EP 29. Field distribution for deep brain stimulation using an anatomical partially anisotropic volume conductor model of the rat brain

Abstract

Introduction Deep brain stimulation (DBS) is a common therapy for the late-stage treatment of Parkinson’s disease. In order to explore clinically relevant questions, DBS is studied both in vivo in animal models and in silico in computational models. Objectives Creating an anatomically realistic volume conductor model (VCM) of the rat brain allows for a close interrelationship of in vivo and in silico models. Thus, an optimization of the stimulation field distribution and an improvement of DBS in animal models is facilitated. Various quantities affect the resulting spatial distribution of the stimulation field in a VCM, namely the specific topology of the compartments and the electric properties of brain tissue (e.g., its anisotropy). Methods Based on the quasi-static modeling approach Laplace equation div( σ )grad(Φ) = 0 is solved, with σ as electric conductivity and Φ as electric potential. The potential distribution evolved by DBS is computed with COMSOL Multiphysics® (Comsol). With the digital rat brain atlas in Papp et al., 2014 , the target region for DBS is assembled as three-dimensional structures. Modeled grey matter nuclei are the subthalamic nucleus (STN) and the entopeduncular nucleus (EPN). In the cubic region of interest (3 mm edge length) all white matter structures and cerebrospinal fluid cavities are included. Whilst the electrical conductivities of grey matter may be assumed as isotropic, for white matter an anisotropic conductivity should be assigned. By assuming that white matter has a ten times higher longitudinal conductivity along the axonal fibers than in transverse direction ( Tuch et al., 2001 ), the conductivity tensor is defined. The orientation of the anisotropic properties follows curvilinear coordinates. These coordinates are computed by using the diffusion method implemented in Comsol by solving Laplace’s equation, −grad(U) = 0, where the gradient of the solution U forms the first basis vector of the coordinate system. Thereby the anisotropy follows the shape of the white matter fiber bundles. The bipolar electrode model and the stimulation parameters are based on the in vivo model in Badstubner, 2013 . Results In this model, an anisotropic conductivity following curvilinear coordinates is implemented in the corticofugal pathway (CP). In Fig. 1 the periprosthetic potential either for the fully isotropic or partially anisotropic model is compared. Here, the relative difference of the potential Φ is the difference between a baseline model, with a homogeneous conductivity in all structures, and both heterogeneous models. The relative difference varies up to 15% and 60% in the isotropic and anisotropic case, respectively. Conclusion Our results suggest that neglecting an anatomically realistic anisotropy would lead to incorrect assessments of the neuronal activation.