A Three-Dimensional Model of Skeletal Muscle Tissues

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-05-07 DOI:10.1137/22m1506985

Javier A. Almonacid, Sebastián A. Domínguez-Rivera, Ryan N. Konno, Nilima Nigam, Stephanie A. Ross, Cassidy Tam, James M. Wakeling

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引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. Skeletal muscles are living tissues that can undergo large deformations in short periods of time and that can be activated to produce force. In this paper we use the principles of continuum mechanics to propose a dynamic, fully nonlinear, and three-dimensional model to describe the deformation of these tissues. We model muscles as a fiber-reinforced composite and transversely isotropic material. We introduce a flexible computational framework to approximate the deformations of skeletal muscle to provide new insights into the underlying mechanics of these tissues. The model parameters and mechanical properties are obtained through experimental data and can be specified locally. A semi-implicit in-time, conforming, finite element in space scheme is used to approximate the solutions to the governing nonlinear dynamic model. We provide a series of numerical experiments demonstrating the application of this framework to relevant problems in biomechanics and also discuss questions around model validation.

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骨骼肌组织的三维模型

SIAM 应用数学期刊》，提前印刷。摘要骨骼肌是一种活的组织，可在短时间内发生巨大变形，并可被激活以产生力。在本文中，我们利用连续介质力学原理提出了一种动态、完全非线性的三维模型来描述这些组织的变形。我们将肌肉建模为纤维增强复合材料和横向各向同性材料。我们引入了一个灵活的计算框架来逼近骨骼肌的变形，从而为这些组织的基本力学提供新的见解。模型参数和力学性能是通过实验数据获得的，并可在本地指定。采用半隐式时间、符合、空间有限元方案来近似求解非线性动态模型。我们提供了一系列数值实验，展示了这一框架在生物力学相关问题中的应用，并讨论了围绕模型验证的问题。

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来源期刊

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.