Conductivity mapping of biological tissue using diffusion MRI

The impact of brain lesions on tDCS-induced electric fields

Transcranial direct current stimulation (tDCS) can enhance motor and language rehabilitation after stroke. Though brain lesions distort tDCS-induced electric field (E-field), systematic accounts remain limited. Using electric field modelling, we investigated the effect of 630 synthetic lesions on E-field magnitude in the region of interest (ROI). Models were conducted for two tDCS montages targeting either primary motor cortex (M1) or Broca's area (BA44). Absolute E-field magnitude in the ROI differed by up to 42% compared to the non-lesioned brain depending on lesion size, lesion-ROI distance, and lesion conductivity value. Lesion location determined the sign of this difference: lesions in-line with the predominant direction of current increased E-field magnitude in the ROI, whereas lesions located in the opposite direction decreased E-field magnitude. We further explored how individualised tDCS can control lesion-induced effects on E-field. Lesions affected the individualised electrode configuration needed to maximise E-field magnitude in the ROI, but this effect was negligible when prioritising the maximisation of radial inward current. Lesions distorting tDCS-induced E-field, is likely to exacerbate inter-individual variability in E-field magnitude. Individualising electrode configuration and stimulator output can minimise lesion-induced variability but requires improved estimates of lesion conductivity. Individualised tDCS is critical to overcome E-field variability in lesioned brains.

On Modelling Electrical Conductivity of the Cerebral White Matter

The conductivity, in general, of the brain tissues is a characteristic key of functional cerebral changes. White matter electric conductivity appears to be extremely anisotropic, so a tensor (matrix) is needed to describe it. Traditional methods of imaging brain electrical properties fail to capture it and required the interpolation of the diffusion matrix. The electrochemical model is suitable for analysis, while, on the other hand, the volume fraction model is suitable for studying the effect of white matter structural changes in relation to electrical conductivity. It adopts a relevant algorithm, based upon a linear conductivity-to-diffusivity relationship and a volume constraint, respectively. It incorporates the effects of the partial volume of the cerebrospinal fluid and the structure of the neuronal fiber crossing, which was not achieved by the existing algorithms, accomplishing a more accurate estimation of the anisotropic conductivity of the white matter. Diffusion matrix imaging is a powerful noninvasive method for characterizing neuronal tissue in the human brain. The ultimate goal is to study and draw appropriate conclusions, regarding the molecule diffusion in the brain under normal physiological conditions and the changes that occur in development, diseases, and aging. The ability to measure the electrical conductivity of brain tissues in a noninvasive way also helps in characterizing endogenous currents by measuring the associated electromagnetic fields.

Magnetic Resonance Electrical Impedance Tomography

Magnetic Resonance Electrical Impedance Tomography (MREIT) is a high-resolution bioimpedance imaging technique that has developed over a period beginning in the early 1990s to measure low-frequency (<1 kHz) tissue electrical properties. Low-frequency electrical properties are particularly important because they provide valuable information on cell structures and ionic composition of tissues, which may be very useful for diagnostic purposes. MREIT uses one component of the magnetic flux density data induced due to an exogenous-current administration, measured using an MRI machine, to reconstruct isotropic or anisotropic electrical property distributions. The MREIT technique typically requires two linearly independent current administrations to reconstruct conductivity uniquely. Since its invention, researchers have explored its potential for measuring electrical conductivity in regions such as the brain and muscle tissue. It has also been investigated in disease models, for example, cerebral ischemia and early tumor detection. In this chapter, we aim to provide a solid foundation of the different MREIT image reconstruction algorithms, including both isotropic and anisotropic conductivity reconstruction approaches. We will also explore the newly developed diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT) method, a practical method for anisotropic tissue property imaging, at the end of the chapter.

Magnetic-resonance-based measurement of electromagnetic fields and conductivity in vivo using single current administration-A machine learning approach

Diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT) is a newly developed technique that combines MR-based measurements of magnetic flux density with diffusion tensor MRI (DT-MRI) data to reconstruct electrical conductivity tensor distributions. DT-MREIT techniques normally require injection of two independent current patterns for unique reconstruction of conductivity characteristics. In this paper, we demonstrate an algorithm that can be used to reconstruct the position dependent scale factor relating conductivity and diffusion tensors, using flux density data measured from only one current injection. We demonstrate how these images can also be used to reconstruct electric field and current density distributions. Reconstructions were performed using a mimetic algorithm and simulations of magnetic flux density from complementary electrode montages, combined with a small-scale machine learning approach. In a biological tissue phantom, we found that the method reduced relative errors between single-current and two-current DT-MREIT results to around 10%. For in vivo human experimental data the error was about 15%. These results suggest that incorporation of machine learning may make it easier to recover electrical conductivity tensors and electric field images during neuromodulation therapy without the need for multiple current administrations.

