Inhomogeneous Volume Conductor Research Articles

Sensitivity Analysis of the Tetrapolar Electrical Impedance Measurement Systems Using COMSOL Multiphysics for the non-uniform and Inhomogeneous Medium

One of the major problems with Electrical Impedance Tomography (EIT) is the lack of spatial sensitivity within the measured volume. In this paper, sensitivity distribution of the tetrapolar impedance measurement system was visualized considering a cylindrical phantom consisting of homogeneous and inhomogeneous medium. Previously, sensitivity distribution was analysed analytically only for the homogeneous medium considering simple geometries and the distribution was found to be complex1,2. However, for the inhomogeneous volume conductors sensitivity analysis needs to be done using finite element method (FEM). In this paper, the results of sensitivity analysis based on finite element method using COMSOL Multiphysics simulation software are presented. A cylindrical non-uniform, inhomogeneous phantom, which mimics the human upper arm, was chosen to do the experiments by varying different parameters of interest. A successful method for controlling the region of interest was found where the sensitivity was maximum. Refining the finite element mesh size and introducing multifrequency input current (up to 1 MHz) this simulation method can be further improved.Dhaka Univ. J. Sci. 64(1): 7-13, 2016 (January)

Signal and Noise Covariance Estimation Based on ICA for High-Resolution Cortical Dipole Imaging

We investigated suitable spatial inverse filters for cortical dipole imaging from the scalp electroencephalogram (EEG). The effects of incorporating statistical information of signal and noise into inverse procedures were examined by computer simulations and experimental studies. The parametric projection filter (PPF) and parametric Wiener filter (PWF) were applied to an inhomogeneous three-sphere volume conductor head model. The noise covariance matrix was estimated by applying independent component analysis (ICA) to scalp potentials. The present simulation results suggest that the PPF and the PWF provided excellent performance when the noise covariance was estimated from the differential noise between EEG and the separated signal using ICA and the signal covariance was estimated from the separated signal. Moreover, the spatial resolution of the cortical dipole imaging was improved while the influence of noise was suppressed by including the differential noise at the instant of the imaging and by adjusting the duration of noise sample according to the signal to noise ratio. We applied the proposed imaging technique to human experimental data of visual evoked potential and obtained reasonable results that coincide to physiological knowledge.

Effects of stimulus parameters and tissue inhomogeneity on nerve excitation processes in magnetic stimulation of the brain: A simulation study

In this study, we used a computer simulation to investigate the nerve excitation processes of the nerve axon in an inhomogeneous volume conductor in magnetic stimulation. We assumed that the nerve axon was located in an inhomogeneous conducting medium with two regions having different conductivities that simulate different tissue types. The distribution of induced electric fields was calculated with the finite element method. The nerve fiber was modeled after equivalent electrical circuits having active nodes of Ranvier. We observed the excitation threshold when the coil current waveforms and direction are changed with varying the electrical properties of the tissue. The simulation results show that the threshold is lower when biphasic waveforms are used and that the optimal current direction depends on tissue conductivity. The results also suggest that the nerve is excited even when the coil current flow is perpendicular to the axon in inhomogeneous conducting media. The results in this study give useful information to explain the experimental results in magnetic stimulation of the brain.

Signal strength versus cuff length in nerve cuff electrode recordings.

When a nerve cuff electrode is used for the recording of signals from peripheral nerves, cuff dimensions have to be chosen. Traditionally, the peak-to-peak amplitude of the single-fiber action potential (SFAP) is optimized through the choice of cuff diameter and cuff length. In this paper, the dependency of the root-mean-square (RMS) value of the nerve signal on the cuff dimensions was studied and compared with the peak-to-peak value of the SFAP. A simple approximation for signal optimization by cuff dimensioning is suggested. The results were obtained from modeled SFAPs and from the electroneurogram (ENG) created by superimposed SFAPs, obtained from an inhomogeneous volume conductor model. The results show that the RMS value of the nerve signal is considerably more sensitive to the cuff length than the SFAP peak-to-peak amplitude, and that the RMS of the ENG is a linear function of the fiber diameter.

