PDE-constrained shape registration to characterize biological growth and morphogenesis from imaging data
PDE-constrained shape registration to characterize biological growth and morphogenesis from imaging data
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PDE 约束形状配准，用于根据成像数据表征生物生长和形态发生
DOI：
10.1007/s00366-022-01682-x
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发表时间：
2022
影响因子：
8.7
通讯作者：
Tepole, Adrian Buganza
中科院分区：
文献类型：
--
作者：
Pawar, Aishwarya;Li, Linlin;Gosain, Arun K.;Umulis, David M.;Tepole, Adrian Buganza
我们提出了一种基于偏微分方程约束的形状配准算法，该算法从成像数据中捕捉生物组织的变形和生长。形状配准是通过空间变换函数来评估几何图形对之间的最佳对齐的过程。我们从以前报道的工作开始，使用3D张量积B样条基函数来对3D空间进行内插。这里，由描述组织形状的隐函数组成的B-样条控制点的移动产生总变形梯度场。然后，变形梯度被分为增长贡献和弹性贡献。增长张量捕捉质量的增加，即增长，并根据本构方程演化，本构方程通常是弹性变形的函数。材料中的应力是由变形的弹性部分单独产生的。配准的结果是通过最小化总能量泛函来获得的，该总能量泛函包括：反映形状之间的相似性的距离度量，以及考虑组织生长的总弹性能量。我们应用所提出的形状配准框架来研究斑马鱼胚胎的外胚化过程和皮肤重建手术中的组织扩张。我们预计，我们的PDE约束形状配准方法将提高我们对生物和医学问题的理解，在这些问题中，组织会随着时间的推移经历极端的变形。
We propose a PDE-constrained shape registration algorithm that captures the deformation and growth of biological tissue from imaging data. Shape registration is the process of evaluating optimum alignment between pairs of geometries through a spatial transformation function. We start from our previously reported work, which uses 3D tensor product B-spline basis functions to interpolate 3D space. Here, the movement of the B-spline control points, composed of an implicit function describing the shape of the tissue, yields the total deformation gradient field. The deformation gradient is then split into growth and elastic contributions. The growth tensor captures the addition of mass, i.e. growth, and evolves according to a constitutive equation which is usually a function of the elastic deformation. Stress is generated in the material due to the elastic component of the deformation alone. The result of the registration is obtained by minimizing a total energy functional which includes: a distance measure reflecting similarity between the shapes, and the total elastic energy accounting for the growth of the tissue. We apply the proposed shape registration framework to study zebrafish embryo epiboly process and tissue expansion during skin reconstruction surgery. We anticipate that our PDE-constrained shape registration method will improve our understanding of biological and medical problems in which tissues undergo extreme deformations over time.
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