Deterministic-Stochastic Modeling of Transcranial Magnetic Stimulation featuring the Use of Method of Moments and Stochastic Collocation

Abstract

This work examines the influence of the human brain tissue parameters’ uncertainty and the stimulation coil positioning variations within the framework of transcranial magnetic stimulation (TMS). A combination of deterministic modelling and the stochastic collocation method (SCM) is used for the assessment of the input parameter uncertainties’ effects on several outputs of interest: the induced electric field and the related electric current density in the homogeneous human brain model, as well as the maximum values of electric field, magnetic flux density and the induced electric current density. The deterministic model features the formulation based on the surface integral equation approach whose numerical solution is carried out using the method of moments. The SCM shows satisfactory convergence in the assessment of the stochastic mean, variance and standard deviation for the output parameters of interest. Confidence intervals are computed, and the impact of input permittivity, conductivity and coil positioning is assessed. It is found that due to a non- symmetric nature of the utilised brain model the highest electric field variance is shifted from the expected location directly under the coil geometric centre.

Mario Cvetković

Associate Professor | Department of Electrical Engineering Fundamentals

Associate professor at FESB in Split, with a research focus on numerical modeling including finite element and moment methods, computational bioelectromagnetics and heat transfer related phenomena. He is involved in IEEE’s ICES Technical Committee 95, various international projects and is committed to advancing both knowledge and practical applications in electromagnetic safety and biomedical engineering.