Series solutions of nonlinear coupled equations in tissue engineering

The objective of this article was to simulate a mathematical model of diffusive transport of nutrients which affects the nonlinear cell proliferation rate. The governing coupled equations are solved under the assumption that the nutrient delivery to the scaffold is purely depends on diffusion. The h...

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Bibliographic Details
Published inAlexandria engineering journal Vol. 57; no. 3; pp. 2069 - 2075
Main Authors Kousar, N., Mahmood, R., Nawaz, A.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.09.2018
Elsevier
Subjects
Homotopy analysis method
Scaffold
Series solution
Tissue engineering
Scaffold
Tissue engineering
Homotopy analysis method
Series solution
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Summary:The objective of this article was to simulate a mathematical model of diffusive transport of nutrients which affects the nonlinear cell proliferation rate. The governing coupled equations are solved under the assumption that the nutrient delivery to the scaffold is purely depends on diffusion. The homotopy analysis method (HAM) is applied to find the approximate series solution for the nonlinear coupled PDEs. This method is very powerful analytical tool for solving nonlinear and coupled equations. The results are obtained of different physical parameters for the uniform cell seeding strategy. The results show the appearance of cell proliferated regions near the nutrient supply. We have compared our results with the results given in the literature (Lewis et al., 2005). Upto the best of author’s knowledge, no series solution is found so far in the literature for this tissue engineering model.
ISSN:1110-0168
DOI:10.1016/j.aej.2017.05.023