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.

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.

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 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.

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.

Modelling surface potentials from intracochlear electrical stimulation.

Volume conduction models were used qualitatively to model surface potentials from cochlear implant patients recorded earlier by the authors. These recorded potentials reflected the equivalent dipole orientation in the head in patients who are deaf due to otosclerosis, but increased uniformly with the distance between the stimulating electrodes along the basilar membrane in other patients, which suggested a low and high resistivity of the cochlear bone, respectively. Several models of the head were constructed, with compartments representing the skin, skull, brain, cochlea, internal and external ear canal. In the "petrous bone" model, the cochlea was modelled as a cavity in a bony layer surrounded by the brain compartment. Of all models, the petrous bone model using a high resistivity ratio (1:100) between the bony and the other compartments was the only one that produced outcomes similar to the potentials observed in non-otosclerosis patients. In conclusion, the results suggested that the surface potentials observed in non-otosclerosis patients are sufficiently explained by a high impedance between cochlear turns and a non-specific return of current via the wall of the petrous bone into the larger brain compartment.

Interictal spike localization using a standard realistic head model: simulations and analysis of clinical data.

OBJECTIVES: In this paper realistic and standard realistic head models were applied to neural source localization. METHODS: Three different triangulated head structures; the brain, the skull and the scalp were constructed from MRI information of each patient. For each subject the exact positions of the electrodes were digitized. RESULTS: The influence of the number of triangles and of the skull conductivity on the accuracy of the method was tested. The use of a standard realistic head model instead of spherical models is proposed in cases where detailed MRI information is not available, and the accuracy of this procedure is tested with dipole simulations. These techniques were applied also to EEG signals from 3 patients with focal epilepsy. In all cases the neural activity was assumed to be confined to a small portion of cortical tissue, so that the neural generator was approximated to a current dipole. The realistic head model localization is discussed on the basis of neuroimaging information. CONCLUSIONS: We show that the standard realistic head model is two or 3 times better than the spherical model for dipole localization and we propose it as a good alternative to the spherical model for EEG data processing, in cases where full MRI information is not available.

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.

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.

The effect of separate red blood cells on capillary tissue oxygenation calculated with a numerical model.

In simplified models that describe large quantities of capillaries the capillary content is considered to be homogeneous for oxygen transport; but, in reality, the capillaries contain discrete red blood cells (RBCs), and this discreteness will affect oxygen transport from the capillary to the tissue. This was previously investigated with an analytical model, where RBCs were modelled as point-like sources. A numerical approach is used in this investigation, and the results are compared with the analytical model. In both models the effect of the particulate nature of blood depends on the haematocrit and on the RBC velocity. There is only a minor difference between the two models. For rat hearts, the correction factor used in this study, the extraction pressure, can be up to 3 kPa (23 mmHg).

[Localization of brain electric sources in patients with focal epilepsy]. / Localização de fontes eléctricas cerebrais em doentes com epilepsia focal.

In this paper we discuss a non-invasive method to localize neural electrical sources using EEG data. In this method, the human head is modelled by a set of four concentric spheres with different conductivities which represent the scalp, the skull, the CSF and the brain or by three triangulated surfaces which approximate the exact head shape (in this model we do not consider the CSF layer) using NMR images. In this case the computer effort is very high, since the calculations imply thousands of equations. Therefore, the number of research groups working with this improved model, in the world, is very small. In both models, we assume that the neural source is a current dipole. This makes the model suitable for cases where the active brain areas are limited and localized. We discuss some error factors associated with the method, as the geometry of the head, the conductivity of the different layers and the number of electrodes used in the EEG measurements. Comparing the more realistic head model, with the spherical one we often have differences of 1-2 cm. However, we can reach even more pronounced differences in the frontal areas. Concerning the skull conductivity, we realized that it could introduce errors of 1-2 cm. We observed that at least 50 electrodes should be used only since 21 electrodes could imply errors of about 0.5 cm. The method was applied, both in the spherical version and the realistic one, to clinical cases of focal epileptic patients. The results are discussed in terms of the other clinical information available and they are coherent with the remaining clinical data.

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.

Reconsidering the effect of local plasma convection in a classical model of oxygen transport in capillaries.

In 1970, Aroesty and Gross investigated the influence of local plasma convection in between two successive red blood cells (RBC) in a capillary on the local oxygen transfer into tissue by combining convectional and diffusional oxygen transport. They concluded that the effect of local plasma convection on oxygen transport in the capillaries was insignificant. Here it is shown that this result was due to their choice of flat oxygen concentration profiles as boundary conditions. In fact, the plasma motion can be of importance when more realistic oxygen concentrations are used as boundary conditions. The fluxes of oxygen through the capillary wall could be up to 50% larger as compared to those of Aroesty and Gross, especially for low hematocrit values and for maximally working muscle. Since the boundary concentrations in the model of the current paper are fixed, chosen not to be influenced by the transport processes, calculations will not show to what extent motion really enhances the oxygen transport, and should be considered as rough indications of the effect of plasma motion. The results in this investigation indicate that in capillaries motion has to be taken into account under conditions of low hematocrit or high RBC velocity.

The effect of blood flow on oxygen extraction pressures calculated in a model of pointlike erythrocyte sources for rat heart.

A mathematical description of pericapillary oxygen gradients that takes into account the particulate nature of blood is possible in terms of erythrocytes as pointlike sources. The formulation in terms of quasi-stationary sources [1] is extended to account for moving erythrocytes. The extended model is semianalytical and can be used to estimate the extraction pressure (EP), which quantifies the effect on partial pressure of oxygen (pO2) in the tissue far from the erythrocytes. Simulations have been done for rat heart muscle tissue around a capillary. For low hematocrit (Hct; 20%) and low blood velocity EP is highest, higher than the pO2 drop in a surrounding typical tissue cylinder. This means that the impediment to O2 release close to the capillary can be larger than that to transport further into the tissue. Increasing the hematocrit decreases EP, that is, it facilitates O2 release. Increasing the blood velocity decreases EP at low Hct values but has the opposite effect at high Hct values (> 35%). For zero velocity, results are the same as with the quasi-stationary model.