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.

Geometry and structure of the arterial wall are maintained through continuous growth and remodeling (G&R). To understand these processes, mathematical models have been proposed in which the outcome of G&R depends on a mechanical stimulus through evolution equations. Rate parameters in these equations cannot be determined easily from experimental data. Assuming that the healthy artery is stable against remodeling, a physiologically acceptable range for the two rate parameters in the framework of an existing model of arterial G&R is determined here. The model is explicitly evaluated for the example of a cylindrical blood vessel, both thick-walled and thin-walled. For the thin-walled vessel a criterion for stability against remodeling is derived by means of a linear stability approach, and is expressed in terms of the ratio of the rates of remodeling parameters. It is shown that this criterion is equivalent to the condition that the physiological healthy state of the artery can be reached, implying that if the healthy state exists then it is stable. Explicit numerical results are presented for a typical cerebral artery and an abdominal aorta.

A continuum-mechanics approach for the derivation of a model for the behavior, that is, the growth and remodeling, of an arterial tissue under a mechanical load is presented. This behavior exhibits an interplay between two phenomena: continuum mechanics and biology. The tissue is modeled as a continuous mixture of two components: elastin and collagen. Both components are incompressible, but the tissue as a whole can show volumetric growth due to the creation of collagen. Collagen is a fibrous structure, having a strain-induced preferred orientation. Remodeling of the tissue incorporates degradation of elastin and strain-induced creation and degradation of collagen fibers. Both elastin and collagen are considered to be nonlinear elastic media; elastin as a neo-Hookean material and collagen fibers behaving according to an exponential law. The modeling is based on the classical balance laws of mass and momentum.

Living tissues continuously undergo growth, i.e. a change in mass, and remodeling, i.e. reorganization or renovation. Modeling both growth and remodeling (G&R) of the vascular tissue is aimed to provide insight into the adaptation of the tissue, in the healthy and diseased state, and upon surgical intervention. An important aspect is the description of remodeling of collagen fiber direction. Whereas a phenomenological approach for that is suggested in [2], in this study we adopt an approach towards more microstructural approach, along the model in [1].