On the Volume Conduction Model Validation with Stereo EEG Data

Volume conduction can be defined as the transmission of electric potential and magnetic field generated by a primary current source of brain activation in the surrounding medium, i.e., the human head. Volume conduction simulations are based on sophisticated models whose construction represents a current challenge within the neuroscientific community. Volume conduction models are used in various applications such as electroencephalography (EEG) or magnetoencephalography (MEG) source reconstruction, or in the optimization of the electrode placement in a transcranial electrical stimulation session. Clinical applications based on volume conduction models are, for example, the localization of the epileptogenic zone, i.e., the brain area responsible for the generation of seizures, in the presurgical assessment of focal drug-resistant epilepsy patients, and the antidepressant effects given by transcranial electrical stimulation. Increasing the accuracy of volume conduction simulations is therefore crucial. To the best of our knowledge, the accuracy of volume conduction models have never been validated directly with actual measurements in human patients. The main goal of this thesis is to describe a first attempt to validate volume conduction modeling using electric stimulation stereo-encephalografic (sEEG) data. This work therefore is focused on the research, investigation and test of tools and methods which can be used to describe the accuracy of volume conduction models used in both clinical and basic research. Given a dataset of one pharmaco-resistant epilepsy patient, composed by the anatomical T1 weighted magnetic resonance image (MRI), the electrophysiological signal recorded during electric brain stimulation sessions with sEEG technique and sEEG contact positions extracted by post-implantation CT image, the analysis conducted in this work can be split into three main steps. First, we built volume conduction head models and we simulated the electric potentials during the electric brain stimulations. In this step, we solved the so-called (s)EEG forward problem by means of the finite element method in its classical formulation, and we considered three different conductivity profile to assign to the computational domain, individually extracted by the T1-w MRI. Moreover we computed the solution in meshes with two different resolution, i.e., 1 mm and 2 mm, with three different ways to model the source term, i.e., the partial integration approach, the subtraction approach and Venant\u2019s approach. Second, we extracted the responses to the electric brain stimulations from the actual sEEG measurements. Particular emphasis in this step was given to the optimal referencing systems of sEEG electrodes. Third, we compared the simulated and measured potentials for each of the three volume conduction head models, both in a single shaft and global comparison. The comparison results in overall high relative differences, with only slight modulations given by the distance from the stimulation site, the underlying volume conduction head model used and the compartment where the dipolar source is located. Simulation results show that the computation of sEEG forward problem solution is feasible with the same scheme adopted for scalp EEG in the duneuro software (http:// duneuro.org/), and it is stable for different mesh resolutions and source models also for intracranial electrodes, i.e., for electrodes close to the source positions. From this first validation attempt, we can conclude that the distance contact-source modulates the relative error between measured and simulated potential; for the contacts in the white matter compartment we observed the most accurate results, and the results relative to the three and four compartment results were more accurate than the ones relative to the five compartment results. While we achieved topographical errors within 10% for most of the shafts, the amplitude of simulated and measured potentials notably differs

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

How to assess the accuracy of volume conduction models? A validation study with stereotactic EEG data

Introduction: Volume conduction models of the human head are used in various neuroscience fields, such as for source reconstruction in EEG and MEG, and for modeling the effects of brain stimulation. Numerous studies have quantified the accuracy and sensitivity of volume conduction models by analyzing the effects of the geometrical and electrical features of the head model, the sensor model, the source model, and the numerical method. Most studies are based on simulations as it is hard to obtain sufficiently detailed measurements to compare to models. The recording of stereotactic EEG during electric stimulation mapping provides an opportunity for such empirical validation. Methods: In the study presented here, we used the potential distribution of volume-conducted artifacts that are due to cortical stimulation to evaluate the accuracy of finite element method (FEM) volume conduction models. We adopted a widely used strategy for numerical comparison, i.e., we fixed the geometrical description of the head model and the mathematical method to perform simulations, and we gradually altered the head models, by increasing the level of detail of the conductivity profile. We compared the simulated potentials at different levels of refinement with the measured potentials in three epilepsy patients. Results: Our results show that increasing the level of detail of the volume conduction head model only marginally improves the accuracy of the simulated potentials when compared to in-vivo sEEG measurements. The mismatch between measured and simulated potentials is, throughout all patients and models, maximally 40 microvolts (i.e., 10% relative error) in 80% of the stimulation-recording combination pairs and it is modulated by the distance between recording and stimulating electrodes. Discussion: Our study suggests that commonly used strategies used to validate volume conduction models based solely on simulations might give an overly optimistic idea about volume conduction model accuracy. We recommend more empirical validations to be performed to identify those factors in volume conduction models that have the highest impact on the accuracy of simulated potentials. We share the dataset to allow researchers to further investigate the mismatch between measurements and FEM models and to contribute to improving volume conduction models.</p

CutFEM forward modeling for EEG source analysis

IntroductionSource analysis of Electroencephalography (EEG) data requires the computation of the scalp potential induced by current sources in the brain. This so-called EEG forward problem is based on an accurate estimation of the volume conduction effects in the human head, represented by a partial differential equation which can be solved using the finite element method (FEM). FEM offers flexibility when modeling anisotropic tissue conductivities but requires a volumetric discretization, a mesh, of the head domain. Structured hexahedral meshes are easy to create in an automatic fashion, while tetrahedral meshes are better suited to model curved geometries. Tetrahedral meshes, thus, offer better accuracy but are more difficult to create.MethodsWe introduce CutFEM for EEG forward simulations to integrate the strengths of hexahedra and tetrahedra. It belongs to the family of unfitted finite element methods, decoupling mesh and geometry representation. Following a description of the method, we will employ CutFEM in both controlled spherical scenarios and the reconstruction of somatosensory-evoked potentials.ResultsCutFEM outperforms competing FEM approaches with regard to numerical accuracy, memory consumption, and computational speed while being able to mesh arbitrarily touching compartments.DiscussionCutFEM balances numerical accuracy, computational efficiency, and a smooth approximation of complex geometries that has previously not been available in FEM-based EEG forward modeling