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

IF 5 Q1 ENGINEERING, BIOMEDICAL BME frontiers Pub Date : 2022-01-01 DOI:10.34133/2022/9868673
Michael Miller, Daniel Tward, Alain Trouvé
{"title":"Molecular Computational Anatomy: Unifying the Particle to Tissue Continuum via Measure Representations of the Brain.","authors":"Michael Miller,&nbsp;Daniel Tward,&nbsp;Alain Trouvé","doi":"10.34133/2022/9868673","DOIUrl":null,"url":null,"abstract":"<p><strong>Objective: </strong>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.</p><p><strong>Impact statement: </strong>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.</p><p><strong>Introduction: </strong>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.</p><p><strong>Methods: </strong>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.</p><p><strong>Results: </strong>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.</p><p><strong>Conclusions: </strong>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.</p>","PeriodicalId":72430,"journal":{"name":"BME frontiers","volume":"2022 ","pages":""},"PeriodicalIF":5.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10193958/pdf/","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"BME frontiers","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.34133/2022/9868673","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, BIOMEDICAL","Score":null,"Total":0}
引用次数: 3

Abstract

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.

Abstract Image

Abstract Image

Abstract Image

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
分子计算解剖学:通过大脑的测量表征统一粒子到组织连续体。
目的:本研究的目的是将空间转录组学和细胞尺度组织学的分子表征与计算解剖学的组织尺度相统一,用于脑制图。影响陈述:我们提出了一种统一的表征理论,该理论基于微观尺度确定性结构和功能的几何变分度量,具有空间聚集组织尺度的统计集合。在计算解剖学中,跨坐标系统的映射使我们能够在毫米尺度上理解大脑的结构和功能特性。数字病理学和空间转录组学的新测量技术使我们能够基于蛋白质和转录组功能同一性来测量脑分子和细胞。我们目前还没有数学表示来一致地整合组织极限与分子粒子描述。这里导出的形式化展示了从量子化粒子的分子尺度(使用狄拉克首先引入的数学结构作为一类广义函数)到组织尺度(最初由欧拉引入的流体方法)的一致过渡的方法。方法:介绍了基于广义函数和统计力学的两种数学方法。我们使用几何变量,空间和功能的乘积度量,来表示微尺度上的功能状态-电生理学,分子组织学-与类似玻尔兹曼的程序相结合,从确定性粒子描述传递到组织尺度上功能状态的经验概率。结果:我们的空间函数变量表示提供了一种从分子尺度到组织尺度的方法,该方法是由非线性功能特征映射组成的线性空间尺度级联。遵循级联意味着每个尺度都是一个几何测量,因此可以引入一个通用的测量规范家族,量化轨道中大脑之间的测地连接,而不依赖于探测技术,无论是RNA身份,Tau或淀粉样蛋白组织,尖峰序列还是密集的MR图像。结论:我们展示了基于几何测量表征的分子和组织尺度的统一脑映射理论。我们把粒子和细胞尺度的组织尺度的一致聚集称为分子计算解剖学。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
7.10
自引率
0.00%
发文量
0
审稿时长
16 weeks
期刊最新文献
A Novel System for Fabricating Microspheres with Microelectromechanical System-Based Bioprinting Technology. A Janus Adhesive Hydrogel with Integrated Attack and Defense for Bacteria Killing and Antifouling. Cationized Decalcified Bone Matrix for Infected Bone Defect Treatment. Functional Neural Networks in Human Brain Organoids. What Is the Magical Cavitation Bubble: A Holistic Perspective to Trigger Advanced Bubbles, Nano-Sonocatalysts, and Cellular Sonosensitizers.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1