect morphological abnormalities by eliminating variation in the data that is irrelevant and confounds underlying subtle morphological characteristics. Finally, we show that higher classification rates between a group of normal brains and a group of brains with localized atrophy are obtained if we use nonmetric distances between AECs instead of conventional Euclidean distances between individual morphological measurements. The results confirm that this representation can improve the results compared to conventional analysis, but also highlight limitations of the current approach and point to directions of further development of this general morphological analysis framework.

This paper addresses the problem of statistical analysis of diffusion tensor magnetic resonance images (DT-MRI). DT-MRI cannot be analyzed by commonly used linear methods, due to the inherent nonlinearity of tensors, which are restricted to lie on a nonlinear submanifold of the space in which they are defined, namely R6. We estimate this submanifold using the Isomap manifold learning technique and perform tensor calculations using geodesic distances along this manifold. Multivariate statistics used in group analyses also use geodesic distances between tensors, thereby warranting that proper estimates of means and covariances are obtained via calculations restricted to the proper subspace of R6. Experimental results on data with known ground truth show that the proposed statistical analysis method properly captures statistical relationships among tensor image data, and it identifies group differences. Comparisons with standard statistical analyses that rely on Euclidean, rather than geodesic distances, are also discussed.

In this paper, a method for maximizing the probability of prostate cancer detection via biopsy is presented, by combining image analysis and optimization techniques. This method consists of three major steps. First, a statistical atlas of the spatial distribution of prostate cancer is constructed from histological images obtained from radical prostatectomy specimen. Second, a probabilistic optimization framework is employed to optimize the biopsy strategy, so that the probability of cancer detection is maximized under needle placement uncertainties. Finally, the optimized biopsy strategy generated in the atlas space is mapped to a specific patient space using an automated segmentation and elastic registration method. Cross-validation experiments showed that the predictive power of the optimized biopsy strategy for cancer detection reached the 94%-96% levels for 6-7 biopsy cores, which is significantly better than standard random-systematic biopsy protocols, thereby encouraging further investigation of optimized biopsy strategies in prospective clinical studies.

We propose a method to simulate atrophy and other similar volumetric change effects on medical images. Given a desired level of atrophy, we find a dense warping deformation that produces the corresponding levels of volumetric loss on the labeled tissue using an energy minimization strategy. Simulated results on a real brain image indicate that the method generates realistic images of tissue loss. The method does not make assumptions regarding the mechanics of tissue deformation, and provides a framework where a pre-specified pattern of atrophy can readily be simulated. Furthermore, it provides exact correspondences between images prior and posterior to the atrophy that can be used to evaluate provisional image registration and atrophy quantification algorithms.

Most methods for structure-function analysis of the brain in medical images are usually based on voxel-wise statistical tests performed on registered magnetic resonance (MR) images across subjects. A major drawback of such methods is the inability to accurately locate regions that manifest nonlinear associations with clinical variables. In this paper, we propose Bayesian morphological analysis methods, based on a Bayesian-network representation, for the analysis of MR brain images. First, we describe how Bayesian networks (BNs) can represent probabilistic associations among voxels and clinical (function) variables. Second, we present a model-selection framework, which generates a BN that captures structure-function relationships from MR brain images and function variables. We demonstrate our methods in the context of determining associations between regional brain atrophy (as demonstrated on MR images of the brain), and functional deficits. We employ two data sets for this evaluation: the first contains MR images of 11 subjects, where associations between regional atrophy and a functional deficit are almost linear; the second data set contains MR images of the ventricles of 84 subjects, where the structure-function association is nonlinear. Our methods successfully identify voxel-wise morphological changes that are associated with functional deficits in both data sets, whereas standard statistical analysis (i.e., t-test and paired t-test) fails in the nonlinear-association case.

We propose a method for enforcing topology preservation and smoothness onto a given displacement field. We first analyze the conditions for topology preservation on two- and three-dimensional displacement fields over a discrete rectangular grid. We then pose the problem of finding the closest topology preserving displacement field in terms of its complete set of gradients, which we later solve using a cyclic projections framework. Adaptive smoothing of a displacement field is then formulated as an extension of topology preservation, via constraints imposed on the Jacobian of the displacement field. The simulation results indicate that this technique is a fast and reliable method to estimate a topology preserving displacement field from a noisy observation that does not necessarily preserve topology. They also show that the proposed smoothing method can render morphometric analysis methods that are based on displacement field of shape transformations more robust to noise without removing important morphologic characteristics.

