Quantification of uncertainties in brain tissue conductivity in a heterogeneous model of deep brain stimulation using a non-intrusive projection approach

The aim of this study was to examine the effects of uncertainty of the conductivity values on the resulting field distribution in a heterogeneous finite element model of deep brain stimulation (DBS). A non-intrusive projection method was used by expanding the input random variables and the resulting potential on a multidimensional basis called the Polynomial Chaos (PC). The finite element model incorporates an accurate model of a DBS electrode used in clinical treatment extended by an encapsulation layer around the electrode body. Areas of grey matter, white matter and cerebrospinal fluid were derived from averaged magnetic resonance imaging (MRI). The uncertainties of the conductivity values of these tissue types were modelled as uniform random variables using data from literature to obtain their upper and lower boundaries.