A Methodology to Empirically Compare Computational Bioelectromagnetics Methods: Evaluation of Three Competitive Methods

A methodology for objective empirical comparisons of competitive computational methods for solving bioelectromagnetics problems is presented. The proposed comparison methodology consists of three steps: 1) a problem of interest is identified, models that represent the range of possible model fidelities are chosen, quantities of interest are clearly specified, and precise quantitative measures of computational costs and errors (including when a reliable reference is missing) are defined; 2) multiple methods are used to solve the problem; for each solution, computational costs are measured and errors in the quantities of interest are calculated; and 3) error-versuscost tradeoffs of the methods are compared. To demonstrate the methodology's effectiveness, the power absorbed in a human model illuminated by an impressed time-harmonic Hertzian dipole in the ultrahigh-frequency band is computed by solving the problem of interest using three competitive methods [adaptive integral method (AIM), generalized minimal residual fast Fourier transform method, and finite-difference time-domain method], and the methods' performances are compared. For example, the comparison reveals that for the baseline case of a spherical head phantom, AIM with a surface-based model has 100-300× faster solution time for ~5% error or, alternatively, has 2.5-3× less error for ~10
⁴
s solution time versus the other numerical methods.