A novel bounded EIT protocol to generate inhomogeneous skull conductivity maps non-invasively.

Electrical Impedance Tomography (EIT) can be used to estimate the electrical properties of the head tissues in a parametric approach. This modality is called parametric EIT or bounded EIT (bEIT). Typical bEIT protocols alternate between several current injection patterns with two current injection electrodes each: one source and one sink ("1-to-1"), while the rest of the electrodes measure the resulting electric potential. Then, one value of conductivity per tissue (e.g. scalp and/or skull) is estimated independently for each current injection pair. With these protocols, it is difficult to obtain local estimates of the skull tissue. Thus, the grand average of the estimates obtained from each pair is assigned to each tissue modeling them as homogeneous. However, it is known that these tissues are inhomogeneous within the same subject. We propose the use of current injection patterns with one source and many sinks ("1to-N") located at the opposite side of the head to build individual and inhomogeneous skull conductivity maps. We validate the method with simulations and compare its performance with equivalent maps generated by using the classical "1-to-1" patterns. The map generated by the novel method shows better spatial correlation with the more conductive spongy bone presence.Clinical Relevance- The novel bEIT protocol allows to map individual head models with spatially resolved skull conductivities in vivo and non-invasively for use in electroencephalography (EEG) source localization, transcranial electrical stimulation (TES) dose calculations and TES pattern optimization, without the risk of ionizing radiation associated with computed tomography (CT) scans.

Unification of optimal targeting methods in transcranial electrical stimulation.

One of the major questions in high-density transcranial electrical stimulation (TES) is: given a region of interest (ROI) and electric current limits for safety, how much current should be delivered by each electrode for optimal targeting of the ROI? Several solutions, apparently unrelated, have been independently proposed depending on how "optimality" is defined and on how this optimization problem is stated mathematically. The least squares (LS), weighted LS (WLS), or reciprocity-based approaches are the simplest ones and have closed-form solutions. An extended optimization problem can be stated as follows: maximize the directional intensity at the ROI, limit the electric fields at the non-ROI, and constrain total injected current and current per electrode for safety. This problem requires iterative convex or linear optimization solvers. We theoretically prove in this work that the LS, WLS and reciprocity-based closed-form solutions are specific solutions to the extended directional maximization optimization problem. Moreover, the LS/WLS and reciprocity-based solutions are the two extreme cases of the intensity-focality trade-off, emerging under variation of a unique parameter of the extended directional maximization problem, the imposed constraint to the electric fields at the non-ROI. We validate and illustrate these findings with simulations on an atlas head model. The unified approach we present here allows a better understanding of the nature of the TES optimization problem and helps in the development of advanced and more effective targeting strategies.

Skull Modeling Effects in Conductivity Estimates Using Parametric Electrical Impedance Tomography.

OBJECTIVE: To estimate scalp, skull, compact bone, and marrow bone electrical conductivity values based on electrical impedance tomography (EIT) measurements, and to determine the influence of skull modeling details on the estimates. METHODS: We collected EIT data with 62 current injection pairs and built five 6-8 million finite element (FE) head models with different grades of skull simplifications for four subjects, including three whose head models serve as Atlases in the scientific literature and in commercial equipment (Colin27 and EGI's Geosource atlases). We estimated electrical conductivity of the scalp, skull, marrow bone, and compact bone tissues for each current injection pair, each model, and each subject. RESULTS: Closure of skull holes in FE models, use of simplified four-layer boundary element method-like models, and neglecting the CSF layer produce an overestimation of the skull conductivity of 10%, 10%-20%, and 20%-30%, respectively (accumulated overestimation of 50%-70%). The average extracted conductivities are 288 ± 53 (the scalp), 4.3 ± 0.08 (the compact bone), and 5.5 ± 1.25 (the whole skull) mS/m. The marrow bone estimates showed large dispersion. CONCLUSION: Present EIT estimates for the skull conductivity are lower than typical literature reference values, but previous in vivo EIT results are likely overestimated due to the use of simpler models. SIGNIFICANCE: Typical literature values of 7-10 mS/m for skull conductivity should be replaced by the present estimated values when using detailed skull head models. We also provide subject specific conductivity estimates for widely used Atlas head models.

Slow-Frequency Pulsed Transcranial Electrical Stimulation for Modulation of Cortical Plasticity Based on Reciprocity Targeting with Precision Electrical Head Modeling.

