Volume Conductor Model Research Articles

Influence of Modeling Errors on the Initial Estimate for Nonlinear Myocardial Activation Times Imaging Calculated With Fastest Route Algorithm.

Noninvasive reconstruction of cardiac electrical activity has a great potential to support clinical decision making, planning, and treatment. Recently, significant progress has been made in the estimation of the cardiac activation from body surface potential maps (BSPMs) using boundary element method (BEM) with the equivalent double layer (EDL) as a source model. In this formulation, noninvasive assessment of activation times results in a nonlinear optimization problem with an initial estimate calculated with the fastest route algorithm (FRA). Each FRA-simulated activation sequence is converted into the ECG. The best initialization is determined by the sequence providing the highest correlation between predicted and measured potentials. We quantitatively assess the effects of the forward modeling errors on the FRA-based initialization. We present three simulation setups to investigate the effects of volume conductor model simplifications, neglecting the cardiac anisotropy and geometrical errors on the localization of ectopic beats starting on the ventricular surface. For the analysis, 12-lead ECG and 99 electrodes BSPM system were used. The areas in the heart exposing the largest localization errors were volume conductor model and electrode configuration specific with an average error <10mm. The results show the robustness of the FRA-based initialization with respect to the considered modeling errors.

Using reciprocity for relating the simulation of transcranial current stimulation to the EEG forward problem

To explore the relationship between transcranial current stimulation (tCS) and the electroencephalography (EEG) forward problem, we investigate and compare accuracy and efficiency of a reciprocal and a direct EEG forward approach for dipolar primary current sources both based on the finite element method (FEM), namely the adjoint approach (AA) and the partial integration approach in conjunction with a transfer matrix concept (PI). By analyzing numerical results, comparing to analytically derived EEG forward potentials and estimating computational complexity in spherical shell models, AA turns out to be essentially identical to PI. It is then proven that AA and PI are also algebraically identical even for general head models. This relation offers a direct link between the EEG forward problem and tCS. We then demonstrate how the quasi-analytical EEG forward solutions in sphere models can be used to validate the numerical accuracies of FEM-based tCS simulation approaches. These approaches differ with respect to the ease with which they can be employed for realistic head modeling based on MRI-derived segmentations. We show that while the accuracy of the most easy to realize approach based on regular hexahedral elements is already quite high, it can be significantly improved if a geometry-adaptation of the elements is employed in conjunction with an isoparametric FEM approach. While the latter approach does not involve any additional difficulties for the user, it reaches the high accuracies of surface-segmentation based tetrahedral FEM, which is considerably more difficult to implement and topologically less flexible in practice. Finally, in a highly realistic head volume conductor model and when compared to the regular alternative, the geometry-adapted hexahedral FEM is shown to result in significant changes in tCS current flow orientation and magnitude up to 45° and a factor of 1.66, respectively.

IMPROVING THE DIAGNOSIS OF ACUTE MYOCARDIAL INFARCTION BY DERIVING EPICARDIAL POTENTIALS FROM THE BODY SURFACE POTENTIAL MAP USING INVERSE ELECTROCARDIOGRAPHY AND AN INDIVIDUALIZED TORSO MODEL

