In silico study of the effects of cerebral circulation on source localization using a dynamical anatomical atlas of the human head

Objective. This study focuses on the effects of dynamical vascular modeling on source localization errors in electroencephalography (EEG). Our aim of this in silico study is to (a) find out the effects of cerebral circulation on the accuracy of EEG source localization estimates, and (b) evaluate its relevance with respect to measurement noise and interpatient variation. Approach. We employ a four-dimensional (3D + T) statistical atlas of the electrical properties of the human head with a cerebral circulation model to generate virtual patients with different cerebral circulatory conditions for EEG source localization analysis. As source reconstruction techniques, we use the linearly constraint minimum variance (LCMV) beamformer, standardized low-resolution brain electromagnetic tomography (sLORETA), and the dipole scan (DS). Main results. Results indicate that arterial blood flow affects source localization at different depths and with varying significance. The average flow rate plays an important role in source localization performance, while the pulsatility effects are very small. In cases where a personalized model of the head is available, blood circulation mismodeling causes localization errors, especially in the deep structures of the brain where the main cerebral arteries are located. When interpatient variations are considered, the results show differences up to 15 mm for sLORETA and LCMV beamformer and 10 mm for DS in the brainstem and entorhinal cortices regions. In regions far from the main arteries vessels, the discrepancies are smaller than 3 mm. When measurement noise is added and interpatient differences are considered in a deep dipolar source, the results indicate that the effects of conductivity mismatch are detectable even for moderate measurement noise. The signal-to-noise ratio limit for sLORETA and LCMV beamformer is 15 dB, while the limit is under 30 dB for DS. Significance. Localization of the brain activity via EEG constitutes an ill-posed inverse problem, where any modeling uncertainty, e.g. a slight amount of noise in the data or material parameter discrepancies, can lead to a significant deviation of the estimated activity, especially in the deep structures of the brain. Proper modeling of the conductivity distribution is necessary in order to obtain an appropriate source localization. In this study, we show that the conductivity of the deep brain structures is particularly impacted by blood flow-induced changes in conductivity because large arteries and veins access the brain through that region.Peer reviewe

Electrical Stimulation of the Human Cerebral Cortex by Extracranial Muscle Activity: Effect Quantification With Intracranial EEG and FEM Simulations

Objective: Electric fields (EF) of approx. 0.2 V/m have been shown to be sufficiently strong to both modulate neuronal activity in the cerebral cortex and have measurable effects on cognitive performance. We hypothesized that the EF caused by the electrical activity of extracranial muscles during natural chewing may reach similar strength in the cerebral cortex and hence might act as an endogenous modality of brain stimulation. Here, we present first steps toward validating this hypothesis. Methods: Using a realistic volume conductor head model of an epilepsy patient having undergone intracranial electrode placement and utilizing simultaneous intracranial and extracranial electrical recordings during chewing, we derive predictions about the chewing-related cortical EF strength to be expected in healthy individuals. Results: We find that in the region of the temporal poles, the expected EF strength may reach amplitudes in the order of 0.1-1 V/m. Conclusion: The cortical EF caused by natural chewing could be large enough to modulate ongoing neural activity in the cerebral cortex and influence cognitive performance. Significance: The present study lends first support for the assumption that extracranial muscle activity might represent an endogenous source of electrical brain stimulation. This offers a new potential explanation for the puzzling effects of gum chewing on cognition, which have been repeatedly reported in the literature

Forward volumetric modeling framework for realistic head models towards accurate EEG source localization

