Interactive computation and visualization of deep brain stimulation effects using Duality.

Deep brain stimulation (DBS) is an established treatment for movement disorders such as Parkinson's disease or essential tremor. Currently, the selection of optimal stimulation settings is performed by iteratively adjusting the stimulation parameters and is a time consuming procedure that requires multiple clinic visits of several hours. Recently, computational models to predict and visualize the effect of DBS have been developed with the goal to simplify and accelerate this procedure by providing visual guidance and such models have been made available also on mobile devices. However, currently available visualization software still either lacks mobility, i.e., it is running on desktop computers and not easily available in clinical praxis, or flexibility, as the simulations that are visualized on mobile devices have to be precomputed. The goal of the pipeline presented in this paper is to close this gap: Using Duality, a newly developed software for the interactive visualization of simulation results, we implemented a pipeline that allows to compute DBS simulations in near-real time and instantaneously visualize the result on a tablet computer. Therefore, a client-server setup is used, so that the visualization and user interaction occur on the tablet computer, while the computations are carried out on a remote server. We present two examples for the use of Duality, one for postoperative programming and one for the planning of DBS surgery in a pre- or intraoperative setting. We carry out a performance analysis and present the results of a case study in which the pipeline for postoperative programming was applied.

A Mixed Finite Element Method to Solve the EEG Forward Problem.

Finite element methods have been shown to achieve high accuracies in numerically solving the EEG forward problem and they enable the realistic modeling of complex geometries and important conductive features such as anisotropic conductivities. To date, most of the presented approaches rely on the same underlying formulation, the continuous Galerkin (CG)-FEM. In this article, a novel approach to solve the EEG forward problem based on a mixed finite element method (Mixed-FEM) is introduced. To obtain the Mixed-FEM formulation, the electric current is introduced as an additional unknown besides the electric potential. As a consequence of this derivation, the Mixed-FEM is, by construction, current preserving, in contrast to the CG-FEM. Consequently, a higher simulation accuracy can be achieved in certain scenarios, e.g., when the diameter of thin insulating structures, such as the skull, is in the range of the mesh resolution. A theoretical derivation of the Mixed-FEM approach for EEG forward simulations is presented, and the algorithms implemented for solving the resulting equation systems are described. Subsequently, first evaluations in both sphere and realistic head models are presented, and the results are compared to previously introduced CG-FEM approaches. Additional visualizations are shown to illustrate the current preserving property of the Mixed-FEM. Based on these results, it is concluded that the newly presented Mixed-FEM can at least complement and in some scenarios even outperform the established CG-FEM approaches, which motivates a further evaluation of the Mixed-FEM for applications in bioelectromagnetism.

Electroencephalography (EEG) forward modeling via H(div) finite element sources with focal interpolation.

The goal of this study is to develop focal, accurate and robust finite element method (FEM) based approaches which can predict the electric potential on the surface of the computational domain given its structure and internal primary source current distribution. While conducting an EEG evaluation, the placement of source currents to the geometrically complex grey matter compartment is a challenging but necessary task to avoid forward errors attributable to tissue conductivity jumps. Here, this task is approached via a mathematically rigorous formulation, in which the current field is modeled via divergence conforming H(div) basis functions. Both linear and quadratic functions are used while the potential field is discretized via the standard linear Lagrangian (nodal) basis. The resulting model includes dipolar sources which are interpolated into a random set of positions and orientations utilizing two alternative approaches: the position based optimization (PBO) and the mean position/orientation (MPO) method. These results demonstrate that the present dipolar approach can reach or even surpass, at least in some respects, the accuracy of two classical reference methods, the partial integration (PI) and St. Venant (SV) approach which utilize monopolar loads instead of dipolar currents.

Using reciprocity for relating the simulation of transcranial current stimulation to the EEG forward problem.