Epicardial potentials (EP) derived from the body surface potential map (BSPM) improve acute myocardial infarction (AMI) diagnosis. In this study, we compared EP derived from the 80-lead BSPM using a standard thoracic volume conductor model (TVCM) with those derived using a patient-specific torso model (PSTM) based on body mass index (BMI). Patients presenting to ED between August 2009 and August 2011 with acute ischaemic-type chest pain at rest were enrolled. At first medical contact, 12-lead ECG and BSPM were recorded. BMI for each patient was calculated. Cardiac troponin-T (cTnT) was sampled 12h after symptom onset. Patients were excluded from analysis if they had any electrocardiographic confounders to interpretation of the ST-segment. A cardiologist assessed the 12-lead ECG for STEMI by Minnesota criteria and BSPM. BSPM ST-elevation (STE) was ≥0.2mV in anterior, ≥0.1mV in lateral, inferior, RV or high right anterior and ≥0.05mV in posterior territories. To derive EP, the BSPM data were interpolated to yield values at 352-nodes of a Dalhousie torso. Using an inverse solution based on the boundary element method, EP at 98 cardiac nodes positioned within a standard TVCM were derived. The TVCM was then scaled to produce a PSTM, using a model developed from CT in 48 patients of varying BMI, and EP re-calculated. EP ≥0.3mV defined STE. A cardiologist blinded to both the 12-lead ECG and BSPM interpreted the EP map. AMI was defined as cTnT ≥0.1µg/L. Enrolled were 400 patients (age 62 ± 13 yrs; 57% male): 80 patients had exclusion criteria. Of the remaining 320 patients, BMI was 27.8 ± 5.6kg m-2. Of these, 180 (56%) had AMI. Overall, 132 had Minnesota STEMI on ECG (sensitivity 65%, sensitivity 89%) and 160 had BSPM STE (sensitivity 81%, specificity 90%). EP STE occurred in 165 patients using TVCM (sensitivity 88%, specificity 95%, p<0.001) and in 206 patients using PSTM (sensitivity 98%, specificity 79%, p<0.001). Of those with EP <0.3mV using TVCM and AMI (n=22), all had EP ≥0.3mV when an individualised PSTM was used. Among patients presenting with ischaemic-type chest pain at rest, EP derived from BSPM using a novel PSTM significantly improves sensitivity for AMI diagnosis.

Current use of imaging and electromagnetic source localization procedures in epilepsy surgery centers across Europe.

In 2014 the European Union-funded E-PILEPSY project was launched to improve awareness of, and accessibility to, epilepsy surgery across Europe. We aimed to investigate the current use of neuroimaging, electromagnetic source localization, and imaging postprocessing procedures in participating centers. A survey on the clinical use of imaging, electromagnetic source localization, and postprocessing methods in epilepsy surgery candidates was distributed among the 25 centers of the consortium. A descriptive analysis was performed, and results were compared to existing guidelines and recommendations. Response rate was 96%. Standard epilepsy magnetic resonance imaging (MRI) protocols are acquired at 3 Tesla by 15 centers and at 1.5 Tesla by 9 centers. Three centers perform 3T MRI only if indicated. Twenty-six different MRI sequences were reported. Six centers follow all guideline-recommended MRI sequences with the proposed slice orientation and slice thickness or voxel size. Additional sequences are used by 22 centers. MRI postprocessing methods are used in 16 centers. Interictal positron emission tomography (PET) is available in 22 centers; all using 18F-fluorodeoxyglucose (FDG). Seventeen centers perform PET postprocessing. Single-photon emission computed tomography (SPECT) is used by 19 centers, of which 15 perform postprocessing. Four centers perform neither PET nor SPECT in children. Seven centers apply magnetoencephalography (MEG) source localization, and nine apply electroencephalography (EEG) source localization. Fourteen combinations of inverse methods and volume conduction models are used. We report a large variation in the presurgical diagnostic workup among epilepsy surgery centers across Europe. This diversity underscores the need for high-quality systematic reviews, evidence-based recommendations, and harmonization of available diagnostic presurgical methods.

The New York Head—A precise standardized volume conductor model for EEG source localization and tES targeting

In source localization of electroencephalograpic (EEG) signals, as well as in targeted transcranial electric current stimulation (tES), a volume conductor model is required to describe the flow of electric currents in the head. Boundary element models (BEM) can be readily computed to represent major tissue compartments, but cannot encode detailed anatomical information within compartments. Finite element models (FEM) can capture more tissue types and intricate anatomical structures, but with the higher precision also comes the need for semi-automated segmentation, and a higher computational cost. In either case, adjusting to the individual human anatomy requires costly magnetic resonance imaging (MRI), and thus head modeling is often based on the anatomy of an ‘arbitrary’ individual (e.g. Colin27). Additionally, existing reference models for the human head often do not include the cerebro-spinal fluid (CSF), and their field of view excludes portions of the head and neck—two factors that demonstrably affect current-flow patterns. Here we present a highly detailed FEM, which we call ICBM-NY, or "New York Head". It is based on the ICBM152 anatomical template (a non-linear average of the MRI of 152 adult human brains) defined in MNI coordinates, for which we extended the field of view to the neck and performed a detailed segmentation of six tissue types (scalp, skull, CSF, gray matter, white matter, air cavities) at 0.5mm3 resolution. The model was solved for 231 electrode locations. To evaluate its performance, additional FEMs and BEMs were constructed for four individual subjects. Each of the four individual FEMs (regarded as the ‘ground truth’) is compared to its BEM counterpart, the ICBM-NY, a BEM of the ICBM anatomy, an ‘individualized’ BEM of the ICBM anatomy warped to the individual head surface, and FEMs of the other individuals. Performance is measured in terms of EEG source localization and tES targeting errors. Results show that the ICBM-NY outperforms FEMs of mismatched individual anatomies as well as the BEM of the ICBM anatomy according to both criteria. We therefore propose the New York Head as a new standard head model to be used in future EEG and tES studies whenever an individual MRI is not available. We release all model data online at neuralengr.com/nyhead/ to facilitate broad adoption.

