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".

Molecular Computational Anatomy: Unifying the Particle to Tissue Continuum via Measure Representations of the Brain

OBJECTIVE

The objective of this research is to unify the molecular representations of spatial transcriptomics and cellular scale histology with the tissue scales of computational anatomy for brain mapping.

IMPACT STATEMENT

We present a unified representation theory for brain mapping based on geometric varifold measures of the microscale deterministic structure and function with the statistical ensembles of the spatially aggregated tissue scales.

INTRODUCTION

Mapping across coordinate systems in computational anatomy allows us to understand structural and functional properties of the brain at the millimeter scale. New measurement technologies in digital pathology and spatial transcriptomics allow us to measure the brain molecule by molecule and cell by cell based on protein and transcriptomic functional identity. We currently have no mathematical representations for integrating consistently the tissue limits with the molecular particle descriptions. The formalism derived here demonstrates the methodology for transitioning consistently from the molecular scale of quantized particles-using mathematical structures as first introduced by Dirac as the class of generalized functions-to the tissue scales with methods originally introduced by Euler for fluids.

METHODS

We introduce two mathematical methods based on notions of generalized functions and statistical mechanics. We use geometric varifolds, a product measure on space and function, to represent functional states at the micro-scales-electrophysiology, molecular histology-integrated with a Boltzmann-like program to pass from deterministic particle descriptions to empirical probabilities on the functional states at the tissue scales.

RESULTS

Our space-function varifold representation provides a recipe for traversing from molecular to tissue scales in terms of a cascade of linear space scaling composed with nonlinear functional feature mapping. Following the cascade implies every scale is a geometric measure so that a universal family of measure norms can be introduced which quantifies the geodesic connection between brains in the orbit independent of the probing technology, whether it be RNA identities, Tau or amyloid histology, spike trains, or dense MR imagery.

CONCLUSIONS

We demonstrate a unified brain mapping theory for molecular and tissue scales based on geometric measure representations. We call the consistent aggregation of tissue scales from particle and cellular scales, molecular computational anatomy.

The Inherent Coupling of Intrinsically Disordered Regions in the Multidomain Receptor Tyrosine Kinase KIT

RTK KIT regulates a variety of crucial cellular processes via its cytoplasmic domain (CD), which is composed of the tyrosine kinase domain, crowned by the highly flexible domains—the juxtamembrane region, kinase insertion domain, and C-tail, which are key recruitment regions for downstream signalling proteins. To prepare a structural basis for the characterization of the interactions of KIT with its signalling proteins (KIT INTERACTOME), we generated the 3D model of the full-length CD attached to the transmembrane helix. This generic model of KIT in inactive state was studied by molecular dynamics simulation under conditions mimicking the natural environment of KIT. With the accurate atomistic description of the multidomain KIT dynamics, we explained its intrinsic (intra-domain) and extrinsic (inter-domain) disorder and represented the conformational assemble of KIT through free energy landscapes. Strongly coupled movements within each domain and between distant domains of KIT prove the functional interdependence of these regions, described as allosteric regulation, a phenomenon widely observed in many proteins. We suggested that KIT, in its inactive state, encodes all properties of the active protein and its post-transduction events.

Folding and Intrinsic Disorder of the Receptor Tyrosine Kinase KIT Insert Domain Seen by Conventional Molecular Dynamics Simulations

The kinase insert domain (KID) of RTK KIT is the key recruitment region for downstream signalling proteins. KID, studied by molecular dynamics simulations as a cleaved polypeptide and as a native domain fused to KIT, showed intrinsic disorder represented by a set of heterogeneous conformations. The accurate atomistic models showed that the helical fold of KID is mainly sequence dependent. However, the reduced fold of the native KID suggests that its folding is allosterically controlled by the kinase domain. The tertiary structure of KID represents a compact array of highly variable α- and 3₁₀-helices linked by flexible loops playing a principal role in the conformational diversity. The helically folded KID retains a collapsed globule-like shape due to non-covalent interactions associated in a ternary hydrophobic core. The free energy landscapes constructed from first principles-the size, the measure of the average distance between the conformations, the amount of helices and the solvent-accessible surface area-describe the KID disorder through a collection of minima (wells), providing a direct evaluation of conformational ensembles. We found that the cleaved KID simulated with restricted N- and C-ends better reproduces the native KID than the isolated polypeptide. We suggest that a cyclic, generic KID would be best suited for future studies of KID f post-transduction effects.

