Use of a priori information in estimating tissue resistivities--application to human data in vivo

CutFEM-based MEG forward modeling improves source separability and sensitivity to quasi-radial sources: A somatosensory group study

Source analysis of magnetoencephalography (MEG) data requires the computation of the magnetic fields induced by current sources in the brain. This so-called MEG forward problem includes an accurate estimation of the volume conduction effects in the human head. Here, we introduce the Cut finite element method (CutFEM) for the MEG forward problem. CutFEM's meshing process imposes fewer restrictions on tissue anatomy than tetrahedral meshes while being able to mesh curved geometries contrary to hexahedral meshing. To evaluate the new approach, we compare CutFEM with a boundary element method (BEM) that distinguishes three tissue compartments and a 6-compartment hexahedral FEM in an n = 19 group study of somatosensory evoked fields (SEF). The neural generators of the 20 ms post-stimulus SEF components (M20) are reconstructed using both an unregularized and a regularized inversion approach. Changing the forward model resulted in reconstruction differences of about 1 centimeter in location and considerable differences in orientation. The tested 6-compartment FEM approaches significantly increase the goodness of fit to the measured data compared with the 3-compartment BEM. They also demonstrate higher quasi-radial contributions for sources below the gyral crowns. Furthermore, CutFEM improves source separability compared with both other approaches. We conclude that head models with 6 compartments rather than 3 and the new CutFEM approach are valuable additions to MEG source reconstruction, in particular for sources that are predominantly radial.

Modification of brain conductivity in human focal epilepsy: A model-based estimation from stereoelectroencephalography

OBJECTIVE

We have developed a novel method for estimating brain tissue electrical conductivity using low-intensity pulse stereoelectroencephalography (SEEG) stimulation coupled with biophysical modeling. We evaluated the hypothesis that brain conductivity is correlated with the degree of epileptogenicity in patients with drug-resistant focal epilepsy.

METHODS

We used bipolar low-intensity biphasic pulse stimulation (.2 mA) followed by a postprocessing pipeline for estimating brain conductivity. This processing is based on biophysical modeling of the electrical potential induced in brain tissue between the stimulated contacts in response to pulse stimulation. We estimated the degree of epileptogenicity using a semi-automatic method quantifying the dynamic of fast discharge at seizure onset: the epileptogenicity index (EI). We also investigated how the location of stimulation within specific anatomical brain regions or within lesional tissue impacts brain conductivity.

RESULTS

We performed 1034 stimulations of 511 bipolar channels in 16 patients. We found that brain conductivity was lower in the epileptogenic zone (EZ; unpaired median difference = .064, p < .001) and inversely correlated with the epileptogenic index value (p < .001, Spearman rho = -.32). Conductivity values were also influenced by anatomical site, location within lesion, and delay between SEEG electrode implantation and stimulation, and had significant interpatient variability. Mixed model multivariate analysis showed that conductivity is significantly associated with EI (F = 13.45, p < .001), anatomical regions (F = 5.586, p < .001), delay since implantation (F = 14.71, p = .003), and age at SEEG (F = 6.591, p = .027), but not with the type of lesion (F = .372, p = .773) or the delay since last seizure (F = 1.592, p = .235).

SIGNIFICANCE

We provide a novel model-based method for estimating brain conductivity from SEEG low-intensity pulse stimulations. The brain tissue conductivity is lower in EZ as compared to non-EZ. Conductivity also varies significantly across anatomical brain regions. Involved pathophysiological processes may include changes in the extracellular space (especially volume or tortuosity) in epileptic tissue.

