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Abstract This paper explicates a solution to building correspondences between molecular-scale transcriptomics and tissue-scale atlases. This problem arises in atlas construction and cross-specimen/technology alignment where specimens per emerging technology remain sparse and conventional image representations cannot efficiently model the high dimensions from subcellular detection of thousands of genes. We address these challenges by representing spatial transcriptomics data as generalized functions encoding position and high-dimensional feature (gene, cell type) identity. We map onto low-dimensional atlas ontologies by modeling regions as homogeneous random fields with unknown transcriptomic feature distribution. We solve simultaneously for the minimizing geodesic diffeomorphism of coordinates through LDDMM and for these latent feature densities. We map tissue-scale mouse brain atlases to gene-based and cell-based transcriptomics data from MERFISH and BARseq technologies and to histopathology and cross-species atlases to illustrate integration of diverse molecular and cellular datasets into a single coordinate system as a means of comparison and further atlas construction.

We describe coordinate systems adapted for the space between two surfaces, such as those delineating the highly folded cortex in mammalian brains. These systems are estimated in order to satisfy geometric priors, including streamline normality or equivolumetric conditions on layers. We give a precise mathematical formulation of these problems, and present numerical simulations based on diffeomorphic registration methods, comparing them with recent approaches.Our method involves • Diffeomorphic registration of inner and outer folded folded surfaces. • Followed by equivolumetric reparametrization of layers to yield coordinate system.

Summary: Many gene signatures have been developed by applying machine learning (ML) on omics profiles, however, their clinical utility is often hindered by limited interpretability and unstable performance. Here, we show the importance of embedding prior biological knowledge in the decision rules yielded by ML approaches to build robust classifiers. We tested this by applying different ML algorithms on gene expression data to predict three difficult cancer phenotypes: bladder cancer progression to muscle-invasive disease, response to neoadjuvant chemotherapy in triple-negative breast cancer, and prostate cancer metastatic progression. We developed two sets of classifiers: mechanistic, by restricting the training to features capturing specific biological mechanisms; and agnostic, in which the training did not use any a priori biological information. Mechanistic models had a similar or better testing performance than their agnostic counterparts, with enhanced interpretability. Our findings support the use of biological constraints to develop robust gene signatures with high translational potential.

Changes in the brain of patients with Huntington's disease (HD) begin years before clinical onset, so it remains critical to identify biomarkers to track these early changes. Metrics derived from tensor modeling of diffusion-weighted MRIs (DTI), that indicate the microscopic brain structure, can add important information to regional volumetric measurements. This study uses two large-scale longitudinal, multicenter datasets, PREDICT-HD and IMAGE-HD, to trace changes in DTI of HD participants with a broad range of CAP scores (a product of CAG repeat expansion and age), including those with pre-manifest disease (i.e., prior to clinical onset). Utilizing a fully automated data-driven approach to study the whole brain divided in regions of interest, we traced changes in DTI metrics (diffusivity and fractional anisotropy) versus CAP scores, using sigmoidal and linear regression models. We identified points of inflection in the sigmoidal regression using change-point analysis. The deep gray matter showed more evident and earlier changes in DTI metrics over CAP scores, compared to the deep white matter. In the deep white matter, these changes were more evident and occurred earlier in superior and posterior areas, compared to anterior and inferior areas. The curves of mean diffusivity vs. age of HD participants within a fixed CAP score were different from those of controls, indicating that the disease has an additional effect to age on the microscopic brain structure. These results show the regional and temporal vulnerability of the white matter and deep gray matter in HD, with potential implications for experimental therapeutics.