Proceedings of the First Workshop Organized by the IAFSS Working Group on Measurement and Computation of Fire Phenomena (MaCFP)

This paper provides a report of the discussions held at the first workshop on Measurement and Computation of Fire Phenomena (MaCFP) on June 10-11 2017. The first MaCFP work-shop was both a technical meeting for the gas phase subgroup and a planning meeting for the condensed phase subgroup. The gas phase subgroup reported on a first suite of experimental- computational comparisons corresponding to an initial list of target experiments. The initial list of target experiments identifies a series of benchmark configurations with databases deemed suitable for validation of fire models based on a Computational Fluid Dynamics approach. The simulations presented at the first MaCFP workshop feature fine grid resolution at the millimeter- or centimeter- scale: these simulations allow an evaluation of the performance of fire models under high-resolution conditions in which the impact of numerical errors is reduced and many of the discrepancies between experimental data and computational results may be attributed to modeling errors. The experimental-computational comparisons are archived on the MaCFP repository [1]. Furthermore, the condensed phase subgroup presented a review of the main issues associated with measurements and modeling of pyrolysis phenomena. Overall, the first workshop provided an illustration of the potential of MaCFP in providing a response to the general need for greater levels of integration and coordination in fire research, and specifically to the particular needs of model validation.

Age and Glaucoma-Related Characteristics in Retinal Nerve Fiber Layer and Choroid: Localized Morphometrics and Visualization Using Functional Shapes Registration

Optical coherence tomography provides high-resolution 3D imaging of the posterior segment of the eye. However, quantitative morphological analysis, particularly relevant in retinal degenerative diseases such as glaucoma, has been confined to simple sectorization and averaging with limited spatial sensitivity for detection of clinical markers. In this paper, we present point-wise analysis and visualization of the retinal nerve fiber layer and choroid from cross-sectional data using functional shapes (fshape) registration. The fshape framework matches two retinas, or generates a mean of multiple retinas, by jointly optimizing the surface geometry and functional signals mapped on the surface. We generated group-wise mean retinal nerve fiber layer and choroidal surfaces with the respective layer thickness mapping and showed the difference by age (normal, younger vs. older) and by disease (age-matched older, normal vs. glaucomatous) in the two layers, along with a more conventional sector-based analysis for comparison. The fshape results visualized the detailed spatial patterns of the differences between the age-matched normal and glaucomatous retinal nerve fiber layers, with the glaucomatous layers most significantly thinner in the inferior region close to Bruch's membrane opening. Between the young and older normal cases, choroid was shown to be significantly thinner in the older subjects across all regions, but particularly in the nasal and inferior regions. The results demonstrate a comprehensive and detailed analysis with visualization of morphometric patterns by multiple factors.

Amotl1 mediates sequestration of the Hippo effector Yap1 downstream of Fat4 to restrict heart growth

Although in flies the atypical cadherin Fat is an upstream regulator of Hippo signalling, the closest mammalian homologue, Fat4, has been shown to regulate tissue polarity rather than growth. Here we show in the mouse heart that Fat4 modulates Hippo signalling to restrict growth. Fat4 mutant myocardium is thicker, with increased cardiomyocyte size and proliferation, and this is mediated by an upregulation of the transcriptional activity of Yap1, an effector of the Hippo pathway. Fat4 is not required for the canonical activation of Hippo kinases but it sequesters a partner of Yap1, Amotl1, out of the nucleus. The nuclear translocation of Amotl1 is accompanied by Yap1 to promote cardiomyocyte proliferation. We, therefore, identify Amotl1, which is not present in flies, as a mammalian intermediate for non-canonical Hippo signalling, downstream of Fat4. This work uncovers a mechanism for the restriction of heart growth at birth, a process which impedes the regenerative potential of the mammalian heart.

Identification of the functional states of human vitamin K epoxide reductase from molecular dynamics simulations

The functionally-related states of hVKORC1 predicted from MD conformations were assigned by probing their affinity to vitamin K and validated through analysis of its binding energy with VKAs.