Constructing a three-dimensional electrical model of a living cochlear implant user's cochlea.

Hearing performance varies greatly among users of cochlear implants. Current three-dimensional cochlear models that predict the electrical fields inside a stimulated cochlea and their effect on neural excitation are generally based on a generic human or guinea pig cochlear shape that does not take inter-user morphological variations into account. This precludes prediction of user-specific performance. The aim of this study is to develop a model of the implanted cochlea of a specific living human individual and to assess if the inclusion of morphological variations in cochlear models affects predicted outcomes significantly. Five three-dimensional electric volume conduction models of the implanted cochleae of individual living users were constructed from standard CT scan data. These models were embedded in head models that include monopolar return electrodes in accurate anatomic positions. Potential distributions and neural excitation patterns were predicted for each of the models. Modeled potential distributions and neural excitation profiles (threshold amplitudes, center frequencies, and bandwidths) are affected by user-specific cochlear morphology and electrode placement within the cochlea. This work suggests that the use of user-specific models is indicated when more detailed analysis is required than what is available from generic models. Copyright © 2015 John Wiley & Sons, Ltd.

Abstract 18237: Non-invasive Three Dimensional Imaging of Ventricular Arrhythmias: In-procedure Simultaneous Mapping of Ventricular Tachycardia and Premature Ventricular Complexes

Introduction: Noninvasive activation imaging and the identification of initiation sites or reentrant circuits are highly desirable for aiding catheter ablative treatment of ventricular arrhythmia. While approaches are being developed to image epicardial potential, Cardiac Electrical Sparse Imaging (CESI), a 3-dimensional noninvasive activation imaging technique offers insight into intramural activation. In this study, we report the first clinical study of the CESI technique with in-procedure simultaneous mapping of Ventricular Tachycardia (VT) and Premature Ventricular Complexes (PVCs). Methods: Body surface potential maps (BSPMs) were recorded using 170±9 electrodes in 4 patients (2 males, 2 females, age 53±5) with VT and/or PVC in the EP lab simultaneously with CARTO mapping and ablation. CT or MRI images were obtained for individualized volume conductor modeling. Activation sequences were estimated using CESI upon the 40 isolated PVC or VT beats induced by programmed stimulation or isoproterenol infusion. Imaging results were compared with CARTO map and ablation sites/outcomes. Results: Good concordance was observed between the imaged results and the EP study. A Correlation Coefficient of 0.76±0.04 and Relative Error of 0.22±0.05 were found between the imaged activation sequences and the Local Activation Time maps from CARTO. The imaged initiation sites well co-localized with the ablation outcomes with Localization Error of 8±1.3mm from the last ablation site and 3.3±1.7mm from the nearest ablation site. Conclusions: We demonstrate for the first time that the beat-to-beat 3D activation imaging technique CESI can be applied clinically with simultaneous mapping in the EP lab. The noninvasive imaging results are in good agreement with the EP study and catheter ablation outcome. The promising results suggest CESI warrants further investigation and has the potential to become a clinically useful technology guiding ablation procedures in patients.