Cancer cells display massive dysregulation of key regulatory pathways due to now well-catalogued mutations and other DNA-related aberrations. Moreover, enormous heterogeneity has been commonly observed in the identity, frequency and location of these aberrations across individuals with the same cancer type or subtype, and this variation naturally propagates to the transcriptome, resulting in myriad types of dysregulated gene expression programs. Many have argued that a more integrative and quantitative analysis of heterogeneity of DNA and RNA molecular profiles may be necessary for designing more systematic explorations of alternative therapies and improving predictive accuracy. We introduce a representation of multi-omics profiles which is sufficiently rich to account for observed heterogeneity and support the construction of quantitative, integrated, metrics of variation. Starting from the network of interactions existing in Reactome, we build a library of "paired DNA-RNA aberrations" that represent prototypical and recurrent patterns of dysregulation in cancer; each two-gene "Source-Target Pair" (STP) consists of a "source" regulatory gene and a "target" gene whose expression is plausibly "controlled" by the source gene. The STP is then "aberrant" in a joint DNA-RNA profile if the source gene is DNA-aberrant (e.g., mutated, deleted, or duplicated), and the downstream target gene is "RNA-aberrant", meaning its expression level is outside the normal, baseline range. With M STPs, each sample profile has exactly one of the 2M possible configurations. We concentrate on subsets of STPs, and the corresponding reduced configurations, by selecting tissue-dependent minimal coverings, defined as the smallest family of STPs with the property that every sample in the considered population displays at least one aberrant STP within that family. These minimal coverings can be computed with integer programming. Given such a covering, a natural measure of cross-sample diversity is the extent to which the particular aberrant STPs composing a covering vary from sample to sample; this variability is captured by the entropy of the distribution over configurations. We apply this program to data from TCGA for six distinct tumor types (breast, prostate, lung, colon, liver, and kidney cancer). This enables an efficient simplification of the complex landscape observed in cancer populations, resulting in the identification of novel signatures of molecular alterations which are not detected with frequency-based criteria. Estimates of cancer heterogeneity across tumor phenotypes reveals a stable pattern: entropy increases with disease severity. This framework is then well-suited to accommodate the expanding complexity of cancer genomes and epigenomes emerging from large consortia projects.

This study examines the atrophy patterns in the entorhinal and transentorhinal cortices of subjects that converted from normal cognition to mild cognitive impairment. The regions were manually segmented from 3T MRI, then corrected for variability in boundary definition over time using an automated approach called longitudinal diffeomorphometry. Cortical thickness was calculated by deforming the gray matter-white matter boundary surface to the pial surface using an approach called normal geodesic flow. The surface was parcellated based on four atlases using large deformation diffeomorphic metric mapping. Average cortical thickness was calculated for (1) manually-defined entorhinal cortex, and (2) manually-defined transentorhinal cortex. Group-wise difference analysis was applied to determine where atrophy occurred, and change point analysis was applied to determine when atrophy started to occur. The results showed that by the time a diagnosis of mild cognitive impairment is made, the transentorhinal cortex and entorhinal cortex was up to 0.6 mm thinner than a control with normal cognition. A change point in atrophy rate was detected in the transentorhinal cortex 9–14 years prior to a diagnosis of mild cognitive impairment, and in the entorhinal cortex 8–11 years prior. The findings are consistent with autopsy findings that demonstrate neuronal changes in the transentorhinal cortex before the entorhinal cortex.

Objective: Several models have been proposed for the evolution of Alzheimer’s disease (AD) biomarkers. The aim of this study was to identify changepoints in a range of biomarkers during the preclinical phase of AD.Methods: We examined nine measures based on cerebrospinal fluid (CSF), magnetic resonance imaging (MRI) and cognitive testing, obtained from 306 cognitively normal individuals, a subset of whom subsequently progressed to the symptomatic phase of AD. A changepoint model was used to determine which of the measures had a significant change in slope in relation to clinical symptom onset.Results: All nine measures had significant changepoints, all of which preceded symptom onset, however, the timing of these changepoints varied considerably. A single measure, CSF t-tau, had an early changepoint (34 years prior to symptom onset). A group of measures, including the remaining CSF measures (CSF Abeta and phosphorylated tau) and all cognitive tests had changepoints 10–15 years prior to symptom onset. A second group is formed by medial temporal lobe shape composite measures, with a 6-year time difference between the right and left side (respectively nine and 3 years prior to symptom onset).Conclusion: These findings highlight the long period of time prior to symptom onset during which AD pathology is accumulating in the brain. There are several significant findings, including the early changes in cognition and the laterality of the MRI findings. Additional work is needed to clarify their significance.

This study examines the atrophy rates of subjects with mild cognitive impairment (MCI) compared to controls in four regions within the medial temporal lobe: the transentorhinal cortex (TEC), entorhinal cortex (ERC), hippocampus, and amygdala. These regions were manually segmented and then corrected for undesirable longitudinal variability via Large Deformation Diffeomorphic Metric Mapping (LDDMM) based longitudinal diffeomorphometry. Diffeomorphometry techniques were used to compare thickness measurements in the TEC with the ERC. There were more significant changes in thickness atrophy rate in the TEC than medial regions of the entorhinal cortex. Volume measures were also calculated for all four regions. Classifiers were constructed using linear discriminant analysis to demonstrate that average thickness and atrophy rate of TEC together was the most discriminating measure compared to the thickness and volume measures in the areas examined, in differentiating MCI from controls. These findings are consistent with autopsy findings demonstrating that initial neuronal changes are found in TEC before spreading more medially in the ERC and to other regions in the medial temporal lobe. These findings suggest that the TEC thickness could serve as a biomarker for Alzheimer's disease in the prodromal phase of the disease. Keywords: Entorhinal cortex, Transentorhinal cortex, Mild cognitive impairment, Braak staging, Cortical thickness, Shape analysis, Longitudinal analysis

