Head Tissue Conductivity Research Articles

Assessing the effects of head modelling errors and measurement noise on EEG source localization accuracy in preterm newborns: A single-subject study.

The accuracy of electroencephalogram (EEG) source localization is compromised because of head modelling errors. In this study, we investigated the effect of inaccuracy in the conductivity of head tissues and head model structural deficiencies on the accuracy of EEG source analysis in premature neonates. A series of EEG forward and inverse simulations was performed by introducing structural deficiencies into the reference head models to generate test models, which were then used to investigate head modelling errors caused by cerebrospinal fluid (CSF) exclusion, lack of grey matter (GM)-white matter (WM) distinction, fontanel exclusion and inaccuracy in skull conductivity. The modelling errors were computed between forward and inverse solutions obtained using the reference and test models generated for each deficiency. Our results showed that the exclusion of CSF from the head model had a strong widespread effect on the accuracy of the EEG source localization with position errors lower than 4.17 mm. The GM and WM distinction also caused strong localization errors (up to 3.5mm). The exclusion of fontanels from the head model also strongly affected the accuracy of the EEG source localization for sources located beneath the fontanels with a maximum localization error of 4.37 mm. Similarly, inaccuracies in the skull conductivity caused errors in EEG forward and inverse modelling in sources beneath cranial bones. Our results indicate that the accuracy of EEG source imaging in premature neonates can be largely improved by using head models, which include not only the brain, skull and scalp but also the CSF, GM, WM and fontanels.

Evaluation of skull conductivity using SCALE head tissue conductivity estimation using EEG.

Inaccurate estimation of skull conductivity is the largest impediment to high-resolution EEG source imaging because of its strong influence and wide variability across individuals. Nonetheless, there is yet no widely applied method for noninvasively measuring individual skull conductivity. We presented a skull conductivity and source location estimation algorithm (SCALE) for simultaneously estimating skull conductivity and the cortical distributions of 18-20 effective sources derived from the EEG data by independent component analysis (ICA). SCALE combines a realistic Finite Element Method (FEM) head model built from a magnetic resonance (MR) head image with the effective source scalp maps to estimate brain-to-skull conductivity ratio (BSCR) and to map the effective sources on the cortical surface. To estimate the robustness of SCALE BSCR estimates, we applied SCALE to MR image and high-density EEG data from ten participants, five having data from 2-3 different tasks and sessions. As expected, across participants SCALE BSCR estimates differed widely (mean 32.8, range 18-78). Within-participant SCALE BSCR estimates were far more consistent than between participants. By incorporating SCALE-optimized distributed EEG source localization, stable functional imaging of cortical EEG effective sources can become routine, giving relatively low-cost EEG imaging a spatial resolution compatible with other brain imaging results and uniquely capable for studying brain dynamics supporting thought and action in laboratory, virtual, and natural environments.

Human in-vivo magnetic resonance current density imaging of the brain by optimizing head tissue conductivities

Abstract Introduction: Magnetic resonance current density imaging (MRCDI) aims to reconstruct the current flow of transcranial electrical stimulation (TES) in the brain from MR-measurements of the current-induced magnetic field Bz. Aim: We test the performance of a standard reconstruction algorithm (“projected current density algorithm”, PCD, Jeong et al. 2014) for human brain data. We compare it with current flow simulations using personalized head models. Methods:1. We generated ground-truth data for the TES current flow and Bz-field using a detailed head model and SimNIBS (www.simnibs.org). We applied the PCD algorithm to the Bz -field and quantified the reconstruction performance by comparison with the ground-truth current flow. We additionally compared the PCD results with simulations using a simple head model (“3c” with scalp, bone and a homogeneous intracranial compartment). 2. We reconstructed the current flow from in-vivo MRCDI data (Göksu et al, 2018) with the PCD algorithm. We also used head models of different complexities (“3c” and “4c”: scalp, skull, CSF & brain) and optimized their conductivities to minimize the root-mean-square difference between the measured and simulated Bz. Results: 1. For simulated Bz data, the PCD algorithm only coarsely reconstructed the true current flow. Even the simple head model performed better. 2. For measured Bz data, current flows obtained with personalized head models and fitted conductivities explained the measurements better than the current flow reconstructed with the PCD algorithm. This was already the case for the simple head model (3c). The more detailed model (4c) resulted in further statistically significant improvements. However, for all models, the unexplained variance stayed above the noise floor, indicating remaining differences to unknown true current flow. Conclusions: The PCD algorithm has low accuracy for MRCDI data of the brain. However, MRCDI is useful for evaluations and improvements of current flow simulations with anatomically detailed personalized head models. Keywords: magnetic resonance current density imaging, personalized electric field calculation, dose control, transcranial electrical stimulation

