When to include ECoG electrode properties in volume conduction models.

OBJECTIVE: Implantable electrodes, such as electrocorticography (ECoG) grids, are used to record brain activity in applications like brain computer interfaces. To improve the spatial sensitivity of ECoG grid recordings, electrode properties need to be better understood. Therefore, the goal of this study is to analyze the importance of including electrodes explicitly in volume conduction calculations. APPROACH: We investigated the influence of ECoG electrode properties on potentials in three geometries with three different electrode models. We performed our simulations with FEMfuns, a volume conduction modeling software toolbox based on the finite element method. MAIN RESULTS: The presence of the electrode alters the potential distribution by an amount that depends on its surface impedance, its distance from the source and the strength of the source. Our modeling results show that when ECoG electrodes are near the sources the potentials in the underlying tissue are more uniform than without electrodes. We show that the recorded potential can change up to a factor of 3, if no extended electrode model is used. In conclusion, when the distance between an electrode and the source is equal to or smaller than the size of the electrode, electrode effects cannot be disregarded. Furthermore, the potential distribution of the tissue under the electrode is affected up to depths equal to the radius of the electrode. SIGNIFICANCE: This paper shows the importance of explicitly including electrode properties in volume conduction models for accurately interpreting ECoG measurements.

FEMfuns: A Volume Conduction Modeling Pipeline that Includes Resistive, Capacitive or Dispersive Tissue and Electrodes.

Applications such as brain computer interfaces require recordings of relevant neuronal population activity with high precision, for example, with electrocorticography (ECoG) grids. In order to achieve this, both the placement of the electrode grid on the cortex and the electrode properties, such as the electrode size and material, need to be optimized. For this purpose, it is essential to have a reliable tool that is able to simulate the extracellular potential, i.e., to solve the so-called ECoG forward problem, and to incorporate the properties of the electrodes explicitly in the model. In this study, this need is addressed by introducing the first open-source pipeline, FEMfuns (finite element method for useful neuroscience simulations), that allows neuroscientists to solve the forward problem in a variety of different geometrical domains, including different types of source models and electrode properties, such as resistive and capacitive materials. FEMfuns is based on the finite element method (FEM) implemented in FEniCS and includes the geometry tessellation, several electrode-electrolyte implementations and adaptive refinement options. The Python code of the pipeline is available under the GNU General Public License version 3 at https://github.com/meronvermaas/FEMfuns . We tested our pipeline with several geometries and source configurations such as a dipolar source in a multi-layer sphere model and a five-compartment realistically-shaped head model. Furthermore, we describe the main scripts in the pipeline, illustrating its flexible and versatile use. Provided with a sufficiently fine tessellation, the numerical solution of the forward problem approximates the analytical solution. Furthermore, we show dispersive material and interface effects in line with previous literature. Our results indicate substantial capacitive and dispersive effects due to the electrode-electrolyte interface when using stimulating electrodes. The results demonstrate that the pipeline presented in this paper is an accurate and flexible tool to simulate signals generated on electrode grids by the spatiotemporal electrical activity patterns produced by sources and thereby allows the user to optimize grids for brain computer interfaces including exploration of alternative electrode materials/properties.

Multimodal Source Imaging: Basic Methods, Signal Processing Techniques, and Applications.

Multimodal source imaging is an emerging field in biomedical engineering. Its central goal is to combine different imaging modalities in a single model or data representation, such that the combination provides an enhanced insight into the underlying physiological organ, compared to each modality separately. It requires advanced signal acquisition and processing techniques and has applications in cognitive neuroscience, clinical neuroscience and electrocardiology. Therefore, it belongs to the heart of biomedical engineering.

Source parameter estimation in inhomogeneous volume conductors of arbitrary shape.

In this paper it is demonstrated that the use of a direct matrix inverse in the solution of the forward problem in volume conduction problems greatly facilitates the application of standard, nonlinear parameter estimation procedures for finding the strength as well as the location of current sources inside an inhomogeneous volume conductor of arbitrary shape from potential measurements at the outer surface (inverse procedure). This, in turn, facilitates the inclusion of a priori constraints. Where possible, the performance of the method is compared to that of the Gabor-Nelson method. Applications are in the fields of bioelectricity (e.g., electrocardiography and electroencephalography).

The surface Laplacian of the potential: theory and application.

