Low-Dimensional Stochastic Modeling of the Electrical Properties of Biological Tissues
For biomedical engineers, this method reduces computational burden in uncertainty quantification for electrical tissue models, but the approach is incremental.
The authors reduce the number of random parameters in Cole-Cole models of biological tissue electrical properties using Karhunen-Loeve expansion, enabling uncertainty quantification in deep brain stimulation simulations. Numerical results for a specific electrode design are provided.
Uncertainty quantification plays an important role in biomedical engineering as measurement data is often unavailable and literature data shows a wide variability. Using 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 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.