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

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.

Computational anatomy and geometric shape analysis enables analysis of complex craniofacial phenotypes in zebrafish

Due to the complexity of fish skulls, previous attempts to classify craniofacial phenotypes have relied on qualitative features or 2D landmarks. In this work we aim to identify and quantify differences in 3D craniofacial phenotypes in adult zebrafish mutants. We first estimate a synthetic ‘normative’ zebrafish template using microCT scans from a sample pool of wildtype animals using the Advanced Normalization Tools (ANTs). We apply a computational anatomy (CA) approach to quantify the phenotype of zebrafish with disruptions in bmp1a, a gene implicated in later skeletal development and whose human ortholog when disrupted is associated with Osteogenesis Imperfecta. Compared to controls, the bmp1a fish have larger otoliths and exhibit shape differences concentrated around the operculum, anterior frontal, and posterior parietal bones. Moreover, bmp1a fish differ in the degree of asymmetry. Our CA approach offers a potential pipeline for high throughput screening of complex fish craniofacial phenotypes, especially those of zebrafish which are an important model system for testing genome to phenome relationships in the study of development, evolution, and human diseases.Summary statementA computational anatomy approach offers a potential pipeline for high throughput screening of complex zebrafish craniofacial phenotypes, an important model system for the study of development, evolution, and human diseases.

Perspective for Future Medicine: Multidisciplinary Computational Anatomy-Based Medicine with Artificial Intelligence

Multidisciplinary computational anatomy (MCA) is a new frontier of science that provides a mathematical analysis basis for the comprehensive and useful understanding of “dynamic living human anatomy.” It defines a new mathematical modeling method for the early detection and highly intelligent diagnosis and treatment of incurable or intractable diseases. The MCA is a method of scientific research on innovative areas based on the medical images that are integrated with the information related to: (1) the spatial axis, extending from a cell size to an organ size; (2) the time series axis, extending from an embryo to post mortem body; (3) the functional axis on physiology or metabolism which is reflected in a variety of medical image modalities; and (4) the pathological axis, extending from a healthy physical condition to a diseased condition. It aims to integrate multiple prediction models such as multiscale prediction model, temporal prediction model, anatomy function prediction model, and anatomy-pathology prediction model. Artificial intelligence has been introduced to accelerate the calculation of statistic mathematical analysis. The future perspective is expected to promote the development of human resources as well as a new MCA-based scientific interdisciplinary field composed of mathematical statistics, information sciences, computing data science, robotics, and biomedical engineering and clinical applications. The MCA-based medicine might be one of the solutions to overcome the difficulties in the current medicine.