Feasibility and Accuracy of Cardiac Magnetic Resonance Imaging–Based Whole‐Heart Inverse Potential Mapping of Sinus Rhythm and Idiopathic Ventricular Foci

BackgroundInverse potential mapping (IPM) noninvasively reconstructs cardiac surface potentials using body surface potentials. This requires a volume conductor model (VCM), usually constructed from computed tomography; however, computed tomography exposes the patient to harmful radiation and lacks information about tissue structure. Magnetic resonance imaging (MRI) is not associated with this limitation and might have advantages for mapping purposes. This feasibility study investigated a magnetic resonance imaging–based IPM approach. In addition, the impact of incorporating the lungs and their particular resistivity values was explored.Methods and ResultsThree volunteers and 8 patients with premature ventricular contractions scheduled for ablation underwent 65‐electrode body surface potential mapping. A VCM was created using magnetic resonance imaging. Cardiac surface potentials were estimated from body surface potentials and used to determine the origin of electrical activation. The IPM‐defined origin of sinus rhythm corresponded well with the anatomic position of the sinus node, as described in the literature. In patients, the IPM‐derived premature ventricular contraction focus was 3‐dimensionally located within 8.3±2.7 mm of the invasively determined focus using electroanatomic mapping. The impact of lungs on the IPM was investigated using homogeneous and inhomogeneous VCMs. The inhomogeneous VCM, incorporating lung‐specific conductivity, provided more accurate results compared with the homogeneous VCM (8.3±2.7 and 10.3±3.1 mm, respectively; P=0.043). The interobserver agreement was high for homogeneous (intraclass correlation coefficient 0.862, P=0.003) and inhomogeneous (intraclass correlation coefficient 0.812, P=0.004) VCMs.ConclusionMagnetic resonance imaging–based whole‐heart IPM enables accurate spatial localization of sinus rhythm and premature ventricular contractions comparable to electroanatomic mapping. An inhomogeneous VCM improved IPM accuracy.

The effect of the resistive properties of bone on neural excitation and electric fields in cochlear implant models

The resistivity of bone is the most variable of all the tissues in the human body, ranging from 312 Ω cm to 84,745 Ω cm. Volume conduction models of cochlear implants have generally used a resistivity value of 641 Ω cm for the bone surrounding the cochlea. This study investigated the effect that bone resistivity has on modelled neural thresholds and intracochlear potentials using user-specific volume conduction models of implanted cochleae applying monopolar stimulation. The complexity of the description of the head volume enveloping the cochlea was varied between a simple infinite bone volume and a detailed skull containing a brain volume, scalp and accurate return electrode position. It was found that, depending on the structure of the head model and implementation of the return electrode, different bone resistivity values are necessary to match model predictions to data from literature. Modelled forward-masked spatial tuning curve (fmSTC) widths and slopes and intracochlear electric field profile length constants were obtained for a range of bone resistivity values for the various head models. The predictions were compared to measurements found in literature. It was concluded that, depending on the head model, a bone resistivity value between 3500 Ω cm and 10,500 Ω cm allows prediction of neural and electrical responses that match measured data. A general recommendation is made to use a resistivity value of approximately 10,000 Ω cm for bone volumes in conduction models of the implanted cochlea when neural excitation is predicted and a value of approximately 6500 Ω cm when predicting electric fields inside the cochlear duct.

Brain Source Imaging in Preclinical Rat Models of Focal Epilepsy using High-Resolution EEG Recordings.

Electroencephalogram (EEG) has been traditionally used to determine which brain regions are the most likely candidates for resection in patients with focal epilepsy. This methodology relies on the assumption that seizures originate from the same regions of the brain from which interictal epileptiform discharges (IEDs) emerge. Preclinical models are very useful to find correlates between IED locations and the actual regions underlying seizure initiation in focal epilepsy. Rats have been commonly used in preclinical studies of epilepsy1; hence, there exist a large variety of models for focal epilepsy in this particular species. However, it is challenging to record multichannel EEG and to perform brain source imaging in such a small animal. To overcome this issue, we combine a patented-technology to obtain 32-channel EEG recordings from rodents2 and an MRI probabilistic atlas for brain anatomical structures in Wistar rats to perform brain source imaging. In this video, we introduce the procedures to acquire multichannel EEG from Wistar rats with focal cortical dysplasia, and describe the steps both to define the volume conductor model from the MRI atlas and to uniquely determine the IEDs. Finally, we validate the whole methodology by obtaining brain source images of IEDs and compare them with those obtained at different time frames during the seizure onset.