How Intrinsic Molecular Dynamics Control Intramolecular Communication in Signal Transducers and Activators of Transcription Factor STAT5

Signal Transducer and Activator of Transcription STAT5 is a key mediator of cell proliferation, differentiation and survival. While STAT5 activity is tightly regulated in normal cells, its constitutive activation directly contributes to oncogenesis and is associated with a broad range of hematological and solid tumor cancers. Therefore the development of compounds able to modulate pathogenic activation of this protein is a very challenging endeavor. A crucial step of drug design is the understanding of the protein conformational features and the definition of putative binding site(s) for such modulators. Currently, there is no structural data available for human STAT5 and our study is the first footprint towards the description of structure and dynamics of this protein. We investigated structural and dynamical features of the two STAT5 isoforms, STAT5a and STAT5b, taken into account their phosphorylation status. The study was based on the exploration of molecular dynamics simulations by different analytical methods. Despite the overall folding similarity of STAT5 proteins, the MD conformations display specific structural and dynamical features for each protein, indicating first, sequence-encoded structural properties and second, phosphorylation-induced effects which contribute to local and long-distance structural rearrangements interpreted as allosteric event. Further examination of the dynamical coupling between distant sites provides evidence for alternative profiles of the communication pathways inside and between the STAT5 domains. These results add a new insight to the understanding of the crucial role of intrinsic molecular dynamics in mediating intramolecular signaling in STAT5. Two pockets, localized in close proximity to the phosphotyrosine-binding site and adjacent to the channel for communication pathways across STAT5, may constitute valid targets to develop inhibitors able to modulate the function-related communication properties of this signaling protein.

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.

Hotspot mutations in KIT receptor differentially modulate its allosterically coupled conformational dynamics: impact on activation and drug sensitivity

Receptor tyrosine kinase KIT controls many signal transduction pathways and represents a typical allosterically regulated protein. The mutation-induced deregulation of KIT activity impairs cellular physiological functions and causes serious human diseases. The impact of hotspots mutations (D816H/Y/N/V and V560G/D) localized in crucial regulatory segments, the juxtamembrane region (JMR) and the activation (A-) loop, on KIT internal dynamics was systematically studied by molecular dynamics simulations. The mutational outcomes predicted in silico were correlated with in vitro and in vivo activation rates and drug sensitivities of KIT mutants. The allosteric regulation of KIT in the native and mutated forms is described in terms of communication between the two remote segments, JMR and A-loop. A strong correlation between the communication profile and the structural and dynamical features of KIT in the native and mutated forms was established. Our results provide new insight on the determinants of receptor KIT constitutive activation by mutations and resistance of KIT mutants to inhibitors. Depiction of an intra-molecular component of the communication network constitutes a first step towards an integrated description of vast communication pathways established by KIT in physiopathological contexts.

Receptor tyrosine kinase KIT plays a crucial role in the regulation of cell signaling. This allosterically controlled activity may be affected by gain-of-function mutations that promote the development of several cancers. Identification of the molecular basis of KIT constitutive activation and allosteric regulation has inspired computational study of KIT hotspot mutations. In the present contribution, we investigated the mutation-induced effects on KIT conformational dynamics and intra-protein communication conditionally on the mutation location and the nature of the substituting amino acid. Our data elucidate that all studied mutations stabilize an inactive non-autoinhibited state of KIT over the inactive auto-inhibited state prevalent for the native protein. This shift in the protein conformational landscape promotes KIT constitutive activation. Our in silico analysis established correlations between the structural and dynamical effects induced by oncogenic mutations and the mutants auto-activation rates and drug sensitivities measured in vitro and in vivo. Particularly, the A-loop mutations stabilize the drug-resistant forms, while the JMR mutations may facilitate inhibitors binding to the active site. Cross-correlations established between local and long-range structural and dynamical effects demonstrate the allosteric character of the gain-of-function mutations mode of action.

Morphometry of anatomical shape complexes with dense deformations and sparse parameters