To explore the relationship between transcranial current stimulation (tCS) and the electroencephalography (EEG) forward problem, we investigate and compare accuracy and efficiency of a reciprocal and a direct EEG forward approach for dipolar primary current sources both based on the finite element method (FEM), namely the adjoint approach (AA) and the partial integration approach in conjunction with a transfer matrix concept (PI). By analyzing numerical results, comparing to analytically derived EEG forward potentials and estimating computational complexity in spherical shell models, AA turns out to be essentially identical to PI. It is then proven that AA and PI are also algebraically identical even for general head models. This relation offers a direct link between the EEG forward problem and tCS. We then demonstrate how the quasi-analytical EEG forward solutions in sphere models can be used to validate the numerical accuracies of FEM-based tCS simulation approaches. These approaches differ with respect to the ease with which they can be employed for realistic head modeling based on MRI-derived segmentations. We show that while the accuracy of the most easy to realize approach based on regular hexahedral elements is already quite high, it can be significantly improved if a geometry-adaptation of the elements is employed in conjunction with an isoparametric FEM approach. While the latter approach does not involve any additional difficulties for the user, it reaches the high accuracies of surface-segmentation based tetrahedral FEM, which is considerably more difficult to implement and topologically less flexible in practice. Finally, in a highly realistic head volume conductor model and when compared to the regular alternative, the geometry-adapted hexahedral FEM is shown to result in significant changes in tCS current flow orientation and magnitude up to 45° and a factor of 1.66, respectively.

The role of blood vessels in high-resolution volume conductor head modeling of EEG.

Reconstruction of the electrical sources of human EEG activity at high spatio-temporal accuracy is an important aim in neuroscience and neurological diagnostics. Over the last decades, numerous studies have demonstrated that realistic modeling of head anatomy improves the accuracy of source reconstruction of EEG signals. For example, including a cerebro-spinal fluid compartment and the anisotropy of white matter electrical conductivity were both shown to significantly reduce modeling errors. Here, we for the first time quantify the role of detailed reconstructions of the cerebral blood vessels in volume conductor head modeling for EEG. To study the role of the highly arborized cerebral blood vessels, we created a submillimeter head model based on ultra-high-field-strength (7T) structural MRI datasets. Blood vessels (arteries and emissary/intraosseous veins) were segmented using Frangi multi-scale vesselness filtering. The final head model consisted of a geometry-adapted cubic mesh with over 17×10(6) nodes. We solved the forward model using a finite-element-method (FEM) transfer matrix approach, which allowed reducing computation times substantially and quantified the importance of the blood vessel compartment by computing forward and inverse errors resulting from ignoring the blood vessels. Our results show that ignoring emissary veins piercing the skull leads to focal localization errors of approx. 5 to 15mm. Large errors (>2cm) were observed due to the carotid arteries and the dense arterial vasculature in areas such as in the insula or in the medial temporal lobe. Thus, in such predisposed areas, errors caused by neglecting blood vessels can reach similar magnitudes as those previously reported for neglecting white matter anisotropy, the CSF or the dura - structures which are generally considered important components of realistic EEG head models. Our findings thus imply that including a realistic blood vessel compartment in EEG head models will be helpful to improve the accuracy of EEG source analyses particularly when high accuracies in brain areas with dense vasculature are required.

Investigation of tDCS volume conduction effects in a highly realistic head model.

OBJECTIVE: We investigate volume conduction effects in transcranial direct current stimulation (tDCS) and present a guideline for efficient and yet accurate volume conductor modeling in tDCS using our newly-developed finite element (FE) approach. APPROACH: We developed a new, accurate and fast isoparametric FE approach for high-resolution geometry-adapted hexahedral meshes and tissue anisotropy. To attain a deeper insight into tDCS, we performed computer simulations, starting with a homogenized three-compartment head model and extending this step by step to a six-compartment anisotropic model. MAIN RESULTS: We are able to demonstrate important tDCS effects. First, we find channeling effects of the skin, the skull spongiosa and the cerebrospinal fluid compartments. Second, current vectors tend to be oriented towards the closest higher conducting region. Third, anisotropic WM conductivity causes current flow in directions more parallel to the WM fiber tracts. Fourth, the highest cortical current magnitudes are not only found close to the stimulation sites. Fifth, the median brain current density decreases with increasing distance from the electrodes. SIGNIFICANCE: Our results allow us to formulate a guideline for volume conductor modeling in tDCS. We recommend to accurately model the major tissues between the stimulating electrodes and the target areas, while for efficient yet accurate modeling, an exact representation of other tissues is less important. Because for the low-frequency regime in electrophysiology the quasi-static approach is justified, our results should also be valid for at least low-frequency (e.g., below 100 Hz) transcranial alternating current stimulation.