Tissue engineering mathematical modeling

As mentioned before, HFMB has been used extensively for various purposes, and a considerable amount of mathematical modeling work has been done to analyze the performance of HFMBs, including the ones for enzyme production and cell growth (e.g., Waterland et al., 1974). Based on these previous studies Ye et al. (2006) and Abdullah et al. (2006) have developed a mathematical description of the simplified HFMB for tissue engineering. The model has been developed to describe mass transfer and nutrient distribution profiles in HFMB for growing 3D bone tissues. Also, it has been used to simulate the effects of the important operation parameters on the nutrient and oxygen distribution in the system used for growing bone tissue. 

The effects of blood flow on heat transfer in living tissue have been examined for more than a century, dating back to the experimental studies of Bernard in 1876. Since then, mathematical modeling of the complex thermal interaction between the vasculature and tissue has been a topic of interest for numerous physiologists, physicians, and engineers. A major problem for theoretical prediction of temperature distribution in tissue is the assessment of the effect of blood circulation, which is the dominant mode of heat removal and an important cause of tissue temperature inhomogeneity. 

Chen, Y.H., Zhou, S.W., Li, Q., 2011. Mathematical modeling of degradation for bulk-erosive polymers applications in tissue engineering scaffolds and dmg delivery systems. Acta Biomater. 7, 1140—1149. 

Radisic, M., W. Deen, R. Langer, and G. Vimjak-Novakovic. 2005. Mathematical model of oxygen distribution in engineered cardiac tissue with parallel channel array perfused with culture medium containing oxygen carriers. Am J Physiol Heart Circ Physiol 288 H 1278-H1289. 

Earlier in Chapter 6, we treated some simple electrode/tissue geometries with mathematical analjrtical solutions. Of course, tissue morphology and composition is so that analytical solutions most often cannot be found. It is therefore necessary to take a more engineering approach to make a realistic geometrical model of the tissue and electrode system, inamittance distribution included. Then let a computer calculate current density vectors and equipotential lines on the basis of a chosen mesh. 

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