Brain Waves: Emergence of Localized, Persistent, Weakly Evanescent Cortical Loops

An inhomogeneous anisotropic physical model of the brain cortex is presented that predicts the emergence of nonevanescent (weakly damped) wave-like modes propagating in the thin cortex layers transverse to both the mean neural fiber direction and the cortex spatial gradient. Although the amplitude of these modes stays below the typically observed axon spiking potential, the lifetime of these modes may significantly exceed the spiking potential inverse decay constant. Full-brain numerical simulations based on parameters extracted from diffusion and structural MRI confirm the existence and extended duration of these wave modes. Contrary to the commonly agreed paradigm that the neural fibers determine the pathways for signal propagation in the brain, the signal propagation because of the cortex wave modes in the highly folded areas will exhibit no apparent correlation with the fiber directions. Nonlinear coupling of those linear weakly evanescent wave modes then provides a universal mechanism for the emergence of synchronized brain wave field activity. The resonant and nonresonant terms of nonlinear coupling between multiple modes produce both synchronous spiking-like high-frequency wave activity as well as low-frequency wave rhythms. Numerical simulation of forced multiple-mode dynamics shows that, as forcing increases, there is a transition from damped to oscillatory regime that can then transition quickly to a nonoscillatory state when a critical excitation threshold is reached. The resonant nonlinear coupling results in the emergence of low-frequency rhythms with frequencies that are several orders of magnitude below the linear frequencies of modes taking part in the coupling. The localization and persistence of these weakly evanescent cortical wave modes have significant implications in particular for neuroimaging methods that detect electromagnetic physiological activity, such as EEG and magnetoencephalography, and for the understanding of brain activity in general, including mechanisms of memory.

Universal theory of brain waves: from linear loops to nonlinear synchronized spiking and collective brain rhythms

An inhomogeneous anisotropic physical model of the brain cortex is presented that predicts the emergence of non-evanescent (weakly damped) wave-like modes propagating in the thin cortex layers transverse to both the mean neural fiber direction and to the cortex spatial gradient. Although the amplitude of these modes stays below the typically observed axon spiking potential, the lifetime of these modes may significantly exceed the spiking potential inverse decay constant. Full brain numerical simulations based on parameters extracted from diffusion and structural MRI confirm the existence and extended duration of these wave modes. Contrary to the standard paradigm that the neural fibers determine the pathways for signal propagation in the brain, the signal propagation due to the cortex wave modes in highly folded areas will exhibit no apparent correlation with the fiber directions. The results are consistent with numerous recent experimental animal and human brain studies demonstrating the existence of electrostatic field activity in the form of traveling waves (including studies where neuronal connections were severed) and with wave loop induced peaks observed in EEG spectra. In addition, we demonstrate that the resonant and non-resonant terms of the nonlinear coupling between multiple modes produce both synchronous spiking-like high frequency wave activity as well as low frequency wave rhythms as a result of their unique dispersion properties. Numerical simulation of forced multiple mode dynamics shows that as forcing increases there is a transition from damped to oscillatory regime that subsequently decays away as over-excitation is reached. The resonant nonlinear coupling results in the emergence of low frequency rhythms with frequencies that are several orders of magnitude below the linear frequencies of modes taking part in the coupling. The localization and persistence of these cortical wave modes, and this new mechanism for understanding the nature of spiking behavior, have significant implications in particular for neuroimaging methods that detect electromagnetic physiological activity, such as EEG and MEG, and in general for the understanding of brain activity, including mechanisms of memory.

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.

Solenoidal Micromagnetic Stimulation Enables Activation of Axons With Specific Orientation

Electrical stimulation of the central and peripheral nervous systems - such as deep brain stimulation, spinal cord stimulation, and epidural cortical stimulation are common therapeutic options increasingly used to treat a large variety of neurological and psychiatric conditions. Despite their remarkable success, there are limitations which if overcome, could enhance outcomes and potentially reduce common side-effects. Micromagnetic stimulation (μMS) was introduced to address some of these limitations. One of the most remarkable properties is that μMS is theoretically capable of activating neurons with specific axonal orientations. Here, we used computational electromagnetic models of the μMS coils adjacent to neuronal tissue combined with axon cable models to investigate μMS orientation-specific properties. We found a 20-fold reduction in the stimulation threshold of the preferred axonal orientation compared to the orthogonal direction. We also studied the directional specificity of μMS coils by recording the responses evoked in the inferior colliculus of rodents when a pulsed magnetic stimulus was applied to the surface of the dorsal cochlear nucleus. The results confirmed that the neuronal responses were highly sensitive to changes in the μMS coil orientation. Accordingly, our results suggest that μMS has the potential of stimulating target nuclei in the brain without affecting the surrounding white matter tracts.

Low-Frequency Conductivity Tensor Imaging of the Human Head In Vivo Using DT-MREIT: First Study

We present the first in vivo images of anisotropic conductivity distribution in the human head, measured at a frequency of approximately 10 Hz. We used magnetic resonance electrical impedance tomography techniques to encode phase changes caused by current flow within the head via two independent electrode pairs. These results were then combined with diffusion tensor imaging data to reconstruct full anisotropic conductivity distributions in 5-mm-thick slices of the brains of two participants. Conductivity values recovered in this paper were broadly consistent with literature values. We anticipate that this technique will be of use in many areas of neuroscience, most importantly in functional imaging via inverse electroencephalogram. Future studies will involve pulse sequence acceleration to maximize brain coverage and resolution.

