Estimating stresses driving tissue flows using a stokes inverse problem
Estimating stresses driving tissue flows using a stokes inverse problem
复制标题
使用斯托克斯逆问题估计驱动组织流动的应力
DOI：
10.1080/00207160.2022.2152281
复制
发表时间：
2022
影响因子：
1.8
通讯作者：
Gao Y
中科院分区：
文献类型：
--
作者：
Gao Y
我们提出了一个反问题，从不同发育阶段的组织速度场的测量中推导出鸡胚外胚层原肠胚形成过程中驱动组织流动的应力分布。我们假设胚胎组织可以被描述为一种高粘性流体，用斯托克斯方程来表征。利用最优控制理论，通过最小化目标泛函来确定应力分布，并以应力为控制变量，构造了使数值流速与实验流速数据相匹配的目标泛函。利用拉格朗日乘数法推导了最优性系统。采用有限元法对这些偏微分方程进行数值逼近，并采用共轭梯度算法求解最优控制问题。
We propose an inverse problem to derive the stress distributions that drive the tissue flows during gastrulation in the epiblast of the chick embryo, from measurements of the tissue velocity fields at different stages of development. We assume that the embryonic tissue can be described as a highly viscous fluid, characterized by the Stokes equations. Using the theory of the optimal control, the stress distributions are determined by minimizing an objective functional, which is constructed such that it can match the numerical velocity of the flow with the experimental velocity data by choosing the stress as the control variable. The Lagrange multiplier method is utilized to derive the optimality system. The finite element method is used to approximate these partial differential equations numerically and we use the conjugate gradient algorithm to solve the optimal control problem.