Normal and equivolumetric coordinate systems for cortical areas.

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.

Cross-modality mapping using image varifolds to align tissue-scale atlases to molecular-scale measures with application to 2D brain sections.

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.

Space-feature measures on meshes for mapping spatial transcriptomics.

Advances in the development of largely automated microscopy methods such as MERFISH for imaging cellular structures in mouse brains are providing spatial detection of micron resolution gene expression. While there has been tremendous progress made in the field of Computational Anatomy (CA) to perform diffeomorphic mapping technologies at the tissue scales for advanced neuroinformatic studies in common coordinates, integration of molecular- and cellular-scale populations through statistical averaging via common coordinates remains yet unattained. This paper describes the first set of algorithms for calculating geodesics in the space of diffeomorphisms, what we term space-feature-measure LDDMM, extending the family of large deformation diffeomorphic metric mapping (LDDMM) algorithms to accommodate a space-feature action on marked particles which extends consistently to the tissue scales. It leads to the derivation of a cross-modality alignment algorithm of transcriptomic data to common coordinate systems attached to standard atlases. We represent the brain data as geometric measures, termed as space-feature measures supported by a large number of unstructured points, each point representing a small volume in space and carrying a list of densities of features elements of a high-dimensional feature space. The shape of space-feature measure brain spaces is measured by transforming them by diffeomorphisms. The metric between these measures is obtained after embedding these objects in a linear space equipped with the norm, yielding a so-called "chordal metric".

Preserving Derivative Information while Transforming Neuronal Curves.

The international neuroscience community is building the first comprehensive atlases of brain cell types to understand how the brain functions from a higher resolution, and more integrated perspective than ever before. In order to build these atlases, subsets of neurons (e.g. serotonergic neurons, prefrontal cortical neurons etc.) are traced in individual brain samples by placing points along dendrites and axons. Then, the traces are mapped to common coordinate systems by transforming the positions of their points, which neglects how the transformation bends the line segments in between. In this work, we apply the theory of jets to describe how to preserve derivatives of neuron traces up to any order. We provide a framework to compute possible error introduced by standard mapping methods, which involves the Jacobian of the mapping transformation. We show how our first order method improves mapping accuracy in both simulated and real neuron traces under random diffeomorphisms. Our method is freely available in our open-source Python package brainlit.

Longitudinal imaging highlights preferential basal ganglia circuit atrophy in Huntington's disease.

Huntington's disease is caused by a CAG repeat expansion in the Huntingtin gene (HTT), coding for polyglutamine in the Huntingtin protein, with longer CAG repeats causing earlier age of onset. The variable 'Age' × ('CAG'-L), where 'Age' is the current age of the individual, 'CAG' is the repeat length and L is a constant (reflecting an approximation of the threshold), termed the 'CAG Age Product' (CAP) enables the consideration of many individuals with different CAG repeat expansions at the same time for analysis of any variable and graphing using the CAG Age Product score as the X axis. Structural MRI studies have showed that progressive striatal atrophy begins many years prior to the onset of diagnosable motor Huntington's disease, confirmed by longitudinal multicentre studies on three continents, including PREDICT-HD, TRACK-HD and IMAGE-HD. However, previous studies have not clarified the relationship between striatal atrophy, atrophy of other basal ganglia structures, and atrophy of other brain regions. The present study has analysed all three longitudinal datasets together using a single image segmentation algorithm and combining data from a large number of subjects across a range of CAG Age Product score. In addition, we have used a strategy of normalizing regional atrophy to atrophy of the whole brain, in order to determine which regions may undergo preferential degeneration. This made possible the detailed characterization of regional brain atrophy in relation to CAG Age Product score. There is dramatic selective atrophy of regions involved in the basal ganglia circuit-caudate, putamen, nucleus accumbens, globus pallidus and substantia nigra. Most other regions of the brain appear to have slower but steady degeneration. These results support (but certainly do not prove) the hypothesis of circuit-based spread of pathology in Huntington's disease, possibly due to spread of mutant Htt protein, though other connection-based mechanisms are possible. Therapeutic targets related to prion-like spread of pathology or other mechanisms may be suggested. In addition, they have implications for current neurosurgical therapeutic approaches, since delivery of therapeutic agents solely to the caudate and putamen may miss other structures affected early, such as nucleus accumbens and output nuclei of the striatum, the substantia nigra and the globus pallidus.

