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.

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.

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.

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.

Digitizing omics profiles by divergence from a baseline.

Data collected from omics technologies have revealed pervasive heterogeneity and stochasticity of molecular states within and between phenotypes. A prominent example of such heterogeneity occurs between genome-wide mRNA, microRNA, and methylation profiles from one individual tumor to another, even within a cancer subtype. However, current methods in bioinformatics, such as detecting differentially expressed genes or CpG sites, are population-based and therefore do not effectively model intersample diversity. Here we introduce a unified theory to quantify sample-level heterogeneity that is applicable to a single omics profile. Specifically, we simplify an omics profile to a digital representation based on the omics profiles from a set of samples from a reference or baseline population (e.g., normal tissues). The state of any subprofile (e.g., expression vector for a subset of genes) is said to be "divergent" if it lies outside the estimated support of the baseline distribution and is consequently interpreted as "dysregulated" relative to that baseline. We focus on two cases: single features (e.g., individual genes) and distinguished subsets (e.g., regulatory pathways). Notably, since the divergence analysis is at the individual sample level, dysregulation can be analyzed probabilistically; for example, one can estimate the probability that a gene or pathway is divergent in some population. Finally, the reduction in complexity facilitates a more "personalized" and biologically interpretable analysis of variation, as illustrated by experiments involving tissue characterization, disease detection and progression, and disease-pathway associations.

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.

Regional subcortical shape analysis in premanifest Huntington's disease.

Huntington's disease (HD) involves preferential and progressive degeneration of striatum and other subcortical regions as well as regional cortical atrophy. It is caused by a CAG repeat expansion in the Huntingtin gene, and the longer the expansion the earlier the age of onset. Atrophy begins prior to manifest clinical signs and symptoms, and brain atrophy in premanifest expansion carriers can be studied. We employed a diffeomorphometric pipeline to contrast subcortical structures' morphological properties in a control group with three disease groups representing different phases of premanifest HD (far, intermediate, and near to onset) as defined by the length of the CAG expansion and the participant's age (CAG-Age-Product). A total of 1,428 magnetic resonance image scans from 694 participants from the PREDICT-HD cohort were used. We found significant region-specific atrophies in all subcortical structures studied, with the estimated abnormality onset time varying from structure to structure. Heterogeneous shape abnormalities of caudate nuclei were present in premanifest HD participants estimated furthest from onset and putaminal shape abnormalities were present in participants intermediate to onset. Thalamic, hippocampal, and amygdalar shape abnormalities were present in participants nearest to onset. We assessed whether the estimated progression of subcortical pathology in premanifest HD tracked specific pathways. This is plausible for changes in basal ganglia circuits but probably not for changes in hippocampus and amygdala. The regional shape analyses conducted in this study provide useful insights into the effects of HD pathology in subcortical structures.

Visual Turing test for computer vision systems.

Today, computer vision systems are tested by their accuracy in detecting and localizing instances of objects. As an alternative, and motivated by the ability of humans to provide far richer descriptions and even tell a story about an image, we construct a "visual Turing test": an operator-assisted device that produces a stochastic sequence of binary questions from a given test image. The query engine proposes a question; the operator either provides the correct answer or rejects the question as ambiguous; the engine proposes the next question ("just-in-time truthing"). The test is then administered to the computer-vision system, one question at a time. After the system's answer is recorded, the system is provided the correct answer and the next question. Parsing is trivial and deterministic; the system being tested requires no natural language processing. The query engine employs statistical constraints, learned from a training set, to produce questions with essentially unpredictable answers-the answer to a question, given the history of questions and their correct answers, is nearly equally likely to be positive or negative. In this sense, the test is only about vision. The system is designed to produce streams of questions that follow natural story lines, from the instantiation of a unique object, through an exploration of its properties, and on to its relationships with other uniquely instantiated objects.

Mapping the order and pattern of brain structural MRI changes using change-point analysis in premanifest Huntington's disease.

