Computational Continuum Biomechanics with Application to Swelling Media and Growth Phenomena

Abstract

AbstractBiological tissues, no matter if soft or hard tissues are concerned, basically consist of a solid matrix saturated by an interstitial fluid, which is composed of a liquid solvent and various dissolved solutes. In case of vascular tissues, the blood system including the arteries, the capillary system and the veins has to be added. Based on the complex geometric and biophysical nature ofbiological systems, a biomechanical description is based on a macroscopic, continuum‐mechanical approach proceeding from homogenised microstructures rather than on a full microscopic investigation.Consequently, the present article provides a continuum‐biomechanical approach for the description of biological tissues. This includes the well‐founded framework of the Theory of Porous Media (TPM), which can be seen as an extension of the classical Theory of Mixtures (TM) towards immiscible materials. Based on this approach, which easily can be extended by electro‐chemical information, swelling tissues like the intervertebral disc and growth phenomena like avascular tumour growth and muscle stimulation as the basis of any motion of biological systems can be described. However, as a result of page limitations, the article excludes the incorporation of the blood system into the present modelling and simulation examples as well as the description of any muscle stimulation (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)