Mixed longitudinal and cross-sectional analyses of deep gray matter and white matter using diffusion weighted images in premanifest and manifest Huntington's disease.

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.

CellCover Defines Conserved Cell Types and Temporal Progression in scRNA-seq Data across Mammalian Neocortical Development.

Accurate identification of cell classes across the tissues of living organisms is central in the analysis of growing atlases of single-cell RNA sequencing (scRNA-seq) data across biomedicine. Such analyses are often based on the existence of highly discriminating "marker genes" for specific cell classes which enables a deeper functional understanding of these classes as well as their identification in new, related datasets. Currently, marker genes are defined by methods that serially assess the level of differential expression (DE) of individual genes across landscapes of diverse cells. This serial approach has been extremely useful, but is limited because it ignores possible redundancy or complementarity across genes, that can only be captured by analyzing several genes at the same time. We wish to identify discriminating panels of genes. To efficiently explore the vast space of possible marker panels, leverage the large number of cells often sequenced, and overcome zero-inflation in scRNA-seq data, we propose viewing panel selection as a variation of the "minimal set-covering problem" in combinatorial optimization which can be solved with integer programming. In this formulation, the covering elements are genes, and the objects to be covered are cells of a particular class, where a cell is covered by a gene if that gene is expressed in that cell. Our method, CellCover, identifies a panel of marker genes in scRNA-seq data that covers one class of cells within a population. We apply this method to generate covering marker gene panels which characterize cells of the developing mouse neocortex as postmitotic neurons are generated from neural progenitor cells (NPCs). We show that CellCover captures cell class-specific signals distinct from those defined by DE methods and that CellCover's compact gene panels can be expanded to explore cell type specific function.Transfer learning experiments exploring these covering panels across in vivo mouse, primate, and human scRNA-seq datasets demonstrate that CellCover identifies markers of conserved cell classes in neurogenesis, as well as markers of temporal progression in the molecular identity of these cell types across development of the mammalian neocortex. The gene covering panels we identify across cell types and developmental time can be freely explored in visualizations across all the public data we use in this report at with NeMo Analytics [1] through https://nemoanalytics.org/p?l=CellCover . The code for CellCover is written in R and the Gurobi R interface and is available at [2].

Preserving Derivative Information while Transforming Neuronal Curves.

The international neuroscience community is building the first comprehensive atlases of brain cell types to understand how the brain functions from a higher resolution, and more integrated perspective than ever before. In order to build these atlases, subsets of neurons (e.g. serotonergic neurons, prefrontal cortical neurons etc.) are traced in individual brain samples by placing points along dendrites and axons. Then, the traces are mapped to common coordinate systems by transforming the positions of their points, which neglects how the transformation bends the line segments in between. In this work, we apply the theory of jets to describe how to preserve derivatives of neuron traces up to any order. We provide a framework to compute possible error introduced by standard mapping methods, which involves the Jacobian of the mapping transformation. We show how our first order method improves mapping accuracy in both simulated and real neuron traces, though zeroth order mapping is generally adequate in our real data setting. Our method is freely available in our open-source Python package brainlit.

A Universal Method for Crossing Molecular and Atlas Modalities using Simplex-Based Image Varifolds and Quadratic Programming.

This paper explicates a solution to the problem of building correspondences between molecular-scale transcriptomics and tissue-scale atlases. The central model represents spatial transcriptomics as generalized functions encoding molecular position and high-dimensional transcriptomic-based (gene, cell type) identity. We map onto low-dimensional atlas ontologies by modeling each atlas compartment as a homogeneous random field with unknown transcriptomic feature distribution. The algorithm presented solves simultaneously for the minimizing geodesic diffeomorphism of coordinates and latent atlas transcriptomic feature fractions by alternating LDDMM optimization for coordinate transformations and quadratic programming for the latent transcriptomic variables. We demonstrate the universality of the algorithm in mapping tissue atlases to gene-based and cell-based MERFISH datasets as well as to other tissue scale atlases. The joint estimation of diffeomorphisms and latent feature distributions allows integration of diverse molecular and cellular datasets into a single coordinate system and creates an avenue of comparison amongst atlas ontologies for continued future development.