In pain management as well as other clinical applications of neuromodulation, it is important to consider the timing parameters influencing activity-dependent plasticity, including pulsed versus sustained currents, as well as the spatial action of electrical currents as they polarize the complex convolutions of the cortical mantle. These factors are of course related; studying temporal factors is not possible when the spatial resolution of current delivery to the cortex is so uncertain to make it unclear whether excitability is increased or decreased with anodal vs. cathodal current flow. In the present study we attempted to improve the targeting of specific cortical locations by applying current through flexible source-sink configurations of 256 electrodes in a geodesic array. We constructed a precision electric head model for 12 healthy individuals. Extraction of the individual's cortical surface allowed computation of the component of the induced current that is normal to the target cortical surface. In an effort to replicate the long-term depression (LTD) induced with pulsed protocols in invasive animal research and transcranial magnetic stimulation studies, we applied 100 ms pulses at 1.9 s intervals either in cortical-surface-anodal or cortical-surface-cathodal directions, with a placebo (sham) control. The results showed significant LTD of the motor evoked potential as a result of the cortical-surface-cathodal pulses in contrast to the placebo control, with a smaller but similar LTD effect for anodal pulses. The cathodal LTD after-effect was sustained over 90 min following current injection. These results support the feasibility of pulsed protocols with low total charge in non-invasive neuromodulation when the precision of targeting is improved with a dense electrode array and accurate head modeling.

Transcranial Electrical Neuromodulation Based on the Reciprocity Principle.

A key challenge in multi-electrode transcranial electrical stimulation (TES) or transcranial direct current stimulation (tDCS) is to find a current injection pattern that delivers the necessary current density at a target and minimizes it in the rest of the head, which is mathematically modeled as an optimization problem. Such an optimization with the Least Squares (LS) or Linearly Constrained Minimum Variance (LCMV) algorithms is generally computationally expensive and requires multiple independent current sources. Based on the reciprocity principle in electroencephalography (EEG) and TES, it could be possible to find the optimal TES patterns quickly whenever the solution of the forward EEG problem is available for a brain region of interest. Here, we investigate the reciprocity principle as a guideline for finding optimal current injection patterns in TES that comply with safety constraints. We define four different trial cortical targets in a detailed seven-tissue finite element head model, and analyze the performance of the reciprocity family of TES methods in terms of electrode density, targeting error, focality, intensity, and directionality using the LS and LCMV solutions as the reference standards. It is found that the reciprocity algorithms show good performance comparable to the LCMV and LS solutions. Comparing the 128 and 256 electrode cases, we found that use of greater electrode density improves focality, directionality, and intensity parameters. The results show that reciprocity principle can be used to quickly determine optimal current injection patterns in TES and help to simplify TES protocols that are consistent with hardware and software availability and with safety constraints.

In vivo quantification of intraventricular hemorrhage in a neonatal piglet model using an EEG-layout based electrical impedance tomography array.

Intraventricular hemorrhage (IVH) is a common occurrence in the days immediately after premature birth. It has been correlated with outcomes such as periventricular leukomalacia (PVL), cerebral palsy and developmental delay. The causes and evolution of IVH are unclear; it has been associated with fluctuations in blood pressure, damage to the subventricular zone and seizures. At present, ultrasound is the most commonly used method for detection of IVH, but is used retrospectively. Without the presence of adequate therapies to avert IVH, the use of a continuous monitoring technique may be somewhat moot. While treatments to mitigate the damage caused by IVH are still under development, the principal benefit of a continuous monitoring technique will be in investigations into the etiology of IVH, and its associations with periventricular injury and blood pressure fluctuations. Electrical impedance tomography (EIT) is potentially of use in this context as accumulating blood displaces higher conductivity cerebrospinal fluid (CSF) in the ventricles. We devised an electrode array and EIT measurement strategy that performed well in detection of simulated ventricular blood in computer models and phantom studies. In this study we describe results of pilot in vivo experiments on neonatal piglets, and show that EIT has high sensitivity and specificity to small quantities of blood (<1 ml) introduced into the ventricle. EIT images were processed to an index representing the quantity of accumulated blood (the 'quantity index', QI). We found that QI values were linearly related to fluid quantity, and that the slope of the curve was consistent between measurements on different subjects. Linear discriminant analysis showed a false positive rate of 0%, and receiver operator characteristic analysis found area under curve values greater than 0.98 to administered volumes between 0.5, and 2.0 ml. We believe our study indicates that this method may be well suited to quantitative monitoring of IVH in newborns, simultaneously or interleaved with electroencephalograph assessments.

Optimization of focality and direction in dense electrode array transcranial direct current stimulation (tDCS).

OBJECTIVE: Transcranial direct current stimulation (tDCS) aims to alter brain function non-invasively via electrodes placed on the scalp. Conventional tDCS uses two relatively large patch electrodes to deliver electrical current to the brain region of interest (ROI). Recent studies have shown that using dense arrays containing up to 512 smaller electrodes may increase the precision of targeting ROIs. However, this creates a need for methods to determine effective and safe stimulus patterns as the number of degrees of freedom is much higher with such arrays. Several approaches to this problem have appeared in the literature. In this paper, we describe a new method for calculating optimal electrode stimulus patterns for targeted and directional modulation in dense array tDCS which differs in some important aspects with methods reported to date. APPROACH: We optimize stimulus pattern of dense arrays with fixed electrode placement to maximize the current density in a particular direction in the ROI. We impose a flexible set of safety constraints on the current power in the brain, individual electrode currents, and total injected current, to protect subject safety. The proposed optimization problem is convex and thus efficiently solved using existing optimization software to find unique and globally optimal electrode stimulus patterns. MAIN RESULTS: Solutions for four anatomical ROIs based on a realistic head model are shown as exemplary results. To illustrate the differences between our approach and previously introduced methods, we compare our method with two of the other leading methods in the literature. We also report on extensive simulations that show the effect of the values chosen for each proposed safety constraint bound on the optimized stimulus patterns. SIGNIFICANCE: The proposed optimization approach employs volume based ROIs, easily adapts to different sets of safety constraints, and takes negligible time to compute. An in-depth comparison study gives insight into the relationship between different objective criteria and optimized stimulus patterns. In addition, the analysis of the interaction between optimized stimulus patterns and safety constraint bounds suggests that more precise current localization in the ROI, with improved safety criterion, may be achieved by careful selection of the constraint bounds.

