A novel approach for the recognition, definition and characterization of the critical links between fluid-dynamics and soft tissue biomechanics

Aim of the present chapter is the introduction of fundamental correlations between in vitro cultivating conditions for soft tissues (e.g., cartilaginous tissue), cell response, and resulting morphological properties of the engineered tissue in order to provide strategies for optimal integrated design of bioreactor configuration and biomaterial support that will enhance functional tissue assembly in future applications. Mathematical modeling and numerical simulations are used as relevant and suitable tools in the analysis of such complex dynamics. They are applied to introduce a rigorous framework for better recognition, definition and characterization of some specific links between the biomechanics and biochemistry of soft tissue on one side and the physicochemical features of the supporting environment on the other side, giving emphasis, in particular, to the effect of the fluid-dynamic shear stress (such attention being motivated by the recent experimental evidence that the shear stress exerted on the surface of a tissue specimen by an external moving fluid can induce changes in tissue metabolism and function). The chapter runs as follows: Available data in the literature are initially used to build a set of growth models by analogy with macromolecular crystals. Surface kinetic conditions are defined which are theoretically coupled to the transfer of mass and momentum at the specimen/culture-liquid interface. This leads to a group of differential equations for the nutrient concentration around the sample and for the evolution of tissue mass displacement. Such evolution is then numerically simulated in the context of modern moving boundary CFD (Computational Fluid Dynamics) methods (Volume-of-Fluid and Level-set techniques). Iterative comparison between the CFD simulations and available experimental data is proven to be a novel and relevant means for progressive refinement of the initial theoretically-postulated growth models and the final determination of a precise mathematical formalism for the tissue growth surface kinetics (able to provide effective solutions in practical situations). Some modern concepts such as the particular form of cellular architecture known as “tensegrity” and its role (together with that played by specific transmembrane molecules known as integrins) in determining the response of the cytoskeleton to the application of external stimuli (i.e. the mechanotransduction process) are invoked and used to elaborate some microphysical reasoning for such a mathematical formalism. Beyond relevance to the field of tissue engineering and practical applications, the present chapter also represents a relevant and typical example of situations in which nonlinearities “conspire” to form organized spatial patterns.