Finding point correspondence in anatomical images is a key step in shape analysis and deformable registration. This paper proposes an automatic correspondence detection algorithm for intramodality MR brain images of different subjects using wavelet-based attribute vectors (WAVs) defined on every image voxel. The attribute vector (AV) is extracted from the wavelet subimages and reflects the image structure in a large neighborhood around the respective voxel in a multiscale fashion. It plays the role of a morphological signature for each voxel, and our goal is, therefore, to make it distinctive of the respective voxel. Correspondence is then determined from similarities of AVs. By incorporating the prior knowledge of the spatial relationship among voxels, the ability of the proposed algorithm to find anatomical correspondence is further improved. Experiments with MR images of human brains show that the algorithm performs similarly to experts, even for complex cortical structures.

Active shape models (ASMs) are often limited by the inability of relatively few eigenvectors to capture the full range of biological shape variability. This paper presents a method that overcomes this limitation, by using a hierarchical formulation of active shape models, using the wavelet transform. The statistical properties of the wavelet transform of a deformable contour are analyzed via principal component analysis, and used as priors in the contour's deformation. Some of these priors reflect relatively global shape characteristics of the object boundaries, whereas, some of them capture local and high-frequency shape characteristics and, thus, serve as local smoothness constraints. This formulation achieves two objectives. First, it is robust when only a limited number of training samples is available. Second, by using local statistics as smoothness constraints, it eliminates the need for adopting ad hoc physical models, such as elasticity or other smoothness models, which do not necessarily reflect true biological variability. Examples on magnetic resonance images of the corpus callosum and hand contours demonstrate that good and fully automated segmentations can be achieved, even with as few as five training samples.

This paper presents a statistical shape model for the automatic prostate segmentation in transrectal ultrasound images. A Gabor filter bank is first used to characterize the prostate boundaries in ultrasound images in both multiple scales and multiple orientations. The Gabor features are further reconstructed to be invariant to the rotation of the ultrasound probe and incorporated in the prostate model as image attributes for guiding the deformable segmentation. A hierarchical deformation strategy is then employed, in which the model adaptively focuses on the similarity of different Gabor features at different deformation stages using a multiresolution technique, i.e., coarse features first and fine features later. A number of successful experiments validate the algorithm.

A new approach is presented for elastic registration of medical images, and is applied to magnetic resonance images of the brain. Experimental results demonstrate very high accuracy in superposition of images from different subjects. There are two major novelties in the proposed algorithm. First, it uses an attribute vector, i.e., a set of geometric moment invariants (GMIs) that are defined on each voxel in an image and are calculated from the tissue maps, to reflect the underlying anatomy at different scales. The attribute vector, if rich enough, can distinguish between different parts of an image, which helps establish anatomical correspondences in the deformation procedure; it also helps reduce local minima, by reducing ambiguity in potential matches. This is a fundamental deviation of our method, referred to as the hierarchical attribute matching mechanism for elastic registration (HAMMER), from other volumetric deformation methods, which are typically based on maximizing image similarity. Second, in order to avoid being trapped by local minima, i.e., suboptimal poor matches, HAMMER uses a successive approximation of the energy function being optimized by lower dimensional smooth energy functions, which are constructed to have significantly fewer local minima. This is achieved by hierarchically selecting the driving features that have distinct attribute vectors, thus, drastically reducing ambiguity in finding correspondence. A number of experiments demonstrate that the proposed algorithm results in accurate superposition of image data from individuals with significant anatomical differences.

A method for automated segmentation of major cortical sulci on the outer brain boundary is presented, with emphasis on automatically determining point correspondence and on labeling cortical regions. The method is formulated in a general optimization framework defined on the unit sphere, which serves as parametric domain for convoluted surfaces of spherical topology. A statistical shape model, which includes a network of deformable curves on the unit sphere, seeks geometric features such as high curvature regions and labels such features via a deformation process that is confined within a spherical map of the outer brain boundary. The limitations of the customary spherical coordinate system, which include discontinuities at the poles and nonuniform sampling, are overcome by defining the statistical prior of shape variation in terms of projections of landmark points onto corresponding tangent planes of the sphere. The method is tested against and shown to be as accurate as manually defined segmentations.

Presents a method for optimizing prostate needle biopsy, by creating a statistical atlas of the spatial distribution of prostate cancer from a large patient cohort. In order to remove inter-individual morphological variability and to determine the true variability in the spatial distribution of cancer within the prostate, an adaptive-focus deformable model (AFDM) is first used to register and normalize the prostate samples. A probabilistic method is then developed to select the prostate biopsy strategy that the greatest chance of detecting prostate cancer. For a test set of data from 20 prostate subjects, five needle locations are adequate to detect the tumor 100% of the time. Furthermore, results on the accuracy of deformable registration and the predictive power of our statistically optimized biopsy strategy are presented in this paper.