Does participant’s age impact on tDCS induced fields? Insights from computational simulations

Objective: Understanding the induced current flow from transcranial direct current stimulation (tDCS) is essential for determining the optimal dose and treatment. Head tissue conductivities play a key role in the resulting electromagnetic fields. However, there exists a complicated relationship between skull conductivity and participant age, that remains unclear. We explored how variations in skull electrical conductivities, particularly as a suggested function of age, affected tDCS induced electric fields. Approach: Simulations were employed to compare tDCS outcomes for different intensities across head atlases of varying age. Three databases were chosen to demonstrate differing variability in skull conductivity with age and how this may affect induced fields. Differences in tDCS electric fields due to proposed age-dependent skull conductivity variation, as well as deviations in grey matter, white matter and scalp, were compared and the most influential tissues determined. Main results: tDCS induced peak electric fields significantly negatively correlated with age, exacerbated by employing proposed age-appropriate skull conductivity (according to all three datasets). Uncertainty in skull conductivity was the most sensitive to changes in peak fields with increasing age. These results were revealed to be directly due to changing skull conductivity, rather than head geometry alone. There was no correlation between tDCS focality and age. Significance: Accurate and individualised head anatomy and in vivo skull conductivity measurements are essential for modelling tDCS induced fields. In particular, age should be taken into account when considering stimulation dose to precisely predict outcomes.

A Comparison of Bound-Constrained and Positivity-Constrained Optimization Method to Estimate Head Tissue Conductivities by Scalp Voltage Information

Electrical Impedance Tomography (EIT) is a noninvasive method used to estimate the conductivity of head tissues. Estimation based on the unconstrained Gauss-Newton (GN) method is conventional, but it may result in negative-value or extraordinary high-value estimates, which are unexpected. In this study, the bound-constrained method and the positivity-constrained optimization method were investigated and compared to the unconstrained optimization method. A two-dimensional model was created for conductivity estimation containing five head tissues, i.e., the scalp, the skull, the cerebrospinal fluid (CSF), grey matter (GM), and white matter (WM). The results showed that the accuracy, the robustness, and the estimation convergence of the estimation of this approach were significantly improved by constraining. All unexpected values also disappeared. The investigation proved that very high sensitivity of the skull region caused the unexpected outcome of the unconstrained cases. This high sensitivity can be significantly reduced by constraining. However, a degree of estimation nonlinearity can be increased by constraining as well, causing some estimation accuracies in the case of the positivity-constrained optimization method to be poor. Therefore, it is recommended to use only the bound-constrained optimization method.

Influence of Head Tissue Conductivity Uncertainties on EEG Dipole Reconstruction.

