# Mechanistic Modeling of Longitudinal Shape Changes: equations of motion and inverse problems

arXiv: https://arxiv.org/abs/2003.05512 · HTML: https://mlsanity.com/paper/2003.05512/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2020.

## Built on by (most cited first, 1 of 1)

- [Automatic classification of deformable shapes](https://mlsanity.com/paper/2211.02530/) (2022)

## Abstract (arXiv)

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.