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5 Comparison of Methods

Since we don't have space to give a detailed, quantitative description of each of the previously mentioned methods, we give an abbreviated summary of the applicability of each method in solving different types of bioelectric field problems.

As outlined above, the FD, FE, and BE methods can all be used to approximate the boundary value problems which arise in biomedical research problems. The choice depends on the nature of the problem. The FE and FD methods are similar in that the entire solution domain must be discretized, while with the BE method only the bounding surfaces must be discretized. For regular domains, the FD method is generally the easiest method to code and implement, but the FD method usually requires special modifications to define irregular boundaries, abrupt changes in material properties, and complex boundary conditions. While typically more difficult to implement, the BE and FE methods are preferred for problems with irregular, inhomogeneous domains and mixed boundary conditions. The FE method is superior to the BE method for representing nonlinearity and true anisotropy, while the BE method is superior to FE method for problems where only the boundary solution is of interest or where solutions are wanted in a set of highly irregularly spaced points in the domain. Because the computational mesh is simpler for the BE method than for the FE method, the BE program requires less book-keeping than a FE program. For this reason BE programs are often considered easier to develop than FE programs, however; the difficulties associated with singular integrals in the BE method are often highly underestimated. In general, the FE method is preferred for problems where the domain is highly heterogeneous, whereas the BE method is preferred for highly homogeneous domains.