Validating EEG, MEG and Combined MEG and EEG Beamforming for an Estimation of the Epileptogenic Zone in Focal Cortical Dysplasia

MEG and EEG source analysis is frequently used for the presurgical evaluation of pharmacoresistant epilepsy patients. The source localization of the epileptogenic zone depends, among other aspects, on the selected inverse and forward approaches and their respective parameter choices. In this validation study, we compare the standard dipole scanning method with two beamformer approaches for the inverse problem, and we investigate the influence of the covariance estimation method and the strength of regularization on the localization performance for EEG, MEG, and combined EEG and MEG. For forward modelling, we investigate the difference between calibrated six-compartment and standard three-compartment head modelling. In a retrospective study, two patients with focal epilepsy due to focal cortical dysplasia type IIb and seizure freedom following lesionectomy or radiofrequency-guided thermocoagulation (RFTC) used the distance of the localization of interictal epileptic spikes to the resection cavity resp. RFTC lesion as reference for good localization. We found that beamformer localization can be sensitive to the choice of the regularization parameter, which has to be individually optimized. Estimation of the covariance matrix with averaged spike data yielded more robust results across the modalities. MEG was the dominant modality and provided a good localization in one case, while it was EEG for the other. When combining the modalities, the good results of the dominant modality were mostly not spoiled by the weaker modality. For appropriate regularization parameter choices, the beamformer localized better than the standard dipole scan. Compared to the importance of an appropriate regularization, the sensitivity of the localization to the head modelling was smaller, due to similar skull conductivity modelling and the fixed source space without orientation constraint.

Tissue Temperature Increases by a 10 kHz Spinal Cord Stimulation System: Phantom and Bioheat Model

OBJECTIVE

A recently introduced Spinal Cord Stimulation (SCS) system operates at 10 kHz, faster than conventional SCS systems, resulting in significantly more power delivered to tissues. Using a SCS heat phantom and bioheat multi-physics model, we characterized tissue temperature increases by this 10 kHz system. We also evaluated its Implanted Pulse Generator (IPG) output compliance and the role of impedance in temperature increases.

MATERIALS AND METHODS

The 10 kHz SCS system output was characterized under resistive loads (1-10 KΩ). Separately, fiber optic temperature probes quantified temperature increases (ΔTs) around the SCS lead in specially developed heat phantoms. The role of stimulation Level (1-7; ideal pulse peak-to-peak of 1-7mA) was considered, specifically in the context of stimulation current Root Mean Square (RMS). Data from the heat phantom were verified with the SCS heat-transfer models. A custom high-bandwidth stimulator provided 10 kHz pulses and sinusoidal stimulation for control experiments.

RESULTS

The 10 kHz SCS system delivers 10 kHz biphasic pulses (30-20-30 μs). Voltage compliance was 15.6V. Even below voltage compliance, IPG bandwidth attenuated pulse waveform, limiting applied RMS. Temperature increased supralinearly with stimulation Level in a manner predicted by applied RMS. ΔT increases with Level and impedance until stimulator compliance was reached. Therefore, IPG bandwidth and compliance dampen peak heating. Nonetheless, temperature increases predicted by bioheat multi-physic models (ΔT = 0.64°C and 1.42°C respectively at Level 4 and 7 at the cervical segment; ΔT = 0.68°C and 1.72°C respectively at Level 4 and 7 at the thoracic spinal cord)-within ranges previously reported to effect neurophysiology.

CONCLUSIONS

Heating of spinal tissues by this 10 kHz SCS system theoretically increases quickly with stimulation level and load impedance, while dampened by IPG pulse bandwidth and voltage compliance limitations. If validated in vivo as a mechanism of kHz SCS, bioheat models informed by IPG limitations allow prediction and optimization of temperature changes.

Evaluating Current Density Modeling of Non-Invasive Eye and Brain Electrical Stimulation Using Phosphene Thresholds

Because current flow cannot be measured directly in the intact retina or brain, current density distribution models were developed to estimate it during magnetic or electrical stimulation. A paradigm is now needed to evaluate if current flow modeling can be related to physiologically meaningful signs of true current distribution in the human brain. We used phosphene threshold measurements (PTs) as surrogate markers of current-flow to determine if PTs, evoked by transcranial alternating current stimulation (tACS), can be matched with current density estimates generated by head model-based computer simulations. Healthy, male subjects (n=15) were subjected to three-staged PT measurements comparing six unilateral and one bilateral stimulation electrode montages according to the 10/20 system: Fp2-Suborbital right (So), Fp2-right shoulder (rS), Fp2-Cz, Fp2- O2, So-rS, Cz-F8 and F7-F8. The stimulation frequency was set at 16 Hz. Subjects were asked to report the appearance and localization of phosphenes in their visual field for every montage. Current density models were built using multi-modal imaging data of a standard brain, meshed with isotropic conductivities of different tissues of the head using the SimBio and SCIRun software packages. We observed that lower PTs were associated with higher simulated current levels in the unilateral montages of the model head, and shorter electrode distances to the eye had lower PTs. The lowest mean PT and the lowest variability were found in the F7-F8 montage (95±33 μA). Our results confirm the hypothesis that phosphenes are primarily of retinal origin, and they provide the first in vivo evidence that computer models of current flow using head models are a valid tool to estimate real current flow in the human eye and brain.

