Computational Methods for Soft Tissue Biomechanics

Computational biomechanics provides a framework for modeling the function of tissues that integrates structurally from cell to organ system and functionally across the physiological processes that affect tissue mechanics or are regulated by mechanical for

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Abstract. Computational biomechanics provides a framework for modeling the function of tissues that integrates structurally from cell to organ system and functionally across the physiological processes that affect tissue mechanics or are regulated by mechanical forces. We develop an integrative computational strategy for soft tissue based on the finite element method, using the biomechanics of the heart as a case study.

1 Background A fundamental goal of physiology is to identify how the cellular and molecular structure of tissues and organs gives rise to their function in vivo. Correspondingly, a key goal of in silica physiology is to develop computational models that can predict physiological function from quantitative measurements of tissue, cellular or molecular structure. Computational modeling provides a potentially powerful way to integrate structural properties measured in vitro to physiological functions measured in vivo. It also provides a mechanism to integrate biophysical theory with experimental observation. In this chapter, we are interested in biomechanical function in general, and cardiac biomechanics in particular: i.e. how the cellular and extracellular organization of myocardial tissue is integrated into the pumping function of the whole heart. For example, how does myocardial fiber architecture influence the relationship between the biophysics of crossbridge interaction and the three-dimensional mechanics of the ventricular chambers? The physics of the heart and other organs are complex. Geometry, structure and boundary conditions are often irregular and three-dimensional, non-homogenous and time-varying. Constitutive properties and reaction kinetics are typically nonlinear and time-dependent. Beyond mechanical responses, fundamental physiological functions include electrical, chemical, thermal and transport processes in cells and tissues. Therefore, computational methods are needed to model realistically many of these diverse and multidisciplinary processes encountered in biomechanics and tissue engineering. Structurally based models are usually based on in vitro measurements of anatomy, tissue architecture and material properties, and cell biophysics. Their results must be validated with measurements from experiments conducted in vivo or in the whole isolated organ. This iteration between model and experiment also provides the opportunity for numerical hypothesis testing and in vivo constitutive parameter estimation. Once validated, the computational models have multidisciplinary applications to problems in medicine, surgery and bioengineering like diagnostic imaging, surgical planning and intervention, medical therapy, and biomedicalengineering design for tissue engineering or medical devices. G. A. Holzapfel et al. (eds.), Biomechanics of Soft Tissue in Cardiovascular Systems © Springer-Verlag Wien 2003

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T.P. Usyk and A.D. McCulloch

In addition to structural integration across scales of tissue organization from muscle and cell to organ and system, computational models also provide a