Huntington's disease (HD) is an autosomal dominant neurodegenerative disorder that progressively affects motor, cognitive, and emotional functions. Structural MRI studies have demonstrated brain atrophy beginning many years prior to clinical onset ("premanifest" period), but the order and pattern of brain structural changes have not been fully characterized. In this study, we investigated brain regional volumes and diffusion tensor imaging (DTI) measurements in premanifest HD, and we aim to determine (1) the extent of MRI changes in a large number of structures across the brain by atlas-based analysis, and (2) the initiation points of structural MRI changes in these brain regions. We adopted a novel multivariate linear regression model to detect the inflection points at which the MRI changes begin (namely, "change-points"), with respect to the CAG-age product (CAP, an indicator of extent of exposure to the effects of CAG repeat expansion). We used approximately 300 T1-weighted and DTI data from premanifest HD and control subjects in the PREDICT-HD study, with atlas-based whole brain segmentation and change-point analysis. The results indicated a distinct topology of structural MRI changes: the change-points of the volumetric measurements suggested a central-to-peripheral pattern of atrophy from the striatum to the deep white matter; and the change points of DTI measurements indicated the earliest changes in mean diffusivity in the deep white matter and posterior white matter. While interpretation needs to be cautious given the cross-sectional nature of the data, these findings suggest a spatial and temporal pattern of spread of structural changes within the HD brain. Hum Brain Mapp 38:5035-5050, 2017. © 2017 Wiley Periodicals, Inc.

Hamiltonian Systems and Optimal Control in Computational Anatomy: 100 Years Since D'Arcy Thompson.

The Computational Anatomy project is the morphome-scale study of shape and form, which we model as an orbit under diffeomorphic group action. Metric comparison calculates the geodesic length of the diffeomorphic flow connecting one form to another. Geodesic connection provides a positioning system for coordinatizing the forms and positioning their associated functional information. This article reviews progress since the Euler-Lagrange characterization of the geodesics a decade ago. Geodesic positioning is posed as a series of problems in Hamiltonian control, which emphasize the key reduction from the Eulerian momentum with dimension of the flow of the group, to the parametric coordinates appropriate to the dimension of the submanifolds being positioned. The Hamiltonian viewpoint provides important extensions of the core setting to new, object-informed positioning systems. Several submanifold mapping problems are discussed as they apply to metamorphosis, multiple shape spaces, and longitudinal time series studies of growth and atrophy via shape splines.

An argument for mechanism-based statistical inference in cancer.

Cancer is perhaps the prototypical systems disease, and as such has been the focus of extensive study in quantitative systems biology. However, translating these programs into personalized clinical care remains elusive and incomplete. In this perspective, we argue that realizing this agenda­in particular, predicting disease phenotypes, progression and treatment response for individuals­requires going well beyond standard computational and bioinformatics tools and algorithms. It entails designing global mathematical models over network-scale configurations of genomic states and molecular concentrations, and learning the model parameters from limited available samples of high-dimensional and integrative omics data. As such, any plausible design should accommodate: biological mechanism, necessary for both feasible learning and interpretable decision making; stochasticity, to deal with uncertainty and observed variation at many scales; and a capacity for statistical inference at the patient level. This program, which requires a close, sustained collaboration between mathematicians and biologists, is illustrated in several contexts, including learning biomarkers, metabolism, cell signaling, network inference and tumorigenesis.

The diffeomorphometry of regional shape change rates and its relevance to cognitive deterioration in mild cognitive impairment and Alzheimer's disease.

We proposed a diffeomorphometry-based statistical pipeline to study the regional shape change rates of the bilateral hippocampus, amygdala, and ventricle in mild cognitive impairment (MCI) and Alzheimer's disease (AD) compared with healthy controls (HC), using sequential magnetic resonance imaging (MRI) scans of 713 subjects (3,123 scans in total). The subgroup shape atrophy rates of the bilateral hippocampus and amygdala, as well as the expansion rates of the bilateral ventricles, for a majority of vertices were found to follow the order of AD>MCI>HC. The bilateral hippocampus and the left amygdala were subsegmented into multiple functionally meaningful subregions with the help of high-field MRI scans. The largest group differences in localized shape atrophy rates on the hippocampus were found to occur in CA1, followed by subiculum, CA2, and finally CA3/dentate gyrus, which is consistent with the neurofibrillary tangle accumulation trajectory. Highly nonuniform group differences were detected on the amygdala; vertices on the core amygdala (basolateral and lateral nucleus) revealed much larger atrophy rates, whereas those on the noncore amygdala (mainly centromedial) displayed similar or even smaller atrophy rates in AD relative to HC. The temporal horns of the ventricles were observed to have the largest localized ventricular expansion rate differences; with the AD group showing larger localized expansion rates on the anterior horn and the body part of the ventricles as well. Significant correlations were observed between the localized shape change rates of each of these six structures and the cognitive deterioration rates as quantified by the Alzheimer's Disease Assessment Scale-Cognitive Behavior Section increase rate and the Mini Mental State Examination decrease rate.

Relationship of medial temporal lobe atrophy, APOE genotype, and cognitive reserve in preclinical Alzheimer's disease.