A novel method for calibrating head models to account for variability in conductivity and its evaluation in a sphere model

The accuracy in electroencephalography (EEG) and combined EEG and magnetoencephalography (MEG) source reconstructions as well as in optimized transcranial electric stimulation (TES) depends on the conductive properties assigned to the head model, and most importantly on individual skull conductivity. In this study, we present an automatic pipeline to calibrate head models with respect to skull conductivity based on the reconstruction of the P20/N20 response using somatosensory evoked potentials and fields. In order to validate in a well-controlled setup without interplay with numerical errors, we evaluate the accuracy of this algorithm in a 4-layer spherical head model using realistic noise levels as well as dipole sources at different eccentricities with strengths and orientations related to somatosensory experiments. Our results show that the reference skull conductivity can be reliably reconstructed for sources resembling the generator of the P20/N20 response. In case of erroneous assumptions on scalp conductivity, the resulting skull conductivity parameter counterbalances this effect, so that EEG source reconstructions using the fitted skull conductivity parameter result in lower errors than when using the standard value. We propose an automatized procedure to calibrate head models which only relies on non-invasive modalities that are available in a standard MEG laboratory, measures under in vivo conditions and in the low frequency range of interest. Calibrated head modeling can improve EEG and combined EEG/MEG source analysis as well as optimized TES.

Modulation of Adaptive Cognitive Control by Prefrontal High-Definition Transcranial Direct Current Stimulation in Older Adults

OBJECTIVE

Adaptive cognitive control frequently declines in advanced age. Because high-definition transcranial direct current stimulation (HD-tDCS) of the right dorsolateral prefrontal cortex (DLPFC) improved cognitive control in young adults, we investigated if this montage can also improve cognitive control in older individuals.

METHOD

In a double-blind, sham HD-tDCS controlled, cross-over design, 36 older participants received right DLPFC HD-tDCS during a visual flanker task. Conflict adaptation (CA) effects on response time (RT) and error rates (ER) assessed adaptive cognitive control. Biophysical modeling assessed the magnitude and distribution of induced current in older adults.

RESULTS

Active HD-tDCS enhanced CA in older adults. However, this positive behavioral effect was limited to CA in ER. Similar to results obtained in healthy young adults, current modeling analysis demonstrated focal current delivery to the DLPFC with sufficient magnitude of the induced current to modulate neural function in older adults.

DISCUSSION

This study confirms the effectiveness of HD-tDCS to modulate adaptive cognitive control in advanced age.

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.

In Vivo Estimation of Head Tissue Conductivities Using Bound Constrained Optimization

The conductivity of head tissues was noninvasively estimated using electrical impedance tomography technique. Instead of using conventional unconstrained optimization method to estimate the conductivities, a constrained method with the scaled-logistic function was employed to improve the very high sensitivity of the skull region resulting in accuracy and robustness improvement. Estimation of five conductivities i.e. scalp, skull, cerebrospinal fluid (CSF), grey matter (GM), and white matter (WM) conductivity was investigated by simulation on random and low-value initial guesses. Simulation results showed that the performance of the unconstrained method depended directly to the difference between the exact skull conductivity value and the initial guess value of the skull conductivity. However, the approached constrained method was independent of the guess selection. It can reduce the sensitivity of the skull region by 126 times and reduce the condition number of the sensitivity matrix by 13-17 times. The estimation resulted in only positive and in-range of reported conductivity values. The estimation error of the skull conductivity decreased by 15% and the robustness increased by 2 times. However, the estimation of the CSF, the WM, and the GM may be not reliable due to the very low sensitivity of these regions in both methods.