Brain Source Imaging in Preclinical Rat Models of Focal Epilepsy using High-Resolution EEG Recordings

Electroencephalogram (EEG) has been traditionally used to determine which brain regions are the most likely candidates for resection in patients with focal epilepsy. This methodology relies on the assumption that seizures originate from the same regions of the brain from which interictal epileptiform discharges (IEDs) emerge. Preclinical models are very useful to find correlates between IED locations and the actual regions underlying seizure initiation in focal epilepsy. Rats have been commonly used in preclinical studies of epilepsy1; hence, there exist a large variety of models for focal epilepsy in this particular species. However, it is challenging to record multichannel EEG and to perform brain source imaging in such a small animal. To overcome this issue, we combine a patented-technology to obtain 32-channel EEG recordings from rodents2 and an MRI probabilistic atlas for brain anatomical structures in Wistar rats to perform brain source imaging. In this video, we introduce the procedures to acquire multichannel EEG from Wistar rats with focal cortical dysplasia, and describe the steps both to define the volume conductor model from the MRI atlas and to uniquely determine the IEDs. Finally, we validate the whole methodology by obtaining brain source images of IEDs and compare them with those obtained at different time frames during the seizure onset.

Surface Laplacians (SL) and phase properties of EEG rhythms: Simulated generators in a volume-conduction model

Surface Laplacian (SL) methods offer advantages in spectral analysis owing to the well-known implications of volume conduction. Although recognition of the superiority of SL over reference-dependent measures is widespread, well-reasoned cautions have precluded their universal adoption. Notably, the expected selectivity of SL for superficial rather than deep generators has relegated SL to the role of an add-on to conventional analyses, rather than as an independent area of inquiry, despite empirical findings supporting the consistency and replicability of physiological effects of interest. It has also been reasoned that the contrast-enhancing effects of SL necessarily make it insensitive to broadly distributed generators, including those suspected for oscillatory rhythms such as EEG alpha. These concerns are further exacerbated for phase-sensitive measures (e.g., phase-locking, coherence), where key features of physiological generators have yet to be evaluated. While the neuronal generators of empirically-derived EEG measures cannot be precisely known due to the inverse problem, simple dipole generator configurations can be simulated using a 4-sphere head model and linearly combined. We simulated subdural and deep generators and distributed dipole layers using sine and cosine waveforms, quantified at 67-scalp sites corresponding to those used in previous research. Reference-dependent (nose, average, mastoids reference) EEG and corresponding SL topographies were used to probe signal fidelity in the topography of the measured amplitude spectra, phase and coherence of sinusoidal stimuli at and between “active” recording sites. SL consistently outperformed the conventional EEG measures, indicating that continued reluctance by the research community is unfounded.

Forward Problem of Electrocardiography

The relationship between epicardial and body surface potentials defines the forward problem of electrocardiography. A robust formulation of the forward problem is instrumental to solving the inverse problem, in which epicardial potentials are computed from known body surface potentials. Here, the accuracy of different forward models has been evaluated experimentally. Body surface and epicardial potentials were recorded simultaneously in anesthetized closed-chest pigs (n=5) during sinus rhythm, and epicardial and endocardial ventricular pacing (65 records in total). Body surface potentials were simulated from epicardial recordings using experiment-specific volume conductor models constructed from magnetic resonance imaging. Results for homogeneous (isotropic electric properties) and inhomogeneous (incorporating lungs, anisotropic skeletal muscle, and subcutaneous fat) forward models were compared with measured body surface potentials. Correlation coefficients were 0.85±0.08 across all animals and activation sequences with no significant difference between homogeneous and inhomogeneous solutions (P=0.85). Despite this, there was considerable variance between simulated and measured body surface potential distributions. Differences between the body surface potential extrema predicted with homogeneous forward models were 55% to 78% greater than observed (P<0.05) and attenuation of potentials adjacent to extrema were 10% to 171% greater (P<0.03). The length and orientation of the vector between potential extrema were also significantly different. Inclusion of inhomogeneous electric properties in the forward model reduced, but did not eliminate these differences. These results demonstrate that homogeneous volume conductor models introduce substantial spatial inaccuracies in forward problem solutions. This probably affects the precision of inverse reconstructions of cardiac potentials, in which this assumption is made.