神経磁気刺激における不均一媒質中の神経線維の興奮特性についてのシミュレーションによる検討

神経磁気刺激における不均一媒質中の神経線維の興奮特性についてのシミュレーションによる検討

A model of the electrical volume conductor in the region of the eye in the ELF range

Electrical and magnetic phosphenes are irritations of the eye caused by electric currents or magnetic fields. These are well known effects initially investigated in the early 1900s. Available estimations of the current densities in the eye, based on the assumption of a homogeneous volume conductor, show low thresholds. These outdated thresholds are still an important cornerstone when justifying today's limit values for extremely low-frequency (ELF) fields specified by statutory regulations. In vitro measurements of the complex conductivity of cattle eye are carried out for the ELF range (5–2000 Hz) separated for the different tissues of the eyeball. They do not show peculiarities at 20 Hz which is the threshold minimum for the phosphene generation. The reported conductivity data of the eye region show variations of two orders of magnitude regarding the electrical conductivity of the individual tissue layers. Starting with these new data, a model of the orbita is introduced describing the eye and its periphery as an electrically inhomogeneous volume conductor. This model contains small-scale structures which are expected to behave as good electrical conductors yielding regions of higher field values within the eye. Therefore, earlier models assuming a homogeneous volume conductor can be regarded as oversimplistic.

The effect of subthreshold prepulses on the recruitment order in a nerve trunk analyzed in a simple and a realistic volume conductor model.

The influence of subthreshold depolarizing prepulses on the threshold current-to-distance and the threshold current-to-diameter relationship of myelinated nerve fibers has been investigated. A nerve fiber model was used in combination with both a simple, homogeneous volume conductor model with a point source and a realistic, inhomogeneous volume conductor model of a monofascicular nerve trunk surrounded by a cuff electrode. The models predict that a subthreshold depolarizing prepulse will desensitize Ranvier nodes of fibers in the vicinity of the cathode and thus cause an increase in the threshold current of a subsequent pulse to activate these fibers. If the increase in threshold current of the excited node is large enough, the excitation will be accompanied by a strong hyperpolarization of adjacent nodes, preventing the propagation of action potentials in these fibers. As fibers close to the electrode are more desensitized by prepulses than more distant ones, it is possible to stimulate distant fibers without stimulating such fibers close to the electrode. Moreover, as larger fibers are more desensitized than smaller ones, smaller fibers have lower threshold currents than larger fibers up to a certain distance from the electrode. The realistic model has provided an additional condition for the application of this method to invert nerve fiber recruitment, i.e., real or virtual anodes should be close to the cathode. When using a cuff electrode for this purpose, in the case of monopolar stimulation the cuff length (determining the position of the virtual anodes) should not exceed twice the internodal length of the fibers to be blocked. Similarly, the distance between cathode and anodes should not exceed the internodal length of these fibers when stimulation is to be applied tripolarly.

Electrocardiographic imaging: I. Effect of torso inhomogeneities on body surface electrocardiographic potentials.

Body surface potential maps (BSPMs) and conventional ECG reflect electrical sources generated by cardiac excitation and repolarization and noninvasively provide important diagnostic information about the electrical state of the heart. Because the heart is located within the torso volume conductor, body surface potentials also reflect the effects of torso inhomogeneities, which include blood, lungs, bone, muscle, fat, and fluid. It is necessary to characterize and understand these effects in order to interpret BSPM and ECG in terms of cardiac activity without "contamination" from the inhomogeneous volume conductor. Actual measured epicardial and body surface potentials were obtained during normal sinus rhythm and for different pacing protocols from a Langendorff-perfused dog heart suspended in a human-shaped torso tank. Accurate geometry of the torso inhomogeneities was digitized from the Visual Human Project and appropriately introduced into a computer model of the tank setup. The geometry and electrical properties of the volume conductor could be varied. Both homogeneous and inhomogeneous torsos have major smoothing effects on BSPM, which is of very low resolution compared with its corresponding epicardial potential pattern. Relative to a homogeneous torso, the inhomogeneities have only a minor effect on BSPM patterns. They augment potential magnitudes depending on the pattern of epicardial activation. Variations of geometry and electrical properties within the normal physiologic range have minimal effects. Effects of torso inhomogeneities on 12-lead ECGs are minimal, and the associated ECG changes fall within the range of normal interindividual variations.

Calculating the activating function of nerve excitation in inhomogeneous volume conductor during magnetic stimulation using the finite element method

The first derivative of induced electric field during magnetic stimulation, activating function, is calculated to study the influence of the interface between conductors with different conductivities on nerve excitation. A Neumann type boundary condition is derived for applying the finite element method to calculate the induced electric field. The spatial distributions of induced electric fields and activating functions in homogeneous and inhomogeneous volume conductors are calculated for comparison. The results show that the interface between conductors of different conductivities appears to markedly affect the nerve excitation elicited by magnetic stimulation.

