Doyle Matthew G, Tavoularis Stavros, Bourgault Yves
Department of Mechanical Engineering, University of Ottawa, Ottawa, ON, K1N 6N5, Canada.
J Biomech Eng. 2010 Apr;132(4):041006. doi: 10.1115/1.4001041.
The myocardium of the left ventricle (LV) of the heart comprises layers of muscle fibers whose orientation varies through the heart wall. Because of these fibers, accurate modeling of the myocardium stress-strain behavior requires models that are nonlinear, anisotropic, and time-varying. This article describes the development and testing of a material model of the canine LV myocardium, which will be used in ongoing simulations of the mechanics of the LV with fluid-structure interaction. The model assumes that myocardium deformation has two extreme states: one during which the muscle fibers are fully relaxed, and another during which the muscle fibers are fully contracted. During the second state, the "total" stresses are assumed to be the sum of "passive" stresses, which represent the fully relaxed muscle fibers, and "active" stresses, which are additional stresses due to the contraction of the muscle fibers. The canine LV myocardium is modeled as a transversely isotropic material for which material properties vary in the fiber and cross-fiber directions. The material behavior is considered to be hyperelastic and is modeled by a strain-energy density function in a manner that is an adaptation of an approach based on measurements of the stress-strain behavior of rabbit LV myocardia. A numerical method has been developed to calculate suitable parameter values for the passive material model using previous passive canine LV myocardium stress measurements and taking into account existing physical and numerical constraints. In the absence of published measurements of total canine LV myocardium stresses, a method has been developed to estimate these stresses from available passive and total rabbit LV myocardium stresses and then to calculate active material parameter values. Material parameter values were calculated for passive and active canine LV myocardium. Passive stresses calculated using the model compare well to previous stress measurements while active stresses calculated using the model compare well with those approximated from rabbit measurements. The adapted material model of the canine LV myocardium is deemed to be suitable for use in simulations of the operation of both idealized and realistic canine hearts. The estimated model parameter values can be easily revised to more appropriate ones if measurements of active canine LV myocardium stresses become available. The extension of this material model to a fully orthotropic one is also possible but determination of its parameters would require stress-stretch measurements in the fiber and both cross-fiber directions.
心脏左心室（LV）的心肌由多层肌纤维组成，这些肌纤维的方向贯穿心脏壁而变化。由于这些纤维，要准确模拟心肌的应力 - 应变行为，需要非线性、各向异性和时变的模型。本文描述了犬左心室心肌材料模型的开发与测试，该模型将用于正在进行的左心室力学与流固相互作用的模拟。该模型假设心肌变形有两种极端状态：一种是肌纤维完全松弛的状态，另一种是肌纤维完全收缩的状态。在第二种状态下，“总”应力被假定为“被动”应力（代表完全松弛的肌纤维）与“主动”应力（由于肌纤维收缩产生的附加应力）之和。犬左心室心肌被建模为横观各向同性材料，其材料特性在纤维方向和跨纤维方向有所不同。材料行为被认为是超弹性的，并通过应变能密度函数进行建模，该方式是基于对兔左心室心肌应力 - 应变行为测量的一种方法的改编。已开发出一种数值方法，利用先前的犬左心室心肌被动应力测量值，并考虑现有的物理和数值约束，来计算被动材料模型的合适参数值。在没有已发表的犬左心室心肌总应力测量值的情况下，已开发出一种方法，从现有的兔左心室心肌被动和总应力中估计这些应力，然后计算主动材料参数值。计算了犬左心室心肌被动和主动的材料参数值。使用该模型计算的被动应力与先前的应力测量结果比较吻合，而使用该模型计算的主动应力与从兔测量值近似得到的结果比较吻合。犬左心室心肌的改编材料模型被认为适用于理想化和现实犬心脏运作的模拟。如果有犬左心室心肌主动应力的测量值，估计的模型参数值可以很容易地修订为更合适的值。将该材料模型扩展为完全正交各向异性模型也是可能的，但确定其参数需要在纤维方向和两个跨纤维方向进行应力 - 拉伸测量。
