PT  - JOURNAL ARTICLE
AU  - Michael Miller
AU  - Daniel Tward
AU  - Alain Trouvé
TI  - Hierarchical Computational Anatomy: Unifying the Molecular to Tissue Continuum Via Measure Representations of the Brain
AID  - 10.1101/2021.04.19.440540
DP  - 2021 Jan 01
TA  - bioRxiv
PG  - 2021.04.19.440540
4099  - http://biorxiv.org/content/early/2021/10/15/2021.04.19.440540.short
4100  - http://biorxiv.org/content/early/2021/10/15/2021.04.19.440540.full
AB  - 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 of the micro-scale phenotypes of molecular disease simultaneously with the connectomic scales of complex interacting brain circuits.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 such as spatial transcriptomics allow us to measure the brain cell by cell based on transcriptomic 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 – as first introduced by Dirac as a generalized function – to the continuum and fluid mechanics scales appropriate for tissue.Methods We introduce two methods based on notions of generalized functions and statistical mechanics. We use generalized functions expanded to include functional descriptions - electrophysiology, transcriptomic, molecular histology – to represent the molecular biology scale integrated with a Boltzman like procedure to pass from the sparse particles to empirical probability laws on the functional state of the tissue.Results We demonstrate a unified mapping methodology for transferring molecular information in the transcriptome and histological scales to the human atlas scales for understanding Alzheimer’s disease. Conclusions: We demonstrate a unified brain mapping theory for molecular and tissue scales.Competing Interest StatementUnder a license agreement between AnatomyWorks LLC and the Johns Hopkins University, Dr. Michael I. Miller and the University are entitled to royalty distributions related to technology described in this work. Dr. Miller is a founder of and holds equity in AnatomyWorks LLC. This arrangement has been reviewed and approved by the Johns Hopkins University in accordance with its conflict of interest policies.