Extracellular Total Electrolyte Concentration Imaging for Electrical Brain Stimulation (EBS)

Techniques for electrical brain stimulation (EBS), in which weak electrical stimulation is applied to the brain, have been extensively studied in various therapeutic brain functional applications. The extracellular fluid in the brain is a complex electrolyte that is composed of different types of ions, such as sodium (Na+), potassium (K+), and calcium (Ca+). Abnormal levels of electrolytes can cause a variety of pathological disorders. In this paper, we present a novel technique to visualize the total electrolyte concentration in the extracellular compartment of biological tissues. The electrical conductivity of biological tissues can be expressed as a product of the concentration and the mobility of the ions. Magnetic resonance electrical impedance tomography (MREIT) investigates the electrical properties in a region of interest (ROI) at low frequencies (below 1 kHz) by injecting currents into the brain region. Combining with diffusion tensor MRI (DT-MRI), we analyze the relation between the concentration of ions and the electrical properties extracted from the magnetic flux density measurements using the MREIT technique. By measuring the magnetic flux density induced by EBS, we propose a fast non-iterative technique to visualize the total extracellular electrolyte concentration (EEC), which is a fundamental component of the conductivity. The proposed technique directly recovers the total EEC distribution associated with the water transport mobility tensor.

Patient-specific computational modeling of cortical spreading depression via diffusion tensor imaging

Cortical spreading depression, a depolarization wave originating in the visual cortex and traveling towards the frontal lobe, is commonly accepted as a correlate of migraine visual aura. As of today, little is known about the mechanisms that can trigger or stop such phenomenon. However, the complex and highly individual characteristics of the brain cortex suggest that the geometry might have a significant impact in supporting or contrasting the propagation of cortical spreading depression. Accurate patient-specific computational models are fundamental to cope with the high variability in cortical geometries among individuals, but also with the conduction anisotropy induced in a given cortex by the complex neuronal organisation in the grey matter. In this paper, we integrate a distributed model for extracellular potassium concentration with patient-specific diffusivity tensors derived locally from diffusion tensor imaging data.

The Impact of Anisotropy on the Accuracy of Conductivity Imaging: A Quantitative Validation Study

We present a quantitative validation study to assess the accuracy of low-frequency conductivity imaging methods, based on a testing current measured using Current Density Imaging (CDI). We tested the proposed procedure to study the influence of tissue anisotropy on the accuracy of conductivity reconstruction methods, using a finite element model of anisotropic brain tissue. Simulations were carried out for three different levels of tissue anisotropy to compare the results obtained by our recently developed anisotropic conductivity method with those obtained by our well-established conductivity method that assumes isotropic conductivity. The validation results clearly show that the conductivity imaging method which takes into account tissue anisotropy yields significantly superior accuracy.

Anisotropic Conductivity Tensor Imaging of In Vivo Canine Brain Using DT-MREIT

We present in vivo images of anisotropic electrical conductivity tensor distributions inside canine brains using diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT). The conductivity tensor is represented as a product of an ion mobility tensor and a scale factor of ion concentrations. Incorporating directional mobility information from water diffusion tensors, we developed a stable process to reconstruct anisotropic conductivity tensor images from measured magnetic flux density data using an MRI scanner. Devising a new image reconstruction algorithm, we reconstructed anisotropic conductivity tensor images of two canine brains with a pixel size of 1.25 mm. Though the reconstructed conductivity values matched well in general with those measured by using invasive probing methods, there were some discrepancies as well. The degree of white matter anisotropy was 2 to 4.5, which is smaller than previous findings of 5 to 10. The reconstructed conductivity value of the cerebrospinal fluid was about 1.3 S/m, which is smaller than previous measurements of about 1.8 S/m. Future studies of in vivo imaging experiments with disease models should follow this initial trial to validate clinical significance of DT-MREIT as a new diagnostic imaging modality. Applications in modeling and simulation studies of bioelectromagnetic phenomena including source imaging and electrical stimulation are also promising.

Comparison of electric field strength and spatial distribution of electroconvulsive therapy and magnetic seizure therapy in a realistic human head model

BACKGROUND

This study examines the strength and spatial distribution of the electric field induced in the brain by electroconvulsive therapy (ECT) and magnetic seizure therapy (MST).

METHODS

The electric field induced by standard (bilateral, right unilateral, and bifrontal) and experimental (focal electrically administered seizure therapy and frontomedial) ECT electrode configurations as well as a circular MST coil configuration was simulated in an anatomically realistic finite element model of the human head. Maps of the electric field strength relative to an estimated neural activation threshold were used to evaluate the stimulation strength and focality in specific brain regions of interest for these ECT and MST paradigms and various stimulus current amplitudes.

RESULTS

The standard ECT configurations and current amplitude of 800-900mA produced the strongest overall stimulation with median of 1.8-2.9 times neural activation threshold and more than 94% of the brain volume stimulated at suprathreshold level. All standard ECT electrode placements exposed the hippocampi to suprathreshold electric field, although there were differences across modalities with bilateral and right unilateral producing respectively the strongest and weakest hippocampal stimulation. MST stimulation is up to 9 times weaker compared to conventional ECT, resulting in direct activation of only 21% of the brain. Reducing the stimulus current amplitude can make ECT as focal as MST.

CONCLUSIONS

The relative differences in electric field strength may be a contributing factor for the cognitive sparing observed with right unilateral compared to bilateral ECT, and MST compared to right unilateral ECT. These simulations could help understand the mechanisms of seizure therapies and develop interventions with superior risk/benefit ratio.

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.

