Low-Dimensional Stochastic Modeling of the Electrical Properties of Biological Tissues

Uncertainty quantification plays an important role in biomedical engineering as measurement data are often unavailable and literature data show a wide variability. Using the state-of-the-art methods, one encounters difficulties when the number of random inputs is large. This is the case, e.g., when using composite Cole-Cole equations to model random electrical properties. It is shown that how the number of parameters can be significantly reduced by the Karhunen-Loeve expansion. The low-dimensional random model is used to quantify uncertainties in the axon activation during deep brain stimulation. Numerical results for a Medtronic 3387 electrode design are given.