Numerical calculation of the potential distribution due to dipole sources in a spherical model of the head

Novel Electrode Placement in Electrical Bioimpedance-Based Stroke Detection: Effects on Current Penetration and Injury Characterization in a Finite Element Model

OBJECTIVE

Reducing time-to-treatment and providing acute management in stroke are essential for patient recovery. Electrical bioimpedance (EBI) is an inexpensive and non-invasive tissue measurement approach that has the potential to provide novel continuous intracranial monitoring-something not possible in current standard-of-care. While extensive previous work has evaluated the feasibility of EBI in diagnosing stroke, high-impedance anatomical features in the head have limited clinical translation.

METHODS

The present study introduces novel electrode placements near highly-conductive cerebral spinal fluid (CSF) pathways to enhance electrical current penetration through the skull and increase detection accuracy of neurologic damage. Simulations were conducted on a realistic finite element model (FEM). Novel electrode placements at the tear ducts, soft palate and base of neck were evaluated. Classification accuracy was assessed in the presence of signal noise, patient variability, and electrode positioning.

RESULTS

Algorithms were developed to successfully determine stroke etiology, location, and size relative to impedance measurements from a baseline scan. Novel electrode placements significantly increased stroke classification accuracy at various levels of signal noise (e.g. p < 0.001 at 40 dB). Novel electrodes also amplified current penetration, with up to 30% increase in current density and 57% increased sensitivity in central intracranial regions (p<0.001).

CONCLUSION

These findings support the use of novel electrode placements in EBI to overcome prior limitations, indicating a potential approach to increasing the technology's clinical utility in stroke identification.

SIGNIFICANCE

A non-invasive EBI monitor for stroke could provide essential timely intervention and care of stroke patients.

Diagnosing and monitoring pleural effusion using parametric electrical impedance tomography - a computational 3D model and preliminary experimental results

PURPOSE

Diagnosing and monitoring pleural effusion (PE) is challenging due unsuitability of existing modalities. In the present study, a novel parametric electrical impedance tomography (pEIT) technique, tailored to a clinically feasible system to diagnose PE is presented.

METHODS

An electrical impedance tomography (EIT) numeric solver was applied to a 3D realistic normal model and five PE models to simulate sets of surface measurements. Simulations were triggered by a series of eight independent projections using five electrodes positioned around the thorax. The relative changes in the potential between the PE models and the normal model were assessed and the error in the estimated PE volume was examined at varying signal to noise ratio (SNR) levels. For experimental feasibility, measurements were performed in four healthy subjects and were correlated with the potentials that were calculated from the normal model.

RESULTS

Relative potential changes were notable (reached until ~55%) and increased with the increasing PE volumes. Maximal error of ± 20 [mL] was obtained for SNR levels >50 [dB]. The feasibility real measurements in healthy subjects showed a strong linear correlation (R² > 0.85) and a successful diagnosis for all subjects.

CONCLUSION

The proposed technique can estimate PE volumes from a redundant set of measurements in a realistic 3D human model and may be utilized for monitoring PE patients.

Monitoring brain damage using bioimpedance technique in a 3D numerical model of the head

Disturbance in the blood supply to the brain causes a stroke or cerebrovascular accident. This can be due to ischemia caused by blockage (thrombosis, arterial embolism) or a hemorrhage. In this study, the feasibility of basic electrical impedance technique for monitoring such damage was analyzed using a computerized model. Simulations were conducted on a realistic 3D numerical model of the head. Tissues were assumed to act as linear isotropic volume conductors, and the quasi-static approximation was applied. Electrical potentials were calculated by solving Poisson's equation, using the finite volume method and the successive over relaxation method. Left-right asymmetry was calculated for several conductivities and volumes of the damaged region. The results were compared with the left-right asymmetry in a head model with normal brain. A negative asymmetry was revealed for blockage (i.e. the potential amplitude over the ischemic hemisphere was greater than that over the intact hemisphere). In case of hemorrhage, a positive asymmetry was found. Furthermore, correlation was found between the location of the damaged region and the electrodes with significant asymmetry. The 3D numerical simulations revealed that the electrical conductivity and the size of the damaged tissue have an effect on the left-right asymmetry of the surface potential.

