Influence of uncertainties in the material properties of brain tissue on the probabilistic volume of tissue activated.

The aim of this study was to examine the influence of uncertainty of the material properties of brain tissue on the probabilistic voltage response and the probabilistic volume of tissue activated (VTA) in a volume conductor model of deep brain stimulation. To quantify the uncertainties of the desired quantities without changing the deterministic model, a nonintrusive projection method was used by approximating these quantities by a polynomial expansion on a multidimensional basis known as polynomial chaos. The coefficients of this expansion were computed with a multidimensional quadrature on sparse Smolyak grids. The deterministic model combines a finite element model based on a digital brain atlas and a multicompartmental model of mammalian nerve fibers. The material properties of brain tissue were modeled as uniform random parameters using data from several experimental studies. Different magnitudes of uncertainty in the material properties were computed to allow predictions on the resulting uncertainties in the desired quantities. The results showed a major contribution of the uncertainties in the electrical conductivity values of brain tissue on the voltage response as well as on the predicted VTA, while the influence of the uncertainties in the relative permittivity was negligible.