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3 Model Construction and Mesh Generation     continued...

There are several different strategies for discretizing the geometry into fundamental elemements. For bioelectric field problems, there are two approaches to mesh construction that have become standard; the divide and conquer (or subsequent subdivision) strategy, and a method based upon finding the dual to the Voronoi diagram, the so-called Delaunay triangulation strategy.

Simply put, in using the divide and conquer strategy one starts with a set of points which define the bounding surface(s) in three dimensions (contours in two dimensions). The volume (surface) is repeatedly divided into smaller regions until a satisfactory discretization level has been achieved (you might be thinking about what kind of stopping criteria should be applied to stop the division). Usually, the domain is broken up into eight-node cubic elements, which can then be subdivided into five (minimally) or six tetrahedral elements for three-dimensional problems and the corresponding quadralaterals and triangles for two-dimensional problems. This methodology has the advantage of being fairly easy to program (also, commercial mesh generators exist for the divide and conquer method). For use in solving bioelectric field problems, its main disadvantage has to do with its inability to control the elements which overlap interior boundaries. A single element may span two different conductive regions, for example, when part of an element represents muscle tissue (which could be anisotropic) and the other part of the element falls into a region representing fat tissue. It then becomes very difficult to assign unique conductivity parameters and at the same time accurately represent the geometry.

(See exercise 8.)