Preserving Derivative Information while Transforming Neuronal Curves.

The international neuroscience community is building the first comprehensive atlases of brain cell types to understand how the brain functions from a higher resolution, and more integrated perspective than ever before. In order to build these atlases, subsets of neurons (e.g. serotonergic neurons, prefrontal cortical neurons etc.) are traced in individual brain samples by placing points along dendrites and axons. Then, the traces are mapped to common coordinate systems by transforming the positions of their points, which neglects how the transformation bends the line segments in between. In this work, we apply the theory of jets to describe how to preserve derivatives of neuron traces up to any order. We provide a framework to compute possible error introduced by standard mapping methods, which involves the Jacobian of the mapping transformation. We show how our first order method improves mapping accuracy in both simulated and real neuron traces under random diffeomorphisms. Our method is freely available in our open-source Python package brainlit.

Using biological constraints to improve prediction in precision oncology.

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.

Longitudinal changes in brain metabolites in healthy controls and patients with first episode psychosis: a 7-Tesla MRS study.

Seven Tesla magnetic resonance spectroscopy (7T MRS) offers a precise measurement of metabolic levels in the human brain via a non-invasive approach. Studying longitudinal changes in brain metabolites could help evaluate the characteristics of disease over time. This approach may also shed light on how the age of study participants and duration of illness may influence these metabolites. This study used 7T MRS to investigate longitudinal patterns of brain metabolites in young adulthood in both healthy controls and patients. A four-year longitudinal cohort with 38 patients with first episode psychosis (onset within 2 years) and 48 healthy controls was used to examine 10 brain metabolites in 5 brain regions associated with the pathophysiology of psychosis in a comprehensive manner. Both patients and controls were found to have significant longitudinal reductions in glutamate in the anterior cingulate cortex (ACC). Only patients were found to have a significant decrease over time in γ-aminobutyric acid, N-acetyl aspartate, myo-inositol, total choline, and total creatine in the ACC. Together we highlight the ACC with dynamic changes in several metabolites in early-stage psychosis, in contrast to the other 4 brain regions that also are known to play roles in psychosis. Meanwhile, glutathione was uniquely found to have a near zero annual percentage change in both patients and controls in all 5 brain regions during a four-year follow-up in young adulthood. Given that a reduction of the glutathione in the ACC has been reported as a feature of treatment-refractory psychosis, this observation further supports the potential of glutathione as a biomarker for this subset of patients with psychosis.

Mechanistic Modeling of Longitudinal Shape Changes: Equations of Motion and Inverse Problems.

This paper examines a longitudinal shape evolution model in which a three-dimensional volume progresses through a family of elastic equilibria in response to the time-derivative of an internal force, or yank, with an additional regularization to ensure diffeomorphic transformations. We consider two different models of yank and address the long time existence and uniqueness of solutions for the equations of motion in both models. In addition, we derive sufficient conditions for the existence of an optimal yank that best describes the change from an observed initial volume to an observed volume at a later time. The main motivation for this work is the understanding of processes such as growth and atrophy in anatomical structures, where the yank could be roughly interpreted as a metabolic event triggering morphological changes. We provide preliminary results on simple examples to illustrate, under this model, the retrievability of some attributes of such events.

Corrigendum to "Robust Diffeomorphic Mapping via Geodesically Controlled Active Shapes".

[This corrects the article DOI: 10.1155/2013/205494.].

Efficient representations of tumor diversity with paired DNA-RNA aberrations.

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.

Entorhinal and Transentorhinal Atrophy in Preclinical Alzheimer's Disease.

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.

Visualising the topography of the acoustic radiation in clinical diffusion tensor imaging scans.