We propose a generic method for the statistical analysis of collections of anatomical shape complexes, namely sets of surfaces that were previously segmented and labeled in a group of subjects. The method estimates an anatomical model, the template complex, that is representative of the population under study. Its shape reflects anatomical invariants within the dataset. In addition, the method automatically places control points near the most variable parts of the template complex. Vectors attached to these points are parameters of deformations of the ambient 3D space. These deformations warp the template to each subject's complex in a way that preserves the organization of the anatomical structures. Multivariate statistical analysis is applied to these deformation parameters to test for group differences. Results of the statistical analysis are then expressed in terms of deformation patterns of the template complex, and can be visualized and interpreted. The user needs only to specify the topology of the template complex and the number of control points. The method then automatically estimates the shape of the template complex, the optimal position of control points and deformation parameters. The proposed approach is completely generic with respect to any type of application and well adapted to efficient use in clinical studies, in that it does not require point correspondence across surfaces and is robust to mesh imperfections such as holes, spikes, inconsistent orientation or irregular meshing. The approach is illustrated with a neuroimaging study of Down syndrome (DS). The results demonstrate that the complex of deep brain structures shows a statistically significant shape difference between control and DS subjects. The deformation-based modelingis able to classify subjects with very high specificity and sensitivity, thus showing important generalization capability even given a low sample size. We show that the results remain significant even if the number of control points, and hence the dimension of variables in the statistical model, are drastically reduced. The analysis may even suggest that parsimonious models have an increased statistical performance. The method has been implemented in the software Deformetrica, which is publicly available at www.deformetrica.org.

Diffeomorphometry and geodesic positioning systems for human anatomy

The Computational Anatomy project has largely been a study of large deformations within a Riemannian framework as an efficient point of view for generating metrics between anatomical configurations. This approach turns D'Arcy Thompson's comparative morphology of human biological shape and form into a metrizable space. Since the metric is constructed based on the geodesic length of the flows of diffeomorphisms connecting the forms, we call it diffeomorphometry. Just as importantly, since the flows describe algebraic group action on anatomical submanifolds and associated functional measurements, they become the basis for positioning information, which we term geodesic positioning. As well the geodesic connections provide Riemannian coordinates for locating forms in the anatomical orbit, which we call geodesic coordinates. These three components taken together - the metric, geodesic positioning of information, and geodesic coordinates - we term the geodesic positioning system. We illustrate via several examples in human and biological coordinate systems and machine learning of the statistical representation of shape and form.

Toward a comprehensive framework for the spatiotemporal statistical analysis of longitudinal shape data

This paper proposes an original approach for the statistical analysis of longitudinal shape data. The proposed method allows the characterization of typical growth patterns and subject-specific shape changes in repeated time-series observations of several subjects. This can be seen as the extension of usual longitudinal statistics of scalar measurements to high-dimensional shape or image data. The method is based on the estimation of continuous subject-specific growth trajectories and the comparison of such temporal shape changes across subjects. Differences between growth trajectories are decomposed into morphological deformations, which account for shape changes independent of the time, and time warps, which account for different rates of shape changes over time. Given a longitudinal shape data set, we estimate a mean growth scenario representative of the population, and the variations of this scenario both in terms of shape changes and in terms of change in growth speed. Then, intrinsic statistics are derived in the space of spatiotemporal deformations, which characterize the typical variations in shape and in growth speed within the studied population. They can be used to detect systematic developmental delays across subjects. In the context of neuroscience, we apply this method to analyze the differences in the growth of the hippocampus in children diagnosed with autism, developmental delays and in controls. Result suggest that group differences may be better characterized by a different speed of maturation rather than shape differences at a given age. In the context of anthropology, we assess the differences in the typical growth of the endocranium between chimpanzees and bonobos. We take advantage of this study to show the robustness of the method with respect to change of parameters and perturbation of the age estimates.

Diffeomorphic brain registration under exhaustive sulcal constraints

The alignment and normalization of individual brain structures is a prerequisite for group-level analyses of structural and functional neuroimaging data. The techniques currently available are either based on volume and/or surface attributes, with limited insight regarding the consistent alignment of anatomical landmarks across individuals. This article details a global, geometric approach that performs the alignment of the exhaustive sulcal imprints (cortical folding patterns) across individuals. This DIffeomorphic Sulcal-based COrtical (DISCO) technique proceeds to the automatic extraction, identification and simplification of sulcal features from T1-weighted Magnetic Resonance Image (MRI) series. These features are then used as control measures for fully-3-D diffeomorphic deformations. Quantitative and qualitative evaluations show that DISCO correctly aligns the sulcal folds and gray and white matter volumes across individuals. The comparison with a recent, iconic diffeomorphic approach (DARTEL) highlights how the absence of explicit cortical landmarks may lead to the misalignment of cortical sulci. We also feature DISCO in the automatic design of an empirical sulcal template from group data. We also demonstrate how DISCO can efficiently be combined with an image-based deformation (DARTEL) to further improve the consistency and accuracy of alignment performances. Finally, we illustrate how the optimized alignment of cortical folds across subjects improves sensitivity in the detection of functional activations in a group-level analysis of neuroimaging data.