A framework for modeling and predicting anatomical deformations is presented, and tested on simulated images. Although a variety of deformations can be modeled in this framework, emphasis is placed on surgical planning, and particularly on modeling and predicting changes of anatomy between preoperative and intraoperative positions, as well as on deformations induced by tumor growth. Two methods are examined. The first is purely shape-based and utilizes the principal modes of co-variation between anatomy and deformation in order to statistically represent deformability. When a patient's anatomy is available, it is used in conjunction with the statistical model to predict the way in which the anatomy will/can deform. The second method is related, and it uses the statistical model in conjunction with a biomechanical model of anatomical deformation. It examines the principal modes of co-variation between shape and forces, with the latter driving the biomechanical model, and thus predicting deformation. Results are shown on simulated images, demonstrating that systematic deformations, such as those resulting from change in position or from tumor growth, can be estimated very well using these models. Estimation accuracy will depend on the application, and particularly on how systematic a deformation of interest is.

This paper presents a deformable model for automatically segmenting brain structures from volumetric magnetic resonance (MR) images and obtaining point correspondences, using geometric and statistical information in a hierarchical scheme. Geometric information is embedded into the model via a set of affine-invariant attribute vectors, each of which characterizes the geometric structure around a point of the model from a local to a global scale. The attribute vectors, in conjunction with the deformation mechanism of the model, warranty that the model not only deforms to nearby edges, as is customary in most deformable surface models, but also that it determines point correspondences based on geometric similarity at different scales. The proposed model is adaptive in that it initially focuses on the most reliable structures of interest, and gradually shifts focus to other structures as those become closer to their respective targets and, therefore, more reliable. The proposed techniques have been used to segment boundaries of the ventricles, the caudate nucleus, and the lenticular nucleus from volumetric MR images.

An active contour (snake) model is presented, with emphasis on medical imaging applications. There are three main novelties in the proposed model. First, an attribute vector is used to characterize the geometric structure around each point of the snake model; the deformable model then deforms in a way that seeks regions with similar attribute vectors. This is in contrast to most deformable models which deform to nearby edges without considering geometric structure, and it was motivated by the need to establish point-correspondences that have anatomical meaning. Second, an adaptive-focus statistical model has been suggested which allows the deformation of the active contour in each stage to be influenced primarily by the most reliable matches. Third, a deformation mechanism that is robust to local minima is proposed by evaluating the snake energy function on segments of the snake at a time, instead of individual points. Various experimental results show the effectiveness of the proposed model.

We present a data mining process for discovering associations between structures and functions of the human brain.Our approach is through the study of lesioned (abnormal) structures and associated functional deficits (disorders).For this purpose we have developed a BRAinImage Database (BRAID) that integrates image processing and visualization capabilities with statistical analysis of spatial and clinical data, providing access via extended SQL through a web interface.We present visualization and statistical methods for mining lesion-deficit associations.We consider issues of scalability and morphological variability.We demonstrate the use of the proposed mining methods by applying them to epidemiological data finding clinically meaningful associations.

A general active contour formulation is considered and a convexity analysis of its energy function is presented. Conditions under which this formulation has a unique solution are derived; these conditions involve both the active contour energy potential and the regularization parameters. This analysis is then applied to four particular active contour formulations, revealing important characteristics about their convexity, and suggesting that external potentials involving center-of-mass computations may be better behaved than the usual potentials based on image gradients. Our analysis also provides an explanation for the poor convergence behavior at concave boundaries and suggests an alternate algorithm for approaching these types of boundaries.

A biomechanical model of the brain is presented, using a finite-element formulation. Emphasis is given to the modeling of the soft-tissue deformations induced by the growth of tumors and its application to the registration of anatomical atlases, with images from patients presenting such pathologies. First, an estimate of the anatomy prior to the tumor growth is obtained through a simulated biomechanical contraction of the tumor region. Then a normal-to-normal atlas registration to this estimated pre-tumor anatomy is applied. Finally, the deformation from the tumor-growth model is applied to the resultant registered atlas, producing an atlas that has been deformed to fully register to the patient images. The process of tumor growth is simulated in a nonlinear optimization framework, which is driven by anatomical features such as boundaries of brain structures. The deformation of the surrounding tissue is estimated using a nonlinear elastic model of soft tissue under the boundary conditions imposed by the skull, ventricles, and the falx and tentorium. A preliminary two-dimensional (2-D) implementation is presented in this paper, and tested on both simulated and patient data. One of the long-term goals of this work is to use anatomical brain atlases to estimate the locations of important brain structures in the brain and to use these estimates in presurgical and radiosurgical planning systems.