In-vivo measurements of human brain tissue conductivity using focal electrical current injection through intracerebral multicontact electrodes

In-vivo measurements of human brain tissue conductivity at body temperature were conducted using focal electrical currents injected through intracerebral multicontact electrodes. A total of 1,421 measurements in 15 epileptic patients (age: 28 ± 10) using a radiofrequency generator (50 kHz current injection) were analyzed. Each contact pair was classified as being from healthy (gray matter, n = 696; white matter, n = 530) or pathological (epileptogenic zone, n = 195) tissue using neuroimaging analysis of the local tissue environment and intracerebral EEG recordings. Brain tissue conductivities were obtained using numerical simulations based on conductivity estimates that accounted for the current flow in the local brain volume around the contact pairs (a cube with a side length of 13 mm). Conductivity values were 0.26 S/m for gray matter and 0.17 S/m for white matter. Healthy gray and white matter had statistically different median impedances (P < 0.0001). White matter conductivity was found to be homogeneous as normality tests did not find evidence of multiple subgroups. Gray matter had lower conductivity in healthy tissue than in the epileptogenic zone (0.26 vs. 0.29 S/m; P = 0.012), even when the epileptogenic zone was not visible in the magnetic resonance image (MRI) (P = 0.005). The present in-vivo conductivity values could serve to create more accurate volume conduction models and could help to refine the identification of relevant intracerebral contacts, especially when located within the epileptogenic zone of an MRI-invisible lesion. Hum Brain Mapp 38:974-986, 2017. © 2016 Wiley Periodicals, Inc.

Simultaneous head tissue conductivity and EEG source location estimation

Accurate electroencephalographic (EEG) source localization requires an electrical head model incorporating accurate geometries and conductivity values for the major head tissues. While consistent conductivity values have been reported for scalp, brain, and cerebrospinal fluid, measured brain-to-skull conductivity ratio (BSCR) estimates have varied between 8 and 80, likely reflecting both inter-subject and measurement method differences. In simulations, mis-estimation of skull conductivity can produce source localization errors as large as 3cm. Here, we describe an iterative gradient-based approach to Simultaneous tissue Conductivity And source Location Estimation (SCALE). The scalp projection maps used by SCALE are obtained from near-dipolar effective EEG sources found by adequate independent component analysis (ICA) decomposition of sufficient high-density EEG data. We applied SCALE to simulated scalp projections of 15cm(2)-scale cortical patch sources in an MR image-based electrical head model with simulated BSCR of 30. Initialized either with a BSCR of 80 or 20, SCALE estimated BSCR as 32.6. In Adaptive Mixture ICA (AMICA) decompositions of (45-min, 128-channel) EEG data from two young adults we identified sets of 13 independent components having near-dipolar scalp maps compatible with a single cortical source patch. Again initialized with either BSCR 80 or 25, SCALE gave BSCR estimates of 34 and 54 for the two subjects respectively. The ability to accurately estimate skull conductivity non-invasively from any well-recorded EEG data in combination with a stable and non-invasively acquired MR imaging-derived electrical head model could remove a critical barrier to using EEG as a sub-cm(2)-scale accurate 3-D functional cortical imaging modality.

Determination of head conductivity frequency response in vivo with optimized EIT-EEG

Electroencephalography (EEG) benefits from accurate head models. Dipole source modelling errors can be reduced from over 1cm to a few millimetres by replacing generic head geometry and conductivity with tailored ones. When adequate head geometry is available, electrical impedance tomography (EIT) can be used to infer the conductivities of head tissues. In this study, the boundary element method (BEM) is applied with three-compartment (scalp, skull and brain) subject-specific head models. The optimal injection of small currents to the head with a modular EIT current injector, and voltage measurement by an EEG amplifier is first sought by simulations. The measurement with a 64-electrode EEG layout is studied with respect to three noise sources affecting EIT: background EEG, deviations from the fitting assumption of equal scalp and brain conductivities, and smooth model geometry deviations from the true head geometry. The noise source effects were investigated depending on the positioning of the injection and extraction electrode and the number of their combinations used sequentially. The deviation from equal scalp and brain conductivities produces rather deterministic errors in the three conductivities irrespective of the current injection locations. With a realistic measurement of around 2 min and around 8 distant distinct current injection pairs, the error from the other noise sources is reduced to around 10% or less in the skull conductivity. The analysis of subsequent real measurements, however, suggests that there could be subject-specific local thinnings in the skull, which could amplify the conductivity fitting errors. With proper analysis of multiplexed sinusoidal EIT current injections, the measurements on average yielded conductivities of 340 mS/m (scalp and brain) and 6.6 mS/m (skull) at 2 Hz. From 11 to 127 Hz, the conductivities increased by 1.6% (scalp and brain) and 6.7% (skull) on the average. The proper analysis was ensured by using recombination of the current injections into virtual ones, avoiding problems in location-specific skull morphology variations. The observed large intersubject variations support the need for in vivo measurement of skull conductivity, resulting in calibrated subject-specific head models.

