A method for simulating the growth of cells on a general surface using the finite element method

The growth of cells on a surface coated with a nutrient is a technique widely used for tissue regeneration. A system of reaction-diffusion equations is used to model the densities of both the cells and the nutrient. This paper presents a finite element method for solving the equations on a general surface which is approximated by a set of flat triangular elements. A change of variables is used to convert the diffusion equations expressed in local coordinates on each element into the equivalent equation expressed in terms of the global coordinates. The methods are illustrated with some typical examples.