PURPOSE: It has long been thought that the acoustic radiation (AR) white matter fibre tract from the medial geniculate body of the thalamus to the Heschl's gyrus cannot be reconstructed via single-fibre analysis of clinical diffusion tensor imaging (DTI) scans. A recently developed single-fibre probabilistic method suggests otherwise. The method uses dynamic programming (DP) to compute the most probable paths between two regions of interest. This study aims to observe the ability of single-fibre probabilistic analysis via DP to visualise the AR in clinical DTI scans from legacy pilot cohorts of subjects with normal hearing (NH) and profound hearing loss (HL). METHODS: Single-fibre probabilistic analysis via DP was applied to reconstruct 3D models of the AR in the two cohorts. DTI and T1 data at 1.5 T for subjects with NH (n = 11) and HL (n = 5), as well as 3 T for NH (n = 1) and HL (n = 1), were used. RESULTS: The topographical features of AR previously observed in post-mortem and multi-fibre analyses can be visualised in DTI scans of 16 subjects and 2 atlases with a success rate of 100%. Relative to MNI coordinates, there was no significant difference in the varifold distances between the topography of the tracts in the 1.5 T cohort. CONCLUSION: The AR can be visualised in clinical 1.5 T and 3 T DTI scans using single-fibre probabilistic analysis via DP, hence, the potential for DP to visualise the AR in medical and pre-surgical applications in pathologies such as vestibular schwannoma, multiple sclerosis, thalamic tumours and stroke as well as hearing loss.

Revisiting the tumorigenesis timeline with a data-driven generative model.

Cancer is driven by the sequential accumulation of genetic and epigenetic changes in oncogenes and tumor suppressor genes. The timing of these events is not well understood. Moreover, it is currently unknown why the same driver gene change appears as an early event in some cancer types and as a later event, or not at all, in others. These questions have become even more topical with the recent progress brought by genome-wide sequencing studies of cancer. Focusing on mutational events, we provide a mathematical model of the full process of tumor evolution that includes different types of fitness advantages for driver genes and carrying-capacity considerations. The model is able to recapitulate a substantial proportion of the observed cancer incidence in several cancer types (colorectal, pancreatic, and leukemia) and inherited conditions (Lynch and familial adenomatous polyposis), by changing only 2 tissue-specific parameters: the number of stem cells in a tissue and its cell division frequency. The model sheds light on the evolutionary dynamics of cancer by suggesting a generalized early onset of tumorigenesis followed by slow mutational waves, in contrast to previous conclusions. Formulas and estimates are provided for the fitness increases induced by driver mutations, often much larger than previously described, and highly tissue dependent. Our results suggest a mechanistic explanation for why the selective fitness advantage introduced by specific driver genes is tissue dependent.

Grant Report on PREDICT-ADFTD: Multimodal Imaging Prediction of AD/FTD and Differential Diagnosis.

We report on the ongoing project "PREDICT-ADFTD: Multimodal Imaging Prediction of AD/FTD and Differential Diagnosis" describing completed and future work supported by this grant. This project is a multi-site, multi-study collaboration effort with research spanning seven sites across the US and Canada. The overall goal of the project is to study neurodegeneration within Alzheimer's Disease, Frontotemporal Dementia, and related neurodegenerative disorders, using a variety of brain imaging and computational techniques to develop methods for the early and accurate prediction of disease and its course. The overarching goal of the project is to develop the earliest and most accurate biomarker that can differentiate clinical diagnoses to inform clinical trials and patient care. In its third year, this project has already completed several projects to achieve this goal, focusing on (1) structural MRI (2) machine learning and (3) FDG-PET and multimodal imaging. Studies utilizing structural MRI have identified key features of underlying pathology by studying hippocampal deformation that is unique to clinical diagnosis and also post-mortem confirmed neuropathology. Several machine learning experiments have shown high classification accuracy in the prediction of disease based on Convolutional Neural Networks utilizing MRI images as input. In addition, we have also achieved high accuracy in predicting conversion to DAT up to five years in the future. Further, we evaluated multimodal models that combine structural and FDG-PET imaging, in order to compare the predictive power of multimodal to unimodal models. Studies utilizing FDG-PET have shown significant predictive ability in the prediction and progression of disease.

Identifying Changepoints in Biomarkers During the Preclinical Phase of Alzheimer's Disease.

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.