Real time estimation of generation, extinction and flow of muscle fibre action potentials in high density surface EMG

PurposeDeveloping a real time method to estimate generation, extinction and propagation of muscle fibre action potentials from bi-dimensional and high density surface electromyogram (EMG). MethodA multi-frame generalization of an optical flow technique including a source term is considered. A model describing generation, extinction and propagation of action potentials is fit to epochs of surface EMG. ResultsThe algorithm is tested on simulations of high density surface EMG (inter-electrode distance equal to 5mm) from finite length fibres generated using a multi-layer volume conductor model. The flow and source term estimated from interference EMG reflect the anatomy of the muscle, i.e. the direction of the fibres (2° of average estimation error) and the positions of innervation zone and tendons under the electrode grid (mean errors of about 1 and 2mm, respectively). The global conduction velocity of the action potentials from motor units under the detection system is also obtained from the estimated flow. The processing time is about 1ms per channel for an epoch of EMG of duration 150ms. ConclusionsA new real time image processing algorithm is proposed to investigate muscle anatomy and activity. Potential applications are proposed in prosthesis control, automatic detection of optimal channels for EMG index extraction and biofeedback.

Modelling extracellular electrical stimulation: III. Derivation and interpretation of neural tissue equations

Objective. A common approach in modelling extracellular electrical stimulation is to represent neural tissue by a volume conductor when calculating the activating function as the driving term in a cable equation for the membrane potential. This approach ignores the cellular composition of tissue, including the neurites and their combined effect on the extracellular potential. This has a number of undesirable consequences. First, the two natural and equally valid choices of boundary conditions for the cable equation (i.e. using either voltage or current) lead to two mutually inconsistent predictions of the membrane potential. Second, the spatio-temporal distribution of the extracellular potential can be strongly affected by the combined cellular composition of the tissue. In this paper, we develop a mean field volume conductor theory to overcome these shortcomings of available models. Approach. This method connects the microscopic properties of the constituent fibres to the macroscopic electrical properties of the tissue by introducing an admittivity kernel for the neural tissue that is non-local, non-instantaneous and anisotropic. This generalizes the usual tissue conductivity. A class of bidomain models that is mathematically equivalent to this class of self-consistent volume conductor models is also presented. The bidomain models are computationally convenient for simulating the activation map of neural tissue using numerical methods such as finite element analysis. Main results. The theory is first developed for tissue composed of identical, parallel fibres and then extended to general neural tissues composed of mixtures of neurites with different and arbitrary orientations, arrangements and properties. Equations describing the extracellular and membrane potential for the longitudinal and transverse modes of stimulation are derived. Significance. The theory complements our earlier work, which developed extensions to cable theory for the micro-scale equations of neural stimulation that apply to individual fibres. The modelling framework provides a number of advantages over other approaches currently adopted in the literature and, therefore, can be used to accurately estimate the membrane potential generated by extracellular electrical stimulation.

Modelling extracellular electrical stimulation: IV. Effect of the cellular composition of neural tissue on its spatio-temporal filtering properties

Objective. The objective of this paper is to present a concrete application of the cellular composite model for calculating the membrane potential, described in an accompanying paper. Approach. A composite model that is used to determine the membrane potential for both longitudinal and transverse modes of stimulation is demonstrated. Main results. Two extreme limits of the model, near-field and far-field for an electrode close to or distant from a neuron, respectively, are derived in this paper. Results for typical neural tissue are compared using the composite, near-field and far-field models as well as the standard isotropic volume conductor model. The self-consistency of the composite model, its spatial profile response and the extracellular potential time behaviour are presented. The magnitudes of the longitudinal and transverse components for different values of electrode-neurite separations are compared. Significance. The unique features of the composite model and its simplified versions can be used to accurately estimate the spatio-temporal response of neural tissue to extracellular electrical stimulation.

Volume conductor model of transcutaneous electrical stimulation with kilohertz signals

Objective. Incorporating high-frequency components in transcutaneous electrical stimulation (TES) waveforms may make it possible to stimulate deeper nerve fibers since the impedance of tissue declines with increasing frequency. However, the mechanisms of high-frequency TES remain largely unexplored. We investigated the properties of TES with frequencies beyond those typically used in neural stimulation. Approach. We implemented a multilayer volume conductor model including dispersion and capacitive effects, coupled to a cable model of a nerve fiber. We simulated voltage- and current-controlled transcutaneous stimulation, and quantified the effects of frequency on the distribution of potentials and fiber excitation. We also quantified the effects of a novel transdermal amplitude modulated signal (TAMS) consisting of a non-zero offset sinusoidal carrier modulated by a square-pulse train. Main results. The model revealed that high-frequency signals generated larger potentials at depth than did low frequencies, but this did not translate into lower stimulation thresholds. Both TAMS and conventional rectangular pulses activated more superficial fibers in addition to the deeper, target fibers, and at no frequency did we observe an inversion of the strength–distance relationship. Current regulated stimulation was more strongly influenced by fiber depth, whereas voltage regulated stimulation was more strongly influenced by skin thickness. Finally, our model reproduced the threshold-frequency relationship of experimentally measured motor thresholds. Significance. The model may be used for prediction of motor thresholds in TES, and contributes to the understanding of high-frequency TES.

