Interpretation of skeletal muscle four-electrode impedance measurements using spatial and temporal frequency-dependent conductivities

Electrode systems for measuring cardiac impedances using optical transmembrane potential sensors and interstitial electrodes--theoretical design

The cardiac electrical substrate is a challenge to direct measurement of its properties. Optical technology together with the capability to fabricate small electrodes at close spacings opens new possibilities. Here, those possibilities are explored from a theoretical viewpoint. It appears that with careful measurements from a well-designed set of electrodes one can obtain structural conductivities, separating intracellular from interstitial values, and longitudinal from transverse. Resting membrane resistance also can be obtained.

An averaging two-electrode probe for monitoring changes in myocardial conductivity evoked by ischemia

This paper considers the applicability of effective conductivity measurements for monitoring physiological and/or pathological phenomena induced by ischemia in the myocardium. The sensitivity of a probe, calculated by means of the finite element method, to changes in the conductivity of the tissue examined is defined for this purpose. Probes developed by Schafer and collaborators (1995) and in our own departments have been examined on the basis of this sensitivity. