Influence of Uncertainties in the Material Properties of Brain Tissue on the Probabilistic Volume of Tissue Activated

Abstract

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.

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

“…The former results in a high computational complexity, whereas a possible correlation of the inputs cannot be handled by many state-of-the-art uncertainty quantification methods. In the following we apply the discrete Karhunen-Loève expansion (KLE) to reduce the number of random variables in (2). Although, the KLE is readily applicable to random fields such as (2), we consider its discrete variant, also referred to as principal component analysis.…”

“…The methods presented in this section assume independence of the inputs. Unfortunately, the KLE as presented in Section III applied to both the permittivity and the conductivity does not ensure independence of the parameters, as both are modeled by the same random process (2). An extension to obtain uncorrelated and independent electrical parameters at the same time is possible but beyond the scope of this paper.…”

“…Simulation details are summarized as follows: the electrode model, which represents the Medtronic 3387 electrode design commonly used in human DBS [2], was encapsulated by a 0.2 mm thick tissue layer, which is formed due to body reactions at the interface between the electrode and the brain tissue [12]. Cathodal current-controlled square-wave stimulation pulses with a frequency of 130 Hz and a pulse duration of 60 µs, as used in clinical practice [2], were applied. The model equation (10) was discretized with 27,000 elements and solved using the software COMSOL Multiphysics R at N = 3846 frequency points in the considered frequency range.…”

“…T HE electrical properties of biological tissue are based on experimental data and are subject to large variability in literature [1], [2], which arises from difficulties associated with the measuring process. Their properties vary over frequency and exhibit a non-symmetrical distribution of relaxation times, which can be described by composite Cole-Cole equations.…”

Adaptive Estimation of the Neural Activation Extent in Computational Volume Conductor Models of Deep Brain Stimulation

“…The field solution in the target area is commonly computed by creating a volume conductor model of the DBS electrode and the surrounding tissue. For solving the governing equations, which are typically the stationary current field or electro-quasistatic equation for DBS applications [7], [10], often commercial software solutions, such as COMSOL Multiphysics R (http://www.comsol.com) are used [5], [7], [8], [11], [12], [13], while, to our knowledge, no studies employing open-source solutions on the field model have been published in scientific journals yet. Regarding the coupling of the neuronal activation in axon models and the extracellular field distribution, a Python package with the purpose to compute the local field potentials for a given axon distribution of defined activation was presented in [14].…”