Assessment of cardiac stroke volume in patients with implanted cardiac pacemaker using parametric electrical impedance tomography: a theoretical 2D study

The present theoretical study examines the ability to estimate cardiac stroke volume (CSV) in patients with implanted cardiac pacemaker using parametric electrical impedance tomography (pEIT) in a 2D computerized model of the thorax. CSV is a direct indicator of the cardiac pumping efficiency. The commonly used methods for measuring CSV require the invasive procedure of right heart catheterization or use expensive imaging techniques (i.e., MRI). Hence, experience with these techniques for diagnosis and monitoring has been limited to hospitalized patients. In the present study, pEIT scheme was applied in a computerized 2D model of the human thorax with implanted cardiac device to determine the left ventricular (LV) volume at different cardiac cycle phases. The LV was simulated as a prolate ellipse with its axes' lengths as the reconstruction parameters while all other geometries and conductivity values remained constant. An optimization was carried out in order to ensure that the ellipse is the appropriate model for the LV at each cardiac cycle phase. LV volumes calculated by both the pEIT algorithm and the ellipsoid model are consistent. A high correlation (ρ = 0.99) between the true and reconstructed volumes was found. The SV calculation error was ∼1%. The results suggest that the LV volume can be estimated using the pEIT method in a 2D computerized model, and that the method has the potential to be used for monitoring patients with implanted cardiac pacemaker.

Bioimpedance technique for monitoring cerebral artery stenosis in a 3D numerical model of the head

Insufficient blood supply to the brain causes a transient ischemic attack (TIA) or a stroke. One of the causes to insufficient blood supply is cerebral artery stenosis. In this study, the feasibility of bioimpedance for monitoring such stenosis was analyzed. Simulations were conducted on a realistic numerical model of the head, focusing on the left middle cerebral artery (LMCA). Tissues were assumed to act as linear isotropic volume conductors, and the quasi-static approximation was applied. Electrical potentials were calculated by solving Poisson's equation, using the finite volume method (FVM) and the successive over relaxation (SOR) method. The best sensitivity found was 0.471 μV/% stenosis, using this electrode configuration: one injector near the left eye and the other injector near the right ear, one measurement position near the left eye and the other one in the right ear, keeping a distance of at least 2.5 cm between measurement and injection positions. The maximal sensitivity achieved in the numerical model under the applied assumptions supports the feasibility of bioimpedance technique for monitoring cerebral artery stenosis. However, according to sensitivity [1/m(4)] maps, calculated for the preferable electrode configurations, the measurements' specificity to the stenosis degree might be inadequate and should be further studied.

Subthreshold parameters of cardiac tissue in a bi-layer computer model of heart failure

Current density threshold and liminal area are subthreshold parameters of the cardiac tissue that indicate its susceptibility to external and internal stimulations. Extensive experimental and theoretical research has been conducted to quantify these two parameters in normal conditions for both animal and human models. Here we employed a 2D numerical model of human cardiac tissue to assess these subthreshold parameters under the pathological conditions of heart failure and fibrosis. Stimuli were applied over an area ranging from 0.04 to 1 mm² using various pulse durations. The current density threshold decreased with increasing stimulation area or pulse duration. No significant changes were found in both parameters between control conditions and heart failure in the atrial tissue, while in the ventricular tissue, heart failure resulted in significantly reduced excitability with higher stimulation current magnitudes needed for excitation and larger liminal areas. This results from the specific ionic remodeling in ventricular heart failure that affects both subthreshold active currents such as I(K₁) and connexin 43 conductance. In fibrosis, increased fibroblast to myocyte coupling coefficient had a non-linear influence on current density thresholds, with an initial increase of current magnitude followed by a relaxation phase down to the current magnitude threshold for the control condition with no fibrosis. The results show that subthreshold excitation properties of the myocardium are influenced in a complex, non-linear manner by cardiac pathologies. Such observations may contribute to our understanding of impulse capturing properties, relevant, for example, for the generation of ectopic foci-originated arrhythmias and for the efficient design of cardiac stimulating electrodes.