The use of the surface Laplacian of the potential (Ls) in bioelectricity is discussed. Different estimates of Ls, in particular the field measured by coaxial electrodes, are compared to that of the true Laplacian. A method to compute Ls on the surface of an inhomogeneous volume conductor of arbitrary shape resulting from assumed electrical sources in introduced. In two applications the sensitivity of the body surface Laplacian is carried to that of body surface potentials. This comparison is carried out for dipolar sources within the human brain as well as for distributed sources within the heart.

The conductivity of the human skull: results of in vivo and in vitro measurements.

The conductivity of the human skull was measured both in vitro and in vivo. The in vitro measurement was performed on a sample of fresh skull placed within a saline environment. For the in vivo measurement a small current was passed through the head by means of two electrodes placed on the scalp. The potential distribution thus generated on the scalp was measured in two subjects for two locations of the current injecting electrodes. Both methods revealed a skull conductivity of about 0.015 [symbol: see text]/m. For the conductivities of the brain, the skull and the scalp a ratio of 1:1/15:1 was found. This is consistent with some of the reports on conductivities found in the literature, but differs considerably from the ratio 1:1/80:1 commonly used in neural source localization. An explanation is provided for this discrepancy, indicating that the correct ratio is 1:1/15:1.

The inverse problem in electroretinography: a study based on skin potentials and a realistic geometry model.

The problem of obtaining the retinal source distribution that generates the electroretinogram (ERG) from measured skin potentials is addressed. A realistic three-dimensional (3-D) volume conductor model of the head is constructed from magnetic resonance image (MRI) data sets. The skin potential distribution generated in this model by a dipole layer source at the retina is computed by using the boundary element method (BEM). The influence of the various compartments of the complete model on the results was investigated, and a simplified model was defined. An inverse procedure for estimating the source distribution at the retina from ERG's obtained from skin electrodes was developed. The procedure was tested on simulated potentials. A fair correspondence between the original and estimated source distribution was found. Furthermore, the ERG's measured at seven skin electrodes were used to estimate the source distribution at the retina. The ERG potential waveform at an additional skin electrode was computed from this source distribution and compared to the measured potential at this electrode. Again a fair correspondence was obtained. It is concluded that the methods may become a useful tool for clinical applications, i.e., for the assessment of localized defects in retinal function.

Electrical impedance of the cochlear implant lubricants hyaluronic acid, oxycellulose, and glycerin.

Hyaluronic acid (Healon), oxycellulose (hydroxypropyl methylcellulose), and glycerin are lubricants used in cochlear implant surgery for atraumatic deep insertion of the electrode array into the scala tympani. The electrical impedances of these three lubricants were measured to assess possible effects on intraoperative evoked response measurements, such as the electrically evoked stapedius reflex and auditory brain stem response. The impedances of hyaluronic acid, oxycellulose, and saline were very similar and independent of frequency (20 Hz to 1 MHz). Glycerin had an excessively high impedance at low frequencies. A film of hyaluronic acid or oxycellulose around the electrode array immersed in saline did not have any measurable effect on the impedance; a film of glycerin resulted in a strongly reactive polarized layer. However, neither the far-field current spread nor the impedance between stimulated electrodes was affected by any of the lubricants applied as a thin film. This suggests that none of these lubricants affect intraoperative responses, when applied as a thin film.

Investigation of tDCS volume conduction effects in a highly realistic head model.

OBJECTIVE: We investigate volume conduction effects in transcranial direct current stimulation (tDCS) and present a guideline for efficient and yet accurate volume conductor modeling in tDCS using our newly-developed finite element (FE) approach. APPROACH: We developed a new, accurate and fast isoparametric FE approach for high-resolution geometry-adapted hexahedral meshes and tissue anisotropy. To attain a deeper insight into tDCS, we performed computer simulations, starting with a homogenized three-compartment head model and extending this step by step to a six-compartment anisotropic model. MAIN RESULTS: We are able to demonstrate important tDCS effects. First, we find channeling effects of the skin, the skull spongiosa and the cerebrospinal fluid compartments. Second, current vectors tend to be oriented towards the closest higher conducting region. Third, anisotropic WM conductivity causes current flow in directions more parallel to the WM fiber tracts. Fourth, the highest cortical current magnitudes are not only found close to the stimulation sites. Fifth, the median brain current density decreases with increasing distance from the electrodes. SIGNIFICANCE: Our results allow us to formulate a guideline for volume conductor modeling in tDCS. We recommend to accurately model the major tissues between the stimulating electrodes and the target areas, while for efficient yet accurate modeling, an exact representation of other tissues is less important. Because for the low-frequency regime in electrophysiology the quasi-static approach is justified, our results should also be valid for at least low-frequency (e.g., below 100 Hz) transcranial alternating current stimulation.

