A finite element‐based constrained mixture implementation for arterial growth, remodeling, and adaptation: Theory and numerical verification. (24th May 2013)

• Record Type: Journal Article
• Authors: Valentín, A.; Humphrey, J.D.; Holzapfel, G.A.
• Is Part Of: International journal for numerical methods in biomedical engineering. Volume 29:Number 8(2013:Aug.)
• Page Start: 822
• Page End: 849
• Publication Date: 2013-05-24
• Subjects: artery -- stress -- adaptation -- mechanics; Biomedical engineering -- Periodicals; Imaging systems in medicine -- Periodicals; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 610.28
• DOI: 10.1002/cnm.2555
• Languages: English
• ISSNs: 2040-7939

Abstract

SUMMARY: We implemented a constrained mixture model of arterial growth and remodeling in a nonlinear finite element framework to facilitate numerical analyses of diverse cases of arterial adaptation and maladaptation, including disease progression, resulting in complex evolving geometries and compositions. This model enables hypothesis testing by predicting consequences of postulated characteristics of cell and matrix turnover, including evolving quantities and orientations of fibrillar constituents and nonhomogenous degradation of elastin or loss of smooth muscle function. The nonlinear finite element formulation is general within the context of arterial mechanics, but we restricted our present numerical verification to cylindrical geometries to allow comparisons with prior results for two special cases: uniform transmural changes in mass and differential growth and remodeling within a two‐layered cylindrical model of the human aorta. The present finite element model recovers the results of these simplified semi‐inverse analyses with good agreement. Copyright © 2013 John Wiley & Sons, Ltd. Abstract : We present an extended constrained mixture model of arterial growth and remodeling implemented within a nonlinear finite element framework. The model transcends prior approaches by consistently postulating local mechanobiological processes that can recover arterial homeostasis in normalcy but may lead to complex emerging behaviors in response to perturbations. The implementation recovers results from a prior semi‐analytic model and is applicable to more complex cases of arterial G&R.