Electrotonic myofibroblast-to-myocyte coupling increases propensity to reentrant arrhythmias in two-dimensional cardiac monolayers

In pathological conditions such as ischemic cardiomyopathy and heart failure, differentiation of fibroblasts into myofibroblasts may result in myocyte-fibroblast electrical coupling via gap junctions. We hypothesized that myofibroblast proliferation and increased heterocellular coupling significantly alter two-dimensional cardiac wave propagation and reentry dynamics. Co-cultures of myocytes and myofibroblasts from neonatal rat ventricles were optically mapped using a voltage-sensitive dye during pacing and sustained reentry. The myofibroblast/myocyte ratio was changed systematically, and junctional coupling of the myofibroblasts was reduced or increased using silencing RNAi or adenoviral overexpression of Cx43, respectively. Numerical simulations in two-dimensional models were used to quantify the effects of heterocellular coupling on conduction velocity (CV) and reentry dynamics. In both simulations and experiments, reentry frequency and CV diminished with larger myofibroblast/myocyte area ratios; complexity of propagation increased, resulting in wave fractionation and reentry multiplication. The relationship between CV and coupling was biphasic: an initial decrease in CV was followed by an increase as heterocellular coupling increased. Low heterocellular coupling resulted in fragmented and wavy wavefronts; at high coupling wavefronts became smoother. Heterocellular coupling alters conduction velocity, reentry stability, and complexity of wave propagation. The results provide novel insight into the mechanisms whereby electrical myocyte-myofibroblast interactions modify wave propagation and the propensity to reentrant arrhythmias.

Solving the ECG forward problem by means of a meshless finite element method

The conventional numerical computational techniques such as the finite element method (FEM) and the boundary element method (BEM) require laborious and time-consuming model meshing. The new meshless FEM only uses the boundary description and the node distribution and no meshing of the model is required. This paper presents the fundamentals and implementation of meshless FEM and the meshless FEM method is adapted to solve the electrocardiography (ECG) forward problem. The method is evaluated on a single-layer torso model, in which the analytical solution exists, and tested in a realistic geometry homogeneous torso model, with satisfactory results being obtained. The present results suggest that the meshless FEM may provide an alternative for ECG forward solutions.

Induced current bio-impedance technique for monitoring bone mineral density--a simulation model

In this study, the feasibility of using induced current bio-impedance technique as a method to determine and monitor bone mineral density (BMD) was theoretically evaluated using computerized simulation model. A 2D polar coordinates numerical solver was developed using the Finite Volume Method (FVM) in order to simulate the developed potentials over an axial CT cross section of a human thigh. Varying femur BMD were simulated by varying femur relative permittivity values. At the chosen excitation current of 1 ampere at a frequency of 20 kHz, the real component of the surface potential was found to be more sensitive to BMD variation than the imaginary component (3.9 microV g(-1) cm3 compared with 0.174 microV g(-1) cm3). The correlation between varying femur permittivities and the real component of the developed surface potential was found to be quadratic and influenced by the coil geometry and the measuring point location. Measurement sensitivity was improved either by taking the measuring point closer to the femur location or by minimizing the distance between the excitation coil and the femur. These results provide the basic principle that may enable a future use of bio-impedance technique for bone density evaluation and monitoring.

Parametric EIT for monitoring cardiac stroke volume

The bio-impedance technique appears appropriate for non-invasive cardiac stroke volume (SV) measurement, as the thoracic conductivity distribution is altered during the cardiac cycle due to the heart contraction and blood perfusion. In the present work, the feasibility of a parametric electrical impedance tomography (EIT) for assessing the cardiac SV was studied. An impedance model of the thorax was constructed from segmented axial MRI images along 19 phases of the cardiac cycle. The heart was simulated as an ellipsoid, with its axes' lengths set as the reconstruction parameters, while all other tissues' geometry and conductivity values were kept fixed. A Newton-Raphson parametric optimization scheme was utilized, yielding a correlation between the reconstructed and anatomical left ventricular volumes of 0.97 (p = 2 x 10(-11)). An analysis of noise sensitivity showed that the proposed algorithm requires an SNR greater than 65 dB. The simulation results were compared to physical data, collected with a portable EIT system (PulmoTrace, CardioInspect). The validation study was employed for a group of N = 28 healthy patients, and a comparison with impedance cardiography measurements (BioZ, Cardiodynamics) was made, showing a correlation of r = 0.86 (p = 4 x10(-9)). The preliminary results demonstrate that parametric EIT has the potential to measure SV, and may be applicable for both clinical and home environment usage.

