Finite Element Methods for Developmental Biology

Abstract

This chapter outlines the physical basis, formulation, and principal features of finite element methods for developmental biology, and presents solutions to technical difficulties that arise when the methods are applied to developmental biology. The finite element method involves breaking a system or region of interest into finite-sized elements. Equations describing the physical behavior of each element are then written. Finally, systems of equations which describe the behavior of the system are constructed and solved to determine the behavior of the system. The first step in a finite element analysis is to identify the quantities of interest. Next, it is necessary to choose a set of independent quantities (primary quantities) in which all other relevant quantities can be written. These quantities must be sufficient to completely describe the system. In the finite element method, these primary quantities determine the state space available at each node. One of the most important steps in the formulation of a finite element problem is the choice of shape functions. These functions define quantities within a given element in terms of its nodal values.