A model for arterial adaptation combining microstructural collagen remodeling and 3D tissue growth

Abstract

Long-term adaptation of soft tissues is realized through growth and remodeling (G&R). Mathematical models are powerful tools in testing hypotheses on G&R and supporting the design and interpretation of experiments. Most theoretical G&R studies concentrate on description of either growth or remodeling. Our model combines concepts of remodeling of collagen recruitment stretch and orientation suggested by other authors with a novel model of general 3D growth. We translate a growth-induced volume change into a change in shape due to the interaction of the growing tissue with its environment. Our G&R model is implemented in a finite element package in 3D, but applied to two rotationally symmetric cases, i.e., the adaptation towards the homeostatic state of the human aorta and the development of a fusiform aneurysm. Starting from a guessed non-homeostatic state, the model is able to reproduce a homeostatic state of an artery with realistic parameters. We investigate the sensitivity of this state to settings of initial parameters. In addition, we simulate G&R of a fusiform aneurysm, initiated by a localized degradation of the matrix of the healthy artery. The aneurysm stabilizes in size soon after the degradation stops.

Continuum Mixture Models of Biological Growth and Remodeling: Past Successes and Future Opportunities

“…Although based on different constitutive relations, similar constrained mixture models have also been proposed to study arterial mechanics (cf. 41,53,54). Because of the fundamental importance of collagen turnover in these models, the reader is referred to the excellent review by Baaijens et al (39).…”

Modeling of cardiac growth and remodeling of myofiber orientation

“…Several studies have applied this approach in vascular G&R, e.g. Gleason et al, 2004;Baek et al, 2005;Valentin et al, 2009;Machyshyn et al, 2010. Kroon et al (2009b investigated the consequences of using either a fixed reference state or an evolving reference state in simulating LV growth.…”

Emergence of Collagen Orientation Heterogeneity in Healing Infarcts and an Agent-Based Model

“…Some of these models have produced heterogeneous predicted fiber structures, although to our knowledge no prior study has explicitly sought to explain the genesis of experimentally measured heterogeneity. Baaijens and colleagues (35)(36)(37)(38)(39)(40) solved structure-based constitutive relations in continuous or finite-element models of arterial wall and aortic valve, assuming a preferred fiber direction either parallel or in between local principal strain or stress directions. Their models correctly predicted the hammock-like heterogeneous distribution of matrix orientation in heart valves and the helical arrangement of matrix fibers in arterial walls.…”