Contactless bio-impedance monitoring technique for brain cryosurgery in a 3D head model

A contactless induced-current bio-impedance system for monitoring brain cryosurgery procedure was modeled and numerically simulated, where the excitation coil was also performing as the measuring, or pick-up coil. A segmented three-dimensional (3D) MRI database was used for building the volume conductor geometry, and the numerical finite-volume method was employed for solving the forward problem for calculating the scalar potential distribution and the second-order voltage change on the pick-up coil. Several coil configurations were considered, varying in their relative positioning to the 3D head model. For each case, the sensitivity of the measured voltage change on the excitation coil to the volume of a frozen lesion was calculated. The highest sensitivity (1.1 x 10(-5) relative voltage change per mm3 of frozen tissue) was obtained for a coil arrangement where its closest segment to the volume conductor is at the maximum distance away from the frozen region position. The simulated system signal-to-carrier ratio was O(10(-8)).

Influence of the scalp thickness on the intracranial contribution to rheoencephalography

In spite of the great efforts made by the scientific community, up to now there is no agreement about the rheoencephalography (REG) capability to reflect cerebral blood flow (CBF). Moreover, a standard procedure and the optimal electrode arrangement have not been established yet. In a previous study, we found, using a classical four-shell spherical model of the head and solving it by numerical methods that, theoretically, there could exist an electrode arrangement to register an REG II free of extracranial contribution. In this paper, we have studied the influence of scalp thickness on the intracranial contribution to REG II. The study has been performed by solving the head model, using in this case analytical methods, and then estimating the partial contribution of CBF pulsatility to REG for a given set of scalp thicknesses. Although our theoretical results validate the previous finding and suggest that, in some cases, an optimal electrode arrangement to register REG II exists, such an arrangement, and even its existence, is very sensitive to the subject's scalp thickness. According to this, there could not exist a universal electrode arrangement suitable for all individuals to register an REG II free of extracranial contribution, since it depends on the subject's physical constitution. This fact could explain the lack of agreement in the literature about REG interpretation.

Effect of brain damage and source location on left-right asymmetry of visual evoked potentials in a realistic model of the head

The left-right asymmetry of visual evoked potentials (VEP) was studied using a realistic three-dimensional model of the head, constructed from CT scans. The integral equation describing the potential distribution due to an inner current-dipole (simulating the VEP source), inside the biological volume conductor (the head) was solved numerically using the finite volume method. The effect of several structural parameters, such as the natural head geometry, the location and orientation of the current source, and conductivity changes (simulating a brain damage) on the VEP asymmetry was examined. The results revealed that the natural anatomical asymmetry presented in a normal head induces some degree of VEP asymmetry (up to 0.42% at the occipital electrodes), yet the major cause of left-right asymmetry is due to asymmetrical location of the source: up to 6.53% in the O(2)-O(1) electrodes for an angular shift of 3 degrees to the left. It was also found that conductivity changes inside the head have a smaller effect on the VEP asymmetry (up to 3.35% in hemorrhaged brain compared to 1.96% in the normal brain at the C(4)-C(3) electrodes). These findings may help in better understanding VEP sources of asymmetry, originating not only due to cerebral functionality, but from structural parameters as well.

The application of the generalized vector sample pattern matching method for EIT image reconstruction

This paper presents a new application of a generalized vector sample pattern matching (GVSPM) method for image reconstruction of conductivity changes in electrical impedance tomography. GVSPM is an iterative method for linear inverse problems. The key concept of the GVSPM is that the objective function is defined in terms of an angular component between the inner product of the known vector and solution of a system of equations. Comparisons are presented between images of simulated and experimental data, reconstructed using truncated singular value decomposition and GVSPM. In both cases, a normalized sensitivity matrix is constructed using the finite volume method to solve the forward problem.

Evaluation of impedance technique for detecting breast carcinoma using a 2-D numerical model of the torso

Previous experimental studies showed that significant changes occur in the electrical properties of breast cancer tissue compared to the surrounding normal tissue. This phenomenon motivated studies on cancer detection using electrical impedance techniques. In the present study, a two-dimensional model of the torso and a numerical method were used to investigate the changes in the potential distribution as a result of a malignant tissue present in the breast. A transverse MRI image of the woman's torso was scanned. Noise reduction and contour-following algorithms were applied to differentiate between eight compartments in the torso. The extracted tissue types were lungs, blood, ribs, bone marrow of the cord, breast fat, skin, skeletal muscle, and heart muscle. Isotropic homogeneous conductivity was assigned to each one of these compartments. The volume conductor problem was solved numerically using the finite volume method to determine the potential distribution developed due to the dipole source. Cases without and with artificially inserted malignant region with realistic sizes were examined to investigate the sensitivity of impedance techniques to detect breast cancer. Significant changes were detected in the potential distribution inside the volume conductor as a result of the realistic size of breast tumors. A linear relation was found between the surface potential in the vicinity of the tumor region and the size of the tumor. For a small malignant area of 0.22 cm2, the surface potential near the tumor region decreased only slightly from a value of 13.81 mV in the normal case to 13.67 mV (0.14 mV change; 1.0%). For a larger malignant area of 5.43 cm2, the potential decrease was more pronounced, 11.29 mV (2.52 mV change; 18.3%), indicating that realistic sizes of breast tumor result in significant changes in the surface potential. Thus, impedance techniques employed in the present study show very good promise in detecting breast cancer.