Technical aspects of neurostimulation: Focus on equipment, electric field modeling, and stimulation protocols

Neuromodulation is a field of science, medicine, and bioengineering that encompasses implantable and non-implantable technologies for the purpose of improving quality of life and functioning of humans. Brain neuromodulation involves different neurostimulation techniques: transcranial magnetic stimulation (TMS), transcranial direct current stimulation (tDCS), vagus nerve stimulation (VNS), and deep brain stimulation (DBS), which are being used both to study their effects on cognitive brain functions and to treat neuropsychiatric disorders. The mechanisms of action of neurostimulation remain incompletely understood. Insight into the technical basis of neurostimulation might be a first step towards a more profound understanding of these mechanisms, which might lead to improved clinical outcome and therapeutic potential. This review provides an overview of the technical basis of neurostimulation focusing on the equipment, the present understanding of induced electric fields, and the stimulation protocols. The review is written from a technical perspective aimed at supporting the use of neurostimulation in clinical practice.

Experimental implementation of a new method of imaging anisotropic electric conductivities

This paper presents the first experiment of imaging anisotropic impedance using a novel technique called Diffusion Tensor Current Density Impedance Imaging (DTCD-II). A biological anisotropic tissue phantom was constructed and an experimental implementation of the new method was performed. The results show that DT-CD-II is an effective way of non-invasively measuring anisotropic conductivity in biological media. The cross-property factor between the diffusion tensor and the conductivity tensor has been carefully determined from the experimental data, and shown to be spatially inhomogeneous. The results show that this novel imaging approach has the potential to provide valuable new information on tissue properties.

Current Density Imaging During Transcranial Direct Current Stimulation Using DT-MRI and MREIT: Algorithm Development and Numerical Simulations

OBJECTIVE

Transcranial direct current stimulation (tDCS) is a neuromodulatory technique for neuropsychiatric diseases and neurological disorders. In the tDCS treatment, dc current is injected into the head through a pair of electrodes attached on the scalp over a target region. A current density imaging method is needed to quantitatively visualize the internal current density distribution during the tDCS treatment.

METHODS

We developed a novel current density image reconstruction algorithm using 1) a subject specific segmented 3-D head model, 2) diffusion tensor data, and 3) magnetic flux density data induced by the tDCS current. We acquired T1 weighted and diffusion tensor images of the head using the MRI scanner before the treatment. During the treatment, we can measure the induced magnetic flux density data using a magnetic resonance electrical impedance tomography (MREIT) pulse sequence. In this paper, the magnetic flux density data were numerically generated.

RESULTS

Numerical simulation results show that the proposed method successfully recovers the current density distribution including the effects of the anisotropic, as well as isotropic conductivity values of different tissues in the head.

CONCLUSION

The proposed current density imaging method using DT-MRI and MREIT can reliably recover cross-sectional images of the current density distribution during the tDCS treatment.

SIGNIFICANCE

Success of the tDCS treatment depends on a precise determination of the induced current density distribution within different anatomical structures of the brain. Quantitative visualization of the current density distribution in the brain will play an important role in understanding the effects of the electrical stimulation.

Assessment of electric field distribution in anisotropic cortical and subcortical regions under the influence of tDCS

The focus of this study is to estimate the contribution of regional anisotropic conductivity on the spatial distribution of an induced electric field across gray matter (GM), white matter (WM), and subcortical regions under transcranial direct current stimulation (tDCS). The assessment was conducted using a passive high-resolution finite element head model with inhomogeneous and variable anisotropic conductivities derived from the diffusion tensor data. Electric field distribution was evaluated across different cortical as well as subcortical regions under four bicephalic electrode configurations. Results indicate that regional tissue heterogeneity and anisotropy cause the pattern of induced fields to vary in orientation and strength when compared to the isotropic scenario. Different electrode montages resulted in distinct distribution patterns with noticeable variations in field strengths. The effect of anisotropy is highly montage dependent and directional conductivity has a more profound effect in defining the strength of the induced field. The inclusion of anisotropy in the GM and subcortical regions has a significant effect on the strength and spatial distribution of the induced electric field. Under the (C3-Fp2) montage, the inclusion of GM and subcortical anisotropy increased the average percentage difference in the electric field strength of brain from 5% to 34% (WM anisotropy only). In terms of patterns distribution, the topographic errors increased from 9.9% to 40% (WM anisotropy only) across the brain.

Numerical investigation of white matter anisotropic conductivity in defining current distribution under tDCS

The study investigates the impact of white matter directional conductivity on brain current density under the influence of Transcranial direct current stimulation (tDCS). The study employed different conductivity estimation algorithms to represent conductivity distribution in the white matter (WM) of the brain. Two procedures, one mathematically driven and the second one based on the Diffusion tensor imaging (DTI) are considered. The finite element method has been applied to estimate the current density distribution across the head models. Strengths and weaknesses of these algorithms have been compared by analyzing the variation in current density magnitude and distribution patterns with respect to the isotropic case. Results indicate that anisotropy has a profound influence on the strength of current density (up to ≈50% in WM) as it causes current flow to deviate from its isotropically defined path along with diffused distribution patterns across the gray and WM. The extent of this variation is highly correlated with the degree of the anisotropy of the regions. Regions of high anisotropy and models of fixed anisotropic ratio displayed higher and wider degree of variations across the structures (topographic variations up to 48%), respectively. In contrast, models, which are correlated with the magnitude of local diffusion tensor behaved in a less exacerbated manner (≈10% topographic changes in WM). Anisotropy increased the current density strength across the cortical gyri under and between the stimulating electrodes, whereas a significant drop has been recorded in deeper regions of the GM (max % difference ≈±10). In addition, it has been observed that Equivalent isotropic trace algorithm is more suitable to incorporate directional conductivity under tDCS paradigm, than other considered approaches, as this algorithm is computationally less expensive and insensitive to the limiting factor imposed by the volume constraint.

