Mechanistic Modeling of Longitudinal Shape Changes: Equations of Motion and Inverse Problems.

Dai-Ni Hsieh, Sylvain Arguillère, Nicolas Charon, Laurent Younes

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Article in SIAM journal on applied dynamical systems, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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5 · Who and what money

Authors and funding

4 authors.

Dai-Ni HsiehDepartment of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD 21218 USA.

Sylvain ArguillèreLaboratoire Paul Painlevé, University of Lille, Villeneuve d'Ascq Cedex, 59655 France.

Nicolas CharonDepartment of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD 21218 USA.

Laurent YounesDepartment of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD 21218 USA.

Funding

Project 2 MeasurementU19AG033655 · NIA · JOHNS HOPKINS UNIVERSITY · PI MARILYN S. ALBERT, Arnold Bakker · 2014 to 2026

$51.5M

CRCNS US- German Res Prop: functional computational anatomy of the auditory cortex R01DC016784 · NIDCD · JOHNS HOPKINS UNIVERSITY · PI RATNANATHER, JOHN TILAK · 2017 to 2019

$725k

NIA NIH HHS U19 AG033655NIDCD NIH HHS R01 DC016784

6 · The paper itself

Abstract

This paper examines a longitudinal shape evolution model in which a three-dimensional 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.

Indexed as

elastic deformationsexistence of solutionsinverse problemslayered volumesshape analysis

Identifiers

PMID38606305

DOI10.1137/21m1423099

PMCPMC11008764

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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.