A Mixture Model of Arterial Growth and Remodeling in Hypertension: Altered Muscle Tone and Tissue Turnover

Abstract

Hypertension results in a thickening of the arterial wall due to a net increase in wall constituents via a coordinated production and removal of smooth muscle and extracellular matrix. Although many reports address the associated changes in material properties, few models address the biomechanics of the growth and remodeling process. In this paper, we employ a new, fundamentally different approach to modeling arterial adaptation in hypertension. In particular, basic, characteristic features of hypertension are simulated using a constrained mixture model wherein individual constituents can turnover at different rates and can have different natural configurations. We show, for example, that if there is no turnover of elastin (which approximates responses in maturity), the model vessel is able to reduce an early elevation in wall stress via a thickening of the wall even though the adaptation may be suboptimal. Conversely, if all constituents can turnover completely (which may approximate late development), the model vessel can restore the state of stress and material properties to native values. Given the potential of such a model, there is a need for more data on the history of turnover of individual constituents and their individual material properties.

Computational hemodynamic optimization predicts dominant aortic arch selection is driven by embryonic outflow tract orientation in the chick embryo

“…Unlike dynamic models of vascular adaption (Pries et al 1998) and solid mechanics based growth and remodeling simulations (Gleason and Humphrey 2004;Taber 1998a), our method cannot determine the intermediate steps of the growth pathway. In vivo information of microstructural architecture or employing constitutive biomechanical relationships (Holzapfel et al 2000;Holzapfel and Ogden 2010) would augment the present approach.…”

“…Lack of sufficient data on the micro-structural and mechanical properties of the embryonic aortic arches has limited the direct application of available growth rate laws (Rodriguez et al 1994;Taber 1998a) and micro-structurally motivated phenomenological models (Gleason and Humphrey 2004;Humphrey 1999) to arch morphogenesis. An alternative approach is to employ an optimization-based growth strategy to model vessel growth in complex cardiovascular morphologies in response to secondary anatomical alterations and sustained flow and pressure perturbations.…”

Mathematical modeling of collagen turnover in biological tissue

“…Gleason & Humphrey (2004; Klisch et al (2005) follow this approach for constrained mixtures and Ateshian (2007) for reactive mixtures. A key contribution is the work of Fung & Liu (1989), amongst many others, which demonstrates that the volumetric growth of blood vessels induces a change in the natural configuration of the tissue, and induces residual stresses.…”

Computational Simulation of the Adaptive Capacity of Vein Grafts in Response to Increased Pressure

“…The G&R formulation is based on a constrained mixture theory developed for arteries, details of which can be found in prior work [12,14,[19][20][21]. A point-to-point comparison [22] between 2D and 3D models showed that the 2D models accurately predict adaptive changes in geometry and stiffness and thereby capture salient aspects of G&R sufficient for clinical and fluid-structure interaction studies [19,23].…”