Simulation of Body Surface Laplacian Maps during Ventricular Pacing in a 3D Inhomogeneous Heart-Torso Model

A computer simulation study has been conducted to investigate the performance of body surface Laplacian maps (BSLMs) in localizing and imaging spatially separated myocardial electrical events. A cellular automaton model of ventricles simulates cardiac electrical activity using a two-site pacing protocol to induce dual simultaneously active myocardial electrical events. The heart model is embedded in a realistically shaped inhomogeneous volume conductor. The BSLMs are numerically computed from the induced electrical activity in the heart model. The present computer simulation results show that the BSLM can provide better separation and localization of two regional myocardial electrical events as compared with the body surface potential map (BSPM).

The use of the spatial covariance in computing pericardial potentials.

This paper investigates the incorporation of the spatial covariance of the pericardial potentials, assumed known a priori as a regularization function, when computing the pericardial potential distribution from observed body surface potentials. The resulting inverse solutions are compared with those using as a regularization function: 1) the norm of the solution, 2) the norm of the surface Laplacian of the solution, as well as with those based on using the truncated singular value decomposition. The study uses a realistic source model to simulate potentials throughout the QRS-interval. This source is placed in an anatomically accurate inhomogeneous volume conductor model of the torso. The use of a single value of the regularization parameter is shown to be feasible: for data incorporating 2% noise, the use of the spatial covariance is demonstrated to result in a relative error over the entire QRS interval as low as 10%. Major errors are demonstrated to result if the effect of the inhomogeneity of the lungs is ignored. The spatial covariance based inverse is shown to be more robust with respect to the perturbations (noise; inhomogeneity) than the other estimators included in this study.

Effects of coil orientation and magnetic field shield on transcranial magnetic stimulation in cats

To obtain suitable stimulus conditions for transcranial magnetic stimulation, the evoked compound muscle action potential (ECMAP), evoked spinal cord potential (ESCP), and magnetic and electric fields were analyzed in cats with and without the use of a magnetic field shield. Cats were stimulated using a figure 8 magnetic coil placed on the cranium above the motor cortex. The maximum ECMAP amplitude was recorded when the electric current in the coil was in the mediolateral direction, regardless of whether a magnetic shield with a 5 × 5 cm window was used. ECMAP and ESCP thresholds were reduced when magnetic shielding was in place. Due to the edge effect, the strengths of the magnetic and electric fields were highest in the brainstem area, which is an inhomogeneous volume conductor of the cat's cranium. A large induced electric field directed caudally elicited ECMAP and ESCP responses effectively when a magnetic shield with a 5 × 5 cm window was in place. © 1998 John Wiley & Sons, Inc. Muscle Nerve 21: 1172–1180, 1998.

Effects of coil orientation and magnetic field shield on transcranial magnetic stimulation in cats.

To obtain suitable stimulus conditions for transcranial magnetic stimulation, the evoked compound muscle action potential (ECMAP), evoked spinal cord potential (ESCP), and magnetic and electric fields were analyzed in cats with and without the use of a magnetic field shield. Cats were stimulated using a figure 8 magnetic coil placed on the cranium above the motor cortex. The maximum ECMAP amplitude was recorded when the electric current in the coil was in the mediolateral direction, regardless of whether a magnetic shield with a 5 x 5 cm window was used. ECMAP and ESCP thresholds were reduced when magnetic shielding was in place. Due to the edge effect, the strengths of the magnetic and electric fields were highest in the brainstem area, which is an inhomogeneous volume conductor of the cat's cranium. A large induced electric field directed caudally elicited ECMAP and ESCP responses effectively when a magnetic shield with a 5 x 5 cm window was in place.

Determination of the Induced Electric Fields and the Activating Function in an Inhomogeneous Volume Conductor during Magnetic Stimulation

A calculation model is proposed for the induced electric fields and the activating function in inhomogeneous volume conductors during magnetic stimulation. On the basis of the proposed model, the finite element method (FEM) is used to perform numeric calculation for the induced electric fields in an inhomogeneous volume conductor. In order to study the influence of inhomogeneities on nerve excitation, the spatial distribution of the activating function was also calculated. In a comparison of the results with a homogeneous case, the interface between conductors of different conductivities appears to affect markedly the nerve excitation elicited by magnetic stimulation. Theoretical explanations are given for this simulation result.