Evaluation of the impedance technique for cryosurgery in a theoretical model of the head

Bioimpedance is a noninvasive technique that produces information on the electrical characteristics of tissue inside the body from currents injected and electrical potentials measured on the surface of the body. Because freezing causes a large increase in tissue electrical impedance we thought that it may also cause significant changes in the surface electrical potential making the bioimpedance technique suitable for noninvasive monitoring and imaging of cryosurgery. To evaluate the feasibility of the bioimpedance technique in cryosurgery we examined, as a case study, a theoretical model for the electrical potentials during brain cryosurgery. A three-dimensional spherical model was used to calculate the change in the electrical potential distribution in the head as a function of the current source location and the size of the frozen lesion in the brain. The numerical calculations were executed using the finite volume method and the iterative successive over relaxation method. The results demonstrate that, indeed, freezing inside the head produces measurable changes in the electrical potential on the outer surface-the scalp.

Brain evoked potential topographic mapping based on the diffuse approximation

Evoked potential mapping is a convenient technique to describe brain electrical activity using pictorial representation. A new interpolation method based on the diffuse approximation is applied to represent evoked potential distribution over the skull. The method retains most of the attractive features of the finite-element method but does not require explicit elements. In the simulation examples, the human head is assumed to be a single-layer sphere with homogeneous conductivity, and Ary eccentricity transformation is considered to approximate the more realistic three-shell model. The patterns shown in the computed maps suggest the ability of the proposed method to extract coherent information from the data from different electrodes. In the application protocol, visual evoked potentials are used to test the method with a realistic head shape.

A finite volume model of cardiac propagation

This paper describes a two-dimensional cardiac propagation model based on the finite volume method (FVM). This technique, originally derived and applied within the filed of computational fluid dynamics, is well suited to the investigation of conduction in cardiac electrophysiology. Specifically, the FVM permits the consideration of propagation in a realistic structure, subject to arbitrary fiber orientations and regionally defined properties. In this application of the FVM, an arbitrarily shaped domain is decomposed into a set of constitutive quadrilaterals. Calculations are performed in a computational space, in which the quadrilaterals are all represented simply as squares. Results are related to their physical-space equivalents by means of a transformation matrix. The method is applied to a number of cases. First, large-scale propagation is considered, in which a magnetic resonance-imaged cardiac cross-section serves as the governing geometry. Next, conduction is examined in the presence of an isthmus formed by the microvasculature in a slice of papillary muscle tissue. Under ischemic conditions, the safety factor for propagation is seen to be related to orientation of the fibers within the isthmus. Finally, conduction is studied in the presence of an inexcitable obstacle and a curved fiber field. This example illustrates the dramatic influence of the complex orientation of the fibers on the resulting activation pattern. The FVM provides a means of accurately modeling the cardiac structure and can help bridge the gap between computation and experiment in cardiac electrophysiology.

Sensitivity distributions of EEG and MEG measurements

It is generally believed that because the skull has low conductivity to electric current but is transparent to magnetic fields, the measurement sensitivity of the magnetoencephalography (MEG) in the brain region should be more concentrated than that of the electroencephalography (EEG). It is also believed that the information recorded by these techniques is very different. If this were indeed the case, it might be possible to justify the cost of MEG instrumentation which is at least 25 times higher than that of EEG instrumentation. The localization of measurement sensitivity using these techniques was evaluated quantitatively in an inhomogeneous spherical head model using a new concept called half-sensitivity volume (HSV). It is shown that the planar gradiometer has a far smaller HSV than the axial gradiometer. However, using the EEG it is possible to achieve even smaller HSV's than with whole-head planar gradiometer MEG devices. The micro-superconducting quantum interference device (SQUID) MEG device does have HSV's comparable to those of the EEG. The sensitivity distribution of planar gradiometers, however, closely resembles that of dipolar EEG leads and, therefore, the MEG and EEG record the electric activity of the brain in a very similar way.

