Multiscale Modeling of Arterial Adaptations: Incorporating Molecular Mechanisms Within Continuum Biomechanical Models
Continuum level biomechanical models of arterial adaptations are proving themselves vital both for understanding better the progression of disease and for improving the design of clinical interventions. Although these models are most appropriate to the clinical scale of observation, the underlying mechanisms responsible for such remodeling occur at the molecular scale. The goal of this chapter is to review a validated continuum level model of arterial adaptations and to suggest a straightforward approach to incorporate molecular level information within such models. In particular, it is shown that continuum mixture models reveal naturally a means to incorporate molecular information within fundamental constitutive relations within the continuum theory. There is, therefore, significant motivation to continue to formulate molecular level models that are necessary to inform models at scales that address the Physiome.
KeywordsWall Shear Stress Constitutive Relation Soluble Constituent Linear Momentum Balance Arterial Adaptation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This work was supported, in part, via NIH grants HL-086418 and HL-105297.
Baek S, Rajagopal KR, Humphrey JD (2006) A theoretical model of enlarging intracranial fusiform aneurysms. J Biomech Eng 128:142–149
Figueroa CA, Baek S, Taylor CA, Humphrey JD (2009) A computational framework for fluid-solid-growth modeling in cardiovascular simulations. Comput Methods Appl Mech Eng 198:3583–3602
Hayenga HN, Thorne BC, Peirce SM, Humphrey JD (2011) Ensuring congruency in multiscale modeling: towards linking agent based and continuum biomechanical models of arterial adaptation. Ann Biomed Eng 39:2669–2682
Humphrey JD (2002) Cardiovascular solid mechanics. Cells, tissues, and organs. Springer, New York
Humphrey JD (2008a) Mechanisms of arterial remodeling in hypertension: coupled roles of wall shear and intramural stress. Hypertension 52:195–200
Humphrey JD (2008b) Vascular adaptation and mechanical homeostasis at tissue, cellular, and sub-cellular levels. Cell Biochem Biophys 50:53–78
Humphrey JD, Rajagopal KR (2002) A constrained mixture model for growth and remodeling of soft tissues. Math Models Methods Appl Sci 12:407–430
Taylor CA, Humphrey JD (2009) Open problems in computational vascular biomechanics: hemodynamics and arterial wall mechanics. Comput Methods Appl Mech Eng 198:3514–3523
Valentín A, Cardamone L, Baek S, Humphrey JD (2009) Complementary vasoactivity and matrix remodelling in arterial adaptations to altered flow and pressure. J R Soc Interface 6:293–306
Valentín A, Humphrey JD (2009a) Evaluation of fundamental hypotheses underlying constrained mixture models of arterial growth and remodelling. Philos Trans R Soc A 367:3585–3606
Valentín A, Humphrey JD (2009b) Parameter sensitivity study of a constrained mixture model of arterial growth and remodeling. J Biomech Eng 131:101006
© Springer Science+Business Media Dordrecht 2013