Impact of uncertain head tissue conductivity in the optimization of transcranial direct current stimulation for an auditory target

OBJECTIVE

Transcranial direct current stimulation (tDCS) is a non-invasive brain stimulation technique to modify neural excitability. Using multi-array tDCS, we investigate the influence of inter-individually varying head tissue conductivity profiles on optimal electrode configurations for an auditory cortex stimulation.

APPROACH

In order to quantify the uncertainty of the optimal electrode configurations, multi-variate generalized polynomial chaos expansions of the model solutions are used based on uncertain conductivity profiles of the compartments skin, skull, gray matter, and white matter. Stochastic measures, probability density functions, and sensitivity of the quantities of interest are investigated for each electrode and the current density at the target with the resulting stimulation protocols visualized on the head surface.

MAIN RESULTS

We demonstrate that the optimized stimulation protocols are only comprised of a few active electrodes, with tolerable deviations in the stimulation amplitude of the anode. However, large deviations in the order of the uncertainty in the conductivity profiles could be noted in the stimulation protocol of the compensating cathodes. Regarding these main stimulation electrodes, the stimulation protocol was most sensitive to uncertainty in skull conductivity. Finally, the probability that the current density amplitude in the auditory cortex target region is supra-threshold was below 50%.

SIGNIFICANCE

The results suggest that an uncertain conductivity profile in computational models of tDCS can have a substantial influence on the prediction of optimal stimulation protocols for stimulation of the auditory cortex. The investigations carried out in this study present a possibility to predict the probability of providing a therapeutic effect with an optimized electrode system for future auditory clinical and experimental procedures of tDCS applications.

Effect of anatomical variability on electric field characteristics of electroconvulsive therapy and magnetic seizure therapy: a parametric modeling study

Electroconvulsive therapy (ECT) and magnetic seizure therapy (MST) are conventionally applied with a fixed stimulus current amplitude, which may result in differences in the neural stimulation strength and focality across patients due to interindividual anatomical variability. The objective of this study is to quantify the effect of head anatomical variability associated with age, sex, and individual differences on the induced electric field characteristics in ECT and MST. Six stimulation modalities were modeled including bilateral and right unilateral ECT, focal electrically administered seizure therapy (FEAST), and MST with circular, cap, and double-cone coils. The electric field was computed using the finite element method in a parameterized spherical head model representing the variability in the general population. Head tissue layer thicknesses and conductivities were varied to examine the impact of interindividual anatomical differences on the stimulation strength, depth, and focality. Skull conductivity most strongly affects the ECT electric field, whereas the MST electric field is independent of tissue conductivity variation in this model but is markedly affected by differences in head diameter. Focal ECT electrode configurations such as FEAST is more sensitive to anatomical variability than that of less focal paradigms such as BL ECT. In MST, anatomical variability has stronger influence on the electric field of the cap and circular coils compared to the double-cone coil, possibly due to the more superficial field of the former. The variability of the ECT and MST electric fields due to anatomical differences should be considered in the interpretation of existing studies and in efforts to improve dosing approaches for better control of stimulation strength and focality across patients, such as individualization of the current amplitude. The conventional approach to individualizing dosage by titrating the number of pulses cannot compensate for differences in the spatial extent of stimulation that result from anatomical variability.