The influence of sulcus width on simulated electric fields induced by transcranial magnetic stimulation.

Volume conduction models can help in acquiring knowledge about the distribution of the electric field induced by transcranial magnetic stimulation. One aspect of a detailed model is an accurate description of the cortical surface geometry. Since its estimation is difficult, it is important to know how accurate the geometry has to be represented. Previous studies only looked at the differences caused by neglecting the complete boundary between cerebrospinal fluid (CSF) and grey matter (Thielscher et al 2011 NeuroImage 54 234-43, Bijsterbosch et al 2012 Med. Biol. Eng. Comput. 50 671-81), or by resizing the whole brain (Wagner et al 2008 Exp. Brain Res. 186 539-50). However, due to the high conductive properties of the CSF, it can be expected that alterations in sulcus width can already have a significant effect on the distribution of the electric field. To answer this question, the sulcus width of a highly realistic head model, based on T1-, T2- and diffusion-weighted magnetic resonance images, was altered systematically. This study shows that alterations in the sulcus width do not cause large differences in the majority of the electric field values. However, considerable overestimation of sulcus width produces an overestimation of the calculated field strength, also at locations distant from the target location.

Noninvasive detection of epicardial and endocardial activity of the heart.

Determining electrical activation of the heart in a noninvasive way is one of the challenges in cardiac electrophysiology. The ECG provides some, but limited information about the electrical status of the heart. This article describes a method to determine both endocardial and epicardial activation of the heart of an individual patient from 64 electrograms recorded from the body surface. Information obtained in this way might be helpful for the treatment of arrhythmias, to assess the effect of drugs on conduction in the heart and to assess electrical stability of the heart.

Modelling the fetal magnetocardiogram.

During gestation the abdominally recorded fetal ECG (FECG) changes as a result of changes in the conductive medium. In particular, a minimum occurs in the FECG amplitude around 30 weeks of gestation. Based on the results of an extensive FECG study, the effect of these changes on the fetal MCG are simulated. It is shown that the FMCG amplitude is not greatly affected by the changes in the conductive medium. The FMCG waveform, however, is.

ECGSIM: an interactive tool for studying the genesis of QRST waveforms.

BACKGROUND: Discussion about the selection of diagnostic features of the ECG and their possible interpretation would benefit from a model of the genesis of these signals that has a sound basis in electrophysiology as well as in physics. Recent advances in computer technology have made it possible to build a simulation package whereby the genesis of ECG signals can be studied interactively. DESIGN: A numerical method was developed for computing ECG signals on the thorax, as well as electrograms on both endocardium and epicardium. The source representation of the myocardial electric activity is the equivalent double layer. The transfer factors between the electric sources and the resulting potentials on the heart surface as well as on the body surface were computed using a realistic thorax model. RESULTS AND CONCLUSION: The resulting transfer factors were implemented in a simulation program. The program allows the user to make interactive changes in the timing of depolarisation and repolarisation on the ventricular surface, as well as changing the local source strength, and to inspect or document the effect of such changes instantaneously on electrograms and body surface potentials, visualised by waveforms as well as by potential maps and movies. The entire simulation package can be installed free of charge from www.ecgsim.org.

The fetal ECG throughout the second half of gestation.

The results of a study in which multi-lead simultaneous recordings of the abdominal fetal electrocardiogram (FECG) have been made are presented. A homogeneous volume conduction model based on the actual recorded geometry was made. Using this model, fetal vectorcardiograms (FVCGS) were computed. Before 28 weeks of gestation the inter- and intra-individual variability of the observed signals could be removed by computing FVCGs in a fetal reference frame. This opens up the possibility of using the shape of the QRS complex for diagnostic purposes.

The effect of changes in the conductive medium on the fetal ECG throughout gestation.

The electrical conduction of the ECG from the fetal heart to the maternal abdomen has been modelled by using volume conductor models based on the measured actual geometry. The models have been verified by means of multi-lead recordings of the fetal ECG. The results show that early in pregnancy (less than 28 weeks) the conduction can successfully be described by an electrically homogeneous model. Based on this model, a description of the fetal ECG that is independent of the position of the fetus is derived. In late pregnancies, the conduction is dominated by the isolating effect of the vernix caseosa. As the distribution of the vernix over the fetal body is unknown, the shape of the fetal ECG is disturbed in an unintelligible way. As a consequence, caution has to be applied when using the shape of the fetal ECG for diagnostic means.