Reliable EEG source analysis depends on sufficiently detailed and accurate head models. In this study, we investigate how uncertainties inherent to the experimentally determined conductivity values of the different conductive compartments influence the results of EEG source analysis. In a single source scenario, the superficial and focal somatosensory P20/N20 component, we analyze the influence of varying conductivities on dipole reconstructions using a generalized polynomial chaos (gPC) approach. We find that in particular the conductivity uncertainties for skin and skull have a significant influence on the EEG inverse solution, leading to variations in source localization by several centimeters. The conductivity uncertainties for gray and white matter were found to have little influence on the source localization, but a strong influence on the strength and orientation of the reconstructed source, respectively. As the CSF conductivity is most accurately determined of all conductivities in a realistic head model, CSF conductivity uncertainties had a negligible influence on the source reconstruction. This small uncertainty is a further benefit of distinguishing the CSF in realistic volume conductor models.

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.

Abstract #13: Impact of Conductivity Calibrated Individual Head Model on Reciprocity Optimized Transcranial Electrical Stimulation

Introduction: Head modeling is an important part of EEG source localization and optimization in TES allowing to see how much current is delivered to the brain target. Using MRI one can routinely create anatomically accurate individual head models in terms of geometrical precision. However, estimation of subject-specific electrical conductivity values of the head tissues is still a challenge, so usually default values from the literature are used. Bounded Electrical Impedance Tomography (bEIT) allows estimating the head tissue conductivities non-invasively and individually (Fernandez-Corazza et al., 2018. DOI: 10.1109/TBME.2017.2777143) and thus to complement the subject-specific geometry by individual conductivities. In this paper, we estimate the neurostimulation dose differences resulting from using the default literature conductivity values versus calibrated individualized head tissue conductivities.

Fast Approximation of EEG Forward Problem and Application to Tissue Conductivity Estimation.

Bioelectric source analysis in the human brain from scalp electroencephalography (EEG) signals is sensitive to the conductivities of different head tissues. The conductivity of tissues is subject dependent, so non-invasive methods for conductivity estimation are necessary to fine tune EEG models. To do so, the EEG forward problem solution (so-called lead field matrix) must be computed for a large number of conductivity configurations. Computing a lead field requires a matrix inversion which is computationally intensive for realistic head models. Thus, the required time for computing a large number of lead fields can become impractical. In this work, we propose to approximate the lead field matrix for a set of conductivity configurations, using the exact solution only for a small set of support points in the conductivity space. Our approach accelerates the computation time, while controlling the approximation error. Our method is tested on simulated and measured EEG data for brain and skull conductivity estimation. This test demonstrates that the approximation does not introduce any bias and runs significantly faster than if exact lead field were to be computed.

High-resolution EEG source imaging of one-year-old children.

Recently we described an iterative skull conductivity and source location estimation (SCALE) algorithm for simultaneously estimating head tissue conductivities and brain source locations. SCALE uses a realistic FEM forward problem head model and scalp maps of 10 or more near-dipolar sources identified by independent component analysis (ICA) decomposition of sufficient high-density EEG data. In this study, we applied SCALE to 20 minutes of 64-channel EEG data and magnetic resonance (MR) head images from four twelve-months-of-age infants. For each child, we selected 15-16 near-dipolar independent components from multiple-model adaptive mixture ICA (AMICA) decomposition of their EEG data. SCALE converged to brain-to-skull conductivity ratio (BSCR) estimates in the 10-12 range and mostly compact gyral or sulcal cortical distributions for the IC sources.

Effects of uncertainty in head tissue conductivity and complexity on EEG forward modeling in neonates.

