MECHANISTIC MODELING OF LONGITUDINAL SHAPE ...
Document type :
Compte-rendu et recension critique d'ouvrage
DOI :
Title :
MECHANISTIC MODELING OF LONGITUDINAL SHAPE CHANGES: EQUATIONS OF MOTION AND INVERSE PROBLEMS
Author(s) :
Hsieh, Dai-Ni [Auteur]
Arguillère, Sylvain [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Charon, Nicolas [Auteur]
Younes, Laurent [Auteur]
Arguillère, Sylvain [Auteur]
![refId](/themes/Mirage2//images/idref.png)
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Charon, Nicolas [Auteur]
Younes, Laurent [Auteur]
Journal title :
SIAM Journal on Applied Dynamical Systems
Publisher :
Society for Industrial and Applied Mathematics
Publication date :
2021
ISSN :
1536-0040
HAL domain(s) :
Mathématiques [math]/Optimisation et contrôle [math.OC]
Mathématiques [math]/Géométrie différentielle [math.DG]
Mathématiques [math]/Géométrie différentielle [math.DG]
English abstract : [en]
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 ...
Show more >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.Show less >
Show more >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.Show less >
Language :
Anglais
Popular science :
Non
Comment :
41 pages, 11 figures
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