Influence of anisotropic conductivity in the skull and white matter on transcranial direct current stimulation via an anatomically realistic finite element head model

To establish safe and efficient transcranial direct current stimulation (tDCS), it is of particular importance to understand the electrical effects of tDCS in the brain. Since the current density (CD) and electric field (EF) in the brain generated by tDCS depend on various factors including complex head geometries and electrical tissue properties, in this work, we investigated the influence of anisotropic conductivity in the skull and white matter (WM) on tDCS via a 3D anatomically realistic finite element head model. We systematically incorporated various anisotropic conductivity ratios into the skull and WM. The effects of anisotropic tissue conductivity on the CD and EF were subsequently assessed through comparisons to the conventional isotropic solutions. Our results show that the anisotropic skull conductivity significantly affects the CD and EF distribution: there is a significant reduction in the ratio of the target versus non-target total CD and EF on the order of 12-14%. In contrast, the WM anisotropy does not significantly influence the CD and EF on the targeted cortical surface, only on the order of 1-3%. However, the WM anisotropy highly alters the spatial distribution of both the CD and EF inside the brain. This study shows that it is critical to incorporate anisotropic conductivities in planning of tDCS for improved efficacy and safety.

EEG source imaging in epilepsy--practicalities and pitfalls

EEG source imaging (ESI) is a model-based imaging technique that integrates temporal and spatial components of EEG to identify the generating source of electrical potentials recorded on the scalp. Recent advances in computer technologies have made the analysis of ESI data less time-consuming, and have rekindled interest in this technique as a clinical diagnostic tool. On the basis of the available body of evidence, ESI seems to be a promising tool for epilepsy evaluation; however, the precise clinical value of ESI in presurgical evaluation of epilepsy and in localization of eloquent cortex remains to be investigated. In this Review, we describe two fundamental issues in ESI; namely, the forward and inverse problems, and their solutions. The clinical application of ESI in surgical planning for patients with medically refractory focal epilepsy, and its use in source reconstruction together with invasive recordings, is also discussed. As ESI can be used to map evoked responses, we discuss the clinical utility of this technique in cortical mapping-an essential process when planning resective surgery for brain regions that are in close proximity to eloquent cortex.

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.

Regional electric field induced by electroconvulsive therapy in a realistic finite element head model: influence of white matter anisotropic conductivity

We present the first computational study investigating the electric field (E-field) strength generated by various electroconvulsive therapy (ECT) electrode configurations in specific brain regions of interest (ROIs) that have putative roles in the therapeutic action and/or adverse side effects of ECT. This study also characterizes the impact of the white matter (WM) conductivity anisotropy on the E-field distribution. A finite element head model incorporating tissue heterogeneity and WM anisotropic conductivity was constructed based on structural magnetic resonance imaging (MRI) and diffusion tensor MRI data. We computed the spatial E-field distributions generated by three standard ECT electrode placements including bilateral (BL), bifrontal (BF), and right unilateral (RUL) and an investigational electrode configuration for focal electrically administered seizure therapy (FEAST). The key results are that (1) the median E-field strength over the whole brain is 3.9, 1.5, 2.3, and 2.6 V/cm for the BL, BF, RUL, and FEAST electrode configurations, respectively, which coupled with the broad spread of the BL E-field suggests a biophysical basis for observations of superior efficacy of BL ECT compared to BF and RUL ECT; (2) in the hippocampi, BL ECT produces a median E-field of 4.8 V/cm that is 1.5-2.8 times stronger than that for the other electrode configurations, consistent with the more pronounced amnestic effects of BL ECT; and (3) neglecting the WM conductivity anisotropy results in E-field strength error up to 18% overall and up to 39% in specific ROIs, motivating the inclusion of the WM conductivity anisotropy in accurate head models. This computational study demonstrates how the realistic finite element head model incorporating tissue conductivity anisotropy provides quantitative insight into the biophysics of ECT, which may shed light on the differential clinical outcomes seen with various forms of ECT, and may guide the development of novel stimulation paradigms with improved risk/benefit ratio.

Optimum b value for resolving crossing fibers: a study with standard clinical b value using 1.5-T MR

INTRODUCTION

We sought to investigate the optimum b value for resolving crossing fiber using high-angular resolution diffusion imaging (HARDI)-based multi-tensor tractography. The study tested the standard b values that are commonly used in the routine clinical setting.

METHODS

Ten normal volunteers (five men and five women) with a mean age of 26.3 years (range, 22-32 years) were scanned using a 1.5-T clinical magnetic resonance unit. Single-shot echo-planar imaging was used for diffusion-weighted imaging with a diffusion-sensitizing gradient in 32 orientations. The b values of 700, 1,400, 2,100, and 2,800 s/m(2) were used. Data postprocessing was performed using multi-tensor methods. The depiction of the optic nerves, optic tracts, and decussation of superior cerebellar peduncles were assessed.

RESULTS

The depictions of the nerve fibers were independent of the b values tested.

