Multi scale diffeomorphic metric mapping of spatial transcriptomics datasets

Miller, Michael I.; Fan, Jean; Tward, Daniel J.

doi:10.1109/cvprw53098.2021.00504

Cited by 4 publications

(4 citation statements)

References 32 publications

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“…This paper introduces a new class of image-based diffeomorphometry methods which we term Projective LDDMM for aligning sparse sets of image captures to 3D coordinate systems across micron and millimeter scales. We focus particularly on the registration of 3D MRI with 2D digital histology, as representative of the class of multi-scale, multi-modality mapping in biomedical research including traditional light microscopy mapping to dense reference atlases [5, 6, 7, 8], light sheet methods [9, 10], deep tissue imaging [11], and spatial transcriptomics [12, 13, 14, 15]. We formulate the mapping of dense atlases to sparse images problem using the random orbit model of computational anatomy [16, 17, 18, 19] in which the space of dense anatomies is modeled as an orbit of a 3D template under the group of diffeomorphisms.…”

Section: Introductionmentioning

confidence: 99%

Projective LDDMM: Mapping Molecular Digital Pathology with Tissue MRI

Stouffer

Tward

Miller

2022

Preprint

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Reconstructing dense 3D anatomical coordinates from 2D projective measurements has become a central problem in digital pathology for both animal models and human studies. We describe a new family of diffeomorphic mapping technologies called Projective LDDMM which generate diffeomorphic mappings of dense human MRI atlases at tissue scales onto sparse measurements at micron scales associated with histological and more general optical imaging modalities. We solve the problem of dense mapping surjectively onto histological sections by incorporating new technologies for crossing modalities that use non-linear scattering transforms to represent multiple radiomic-like textures at micron scales and incorporating a Gaussian mixture-model frame-work for modelling tears and distortions associated to each section. We highlight the significance of our method through incorporation of neuropathological measures and MRI, as relevant to the development of biomarkers for Alzheimer’s disease and one instance of the integration of imaging data across the scales of clinical imaging and digital pathology.

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Section: Introductionmentioning

confidence: 99%

Projective LDDMM: Mapping Molecular Digital Pathology with Tissue MRI

Stouffer

Tward

Miller

2022

Preprint

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“…Specifically, in our own work on digital pathology for the study of Alzheimer’s disease called the BIOCARD study [ 6 ], we are examining pathological Tau in the medial temporal lobe (MTL) at both the microhistological and macroscopic atlas scales, from 10 to 100 μ m [ 7 , 8 ], extended to the magnetic resonance millimeter scales for examining entire circuits in the MTL. In the mouse cell census project, we are examining single-cell spatial transcriptomics using modern RNA sequencing in dense tissue at the micron scale and its representations in the Allen atlas coordinates [ 9 ].…”

Section: Introductionmentioning

confidence: 99%

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

2022

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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.

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“…Specifically, in our own work digital pathology for the study of Alzheimer’s disease called the BIOCARD study [6], we are examining pathological Tau at both the micro histological and macro atlas scales of Tau particle detections, from 10-100 μ m [7, 8] and to human magnetic resonance millimeter scales for examining entire circuits in the medial temporal lobe. In the mouse cell counting project we are examining single-cell spatial transcriptomics using modern RNA sequencing in dense tissue at the micron scale and its representations in the Allen atlas coordinates [9].…”

Section: Introductionmentioning

confidence: 99%

Hierarchical Computational Anatomy: Unifying the Molecular to Tissue Continuum Via Measure Representations of the Brain

Tward

Trouvé

2021

Preprint

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This paper presents a unified representation of the brain based on mathematical functional measures integrating the molecular and cellular scale descriptions with continuum tissue scale descriptions. We present a fine-to-coarse recipe for traversing the brain as a hierarchy of measures projecting functional description into stable empirical probability laws that unifies scale-space aggregation. The representation uses measure norms for mapping the brain across scales from different measurement technologies. Brainspace is constructed as a metric space with metric comparison between brains provided by a hierarchy of Hamiltonian geodesic flows of diffeomorphisms connecting the molecular and continuum tissue scales. The diffeomorphisms act on the brain measures via the 3D varifold action representing "copy and paste" so that basic particle quantities that are conserved biologically are combined with greater multiplicity and not geometrically distorted. Two applications are examined, the first histological and tissue scale data in the human brain for studying Alzheimer's disease, and the second the RNA and cell signatures of dense spatial transcriptomics mapped to the meso-scales of brain atlases. The representation unifies the classical formalism of computational anatomy for representing continuum tissue scale with non-classical generalized functions appropriate for molecular particle scales.

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Multi scale diffeomorphic metric mapping of spatial transcriptomics datasets

Cited by 4 publications

References 32 publications

Projective LDDMM: Mapping Molecular Digital Pathology with Tissue MRI

Projective LDDMM: Mapping Molecular Digital Pathology with Tissue MRI

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

Hierarchical Computational Anatomy: Unifying the Molecular to Tissue Continuum Via Measure Representations of the Brain

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