Finite element analysis of current pathways with implanted electrodes

Influence of anisotropic conductivity on EEG source reconstruction: investigations in a rabbit model

The aim of our work was to quantify the influence of white matter anisotropic conductivity information on electroencephalography (EEG) source reconstruction. We performed this quantification in a rabbit head using both simulations and source localization based on invasive measurements. In vivo anisotropic (tensorial) conductivity information was obtained from magnetic resonance diffusion tensor imaging and included into a high-resolution finite-element model. When neglecting anisotropy in the simulations, we found a shift in source location of up to 1.3 mm with a mean value of 0.3 mm. The averaged orientational deviation was 10 degree and the mean magnitude error of the dipole was 29%. Source localization of the first cortical components after median and tibial nerve stimulation resulted in anatomically verified dipole positions with no significant anisotropy effect. Our results indicate that the expected average source localization error due to anisotropic white matter conductivity is within the principal accuracy limits of current inverse procedures. However, larger localization errors might occur in certain cases. In contrast, dipole orientation and dipole strength are influenced significantly by the anisotropy. We conclude that the inclusion of tissue anisotropy information improves source estimation procedures.

Deep brain stimulation in movement disorders: stereotactic coregistration of two-dimensional electrical field modeling and magnetic resonance imaging

Object. Adjusting electrical parameters used in deep brain stimulation (DBS) for dystonia remains time consuming and is currently based on clinical observation alone. The goal of this study was to visualize electrical parameters around the electrode, to correlate these parameters with the anatomy of the globus pallidus internus (GPI), and to study the relationship between the volume of stimulated tissue and the electrical parameter settings.

Methods. The authors developed a computer-assisted methodological model for visualizing electrical parameters (the isopotential and the isoelectric field magnitude), with reference to the stereotactic target, for different stimulation settings (monopolar and bipolar) applied during DBS. Electrical field values were correlated with the anatomy of the GPI, which was determined by performing stereotactic magnetic resonance imaging in one reference patient.

By using this method it is possible to compare potential and electrical field distributions for different stimulation modes. In monopolar and bipolar stimulation, the shape and distribution of the potential and electrical field are different and depend on the stimulation voltage. Distributions visualized for patient-specific parameters can be subsequently correlated with anatomical information. The application of this method to one patient demonstrated that the 0.2-V/mm isofield line fits best with the lateral GPI borders at the level of the stimulated contacts.

Conclusions. The electrical field is a crucial parameter because it is assumed to be responsible for triggering action potentials. Electrical field visualization allows the calculation of the stimulated volume for a given isoline. Its application to an entire series of patients may help determine a threshold for obtaining a therapeutic effect, which is currently unknown, and consequently may aid in optimizing parameter settings in individual patients.

Co-registration of stereotactic MRI and isofieldlines during deep brain stimulation

OBJECT

The parameter adjustment process during deep brain stimulation (DBS) for dystonia remains time consuming and based on clinical observation alone. The aim was to correlate the electric field with the GPi anatomy to be able to study the stimulated volume.

METHODS

We developed a computer-assisted method (model) for visualizing electric field in reference to the stereotactic space. Electric field values were correlated with the GPi anatomy (stereotactic Magnetic Resonance Imaging) in one reference patient.

RESULTS

Using this methodology it becomes possible to correlate the electric field distributions for patient specific parameters with the anatomical information. The application to one patient showed that the 0.1V/mm isofieldline fits best with the lateral GPi borders at the level of the stimulated contacts.

CONCLUSIONS

The electric field is a crucial parameter as it is assumed to be responsible for triggering action potentials. Electric field visualisation allows the calculation of the stimulated volume for a given isoline. Its application to our whole patient population might help in determining a threshold for obtaining a therapeutic effect, to date unknown, and consequently in optimizing the parameter setting in each patient.

A realistic three dimensional FEM of the human head

A realistic three-dimensional finite element model (FEM) of the human head has been developed. Separate layers for the scalp, skull, cerebrospinal fluid (CSF) and brain were modelled. Hexahedral elements, a special master matrix assembly technique and an iterative successive over-relaxation (SOR) solution scheme were employed. This approach enabled rapid modelling with minimal memory requirements, which makes this method practical if used for electrical impedance tomography (EIT) or source localization inverse problems. Compared to scalp electrodes, subdural voltage sensing electrodes were three to four times more sensitive close to an oedema or source region, if it was peripheral, but this decreased to 30%-40% for central oedema or source regions. Scalp current injecting electrodes are preferable, since the maximum allowable current is 10 times larger than that of the subdural ones. The distance of voltage sensing electrodes from a region to be imaged highly affects sensitivity, so depth electrodes will be more sensitive, provided that they are close to the region of interest. Finally, the electrode size has significant effects on the input or transfer impedance.

Validation of a detailed computer model for the electric fields in the brain

A computer model has been designed for the calculation of the electrical fields in the head, based on the finite difference method. This method has not previously been applied for head modelling. The model was validated by using three concentric spheres and comparing it with an analytic model. Three levels of accuracy were tested. The forward solutions show that the finite difference algorithm works correctly and, by selecting the size of the volume elements properly, accurate results are obtained. The model will be applied to accurate and realistic geometries of the human head obtained from magnetic resonance images.

