Tissue engineering aims to regenerate, repair or replace organs or defective tissues. This tissue regeneration often occurs in a bioreactor. Important challenges in tissue engineering include ensuring adequate nutrient supply, maintaining the desired cell distribution and achieving sufficiently high cell yield. To put laboratory experiments into a theoretical framework, mathematical modelling of the physical and biochemical processes involved in tissue growth is a useful tool. In this work, we derive and solve a model for a cell-seeded porous scaffold placed in a perfusion bioreactor in which fluid delivers nutrients to the cells. The model describes the key features, including fluid flow, nutrient delivery, cell proliferation and consequent variation of scaffold porosity. Fluid flow through the porous scaffold is modelled by Darcy's law, and nutrient delivery is described by a reaction-advection-diffusion equation. A reaction-diffusion equation describes the evolution of cell density, in which cell proliferation is modelled via logistic growth and cell spreading via non-linear diffusion, which depends on cell density. The effect of shear stress on nutrient consumption and cell proliferation is also included in the model. COMSOL (a commercial finite element solver) is used to solve the model numerically. The results reveal the dependence of the cell distribution and total cell yield on the initial cell density and scaffold porosity. We suggest various seeding strategies and scaffold designs to improve the cell distribution and total cell yield in the engineered tissue construct.

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An innovative extension of the geometric Brownian motion model is developed by incorporating a weighting factor and a stochastic function modeled as a mixture of power and trigonometric functions. Simulations based on this modified Brownian motion model, with optimal weighting factors selected by goodness-of-fit tests, substantially outperform the basic geometric Brownian motion model in terms of fitting the returns distribution of historic data price indices. Furthermore, we attempt to provide an interpretation of the additional stochastic term in relation to irrational behavior in financial markets and outline the importance of this novel model.

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