An integro-partial differential equation for modeling biofluids flow in fractured biomaterials

作者：Zadeh Kouroush Sadegh^*

来源：Journal of Theoretical Biology, 2011, 273(1): 72-79.

DOI：10.1016/j.jtbi.2010.12.039

• Integro-partial differential equation
• Incomplete Beta function
• Porous media
• Finite Element Method (FEM)
• Scaling

A novel mathematical model in the framework of a nonlinear integro-partial differential equation governing biofluids flow in fractured biomaterials is proposed, solved, verified, and evaluated. A semi-analytical solution is derived for the equation, verified by a mass-lumped Galerkin finite element method (FEM), and calibrated with two in vitro experimental datasets. The solution process uses separation of variables and results in explicit expression involving complete and incomplete beta functions. The proposed semi-analytical model shows reasonable agreements with the finite element simulator as well as with two in vitro experimental time series and can be successfully used to simulate biofluids (e.g. water, blood, oil, etc.) flow in natural and synthetic porous biomaterials.

• 出版日期2011-3-21