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

TL;DR

This paper introduces a low-dimensional stochastic modeling approach using Karhunen-Loeve expansion to efficiently quantify uncertainties in the electrical properties of biological tissues, specifically applied to deep brain stimulation.

Contribution

It demonstrates how to reduce the complexity of modeling electrical tissue properties with high variability using low-dimensional representations.

Findings

Karhunen-Loeve expansion reduces parameter count

Uncertainty quantification applied to deep brain stimulation

Numerical results for Medtronic 3387 electrode design

Abstract

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.