Synergetic effects connecting spatial and functional neuroimaging techniques allows reduction of the weakness for single method analysis. Specifically, Electroencephalographic (EEG) Source Imaging (ESI) relating structural head models and distributed source localization techniques improves the time and spatial resolution of single MRI or EEG analysis. The construction of more accurate forward models for ESI solutions, holding better precision and less computational burden is an important task for investigative purposes, but also for surgery planning and disorder treatments. In this regard, we present a novel finite-difference EEG forward problem solution that we called ghost-filling finite difference anisotropic reciprocity method (GFDARM). First, we introduce a finite difference numerical solution for the conservative form of the Poisson equation, using an asymmetric volumetric stencil, together with the transition layer technique to formulate finite differences that properly deal with the considered Newman and Dirichlet boundary conditions. Later, we formulate a solution for an irregular free-form boundary domain, based on a second-order accuracy ghost-filling approximation for the homogeneous Newman flux condition, allowing us to solve the discretized finite differences volume only for the significant potential unknowns. Then we analyze the linear equation system solution and the considerations for a reciprocity solution over the electrodes space. Further, we test our method using a multilayer spherical head model that can include anisotropy and can admit an analytical solution of the Poisson equation. Finally, we analyze a noisy linear equation system to study the numerical stability of the technique in the presence of perturbations. Our results show stability and super-linear convergence. Moreover, validation against an analytical solution shows high correspondence in the potential distribution for a wide range of dipole positions and orientations. As a final stage, we introduce a realistic patient-specific EEG forward modeling pipeline, including anisotropy in the skull and the white matter; MRI segmentation; electrode co-register; voxelwise conductivity definitions; reciprocity space solution; and GFDARM numeric EEG forward solver. Our results using Bayesian model selection for group studies in a random fixed effect analysis show strong evidence in favor of more complex head models, including anisotropic skull and white matter modelingResumen: Los efectos conjuntos conectando técnicas espaciales y funcionales de neuro-imagen permiten el mejoramiento de las características de un solo método. Específicamente, la generación de imágenes de fuentes de activación (ESI) mediante electroencefalografía (EEG) que relaciona modelos estructurales de conductividad y técnicas de localización de fuentes distribuidas, permite un mejoramiento en la resolución espacial, conservando la resolución temporal del EEG. La construcción de modelos de conductividad más precisos, con una mayor precisión y menos carga computacional es una tarea importante para soluciones que emplean ESI, así como para fines de investigación, planificación de cirugía y/o los tratamientos de trastornos neurológicos en general. En este trabajo presentamos una nueva solución del problema directo empleando diferencias finitas, a la que llamamos método de diferencias finitas empleando llenado-fantasma, reciprocidad y anisotropía (GFDARM). Primero, nosotros presentamos una solución numérica de diferencias finitas para la forma conservativa de la ecuación de Poisson, utilizando una plantilla volumétrica asimétrica, junto con la técnica de transición de capas, para formular diferencias finitas que aborden adecuadamente las condiciones de contorno de Newman y Dirichlet. Más adelante, formulamos la solución para una frontera irregular y de forma libre basada en una aproximación de segundo orden de llenado-fantasma que permite cumplir la condición de flujo homogéneo de Newman, lo que nos permite resolver el volumen discretizado solo para las incógnitas de potencial diferentes de cero (significativas). Posteriormente se analiza la solución del sistema de ecuaciones lineales y las consideraciones para una solución de reciprocidad sobre el espacio de los electrodos. Además, realizamos pruebas utilizando un modelo de cabeza esférico multicapa que puede incluir anisotropía y del cual se puede obtener una solución analítica. Finalmente, se analiza la solución del sistema lineal de ecuaciones en presencia de ruido estudiando la estabilidad numérica de la técnica. Nuestros resultados muestran estabilidad y convergencia súper lineal y una alta correspondencia en la distribución de potenciales para una amplia gama de posiciones y orientaciones de dipolos comparando contra una solución analítica esférica. Finalmente se una metodología para el modelado directo de EEG empleando modelos realistas y paciente-específicos, que incluye anisotropía en el cráneo y la materia blanca; segmentación de MRI; co-registro de electrodos; definiciones de conductividad voxel a voxel; solución de espacio de reciprocidad; y solución numérica del problema directo en EEG empleando GFDARM. El desempeño de la técnica y la influencia de los modelos directos realísticos son analizados empleando selección de modelos para estudios de grupos en un marco Bayesiano, los cuales muestran fuerte evidencia a favor de modelos de conductividad más complejos, que incluyan modelado anisótropo del cráneo y la materia blancaDoctorad

