  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.
