A homogenized constrained mixture (and mechanical analog) model for growth and remodeling of soft tissue.
A homogenized constrained mixture (and mechanical analog) model for growth and remodeling of soft tissue.
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DOI：
10.1007/s10237-016-0770-9
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发表时间：
2016-12
影响因子：
3.5
通讯作者：
Humphrey JD
中科院分区：
文献类型：
--
作者：
Cyron CJ;Aydin RC;Humphrey JD
承重软组织的生长和重塑的大多数数学模型基于两种主要方法之一：运动学理论，其指定了组织作为整体的无应力配置的演化方程，或受约束的混合物理论，其指定了大规模生产和去除应力配置内的单个成分的速率。前者是流行的，因为它的概念简单，但在很大程度上依赖于启发式定义的增长;后者是基于生物动机的微力学模型，但遭受较高的计算成本，由于需要跟踪所有过去的配置。在本文中，我们提出了一个时间均匀化的约束混合模型，结合了两种经典方法的优点，即生物动机的微机械基础，一个简单的计算实现，和低计算成本。作为说明性的例子，我们表明，这种方法很好地描述了细胞介导的重塑组织等效物在体外和动脉瘤在体内的生长和重塑。我们还表明，这种均匀化的约束混合模型表明，模型的增长和重塑和粘弹性之间的密切关系。也就是说，组织适应的重要方面可以根据简单的机械模拟模型、麦克斯韦流体（即，串联的弹簧和缓冲器）与代表细胞外基质的细胞介导的机械调节的“运动元件”并联。这种类比允许一个简单的实现均匀化的约束混合物模型在商业上可用的模拟代码，利用现有的模型粘弹性。
Most mathematical models of the growth and remodeling of load-bearing soft tissues are based on one of two major approaches: a kinematic theory that specifies an evolution equation for the stress-free configuration of the tissue as a whole or a constrained mixture theory that specifies rates of mass production and removal of individual constituents within stressed configurations. The former is popular because of its conceptual simplicity, but relies largely on heuristic definitions of growth; the latter is based on biologically motivated micromechanical models, but suffers from higher computational costs due to the need to track all past configurations. In this paper, we present a temporally homogenized constrained mixture model that combines advantages of both classical approaches, namely, a biologically motivated micromechanical foundation, a simple computational implementation, and low computational cost. As illustrative examples, we show that this approach describes well both cell-mediated remodeling of tissue equivalents in vitro and the growth and remodeling of aneurysms in vivo. We also show that this homogenized constrained mixture model suggests an intimate relationship between models of growth and remodeling and viscoelasticity. That is, important aspects of tissue adaptation can be understood in terms of a simple mechanical analog model, a Maxwell fluid (i.e., spring and dashpot in series) in parallel with a “motor element” that represents cell-mediated mechanoregulation of extracellular matrix. This analogy allows a simple implementation of homogenized constrained mixture models within commercially available simulation codes by exploiting available models of viscoelasticity.
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影响因子：
3.8
作者：
Bai Y;Lee PF;Humphrey JD;Yeh AT
通讯作者：
Yeh AT
DOI：
10.1016/j.ijengsci.2014.08.003
发表时间：
2014-12-01
影响因子：
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作者：
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作者：
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DOI：
10.1016/j.cma.2014.01.001
发表时间：
2014-04-15
影响因子：
7.2
作者：
Albero, Antonio Bolea;Ehret, Alexander E.;Boel, Markus
通讯作者：
Boel, Markus