Uncertainty quantification in transcranial magnetic stimulation

In this study, a computational framework for statistically characterizing the region stimulated by TMS is presented. Specifically, given probability density functions (pdfs) of the above uncertain parameters, the framework computes the probability that a cortical region of interest is being stimulated and pdfs for the depth and volume of the stimulated region. To collect this information efficiently, the framework leverages a high dimensional model representation (HDMR) technique that generates parameterized surrogate models for the electric field near the stimulated region. Next, these surrogate models are used in lieu of a computationally expensive electromagnetic simulator while obtaining the statistics of the stimulated regions via traditional Monte-Carlo method. The HDMR technique generates the surrogate models using a series of iteratively constructed component functions. The component functions pertinent to the most strongly interacting uncertain parameters are approximated via a multi-element probabilistic collocation method (Yücel et al., Proc. IEEE Int. Symp. Antennas Propagat., 2012). The accuracy of proposed framework will be demonstrated through the statistical characterization of the stimulated region for commonly performed TMS procedures on concentric spheres and MRI-derived human head models.