The magnetocardiogram as derived from electrocardiographic data.

Magnetocardiographic signals, as present outside the thorax and generated by the depolarization process within the ventricles of the human heart, have been computed by using a model that incorporates the uniform double layer as the exclusive primary source. The volume conductor effects are treated by using an inhomogeneous, multicompartmental model of the thorax, based on "tailored" geometry derived from magnetic resonance imaging. The required activation function, specifying the timing of the ventricular depolarization process, was derived from an inverse procedure that uses as input data electric signals measured at the body surface. Next, the magnetic signals from the same subjects were measured. A close correspondence between computed and measured magnetic signals was observed (relative root mean square residual difference of 0.37). These results demonstrate that magnetocardiograms and electrocardiograms have a common basis and that it is unlikely that prominent sources exist that are electrically silent and yet active in the genesis of the magnetic fields associated with the depolarization process of the heart. Moreover, fresh support is implied for the usefulness of the classical uniform double layer as the electrical source model during ventricular depolarization. The contributions of the secondary sources have previously been found to be a major component of the electric signals; they are now also shown to be a major component of the magnetic signals.

The potential distribution generated by the fetal heart at the maternal abdomen.

The pathways along which the electrical currents generated by the fetal heart are conducted to the surface of the maternal abdomen are not known. As a consequence, in recording the fetal electrocardiogram (FECG) it is hard to predict where electrodes should be placed in order to obtain an optimal signal. The amplitude of the FECG varies with gestation, and there is a large interindividual variability in the amplitude of the FECG and in the optimal recording site among subjects within the same gestational age. Attempts have been made to explain these phenomena in terms of volume conduction. In this research the complete potential distribution on the maternal abdomen is studied in connection with the geometrical configuration of the electrical source (fetal heart) and the volume conductor (surrounding tissues). For a small group of pregnant women the abdominal FECG is recorded simultaneously in 32 leads during a period of about one minute, once every two weeks from 20 weeks of gestation onwards. A spatial filtering technique which combines information of all 32 leads is used to provide a trigger of the fetal QRS complexes. Using this trigger, an average fetal complex is constructed for each lead by time coherent averaging, after subtraction of the maternal contribution. These average fetal complexes are combined to plot the complete potential distribution generated by the fetal heart at the maternal abdomen (fetal body surface map, FBSM) at any given time instant during the fetal cardiac cycle. At these recording sessions the geometry is carefully quantified by making transverse scans every 2 cm with a compound echo scanner. The contours of fetal head and body, the placenta and the uterus are manually drawn on hardcopies of the video display images. Real time echoscopy is used to support the identification of the geometry. The contours are fed into a computer using a graphics tablet. The three dimensional surfaces of fetus, placenta and uterus are separately represented by a triangulation of the respective contour lines. Figures 5 and 6 show an example of the triangulated representation of the recorded geometry. Figure 7 shows the average fetal complexes of an individual at 26 weeks of gestation, plotted at the site where they have been recorded.(ABSTRACT TRUNCATED AT 400 WORDS)

Accuracy of a single equivalent moving dipole model in a realistic anatomic geometry torso model.

In this study, we investigated the accuracy of an algorithm to identify the spatial single equivalent moving dipole parameters in a realistic anatomic geometry torso model from potentials at the body surface. Specifically we investigated the effect of measurement noise, and dipole position and orientation in the accuracy of the algorithm. The boundary element method was used to calculate the forward potential distribution at 64 electrode positions on the body surface due to a point dipole. The mean and standard deviation of the distance of the true (obtained in the forward potential calculation) minus the estimated dipole location (obtained from the inverse algorithm) was estimated for each of the above three cases. Our results indicate that the dipole position has the most significant influence on the accuracy of our inverse algorithm.

Lead system transformation for pooling of body surface map data: a surface Laplacian approach.

In this paper, a method is described to transform Body Surface Map (BSM) data from one lead system to that of another. This enables pooling of BSM data between different centres. The transformation tool is based upon Laplacian interpolation. It is evaluated by inspecting transformations from lead systems having few leads to one having many leads.