Numerical solution of the potential due to dipole sources in volume conductors with arbitrary geometry and conductivity

The integral conservation equation for biological volume conductors with general geometry and arbitrary distribution of electrical conductivity is solved using a finite volume method. An effective conductivity was defined for the boundaries between regions with abrupt change of the conductivity to allow the simultaneous solution of the entire domain although the derivatives are not continuous. The geometrical singularities arising from the spherical topology of the coordinate system are removed using the conservation law. The resulting finite volume solution method is efficient both in central processing unit (CPU) time and memory requirements, allowing the solution of the volume conductor equation using a large number of mesh points (of the order of 10(5)) even on small workstations (like SGI Indigo). It results in very accurate solutions, as several comparisons with analytical solutions of head models reveal. The proposed finite volume method is an attractive alternative to the finite element and boundary element methods that are more common in bioelectric applications.

Effect of source location on the scalp potential asymmetry in a numerical model of the head

The correlation between source asymmetry in the brain and the potential amplitude asymmetry on the scalp was studied by a two-dimensional (2-D) numerical model of the head. The model employed computerized tomography (CT) images to define the different compartments of the head. The source was modeled by a dipole layer in the occiput for an occipital source (visual evoked potential generators) or a dipole layer around the cortex representing spontaneous activity generators. The volume conductor equation for the potential distribution was solved numerically using a finite volume method for two CT images; one had relatively symmetric left-right anatomy while the other had a falx deviation of 6 degrees between the occiput and the nasion-inion line. By examining several arrangements of sources, it has been demonstrated that source asymmetry can cause nonnegligible asymmetry in the potential amplitude at the homotopic points on the scalp. This asymmetry, that is not related to real physiologic or psychological origin, should be taken into consideration in any EEG potential distribution analysis.

Left-right asymmetry of visual evoked potentials in brain-damaged patients: a mathematical model and experimental results

The left-right asymmetry in the potential amplitude on the scalp was studied in poststroke patients by using flash visual evoked potential (VEP) and a numerical two-dimensional model of the head. The left-right asymmetry of the VEP was measured in three patients after thrombosis, in one after hemorrhage, and in one healthy subject. The numerical model used computed tomography images to define the different compartments of the head. The volume conductor equation for the potential distribution created by a dipole source in the occipital region was solved numerically with use of a finite volume method. Left-right asymmetry was calculated with several values of conductivity of the damaged region. The experimental results revealed a negative asymmetry in the three patients after thrombosis (i.e., the potential amplitude over the ischemic hemisphere was smaller than that over the intact hemisphere), whereas, in the patient after hemorrhage, a positive asymmetry was found. Nonsignificant left-right asymmetry was found in the healthy subject. The numerical model revealed that the electrical conductivity of the damaged tissue has a major effect on the left-right asymmetry. Negative asymmetry, such as that found for patients after thrombosis, was obtained when the conductivity of the damaged region was greater than that of the brain, whereas positive asymmetry (hemorrhage patient) was obtained when that conductivity was smaller than that of the brain. This finding indicates that the left-right asymmetry in the scalp VEP of patients after brain damage may be a result of changes in the conductivity of the volume conductor (the ischemic region) between the source and the electrodes.

Correlation between skull thickness asymmetry and scalp potential estimated by a numerical model of the head

The contribution of asymmetric skull thickness to the scalp potential amplitude was investigated numerically. The model consisted of four conductive layers representing the scalp, the skull, the cerebrospinal fluid, and the cortex with a current dipole in the occipital region. The potential created by the dipole was calculated assuming quasistatic formulation and linear media. The governing equation was discretized by the finite volume method to ensure the conservation of fluxes even in regions with abrupt changes of the conductivity. The large set of the algebraic equations for the electric potential was solved iteratively by the successive overrelaxation method. The model confirmed previous experimental studies suggesting that the potential amplitude is 60% smaller on the side with the thicker bone if the asymmetry of the skull thickness exceeds 40%. The model developed suggests that skull thickness asymmetry can create nonnegligible asymmetries in the potential measured on the scalp above homotopic points of the two hemispheres.