Investigations of sensitivity and resolution of ECG and MCG in a realistically shaped thorax model

Solving the inverse problem of electrocardiography (ECG) and magnetocardiography (MCG) is often referred to as cardiac source imaging. Spatial properties of ECG and MCG as imaging systems are, however, not well known. In this modelling study, we investigate the sensitivity and point-spread function (PSF) of ECG, MCG, and combined ECG+MCG as a function of source position and orientation, globally around the ventricles: signal topographies are modelled using a realistically-shaped volume conductor model, and the inverse problem is solved using a distributed source model and linear source estimation with minimal use of prior information. The results show that the sensitivity depends not only on the modality but also on the location and orientation of the source and that the sensitivity distribution is clearly reflected in the PSF. MCG can better characterize tangential anterior sources (with respect to the heart surface), while ECG excels with normally-oriented and posterior sources. Compared to either modality used alone, the sensitivity of combined ECG+MCG is less dependent on source orientation per source location, leading to better source estimates. Thus, for maximal sensitivity and optimal source estimation, the electric and magnetic measurements should be combined.

Generation of field potentials and modulation of their dynamics through volume integration of cortical activity.

Field potentials (FPs) recorded within the brain, often called "local field potentials" (LFPs), are useful measures of net synaptic activity in a neuronal ensemble. However, due to volume conduction, FPs spread beyond regions of underlying synaptic activity, and thus an "LFP" signal may not accurately reflect the temporal patterns of synaptic activity in the immediately surrounding neuron population. To better understand the physiological processes reflected in FPs, we explored the relationship between the FP and its membrane current generators using current source density (CSD) analysis in conjunction with a volume conductor model. The model provides a quantitative description of the spatiotemporal summation of immediate local and more distant membrane currents to produce the FP. By applying the model to FPs in the macaque auditory cortex, we have investigated a critical issue that has broad implications for FP research. We have shown that FP responses in particular cortical layers are differentially susceptible to activity in other layers. Activity in the supragranular layers has the strongest contribution to FPs in other cortical layers, and infragranular FPs are most susceptible to contributions from other layers. To define the physiological processes generating FPs recorded in loci of relatively weak synaptic activity, strong effects produced by synaptic events in the vicinity have to be taken into account. While outlining limitations and caveats inherent to FP measurements, our results also suggest specific peak and frequency band components of FPs can be related to activity in specific cortical layers. These results may help improving the interpretability of FPs.

Electrical stimulation of neural tissue modeled as a cellular composite: point source electrode in an isotropic tissue.

Standard volume conductor models of neural electrical stimulation assume that the electrical properties of the tissue are well described by a conductivity that is smooth and homogeneous at a microscopic scale. However, neural tissue is composed of tightly packed cells whose membranes have markedly different electrical properties to either the intra- or extracellular space. Consequently, the electrical properties of tissue are highly heterogeneous at the microscopic scale: a fact not accounted for in standard volume conductor models. Here we apply a recently developed framework for volume conductor models that accounts for the cellular composition of tissue. We consider the case of a point source electrode in tissue comprised of neural fibers crossing each other equally in all directions. We derive the tissue admittivity (that replaces the standard tissue conductivity) from single cell properties, and then calculate the extracellular potential. Our findings indicate that the cellular composition of tissue affects the spatiotemporal profile of the extracellular potential. In particular, the full solution asymptotically approaches a near-field limit close to the electrode and a far-field limit far from the electrode. The near-field and far-field approximations are solutions to standard volume conductor models, but differ from each other by nearly an order or magnitude. Consequently the full solution is expected to provide a more accurate estimate of electrical potentials over the full range of electrode-neurite separations.