论文标题
纵向形状变化的机械模型：运动方程和反问题
Mechanistic Modeling of Longitudinal Shape Changes: equations of motion and inverse problems
论文作者
论文摘要
本文研究了一个纵向形状进化模型，其中3D体积通过弹性平衡的家族进行，以响应内力或Yank的时间衍生，并进行额外的正则化以确保差异变化。我们考虑了两个不同的洋克模型，并解决了两个模型中运动方程的长时间存在和独特性。此外，我们为存在的最佳洋基提供了足够的条件，该条件最能描述从观察到的初始体积到以后观察到的体积的变化。这项工作的主要动机是对解剖结构中生长和萎缩等过程的理解，在该过程中，可以将洋克大致解释为触发形态变化的代谢事件。我们在简单示例上提供了初步结果，以说明此类事件的某些属性的可检索性。
This paper examines a longitudinal shape evolution model in which a 3D volume progresses through a family of elastic equilibria in response to the time-derivative of an internal force, or yank, with an additional regularization to ensure diffeomorphic transformations. We consider two different models of yank and address the long time existence and uniqueness of solutions for the equations of motion in both models. In addition, we derive sufficient conditions for the existence of an optimal yank that best describes the change from an observed initial volume to an observed volume at a later time. The main motivation for this work is the understanding of processes such as growth and atrophy in anatomical structures, where the yank could be roughly interpreted as a metabolic event triggering morphological changes. We provide preliminary results on simple examples to illustrate, under this model, the retrievability of some attributes of such events.