CONCLUSION

The depiction of crossing fibers by HARDI-based multi-tensor tractography is not substantially influenced by b values ranging from 700 to 2,800 s/m(2). Thus, the optimum b value within this range may be the lowest one considering the higher signal to noise ratio.

Influence of white matter anisotropy on EEG source localization: an experimental study

The goal of this study was to experimentally investigate the influence of the white matter (WM) anisotropy on the EEG source localization. We acquired both visual evoked potential (VEP) and functional MRI (fMRI) data from three human subjects presented with identical visual stimuli. A finite element method (FEM) head model with or without incorporating the WM anisotropy was built to solve the EEG forward problems, and single-dipole source localization was subsequently performed based on the N75 VEP component. The localized dipole positions were quantitatively compared with the locations of the fMRI activations within the primary visual cortex (V1). The results show that the distance between the localized N75 dipole position and the fMRI V1 activation center was slightly smaller when using an anisotropic model than when using an isotropic model. This experimental study suggests that compared to the conventional isotropic model, the anisotropic models incorporating realistic WM anisotropic conductivity distributions do not significantly improve the accuracy of the EEG dipole localization within V1.

Reduced spatial focality of electrical field in tDCS with ring electrodes due to tissue anisotropy

For effective stimulation with tDCS, spatial focality of induced electrical field (EF) is one of the important factors to be considered. Recently, there have been some studies to improve the spatial focality via different types of electrodes and their new configurations: some improvements using ring electrodes were reported over the conventional pad electrodes. However, most of these studies assumed isotropic conductivities in the head. In this work, we have investigated the effect of tissue anisotropy on the spatial focality of tDCS with the 4+1 ring electrode configuration via a 3-D high-resolution finite element (FE) head model with anisotropic conductivities in the skull and white matter. By examining the profiles of the induced EF from the head models with isotropic and anisotropic conductivities respectively, we found that the spatial focality of the induced EF significantly drops and get diffused due to tissue anisotropy. Our analysis suggests that it is critical to incorporate tissue anisotropy in the stimulation of the brain via tDCS.

Influence of white matter anisotropic conductivity on EEG source localization: comparison to fMRI in human primary visual cortex

OBJECTIVE

The goal of this study was to experimentally investigate the influence of the anisotropy of white matter (WM) conductivity on EEG source localization.

METHODS

Visual evoked potentials (VEP) and fMRI data were recorded from three human subjects presented with identical visual stimuli. A finite element method was used to solve the EEG forward problems based on both anisotropic and isotropic head models, and single-dipole source localization was subsequently performed to localize the source underlying the N75 VEP component.

RESULTS

The averaged distances of the localized N75 dipole locations in V1 between the isotropic and anisotropic head models ranged from 0 to 6.22+/-2.83mm. The distances between the localized dipole positions and the centers of the fMRI V1 activations were slightly smaller when using an anisotropic model (7.49+/-1.35-15.70+/-8.60mm) than when using an isotropic model (7.65+/-1.30-15.31+/-9.18mm).

CONCLUSIONS

Anisotropic models incorporating realistic WM anisotropic conductivity distributions do not substantially improve the accuracy of EEG dipole localization in the primary visual cortex using experimental data obtained using visual stimulation.

SIGNIFICANCE

The present study represents the first attempt using a human experimental approach to assess the effects of WM anisotropy on EEG source analysis.

EEG source analysis of epileptiform activity using a 1 mm anisotropic hexahedra finite element head model

The major goal of the evaluation in presurgical epilepsy diagnosis for medically intractable patients is the precise reconstruction of the epileptogenic foci, preferably with non-invasive methods. This paper evaluates whether surface electroencephalography (EEG) source analysis based on a 1 mm anisotropic finite element (FE) head model can provide additional guidance for presurgical epilepsy diagnosis and whether it is practically feasible in daily routine. A 1 mm hexahedra FE volume conductor model of the patient's head with special focus on accurately modeling the compartments skull, cerebrospinal fluid (CSF) and the anisotropic conducting brain tissues was constructed using non-linearly co-registered T1-, T2- and diffusion-tensor-magnetic resonance imaging data. The electrodes of intra-cranial EEG (iEEG) measurements were extracted from a co-registered computed tomography image. Goal function scan (GFS), minimum norm least squares (MNLS), standardized low resolution electromagnetic tomography (sLORETA) and spatio-temporal current dipole modeling inverse methods were then applied to the peak of the averaged ictal discharges EEG data. MNLS and sLORETA pointed to a single center of activity. Moving and rotating single dipole fits resulted in an explained variance of more than 97%. The non-invasive EEG source analysis methods localized at the border of the lesion and at the border of the iEEG electrodes which mainly received ictal discharges. Source orientation was towards the epileptogenic tissue. For the reconstructed superficial source, brain conductivity anisotropy and the lesion conductivity had only a minor influence, whereas a correct modeling of the highly conducting CSF compartment and the anisotropic skull was found to be important. The proposed FE forward modeling approach strongly simplifies meshing and reduces run-time (37 ms for one forward computation in the model with 3.1 million unknowns), corroborating the practical feasibility of the approach.