In this study, we investigated the impact of uncertainty in head tissue conductivities and inherent geometrical complexities including fontanels in neonates. Based on MR and CT coregistered images, we created a realistic neonatal head model consisting of scalp, skull, fontanels, cerebrospinal fluid (CSF), gray matter (GM), and white matter (WM). Using computer simulations, we investigated the effects of exclusion of CSF and fontanels, discrimination between GM and WM, and uncertainty in conductivity of neonatal head tissues on EEG forward modeling. We found that exclusion of CSF from the head model induced the strongest widespread effect on the EEG forward solution. Discrimination between GM and white matter also induced a strong widespread effect, but which was less intense than that of CSF exclusion. The results also showed that exclusion of the fontanels from the neonatal head model locally affected areas beneath the fontanels, but this effect was much less pronounced than those of exclusion of CSF and GM/WM discrimination. Changes in GM/WM conductivities by 25% with respect to reference values induced considerable effects in EEG forward solution, but this effect was more pronounced for GM conductivity. Similarly, changes in skull conductivity induced effects in the EEG forward modeling in areas covered by the cranial bones. The least intense effect on EEG was caused by changes in conductivity of the fontanels. Our findings clearly emphasize the impact of uncertainty in conductivity and deficiencies in head tissue compartments on modeling research and localization of brain electrical activity in neonates. Hum Brain Mapp 37:3604-3622, 2016. © 2016 Wiley Periodicals, Inc.

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 2min 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 340mS/m (scalp and brain) and 6.6mS/m (skull) at 2Hz. From 11 to 127Hz, 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.

The electric field distribution in the brain during TTFields therapy and its dependence on tissue dielectric properties and anatomy: a computational study

Tumor treating fields (TTFields) are a non-invasive, anti-mitotic and approved treatment for recurrent glioblastoma multiforme (GBM) patients. In vitro studies have shown that inhibition of cell division in glioma is achieved when the applied alternating electric field has a frequency in the range of 200 kHz and an amplitude of 1–3 V cm−1. Our aim is to calculate the electric field distribution in the brain during TTFields therapy and to investigate the dependence of these predictions on the heterogeneous, anisotropic dielectric properties used in the computational model.A realistic head model was developed by segmenting MR images and by incorporating anisotropic conductivity values for the brain tissues. The finite element method (FEM) was used to solve for the electric potential within a volume mesh that consisted of the head tissues, a virtual lesion with an active tumour shell surrounding a necrotic core, and the transducer arrays.The induced electric field distribution is highly non-uniform. Average field strength values are slightly higher in the tumour when incorporating anisotropy, by about 10% or less. A sensitivity analysis with respect to the conductivity and permittivity of head tissues shows a variation in field strength of less than 42% in brain parenchyma and in the tumour, for values within the ranges reported in the literature. Comparing results to a previously developed head model suggests significant inter-subject variability.This modelling study predicts that during treatment with TTFields the electric field in the tumour exceeds 1 V cm−1, independent of modelling assumptions. In the future, computational models may be useful to optimize delivery of TTFields.

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 15cm2-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-cm2-scale accurate 3-D functional cortical imaging modality.

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.

Analysis of parametric estimation of head tissue conductivities using Electrical Impedance Tomography

We study the theoretical performance of using Electrical Impedance Tomography (EIT) to measure the conductivity of the main tissues of the head. The governing equations are solved using the Finite Element Method for realistically shaped head models with isotropic and anisotropic electrical conductivities. We focus on the Electroencephalography (EEG) signal frequency range since EEG source localization is the assumed application. We obtain the Cramér-Rao Lower Bound (CRLB) to find the minimum conductivity estimation error expected with EIT measurements. The more convenient electrode pairs selected for current injection from a typical EEG array are determined from the CRLB. Moreover, using simulated data, the Maximum Likelihood Estimator of the conductivity parameters is shown to be close to the CRLB for a relatively low number of measurements. The results support the idea of using EIT as a low-cost and practical tool for individually measure the conductivity of the head tissues, and to use them when solving the EEG source localization. Even when the conductivity of the soft tissues of the head is available from Diffusion Tensor Imaging, EIT can complement the electrical model with the estimation of the skull and scalp conductivities.

Anatomically Accurate Infant Head Models for EEG Source Localization

Children differ from adults in head size, skull morphology, and tissue conductivity. We conducted a simulation to examine the error of source localization when a rescaled adult head model and different skull conductivities are used for EEG source localization in children. We have proven by simulation that source localization accuracy is the best with an infant specific head model including the age specific skull structure and conductivity.

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.