Huntington disease (HD) is a fatal progressive neurodegenerative disorder for which only symptomatic treatment is available. A better understanding of the pathology, and identification of biomarkers will facilitate the development of disease-modifying treatments. HD is potentially a good model of a neurodegenerative disease for development of biomarkers because it is an autosomal-dominant disease with complete penetrance, caused by a single gene mutation, in which the neurodegenerative process can be assessed many years before onset of signs and symptoms of manifest disease. Previous MRI studies have detected abnormalities in gray and white matter starting in premanifest stages. However, the understanding of how these abnormalities are related, both in time and space, is still incomplete. In this study, we combined deep gray matter shape diffeomorphometry and white matter DTI analysis in order to provide a better mapping of pathology in the deep gray matter and subcortical white matter in premanifest HD. We used 296 MRI scans from the PREDICT-HD database. Atrophy in the deep gray matter, thalamus, hippocampus, and nucleus accumbens was analyzed by surface based morphometry, and while white matter abnormalities were analyzed in (i) regions of interest surrounding these structures, using (ii) tractography-based analysis, and using (iii) whole brain atlas-based analysis. We detected atrophy in the deep gray matter, particularly in putamen, from early premanifest stages. The atrophy was greater both in extent and effect size in cases with longer exposure to the effects of the CAG expansion mutation (as assessed by greater CAP-scores), and preceded detectible abnormalities in the white matter. Near the predicted onset of manifest HD, the MD increase was widespread, with highest indices in the deep and posterior white matter. This type of in-vivo macroscopic mapping of HD brain abnormalities can potentially indicate when and where therapeutics could be targeted to delay the onset or slow the disease progression.

This paper uses diffeomorphometry methods to quantify the order in which statistically significant morphometric change occurs in three medial temporal lobe regions, the amygdala, entorhinal cortex (ERC), and hippocampus among subjects with symptomatic and preclinical Alzheimer's disease (AD). Magnetic resonance imaging scans were examined in subjects who were cognitively normal at baseline, some of whom subsequently developed clinical symptoms of AD. The images were mapped to a common template, using shape-based diffeomorphometry. The multidimensional shape markers indexed through the temporal lobe structures were modeled using a changepoint model with explicit parameters, specifying the number of years preceding clinical symptom onset. Our model assumes that the atrophy rate of a considered brain structure increases years before detectable symptoms. The results demonstrate that the atrophy changepoint in the ERC occurs first, indicating significant change 8–10 years prior to onset, followed by the hippocampus, 2–4 years prior to onset, followed by the amygdala, 3 years prior to onset. The ERC is significant bilaterally, in both our local and global measures, with estimates of ERC surface area loss of 2.4% (left side) and 1.6% (right side) annually. The same changepoint model for ERC volume gives 3.0% and 2.7% on the left and right sides, respectively. Understanding the order in which changes in the brain occur during preclinical AD may assist in the design of intervention trials aimed at slowing the evolution of the disease.

This paper presents recent advances in the use of diffeomorphic active shapes which incorporate the conservation laws of large deformation diffeomorphic metric mapping. The equations of evolution satisfying the conservation law are geodesics under the diffeomorphism metric and therefore termed geodesically controlled diffeomorphic active shapes (GDAS). Our principal application in this paper is on robust diffeomorphic mapping methods based on parameterized surface representations of subcortical template structures. Our parametrization of the GDAS evolution is via the initial momentum representation in the tangent space of the template surface. The dimension of this representation is constrained using principal component analysis generated from training samples. In this work, we seek to use template surfaces to generate segmentations of the hippocampus with three data attachment terms: surface matching, landmark matching, and inside-outside modeling from grayscale T1 MR imaging data. This is formulated as an energy minimization problem, where energy describes shape variability and data attachment accuracy, and we derive a variational solution. A gradient descent strategy is employed in the numerical optimization. For the landmark matching case, we demonstrate the robustness of this algorithm as applied to the workflow of a large neuroanatomical study by comparing to an existing diffeomorphic landmark matching algorithm.

3D surfaces are important geometric models for many objects of interest in image analysis and Computational Anatomy. In this paper, we describe a Bayesian inference scheme for estimating a template surface from a set of observed surface data. In order to achieve this, we use the geodesic shooting approach to construct a statistical model for the generation and the observations of random surfaces. We develop a mode approximation EM algorithm to infer the maximum a posteriori estimation of initial momentum μ, which determines the template surface. Experimental results of caudate, thalamus, and hippocampus data are presented.