Combining EEG and MEG for the reconstruction of epileptic activity using a calibrated realistic volume conductor model

To increase the reliability for the non-invasive determination of the irritative zone in presurgical epilepsy diagnosis, we introduce here a new experimental and methodological source analysis pipeline that combines the complementary information in EEG and MEG, and apply it to data from a patient, suffering from refractory focal epilepsy. Skull conductivity parameters in a six compartment finite element head model with brain anisotropy, constructed from individual MRI data, are estimated in a calibration procedure using somatosensory evoked potential (SEP) and field (SEF) data. These data are measured in a single run before acquisition of further runs of spontaneous epileptic activity. Our results show that even for single interictal spikes, volume conduction effects dominate over noise and need to be taken into account for accurate source analysis. While cerebrospinal fluid and brain anisotropy influence both modalities, only EEG is sensitive to skull conductivity and conductivity calibration significantly reduces the difference in especially depth localization of both modalities, emphasizing its importance for combining EEG and MEG source analysis. On the other hand, localization differences which are due to the distinct sensitivity profiles of EEG and MEG persist. In case of a moderate error in skull conductivity, combined source analysis results can still profit from the different sensitivity profiles of EEG and MEG to accurately determine location, orientation and strength of the underlying sources. On the other side, significant errors in skull modeling are reflected in EEG reconstruction errors and could reduce the goodness of fit to combined datasets. For combined EEG and MEG source analysis, we therefore recommend calibrating skull conductivity using additionally acquired SEP/SEF data.

Effects of forward model errors on EEG source localization

Subject-specific four-layer boundary element method (BEM) electrical forward head models for four participants, generated from magnetic resonance (MR) head images using NFT ( www.sccn.ucsd.edu/wiki/NFT ), were used to simulate electroencephalographic (EEG) scalp potentials at 256 recorded electrode positions produced by single current dipoles of a 3-D grid in brain space. Locations of these dipoles were then estimated using gradient descent within five template head models fit to the electrode positions. These were: a spherical model, three-layer and four-layer BEM head models based on the Montreal Neurological Institute (MNI) template head image, and these BEM models warped to the recorded electrode positions. Smallest localization errors (4.1-6.2 mm, medians) were obtained using the electrode-position warped four-layer BEM models, with largest localization errors (~20 mm) for most basal brain locations. When we increased the brain-to-skull conductivity ratio assumed in the template model scalp projections from the simulated value (25:1) to a higher value (80:1) used in earlier studies, the estimated dipole locations moved outwards (12.4 mm, median). We also investigated the effects of errors in co-registering the electrode positions, of reducing electrode counts, and of adding a fifth, isotropic white matter layer to one individual head model. Results show that when individual subject MR head images are not available to construct subject-specific head models, accurate EEG source localization should employ a four- or five-layer BEM template head model incorporating an accurate skull conductivity estimate and warped to 64 or more accurately 3-D measured and co-registered electrode positions.

An extended Kalman filtering approach for the estimation of human head tissue conductivities by using EEG data: a simulation study

In this study, we propose an extended Kalman filter approach for the estimation of the human head tissue conductivities in vivo by using electroencephalogram (EEG) data. Since the relationship between the surface potentials and conductivity distribution is nonlinear, the proposed algorithm first linearizes the system and applies extended Kalman filtering. By using a three-compartment realistic head model obtained from the magnetic resonance images of a real subject, a known dipole assumption and 32 electrode positions, the performance of the proposed method is tested in simulation studies and it is shown that the proposed algorithm estimates the tissue conductivities with less than 1% error in noiseless measurements and less than 5% error when the signal-to-noise ratio is 40 dB or higher. We conclude that the proposed extended Kalman filter approach successfully estimates the tissue conductivities in vivo.

Influence of skull conductivity perturbations on EEG dipole source analysis

PURPOSE

Electroencephalogram (EEG) source analysis is a noninvasive technique used in the presurgical of epilepsy. In this study, the dipole location and orientation errors due to skull conductivity perturbations were investigated in two groups of three-dimensional head models: A spherical head model and a realistic head model.