Registration, atlas estimation and variability analysis of white matter fiber bundles modeled as currents

This paper proposes a generic framework for the registration, the template estimation and the variability analysis of white matter fiber bundles extracted from diffusion images. This framework is based on the metric on currents for the comparison of fiber bundles. This metric measures anatomical differences between fiber bundles, seen as global homologous structures across subjects. It avoids the need to establish correspondences between points or between individual fibers of different bundles. It can measure differences both in terms of the geometry of the bundles (like its boundaries) and in terms of the density of fibers within the bundle. It is robust to fiber interruptions and reconnections. In addition, a recently introduced sparse approximation algorithm allows us to give an interpretable representation of the fiber bundles and their variations in the framework of currents. First, we used this metric to drive the registration between two sets of homologous fiber bundles of two different subjects. A dense deformation of the underlying white matter is estimated, which is constrained by the bundles seen as global anatomical landmarks. By contrast, the alignment obtained from image registration is driven only by the local gradient of the image. Second, we propose a generative statistical model for the analysis of a collection of homologous bundles. This model consistently estimates prototype fiber bundles (called template), which capture the anatomical invariants in the population, a set of deformations, which align the geometry of the template to that of each subject and a set of residual perturbations. The statistical analysis of both the deformations and the residuals describe the anatomical variability in terms of geometry (stretching, torque, etc.) and "texture" (fiber density, etc.). Third, this statistical modeling allows us to simulate new synthetic bundles according to the estimated variability. This gives a way to interpret the anatomical features that the model detects consistently across the subjects. This may be used to better understand the bias introduced by the fiber extraction methods and eventually to give anatomical characterization of the normal or pathological variability of fiber bundles.

DISCO: a coherent diffeomorphic framework for brain registration under exhaustive sulcal constraints

Neuroimaging at the group level requires spatial normalization of individual structural data. We propose a geometric approach that consists in matching a series of cortical surfaces through diffeomorphic registration of their sulcal imprints. The resulting 3D transforms naturally extends to the entire MRI volumes. The Diffeomorphic Sulcal-based COrtical (DISCO) registration integrates two recent technical outcomes: 1) the automatic extraction, identification and simplification of numerous sulci from T1-weighted MRI data series hereby revealing the sulcal imprint and 2) the measure-based diffeomorphic registration of those crucial anatomical landmarks. We show how the DISCO registration may be used to elaborate a sulcal template which optimizes the distribution of constraints over the entire cortical ribbon. DISCO was evaluated through a group of 20 individual brains. Quantitative and qualitative indices attest how this approach may improve both alignment of sulcal folds and overlay of gray and white matter volumes at the group level.

A statistical model of white matter fiber bundles based on currents

The purpose of this paper is to measure the variability of a population of white matter fiber bundles without imposing unrealistic geometrical priors. In this respect, modeling fiber bundles as currents seems particularly relevant, as it gives a metric between bundles which relies neither on point nor on fiber correspondences and which is robust to fiber interruption. First, this metric is included in a diffeomorphic registration scheme which consistently aligns sets of fiber bundles. In particular, we show that aligning directly fiber bundles may solve the aperture problem which appears when fiber mappings are constrained by tensors only. Second, the measure of variability of a population of fiber bundles is based on a statistical model which considers every bundle as a random diffeomorphic deformation of a common template plus a random non-diffeomorphic perturbation. Thus, the variability is decomposed into a geometrical part and a "texture" part. Our results on real data show that both parts may contain interesting anatomical features.

Spatiotemporal atlas estimation for developmental delay detection in longitudinal datasets

We propose a new methodology to analyze the anatomical variability of a set of longitudinal data (population scanned at several ages). This method accounts not only for the usual 3D anatomical variability (geometry of structures), but also for possible changes in the dynamics of evolution of the structures. It does not require that subjects are scanned the same number of times or at the same ages. First a regression model infers a continuous evolution of shapes from a set of observations of the same subject. Second, spatiotemporal registrations deform jointly (1) the geometry of the evolving structure via 3D deformations and (2) the dynamics of evolution via time change functions. Third, we infer from a population a prototype scenario of evolution and its 4D variability. Our method is used to analyze the morphological evolution of 2D profiles of hominids skulls and to analyze brain growth from amygdala of autistics, developmental delay and control children.

