A stress driven growth model for soft tissue considering biological availability

SERGIO OLLER; FACUNDO J. BELLOMO; FRANCISCO ARMERO; LIZ G. NALLIM

IOP Conference Series: Materials Science and Engineering

IOP Publishing

Lugar: Washington DC; Año: 2010 vol. 10 p. 1 - 9

1757-899X

Abstract. Some of the key factors that regulate growth and remodeling of tissues arefundamentally mechanical. However, it is important to take into account the role ofbioavailability together with the stresses and strains in the processes of normal or pathologicalgrowth. In this sense, the model presented in this work is oriented to describe the growth ofsoft biological tissue under "stress driven growth" and depending on the biological availabilityof the organism. The general theoretical framework is given by a kinematic formulation inlarge strain combined with the thermodynamic basis of open systems. The formulation uses amultiplicative decomposition of deformation gradient, splitting it in a growth part and viscoelasticpart. The strains due to growth are incompatible and are controlled by an unbalancedstresses related to a homeostatic state. Growth implies a volume change with an increase ofmass maintaining constant the density. One of the most interesting features of the proposedmodel is the generation of new tissue taking into account the contribution of mass to thesystem controlled through biological availability. Because soft biological tissues in generalhave a hierarchical structure with several components (usually a soft matrix reinforced withcollagen fibers), the developed growth model is suitable for the characterization of the growthof each component. This allows considering a different behavior for each of them in thecontext of a generalized theory of mixtures. Finally, we illustrate the response of the model incase of growth and atrophy with an application example.