Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland.
Centre National de la Recherche Scientifique, CNRS and Institut Camille Jordan, Université Lyon, Lyon, France.
Wiley Interdiscip Rev Syst Biol Med. 2018 Nov;10(6):e1425. doi: 10.1002/wsbm.1425. Epub 2018 Jun 4.
The nonlinear systems models of computational anatomy that have emerged over the past several decades are a synthesis of three significant areas of computational science and biological modeling. First is the algebraic model of biological shape as a Riemannian orbit, a set of objects under diffeomorphic action. Second is the embedding of anatomical shapes into the soft condensed matter physics continuum via the extension of the Euler equations to geodesic, smooth flows with inverses, encoding divergence for the compressibility of atrophy and expansion of growth. Third, is making human shape and form a metrizable space via geodesic connections of coordinate systems. These three themes place our formalism into the modern data science world of personalized medicine supporting inference of high-dimensional anatomical phenotypes for studying neurodegeneration and neurodevelopment. The dynamical systems model of growth and atrophy that emerges is one which is organized in terms of forces, accelerations, velocities, and displacements, with the associated Hamiltonian momentum and the diffeomorphic flow acting as the state, and the smooth vector field the control. The forces that enter the model derive from external measurements through which the dynamical system must flow, and the internal potential energies of structures making up the soft condensed matter. We examine numerous examples on growth and atrophy. This article is categorized under: Analytical and Computational Methods > Computational Methods Laboratory Methods and Technologies > Imaging Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.
过去几十年中出现的计算解剖非线性系统模型是计算科学和生物建模三个重要领域的综合。首先是作为黎曼轨道的生物形状的代数模型，这是一组具有微分同胚作用的对象。其次是通过将欧拉方程扩展到具有逆的测地、光滑流，将解剖形状嵌入到软凝聚态物理连续体中，从而对萎缩的可压缩性和生长的扩张进行编码。第三，通过坐标系的测地线连接，使人类的形状和形态成为可度量的空间。这三个主题将我们的形式主义置于现代数据科学的个性化医学世界中，为研究神经退行性变和神经发育提供高维解剖表型的推断支持。由此产生的生长和萎缩的动力系统模型是根据力、加速度、速度和位移来组织的，具有相关的哈密顿动量和作为状态的微分同胚流，以及作为控制的光滑向量场。进入模型的力源于通过该动力系统必须流动的外部测量，以及构成软凝聚态物质的结构的内部势能。我们检查了许多关于生长和萎缩的例子。本文归类于：分析和计算方法 > 计算方法实验室方法和技术 > 系统属性和过程的成像模型 > 器官、组织和生理模型。
