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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.

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.