Bayesian template estimation in computational anatomy

Templates play a fundamental role in Computational Anatomy. In this paper, we present a Bayesian model for template estimation. It is assumed that observed images I(1), I(2),...,I(N) are generated by shooting the template J through Gaussian distributed random initial momenta theta(1), theta(2),...,theta(N). The template is J modeled as a deformation from a given hypertemplate J(0) with initial momentum mu, which has a Gaussian prior. We apply a mode approximation of the EM (MAEM) procedure, where the conditional expectation is replaced by a Dirac measure at the mode. This leads us to an image matching problem with a Jacobian weight term, and we solve it by deriving the weighted Euler-Lagrange equation. The results of template estimation for hippocampus and cardiac data are presented.

High-resolution 3-D imaging of living cells in suspension using confocal axial tomography

Conventional flow cytometry (FC) methods report optical signals integrated from individual cells at throughput rates as high as thousands of cells per second. This is further combined with the powerful utility to subsequently sort and/or recover the cells of interest. However, these methods cannot extract spatial information. This limitation has prompted efforts by some commercial manufacturers to produce state-of-the-art commercial flow cytometry systems allowing fluorescence images to be recorded by an imaging detector. Nonetheless, there remains an immediate and growing need for technologies facilitating spatial analysis of fluorescent signals from cells maintained in flow suspension. Here, we report a novel methodological approach to this problem that combines micro-fluidic flow, and microelectrode dielectric-field control to manipulate, immobilize and image individual cells in suspension. The method also offers unique possibilities for imaging studies on cells in suspension. In particular, we report the system's immediate utility for confocal "axial tomography" using micro-rotation imaging and show that it greatly enhances 3-D optical resolution compared with conventional light reconstruction (deconvolution) image data treatment. That the method we present here is relatively rapid and lends itself to full automation suggests its eventual utility for 3-D imaging cytometry.

Sparse approximation of currents for statistics on curves and surfaces

Computing, processing, visualizing statistics on shapes like curves or surfaces is a real challenge with many applications ranging from medical image analysis to computational geometry. Modelling such geometrical primitives with currents avoids feature-based approach as well as point-correspondence method. This framework has been proved to be powerful to register brain surfaces or to measure geometrical invariants. However, if the state-of-the-art methods perform efficiently pairwise registrations, new numerical schemes are required to process groupwise statistics due to an increasing complexity when the size of the database is growing. Statistics such as mean and principal modes of a set of shapes often have a heavy and highly redundant representation. We propose therefore to find an adapted basis on which mean and principal modes have a sparse decomposition. Besides the computational improvement, this sparse representation offers a way to visualize and interpret statistics on currents. Experiments show the relevance of the approach on 34 sets of 70 sulcal lines and on 50 sets of 10 meshes of deep brain structures.

Soliton dynamics in computational anatomy

Computational anatomy (CA) has introduced the idea of anatomical structures being transformed by geodesic deformations on groups of diffeomorphisms. Among these geometric structures, landmarks and image outlines in CA are shown to be singular solutions of a partial differential equation that is called the geodesic EPDiff equation. A recently discovered momentum map for singular solutions of EPDiff yields their canonical Hamiltonian formulation, which in turn provides a complete parameterization of the landmarks by their canonical positions and momenta. The momentum map provides an isomorphism between landmarks (and outlines) for images and singular soliton solutions of the EPDiff equation. This isomorphism suggests a new dynamical paradigm for CA, as well as new data representation.

Statistics on diffeomorphisms via tangent space representations

In this paper, we present a linear setting for statistical analysis of shape and an optimization approach based on a recent derivation of a conservation of momentum law for the geodesics of diffeomorphic flow. Once a template is fixed, the space of initial momentum becomes an appropriate space for studying shape via geodesic flow since the flow at any point along the geodesic is completely determined by the momentum at the origin through geodesic shooting equations. The space of initial momentum provides a linear representation of the nonlinear diffeomorphic shape space in which linear statistical analysis can be applied. Specializing to the landmark matching problem of Computational Anatomy, we derive an algorithm for solving the variational problem with respect to the initial momentum and demonstrate principal component analysis (PCA) in this setting with three-dimensional face and hippocampus databases.