Assessing the numerical accuracy of the impedance method

The impedance method has been used extensively to calculate induced electric fields and currents in tissue as a result of applied electromagnetic fields. However, there has previously been no known method for an a priori assessment of the numerical accuracy of the results found by this method. Here, we present a method which permits an a priori assessment of the numerical accuracy of the impedance method applied to physiologically meaningful problems in bioengineering. The assessment method relies on estimating the condition number associated with the impedance matrix for problems with varying shapes, sizes, conductivities, anisotropies, and implementation strategies. Equations have been provided which predict the number of significant figures lost due to poor matrix conditioning as a function of these variables. The results show that, for problems of moderate size and uncomplicated geometry, applied fields should be measured or calculated accurately to at least five or six significant figures. As resolutions are increased and material properties are more widely divergent even more significant figures are needed. The equations provided here should ensure that solutions found from the impedance method are calculated accurately.