The development of algorithms for the spatial transformation and registration of tomographic brain images is a key issue in several clinical and basic science medical applications, including computer-aided neurosurgery, functional image analysis, and morphometrics. This paper describes a technique for the spatial transformation of brain images, which is based on elastically deformable models. A deformable surface algorithm is used to find a parametric representation of the outer cortical surface and then to define a map between corresponding cortical regions in two brain images. Based on the resulting map, a three-dimensional elastic warping transformation is then determined, which brings two images into register. This transformation models images as inhomogeneous elastic objects which are deformed into registration with each other by external force fields. The elastic properties of the images can vary from one region to the other, allowing more variable brain regions, such as the ventricles, to deform more freely than less variable ones. Finally, the framework of prestrained elasticity is used to model structural irregularities, and in particular the ventricular expansion occurring with aging or diseases, and the growth of tumors. Performance measurements are obtained using magnetic resonance images.

The cortical sulci are brain structures resembling thin convoluted ribbons embedded in three dimensions. The importance of the sulci lies primarily in their relation to the cytoarchitectonic and functional organization of the underlying cortex and in their utilization as features in non-rigid registration methods. This paper presents a methodology for extracting parametric representations of the cerebral sulcus from magnetic resonance images. The proposed methodology is based on deformable models utilizing characteristics of the cortical shape. Specifically, a parametric representation of a sulcus is determined by the motion of an active contour along the medial surface of the corresponding cortical fold. The active contour is initialized along the outer boundary of the brain and deforms toward the deep root of a sulcus under the influence of an external force field, restricting it to lie along the medial surface of the particular cortical fold. A parametric representation of the medial surface of the sulcus is obtained as the active contour traverses the sulcus. Based on the first fundamental form of this representation, the location and degree of an interruption of a sulcus can be readily quantified; based on its second fundamental form, shape properties of the sulcus can be determined. This methodology is tested on magnetic resonance images and it is applied to three medical imaging problems: quantitative morphological analysis of the central sulcus; mapping of functional activation along the primary motor cortex and non-rigid registration of brain images.

A general active contour formulation is considered and a convexity analysis of its energy function is presented. Conditions under which this formulation has a unique solution are derived; these conditions involve both the active contour energy potential and the regularization parameters. This analysis is then applied to four particular active contour formulations, revealing important characteristics of their convexity, and suggesting that external potentials involving center of mass computations may be better behaved than the usual potentials based on image gradients. Most importantly, our analysis provides an explanation for the poor convergence behavior at concave boundaries and suggests an alternate algorithm for approaching these types of boundaries.

This paper examines the problem of obtaining a mathematical representation of the outer cortex of the human brain, which is a key problem in several applications, including morphological analysis of the brain, and spatial normalization and registration of brain images. A parameterization of the outer cortex is first obtained using a deformable surface algorithm which, motivated by the structure of the cortex, is constructed to find the central layer of thick surfaces. Based on this parameterization, a hierarchical representation of the outer cortical structure is proposed through its depth map and its curvature maps at various scales. Various experiments on magnetic resonance data are presented.

A new two-stage approach for nonlinear brain image registration is proposed. In the first stage, an active contour algorithm is used to establish a homothetic one-to-one map between a set of region boundaries in two images to be registered. This mapping is used in the second step: a two-dimensional transformation which is based on an elastic body deformation. This method is tested by registering magnetic resonance images to atlas images.

A new active contour model for finding and mapping the outer cortex in brain images is developed. A cross-section of the brain cortex is modeled as a ribbon, and a constant speed mapping of its spine is sought. A variational formulation, an associated force balance condition, and a numerical approach are proposed to achieve this goal. The primary difference between this formulation and that of snakes is in the specification of the external force acting on the active contour. A study of the uniqueness and fidelity of solutions is made through convexity and frequency domain analyses, and a criterion for selection of the regularization coefficient is developed. Examples demonstrating the performance of this method on simulated and real data are provided.

Two new adaptive active contour algorithms for the extraction and mapping of the skeleton of a thick curve are described. They are based on conditions which guarantee uniqueness and fidelity of the solution. Both algorithms modify the regularization constant K/sub o/ in an attempt to maintain convexity of the energy function while simultaneously improving the fidelity of the result. The first algorithm changes K/sub o/ over time while the second adapts K/sub o/ spatially. Both algorithms are evaluated on experiments with synthetic curves; both demonstrate an improved performance compared to a fixed-parameter active contour algorithm.>

A method that simultaneously identifies the central layer of the human cortex and maps it onto the interval