Variation in Reported Human Head Tissue Electrical Conductivity Values

Electromagnetic source characterisation requires accurate volume conductor models representing head geometry and the electrical conductivity field. Head tissue conductivity is often assumed from previous literature, however, despite extensive research, measurements are inconsistent. A meta-analysis of reported human head electrical conductivity values was therefore conducted to determine significant variation and subsequent influential factors. Of 3121 identified publications spanning three databases, 56 papers were included in data extraction. Conductivity values were categorised according to tissue type, and recorded alongside methodology, measurement condition, current frequency, tissue temperature, participant pathology and age. We found variation in electrical conductivity of the whole-skull, the spongiform layer of the skull, isotropic, perpendicularly- and parallelly-oriented white matter (WM) and the brain-to-skull-conductivity ratio (BSCR) could be significantly attributed to a combination of differences in methodology and demographics. This large variation should be acknowledged, and care should be taken when creating volume conductor models, ideally constructing them on an individual basis, rather than assuming them from the literature. When personalised models are unavailable, it is suggested weighted average means from the current meta-analysis are used. Assigning conductivity as: 0.41 S/m for the scalp, 0.02 S/m for the whole skull, or when better modelled as a three-layer skull 0.048 S/m for the spongiform layer, 0.007 S/m for the inner compact and 0.005 S/m for the outer compact, as well as 1.71 S/m for the CSF, 0.47 S/m for the grey matter, 0.22 S/m for WM and 50.4 for the BSCR

Navier-Stokes Modelling of Non-Newtonian Blood Flow in Cerebral Arterial Circulation and its Dynamic Impact on Electrical Conductivity in a Realistic Multi-Compartment Head Model

Background and Objective: This study aims to evaluate the dynamic effect of non-Newtonian cerebral arterial circulation on electrical conductivity distribution (ECD) in a realistic multi-compartment head model. It addresses the importance and challenges associated with electrophysiological modalities, such as transcranial electrical stimulation, electro-magnetoencephalography, and electrical impedance tomography. Factors such as electrical conductivity's impact on forward modeling accuracy, complex vessel networks, data acquisition limitations (especially in MRI), and blood flow phenomena are considered. Methods: The Navier-Stokes equations (NSEs) govern the non-Newtonian flow model used in this study. The solver comprises two stages: the first solves the pressure field using a dynamical pressure-Poisson equation derived from NSEs, and the second updates the velocity field using Leray regularization and the pressure distribution from the first stage. The Carreau-Yasuda model establishes the connection between blood velocity and viscosity. Blood concentration in microvessels is approximated using Fick's law of diffusion, and conductivity mapping is obtained via Archie's law. The head model used corresponds to an open 7 Tesla MRI dataset, differentiating arterial vessels from other structures. Results: The results suggest the establishment of a dynamic model of cerebral blood flow for arterial and microcirculation. Blood pressure and conductivity distributions are obtained through numerically simulated pulse sequences, enabling approximation of blood concentration and conductivity within the brain. Conclusions: This model provides an approximation of dynamic blood flow and corresponding ECD in different brain regions. The advantage lies in its applicability with limited a priori information about blood flow and compatibility with arbitrary head models that distinguish arteries.Comment: 13 pages; 8 figures; 2 tabl

The analytical subtraction approach for solving the forward problem in EEG

Objective: The subtraction approach is known for being a theoretically-rigorous and accurate technique for solving the forward problem in electroencephalography by means of the finite element method. One key aspect of this approach consists of computing integrals of singular kernels over the discretised domain, usually referred to as potential integrals. Several techniques have been proposed for dealing with such integrals, all of them approximating the results at the expense of reducing the accuracy of the solution. In this paper, we derive analytic formulas for the potential integrals, reducing approximation errors to a minimum. Approach: Based on volume coordinates and Gauss theorems, we obtained parametric expressions for all the element matrices needed in the formulation assuming first order basis functions defined on a tetrahedral mesh. This included solving potential integrals over triangles and tetrahedra, for which we found compact and efficient formulas. Main results: Comparison with numerical quadrature schemes allowed to test the advantages of the methodology proposed, which were found of great relevance for highly-eccentric sources, as those found in the somatosensory and visual cortices. Moreover, the availability of compact formulas allowed an efficient implementation of the technique, which resulted in similar computational cost than the simplest numerical scheme. Significance: The analytical subtraction approach is the optimal subtraction-based methodology with regard to accuracy. The computational cost is similar to that obtained with the lowest order numerical integration scheme, making it a competitive option in the field. The technique is highly relevant for improving electromagnetic source imaging results utilising individualised head models and anisotropic electric conductivity fields without imposing impractical mesh requirements