A general constitutive model for vascular tissue considering stress driven growth and biological availability

F. BELLOMO; S. OLLER; F. ARMERO; L. NALLIM

CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES

TECH SCIENCE PRESS

Lugar: Forsyth, GA, USA; Año: 2011 vol. 80 p. 1 - 22

1526-1492

Some of the key factors that regulate growth and remodeling of tissuesare fundamentally mechanical. However, it is important to take into accountthe role of biological availability to generate new tissue together with the stressesand strains in the processes of natural or pathological growth. In this sense, themodel presented in this work is oriented to describe growth of vascular tissue under"stress driven growth" considering biological availability of the organism. Thegeneral theoretical framework is given by a kinematic formulation in large straincombined with the thermodynamic basis of open systems. The formulation uses amultiplicative decomposition of deformation gradient, splitting it in a growth partand visco-elastic part. The strains due to growth are incompatible and are controlledby unbalanced stresses related to a homeostatic state. Growth implies a volume change with an increase of mass maintaining constant the density. One of the most interesting features of the proposed model is the generation of new tissue taking into account the contribution of mass to the system controlled through the biological availability. Because soft biological tissues in general have a hierarchical structure with several components (usually a soft matrix reinforced with collagen fibers), the developed growth model is suitable for the growth characterization of each component. This allows considering a different behavior for each of them in the context of a generalized theory of mixtures.