On the algorithm for computing body surface Laplacians in an inhomogeneous volume conductor of arbitrary shape

In this short communication, a corrected version of algorithm for calculating the body surface Laplacian (BSL) in an inhomogeneous volume conductor of arbitrary shape is described. The present computer simulation results show that the corrected algorithm can give an accurate numerical solution. This algorithm was then applied to examine the effect of the lung inhomogeneity on the BSL's in a realistically shaped torso model. The simulation results show that the low-conductivity lungs have little effect on both topology and magnitudes of body surface Laplacian maps (BSLM's) for a single dipole source.

Importance of soft tissue inhomogeneity in magnetic peripheral nerve stimulation

In magnetic peripheral nerve stimulation with a figure-of-eight coil, a ‘tangential-edge’ coil orientation (the nerve is beneath the coil intersection and perpendicular to the coil wings) is ideal theoretically. However, some experimental results show that strong muscle responses are elicited with a ‘symmetrical-tangential’ coil orientation (the nerve is beneath the coil intersection and parallel to the coil wings), which is inconsistent with the cable theory. We hypothesized that the 10:1 conductivity difference between muscle and fat would cause inconsistent results during magnetic median nerve stimulation in the elbow, which was verified using an inhomogeneous volume conductor model. The induced electric fields were measured in a model composed of saline solutions of different concentrations divided by a cellophane sheet. A nerve was imagined along the boundary between the two solutions, and the coil was held in a ‘symmetrical-tangential’ position. Virtual cathodes, which were off the nerve in the homogeneous model, were on the nerve in the inhomogeneous model. The previous inconsistent results were explained by considering soft tissue inhomogeneity without any modification of the assumption in the cable theory that only the induced electric field component parallel to the nerve is responsible for nerve excitation.

The extracellular potential of a myelinated nerve fiber in an unbounded medium and in nerve cuff models

A model is presented for the calculation of single myelinated fiber action potentials in an unbounded homogeneous medium and in nerve cuff electrodes. The model consists of a fiber model, used to calculate the action currents at the nodes of Ranvier, and a cylindrically symmetrical volume conductor model in which the fiber's nodes are represented as point current sources. The extracellular action potentials were shown to remain unchanged if the fiber diameter and the volume conductor geometry are scaled by the same factor (principle of corresponding states), both in an unbounded homogeneous medium and in an inhomogeneous volume conductor. The influence of several cuff electrode parameters, among others, cuff length and cuff diameter, were studied, and the results were compared, where possible, with theoretical and experimental results as reported in the literature.

Magnetic source imaging in the human heart: estimating cardiac electrical sources from simulated and measured magnetocardiogram data.

The estimation of pseudo primary current dipoles on a 2D-manifold in the atrial and ventricular myocardium and septum, and of the transmembrane potential on the endocardium and epicardium, from the magnetic heart field is investigated. The human thorax surrounding the heart is modelled by an inhomogeneous boundary element volume conductor model, including the outer thorax surface and the surfaces of the lungs. The influence of the blood mass is neglected. In the inverse problem Tikhonov's regularisation is applied. The regularisation parameter is determined by the L-curve method. An algorithm for iterative improvement is applied to estimate the pseudo primary current dipoles. Synthetic magnetic field and electric potential data are generated using a cellular automaton model of the entire human heart. Real world magnetic field data for a normal subject are analysed to demonstrate the practicability and effectiveness of the presented method.

Model of Inhomogeneous Volume Conductors for a Magnetic Nerve Stimulation Mechanism

We measured the electric fields induced by figure-of-eight coils in homogeneous and inhomogeneous volume conductor models. Each model consisted of two troughs separated by a sheet of cellophane. In the inhomogeneous model, one of the two troughs was filled with 0.9% saline solution, and the other with 0.1% saline solution. In the homogeneous model, both troughs were filled with 0.9% saline solution. The figure-of-eight coil was held beneath the troughs with its wings parallel to a boundary between the two troughs. In the inhomogeneous model, the electric field along the boundary and especially its first spatial derivative were markedly elevated in comparison with the corresponding values recorded in the homogeneous model. The response of a nerve fiber to magnetic stimulation in an inhomogeneous medium is different from that in a homogeneous medium.

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.