Method to reduce blur distortion from EEG's using a realistic head model

A mathematical procedure, which we call "Deblurring," was developed to reduce spatial blur distortion of scalp-recorded brain potentials due to transmission through the skull and other tissues. Deblurring estimates potentials at the superficial cerebral cortical surface from EEG's recorded at the scalp using a finite element model of each subject's scalp, skull and cortical surface constructed from their magnetic resonance images (MRI's). Simulations indicate that Deblurring is numerically stable, while a comparison of deblurred data with a direct cortical recording from a neurosurgery patient suggests that the procedure is valid. Application of Deblurring to somatosensory evoked potential data recorded at 124 scalp sites suggests that the method produces a dramatic improvement in spatial detail, and merits further development.

Determination of current density distributions generated by electrical stimulation of the human cerebral cortex

With the use of a 3-dimensional finite element model of the human brain based on structural data from MRI scans, we simulated patterns of current flow in the cerebral hemisphere with different types of electrical stimulation. Five different tissue types were incorporated into the model based on conductivities taken from the literature. The boundary value problem derived from Laplace's equation was solved with a quasi-static approximation. Transcranial electrical stimulation with scalp electrodes was poorly focussed and required high levels of current for stimulation of the cortex. Direct cortical stimulation with bipolar (adjacent) electrodes was found to be very effective in producing localized current flows. Unipolar cortical stimulation (with a more distant reference electrode) produced higher current densities at the same stimulating current as did bipolar stimulation, but stimulated a larger region of the cortex. With the simulated electrodes resting on the pia-arachnoid, as usually occurs clinically, there was significant shunting of the current (7/8 of the total current) through the CSF. Possible changes in electrodes and stimulation parameters that might improve stimulation procedures are considered.

Finite-element model of the human head: scalp potentials due to dipole sources

Three-dimensional finite-element models provide a method to study the relationship between human scalp potentials and neural current sources inside the brain. A new formulation of dipole-like current sources is developed here. Finite-element analyses based on this formulation are carried out for both a three-concentric-spheres model and a human-head model. Differences in calculated scalp potentials between these two models are studied in the context of the forward and inverse problems in EEG. The effects of the eye orbit structure on surface potential distribution are also studied.

The combination method: a numerical technique for electrocardiographic calculations

This paper presents a method for electrocardiographic and other bioelectric calculations combining the Green's function boundary integral technique with the finite element method. Both the boundary integral method and the finite element method have been used extensively in electrocardiography for calculating epicardial and torso potentials. The boundary integral method is well suited for finding potentials in regions of isotropic conductivity and is computationally efficient, requiring unknown potentials to be calculated on the bounding surfaces only. It also compares favorably in accuracy with the finite element method in those regions. The finite element method is used in solving for potentials in regions of anisotropic conductivity since no simplifying assumptions or transformations of anisotropic regions into isotropic regions before solution are required. Combining the two methods, using the boundary integral method in isotropic regions and the finite element method is anisotropic regions, allows the advantages of both methods to be exploited.

Paleocerebellar stimulation induces in vivo release of endogenously synthesized [3H]dopamine and [3H]norepinephrine from rat caudal dorsomedial nucleus accumbens

The influence of cerebellar vermis stimulation on noradrenergic and dopaminergic activity in the nucleus accumbens was investigated in anesthetised rat. Artificial cerebral spinal fluid containing [3H]tyrosine was continuously circulated through a unilateral push-pull cannula implanted in the nucleus accumbens. Fifteen-minute perfusate samples were collected serially for three consecutive 1-h periods designated pre-, during-, and post-stimulation. The stimulation was applied through a bilateral electrode located subdurally over the fifth vermal lobe. The [3H]norepinephrine and [3H]dopamine components in each sample were isolated by alumina extraction and high-pressure liquid chromatographic fractionation, and then quantified by liquid scintillation counting. For cannula locations in the caudal dorsomedial nucleus accumbens, levels of both [3H]catecholamines were found to be significantly higher during stimulation compared to the prestimulation baselines, and [3H]norepinephrine remained significantly elevated through the post-stimulation period. The relative increase during stimulation for [3H]norepinephrine (130%) was nearly twice that for [3H]dopamine (70%). These results indicate that vermal activation can significantly raise both noradrenergic and dopaminergic in vivo activity in the caudal dorsomedial nucleus accumbens, and provide a possible mechanism for explaining previously demonstrated influences of paleocerebellum upon affective components of behavior.

Electric and magnetic fields from two-dimensional anisotropic bisyncytia

Cardiac tissue can be considered macroscopically as a bidomain, anisotropic conductor in which simple depolarization wavefronts produce complex current distributions. Since such distributions may be difficult to measure using electrical techniques, we have developed a mathematical model to determine the feasibility of magnetic localization of these currents. By applying the finite element method to an idealized two-dimensional bisyncytium with anisotropic conductivities, we have calculated the intracellular and extracellular potentials, the current distributions, and the magnetic fields for a circular depolarization wavefront. The calculated magnetic field 1 mm from the tissue is well within the sensitivity of a SQUID magnetometer. Our results show that complex bisyncytial current patterns can be studied magnetically, and these studies should provide valuable insight regarding the electrical anisotropy of cardiac tissue.