MOR-based uncertainty quantification in transcranial magnetic stimulation

Field computation for Transcranial Magnetic Stimulation requires the knowledge of the electrical conductivity profiles in the human head. Unfortunately, the conductivities of the different tissue types are not exactly known and vary from person to person. Consequently, the computation of the electric field in the human brain should incorporate the uncertainty in the conductivity values. In this paper, we compare a non-intrusive polynomial chaos expansion and a new intrusive parametric Model Order Reduction approach for the sensitivity analysis in Transcranial Magnetic Stimulation computations. Our results show that compared to the non-intrusive method, the new intrusive method provides similar results but shows two orders of magnitude reduced computation time. We find monotonically decreasing errors for increasing state-space dimensions, indicating convergence of the new method. For the sensitivity analysis, both Sobol coefficients and sensitivity coefficients indicate that the uncertainty of the white matter conductivity has the largest influence on the uncertainty in the field computation, followed by gray matter and cerebrospinal fluid. Consequently, individual white matter conductivity values should be used in Transcranial Magnetic Stimulation field computations