A new method to derive white matter conductivity from diffusion tensor MRI

We propose a new algorithm to derive the anisotropic conductivity of the cerebral white matter (WM) from the diffusion tensor MRI (DT-MRI) data. The transportation processes for both water molecules and electrical charges are described through a common multicompartment model that consists of axons, glia, or the cerebrospinal fluid (CSF). The volume fraction (VF) of each compartment varies from voxel to voxel and is estimated from the measured diffusion tensor. The conductivity tensor at each voxel is then computed from the estimated VF values and the decomposed eigenvectors of the diffusion tensor. The proposed VF algorithm was applied to the DT-MRI data acquired from two healthy human subjects. The extracted anisotropic conductivity distribution was compared with those obtained by using two existing algorithms, which were based upon a linear conductivity-to-diffusivity relationship and a volume constraint, respectively. The present results suggest that the VF algorithm is capable of incorporating the partial volume effects of the CSF and the intravoxel fiber crossing structure, both of which are not addressed altogether by existing algorithms. Therefore, it holds potential to provide a more accurate estimate of the WM anisotropic conductivity, and may have important applications to neuroscience research or clinical applications in neurology and neurophysiology.

Temporal lobe epilepsy: anatomical and effective connectivity

While temporal lobe epilepsy (TLE) has been treatable with anti-seizure medications over the past century, there still remain a large percentage of patients whose seizures remain untreatable pharmacologically. To better understand and treat TLE, our laboratory uses several in vivo analytical techniques to estimate connectivity in epilepsy. This paper reviews two different connectivity-based approaches with an emphasis on application to the study of epilepsy. First, we present effective connectivity techniques, such as Granger causality, that has been used to assess the dynamic directional relationships among brain regions. These measures are used to better understand how seizure activity initiates, propagates, and terminates. Second, structural techniques, such as magnetic resonance imaging, can be used to assess changes in the underlying neural structures that result in seizure. This paper also includes in vivo epilepsy-centered examples of both effective and anatomical connectivity analysis. These analyses are performed on data collected in vivo from a spontaneously seizing animal model of TLE. Future work in vivo on epilepsy will no doubt benefit from a fusion of these different techniques. We conclude by discussing the interesting possibilities, implications, and challenges that a unified analysis would present.

In vivo measurement of cortical impedance spectrum in monkeys: implications for signal propagation

To combine insights obtained from electric field potentials (LFPs) and neuronal spiking activity (MUA) we need a better understanding of the relative spatial summation of these indices of neuronal activity. Compared to MUA, the LFP has greater spatial coherence, resulting in lower spatial specificity and lower stimulus selectivity. A differential propagation of low- and high-frequency electric signals supposedly underlies this phenomenon, which could result from cortical tissue specifically attenuating higher frequencies, i.e., from a frequency-dependent impedance spectrum. Here we directly measure the cortical impedance spectrum in vivo in monkey primary visual cortex. Our results show that impedance is independent of frequency, is homogeneous and tangentially isotropic within gray matter, and can be theoretically predicted assuming a pure-resistive conductor. We propose that the spatial summation of LFP and MUA is determined by the size of these signals' generators and the nature of neural events underlying them, rather than by biophysical properties of gray matter.

A model for diffusion in white matter in the brain

Diffusion of molecules in brain and other tissues is important in a wide range of biological processes and measurements ranging from the delivery of drugs to diffusion-weighted magnetic resonance imaging. Diffusion tensor imaging is a powerful noninvasive method to characterize neuronal tissue in the human brain in vivo. As a first step toward understanding the relationship between the measured macroscopic apparent diffusion tensor and underlying microscopic compartmental geometry and physical properties, we treat a white matter fascicle as an array of identical thick-walled cylindrical tubes arranged periodically in a regular lattice and immersed in an outer medium. Both square and hexagonal arrays are considered. The diffusing molecules may have different diffusion coefficients and concentrations (or densities) in different domains, namely within the tubes' inner core, membrane, myelin sheath, and within the outer medium. Analytical results are used to explore the effects of a large range of microstructural and compositional parameters on the apparent diffusion tensor and the degree of diffusion anisotropy, allowing the characterization of diffusion in normal physiological conditions as well as changes occurring in development, disease, and aging. Implications for diffusion tensor imaging and for the possible in situ estimation of microstructural parameters from diffusion-weighted MR data are discussed in the context of this modeling framework.

Mapping human brain function with MEG and EEG: methods and validation

We survey the field of magnetoencephalography (MEG) and electroencephalography (EEG) source estimation. These modalities offer the potential for functional brain mapping with temporal resolution in the millisecond range. However, the limited number of spatial measurements and the ill-posedness of the inverse problem present significant limits to our ability to produce accurate spatial maps from these data without imposing major restrictions on the form of the inverse solution. Here we describe approaches to solving the forward problem of computing the mapping from putative inverse solutions into the data space. We then describe the inverse problem in terms of low dimensional solutions, based on the equivalent current dipole (ECD), and high dimensional solutions, in which images of neural activation are constrained to the cerebral cortex. We also address the issue of objective assessment of the relative performance of inverse procedures by the free-response receiver operating characteristic (FROC) curve. We conclude with a discussion of methods for assessing statistical significance of experimental results through use of the bootstrap for determining confidence regions in dipole-fitting methods, and random field (RF) and permutation methods for detecting significant activation in cortically constrained imaging studies.