This study evaluated the utility of baseline and longitudinal magnetic resonance imaging (MRI) measures of medial temporal lobe brain regions collected when participants were cognitively normal and largely in middle age (mean age 57 years) to predict the time to onset of clinical symptoms associated with mild cognitive impairment (MCI). Furthermore, we examined whether the relationship between MRI measures and clinical symptom onset was modified by apolipoprotein E (ApoE) genotype and level of cognitive reserve (CR). MRI scans and measures of CR were obtained at baseline from 245 participants who had been followed for up to 18 years (mean follow-up 11 years). A composite score based on reading, vocabulary, and years of education was used as an index of CR. Cox regression models showed that lower baseline volume of the right hippocampus and smaller baseline thickness of the right entorhinal cortex predicted the time to symptom onset independently of CR and ApoE-ɛ4 genotype, which also predicted the onset of symptoms. The atrophy rates of bilateral entorhinal cortex and amygdala volumes were also associated with time to symptom onset, independent of CR, ApoE genotype, and baseline volume. Only one measure, the left entorhinal cortex baseline volume, interacted with CR, such that smaller volumes predicted symptom onset only in individuals with lower CR. These results suggest that MRI measures of medial temporal atrophy, ApoE-ɛ4 genotype, and the protective effects of higher CR all predict the time to onset of symptoms associated with MCI in a largely independent, additive manner during the preclinical phase of Alzheimer's disease.

Hemodynamics in the Left Atrium and Its Effect on Ventricular Flow Patterns.

In the present study, we investigate the hemodynamics inside left atrium (LA) and understand its impact on the development of ventricular flow patterns. We construct the heart model using dynamic-computed tomographic images and perform simulations using an immersed boundary method based flow solver. We show that the atrial hemodynamics is characterized by a circulatory flow generated by the left pulmonary veins (LPVs) and a direct stream from the right pulmonary veins (RPVs). The complex interaction of the vortex rings formed from each of the PVs leads to vortex breakup and annihilation, thereby producing a regularized flow at the mitral annulus. A comparison of the ventricular flow velocities between the physiological and a simplified pipe-based atrium model shows that the overall differences are limited to about 10% of the peak mitral flow velocity. The implications of this finding on the functional morphology of the left heart as well the computational and experimental modeling of ventricular hemodynamics are discussed.

Shape abnormalities of subcortical and ventricular structures in mild cognitive impairment and Alzheimer's disease: detecting, quantifying, and predicting.

This article assesses the feasibility of using shape information to detect and quantify the subcortical and ventricular structural changes in mild cognitive impairment (MCI) and Alzheimer's disease (AD) patients. We first demonstrate structural shape abnormalities in MCI and AD as compared with healthy controls (HC). Exploring the development to AD, we then divide the MCI participants into two subgroups based on longitudinal clinical information: (1) MCI patients who remained stable; (2) MCI patients who converted to AD over time. We focus on seven structures (amygdala, hippocampus, thalamus, caudate, putamen, globus pallidus, and lateral ventricles) in 754 MR scans (210 HC, 369 MCI of which 151 converted to AD over time, and 175 AD). The hippocampus and amygdala were further subsegmented based on high field 0.8 mm isotropic 7.0T scans for finer exploration. For MCI and AD, prominent ventricular expansions were detected and we found that these patients had strongest hippocampal atrophy occurring at CA1 and strongest amygdala atrophy at the basolateral complex. Mild atrophy in basal ganglia structures was also detected in MCI and AD. Stronger atrophy in the amygdala and hippocampus, and greater expansion in ventricles was observed in MCI converters, relative to those MCI who remained stable. Furthermore, we performed principal component analysis on a linear shape space of each structure. A subsequent linear discriminant analysis on the principal component values of hippocampus, amygdala, and ventricle leads to correct classification of 88% HC subjects and 86% AD subjects.

Regionally selective atrophy of subcortical structures in prodromal HD as revealed by statistical shape analysis.

Huntington disease (HD) is a neurodegenerative disorder that involves preferential atrophy in the striatal complex and related subcortical nuclei. In this article, which is based on a dataset extracted from the PREDICT-HD study, we use statistical shape analysis with deformation markers obtained through "Large Deformation Diffeomorphic Metric Mapping" of cortical surfaces to highlight specific atrophy patterns in the caudate, putamen, and globus pallidus, at different prodromal stages of the disease. On the basis of the relation to cortico-basal ganglia circuitry, we propose that statistical shape analysis, along with other structural and functional imaging studies, may help expand our understanding of the brain circuitry affected and other aspects of the neurobiology of HD, and also guide the most effective strategies for intervention.

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.

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.

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.