METHODS

In each group, the head model had a brain-to-skull conductivity ratio (Rsigma) within the range of 10-40. Solving the forward problem in the head model with skull conductivity perturbations along with the inverse problem in the baseline head model with Rsigma=20 permitted the derivation of the dipole estimation errors.

RESULTS

Perturbations in the skull conductivity generated dipole location and orientation errors: The larger the perturbations, the larger the errors and the error ranges. The dipole orientation error due to skull conductivity perturbations was not great (maximal mean of < 5 degrees) in this study, but the dipole location error was notable (maximal mean of > 5 mm).

CONCLUSIONS

Therefore, the influence of skull conductivity perturbations on EEG dipole source analysis cannot be neglected. This study suggests that it is necessary to measure the skull conductivity of the individual patients in order to achieve accurate EEG source analysis.

Modeling of the human skull in EEG source analysis

We used computer simulations to investigate finite element models of the layered structure of the human skull in EEG source analysis. Local models, where each skull location was modeled differently, and global models, where the skull was assumed to be homogeneous, were compared to a reference model, in which spongy and compact bone were explicitly accounted for. In both cases, isotropic and anisotropic conductivity assumptions were taken into account. We considered sources in the entire brain and determined errors both in the forward calculation and the reconstructed dipole position. Our results show that accounting for the local variations over the skull surface is important, whereas assuming isotropic or anisotropic skull conductivity has little influence. Moreover, we showed that, if using an isotropic and homogeneous skull model, the ratio between skin/brain and skull conductivities should be considerably lower than the commonly used 80:1. For skull modeling, we recommend (1) Local models: if compact and spongy bone can be identified with sufficient accuracy (e.g., from MRI) and their conductivities can be assumed to be known (e.g., from measurements), one should model these explicitly by assigning each voxel to one of the two conductivities, (2) Global models: if the conditions of (1) are not met, one should model the skull as either homogeneous and isotropic, but with considerably higher skull conductivity than the usual 0.0042 S/m, or as homogeneous and anisotropic, but with higher radial skull conductivity than the usual 0.0042 S/m and a considerably lower radial:tangential conductivity anisotropy than the usual 1:10.

Effect of anatomical variability on neural stimulation strength and focality in electroconvulsive therapy (ECT) and magnetic seizure therapy (MST)

We present a quantitative comparison of two metrics-neural stimulation strength and focality-in electrocon-vulsive therapy (ECT) and magnetic seizure therapy (MST) using finite-element method (FEM) simulation in a spherical head model. Five stimulation modalities were modeled, including bilateral ECT, unilateral ECT, focal electrically administered seizure therapy (FEAST), and MST with circular and double-cone coils, with stimulation parameters identical to those applied in clinical practice. We further examine the effect on the stimulation metrics of individual-, sex- and age-related variability in tissue layer thickness and conductivity. Neural stimulation by MST is shown to be more focal and superficial than ECT. This result suggests that it may be advantageous to reduce the current used in ECT. The stimulation strength in MST is also less sensitive to variations in head geometry and tissue conductivity than in ECT. Individualization of pulse amplitude in both ECT and MST could compensate for anatomical variability, which could lead to more consistent clinical outcomes.

Improved EEG source analysis using low-resolution conductivity estimation in a four-compartment finite element head model

Bioelectric source analysis in the human brain from scalp electroencephalography (EEG) signals is sensitive to geometry and conductivity properties of the different head tissues. We propose a low-resolution conductivity estimation (LRCE) method using simulated annealing optimization on high-resolution finite element models that individually optimizes a realistically shaped four-layer volume conductor with regard to the brain and skull compartment conductivities. As input data, the method needs T1- and PD-weighted magnetic resonance images for an improved modeling of the skull and the cerebrospinal fluid compartment and evoked potential data with high signal-to-noise ratio (SNR). Our simulation studies showed that for EEG data with realistic SNR, the LRCE method was able to simultaneously reconstruct both the brain and the skull conductivity together with the underlying dipole source and provided an improved source analysis result. We have also demonstrated the feasibility and applicability of the new method to simultaneously estimate brain and skull conductivity and a somatosensory source from measured tactile somatosensory-evoked potentials of a human subject. Our results show the viability of an approach that computes its own conductivity values and thus reduces the dependence on assigning values from the literature and likely produces a more robust estimate of current sources. Using the LRCE method, the individually optimized four-compartment volume conductor model can, in a second step, be used for the analysis of clinical or cognitive data acquired from the same subject.