Multitensor approach for analysis and tracking of complex fiber configurations

A multidiffusion-tensor model (MDT) is presented containing two anisotropic and one isotropic diffusion tensors. This approach has the ability to detect areas of fiber crossings and resolve the direction of crossing fibers. The mean diffusivity and the ratio of the tensor compartments were merged to one independent parameter by fitting MDT to the diffusion-weighted intensities of a two-point data acquisition scheme. By an F-test between the errors of the standard single diffusion tensor and the more complex MDT, fiber crossings were detected and the more accurate model was chosen voxel by voxel. The performance of crossing detection was compared with the spherical harmonics approach in simulations as well as in vivo. Similar results were found in both methods. The MDT model, however, did not only detect crossings but also yielded the single fiber directions. The FACT algorithm and a probabilistic connectivity algorithm were extended to support the MDT model. For example, a mean angular error smaller than 10 degrees was found for the MDT model in a simulated fiber crossing with an SNR of 80. By tracking the corticospinal tract the MDT-based tracks reached a significantly greater area of the gyrus precentralis.

Reduction of eddy-current-induced distortion in diffusion MRI using a twice-refocused spin echo

Image distortion due to field gradient eddy currents can create image artifacts in diffusion-weighted MR images. These images, acquired by measuring the attenuation of NMR signal due to directionally dependent diffusion, have recently been shown to be useful in the diagnosis and assessment of acute stroke and in mapping of tissue structure. This work presents an improvement on the spin-echo (SE) diffusion sequence that displays less distortion and consequently improves image quality. Adding a second refocusing pulse provides better image quality with less distortion at no cost in scanning efficiency or effectiveness, and allows more flexible diffusion gradient timing. By adjusting the timing of the diffusion gradients, eddy currents with a single exponential decay constant can be nulled, and eddy currents with similar decay constants can be greatly reduced. This new sequence is demonstrated in phantom measurements and in diffusion anisotropy images of normal human brain.

Microwave dielectric measurements and tissue characteristics of the human brain: potential in localizing intracranial tissues

This study describes the measurements of dielectric properties in the microwave range to differentiate various human central nervous structures. Using a vector network analyser transmission and reflection coefficients were measured from 500 MHz to 18 GHz in four human formalin fixed human brains. The positions of the electrodes were marked, and the tissue was histologically stained to visualize the myelo- and the cytoarchitecture as well as the nerve fibre orientation at the electrodes. The profiles of the transmission coefficients showed a characteristic minimum peak. In order to describe this peak, a mathematical function was fitted. Parameters derived from digital image processing were used to characterize the myelo- and cytoarchitecure of the tissue at the electrodes. A multiple regression model, with the frequency at the transmission peak minimum as a dependent variable and two tissue characteristics at the two electrodes as independent variables, showed a multiple regression coefficient of 0.765. A neural network model was able to estimate the frequency at the transmission peak minimum from the tissue characteristics at the electrode. The measurements of dielectric properties are well suited to differentiate distinct intracerebral structures. The method could be used for online monitoring of the needle's position during a stereotactic intervention in neurosurgery.

Conductivity tensor mapping of the human brain using diffusion tensor MRI

Knowledge of the electrical conductivity properties of excitable tissues is essential for relating the electromagnetic fields generated by the tissue to the underlying electrophysiological currents. Efforts to characterize these endogenous currents from measurements of the associated electromagnetic fields would significantly benefit from the ability to measure the electrical conductivity properties of the tissue noninvasively. Here, using an effective medium approach, we show how the electrical conductivity tensor of tissue can be quantitatively inferred from the water self-diffusion tensor as measured by diffusion tensor magnetic resonance imaging. The effective medium model indicates a strong linear relationship between the conductivity and diffusion tensor eigenvalues (respectively, final sigma and d) in agreement with theoretical bounds and experimental measurements presented here (final sigma/d approximately 0.844 +/- 0.0545 S small middle dots/mm(3), r(2) = 0.945). The extension to other biological transport phenomena is also discussed.

Spatiotemporal mapping of brain activity by integration of multiple imaging modalities

Functional magnetic resonance imaging (fMRI) and positron emission tomography measure local changes in brain hemodynamics induced by cognitive or perceptual tasks. These measures have a uniformly high spatial resolution of millimeters or less, but poor temporal resolution (about 1s). Conversely, electroencephalography (EEG) and magnetoencephalography (MEG) measure instantaneously the current flows induced by synaptic activity, but the accurate localization of these current flows based on EEG and MEG data alone remains an unsolved problem. Recently, techniques have been developed that, in the context of brain anatomy visualized with structural MRI, use both hemodynamic and electromagnetic measures to arrive at estimates of brain activation with high spatial and temporal resolution. These methods range from simple juxtaposition to simultaneous integrated techniques. Their application has already led to advances in our understanding of the neural bases of perception, attention, memory and language. Further advances in multi-modality integration will require an improved understanding of the coupling between the physiological phenomena underlying the different signal modalities.

History and future directions of human brain mapping and functional neuroimaging

It has long been known that there is some degree of localisation of function in the human brain, as indicated by the effects of traumatic head injury. Work in the middle of the 20th century, notably the direct cortical stimulation of patients during neurosurgery, suggested that the degree and specificity of such localisation of function were far greater than had earlier been imagined. One problem with the data based on lesions and direct stimulation was that the work depended on the study of what were, by definition, damaged brains. During the second half of the 20th century, a collection of relatively non-invasive tools for assessing and localising human brain function in healthy volunteers has led to an explosion of research in what is often termed "Brain Mapping". The present article reviews some of the history associated with these tools, but emphasises the current state of development with speculation about the future.