Optimizing Stimulus Patterns for Dense Array tDCS With Fewer Sources Than Electrodes Using A branch and Bound Algorithm.

Dense array transcranial direct current stimulation (tDCS) has become of increasing interest as a noninvasive modality to modulate brain function. To target a particular brain region of interest (ROI), using a dense electrode array placed on the scalp, the current injection pattern can be appropriately optimized. Previous optimization methods have assumed availability of individually controlled current sources for each non-reference electrode. This may be costly and impractical in a clinical setting. However, using fewer current sources than electrodes results in a non-convex combinatorial optimization problem. In this paper, we present a novel use of the branch and bound (BB) algorithm to find sub-optimal stimulus patterns with fewer current sources than electrodes. We present simulation results for both focal and spatially extended cortical ROIs. Our results suggest that only a few (2-3) independently controlled current sources can achieve comparable results to a full set (125 sources) to a tolerance of 5%. BB is computationally 3-5 orders of magnitude less demanding than exhaustive search.

EEG source localization: Sensor density and head surface coverage.

BACKGROUND: The accuracy of EEG source localization depends on a sufficient sampling of the surface potential field, an accurate conducting volume estimation (head model), and a suitable and well-understood inverse technique. The goal of the present study is to examine the effect of sampling density and coverage on the ability to accurately localize sources, using common linear inverse weight techniques, at different depths. Several inverse methods are examined, using the popular head conductivity. NEW METHOD: Simulation studies were employed to examine the effect of spatial sampling of the potential field at the head surface, in terms of sensor density and coverage of the inferior and superior head regions. In addition, the effects of sensor density and coverage are investigated in the source localization of epileptiform EEG. RESULTS: Greater sensor density improves source localization accuracy. Moreover, across all sampling density and inverse methods, adding samples on the inferior surface improves the accuracy of source estimates at all depths. COMPARISON WITH EXISTING METHODS: More accurate source localization of EEG data can be achieved with high spatial sampling of the head surface electrodes. CONCLUSIONS: The most accurate source localization is obtained when the voltage surface is densely sampled over both the superior and inferior surfaces.

A 3D finite-difference BiCG iterative solver with the Fourier-Jacobi preconditioner for the anisotropic EIT/EEG forward problem.

The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique.

Automated measurement of skull circumference, cranial index, and braincase volume from pediatric computed tomography.

Normative values of pediatric skull circumference, cranial index, and braincase volume would inform multiple disciplines including neurosurgery, plastic surgery and anthropology. Semi-automated methods exist for obtaining these data but are time consuming and require expertise. We report on a new method for automated extraction of in vivo measures of pediatric crania based on x-ray computed tomography scans (CT). Data were obtained from a clinical image repository for pediatric populations in whom no pathology was noted. The automated process showed good agreement with semi-automated measures, although there was a small bias for both braincase volume and circumference. We developed an open source program to automatically extract measures of skull circumference, cranial index, and braincase volume that are likely to prove useful in multiple disciplines.

Automated measurement of pediatric cranial bone thickness and density from clinical computed tomography.

Skull thickness and density measures of normal pediatric crania would inform multiple disciplines including neurosurgery, optical and magnetoelectrophysiological imaging, and biomechanical modeling of head trauma. We report on a new method for automated extraction of in vivo skull thickness and density measures of pediatric crania based on x-ray computed tomography scans (CT). Data were obtained from a clinical image repository for pediatric populations in whom no pathology was noted. Skull thickness and density measures were systematically obtained across the calvarium. We find a set of measures that correlated with physiological age that are likely to prove useful in multiple disciplines.

Computational modeling of human head electromagnetics for source localization of milliscale brain dynamics.

Understanding the milliscale (temporal and spatial) dynamics of the human brain activity requires high-resolution modeling of head electromagnetics and source localization of EEG data. We have developed an automated environment to construct individualized computational head models from image segmentation and to estimate conductivity parameters using electrical impedance tomography methods. Algorithms incorporating tissue inhomogeneity and impedance anisotropy in electromagnetics forward simulations have been developed and parallelized. The paper reports on the application of the environment in the processing of realistic head models, including conductivity inverse estimation and lead field generation for use in EEG source analysis.