A global sensitivity analysis of three- and four-layer EEG conductivity models

The accuracy of forward models for EEG partly depends on the conductivity values of the head tissues. Yet, the influence of the conductivities on the model output is still not well understood. In this paper, we apply a variance-based sensitivity analysis method to the most common EEG forward models (three or four layers). This method is global because it quantifies the influence of each parameter with all the parameters varying at the same time. With nonlinear models, it helps to understand the interaction between parameters, which is not possible with simple sensitivity analyses (one-at-a-time variations, derivatives, and perturbations). By analyzing the potential topographies at the electrodes, we obtained several results. For a shallow dipole, the EEG topographies are mainly sensitive to the interaction between skull and scalp conductivities. It means that the variability of the EEG topographies is driven mostly by a function of skull and scalp conductivities. Similar results are presented for skull anisotropy and a current injection as performed in electrical impedance tomography. This global sensitivity analysis gives new information about EEG forward models--it identifies the main input parameters that need model refinement--and directions on how to calibrate these models.

Probabilistic forward model for electroencephalography source analysis

Source localization by electroencephalography (EEG) requires an accurate model of head geometry and tissue conductivity. The estimation of source time courses from EEG or from EEG in conjunction with magnetoencephalography (MEG) requires a forward model consistent with true activity for the best outcome. Although MRI provides an excellent description of soft tissue anatomy, a high resolution model of the skull (the dominant resistive component of the head) requires CT, which is not justified for routine physiological studies. Although a number of techniques have been employed to estimate tissue conductivity, no present techniques provide the noninvasive 3D tomographic mapping of conductivity that would be desirable. We introduce a formalism for probabilistic forward modeling that allows the propagation of uncertainties in model parameters into possible errors in source localization. We consider uncertainties in the conductivity profile of the skull, but the approach is general and can be extended to other kinds of uncertainties in the forward model. We and others have previously suggested the possibility of extracting conductivity of the skull from measured electroencephalography data by simultaneously optimizing over dipole parameters and the conductivity values required by the forward model. Using Cramer-Rao bounds, we demonstrate that this approach does not improve localization results nor does it produce reliable conductivity estimates. We conclude that the conductivity of the skull has to be either accurately measured by an independent technique, or that the uncertainties in the conductivity values should be reflected in uncertainty in the source location estimates.

Bio-heat transfer model of deep brain stimulation-induced temperature changes

There is a growing interest in the use of chronic deep brain stimulation (DBS) for the treatment of medically refractory movement disorders and other neurological and psychiatric conditions. Fundamental questions remain about the physiologic effects of DBS. Previous basic research studies have focused on the direct polarization of neuronal membranes by electrical stimulation. The goal of this paper is to provide information on the thermal effects of DBS using finite element models to investigate the magnitude and spatial distribution of DBS-induced temperature changes. The parameters investigated include stimulation waveform, lead selection, brain tissue electrical and thermal conductivities, blood perfusion, metabolic heat generation during the stimulation and lead thermal conductivity/heat dissipation through the electrode. Our results show that clinical DBS protocols will increase the temperature of surrounding tissue by up to 0.8 degrees C depending on stimulation/tissue parameters.

Bio-heat transfer model of deep brain stimulation induced temperature changes

There is a growing interest in the use of chronic deep brain stimulation (DBS) for the treatment of medically refractory movement disorders and other neurological and psychiatric conditions. Fundamental questions remain about the physiologic effects and safety of DBS. Previous basic research studies have focused on the direct polarization of neuronal membranes by electrical stimulation. The goal of this paper is to provide information on the thermal effects of DBS using finite element models to investigate the magnitude and spatial distribution of DBS induced temperature changes. The parameters investigated include: stimulation waveform, lead selection, brain tissue electrical and thermal conductivity, blood perfusion, metabolic heat generation during the stimulation. Our results show that clinical deep brain stimulation protocols will increase the temperature of surrounding tissue by up to 0.8 deg C depending on stimulation/tissue parameters.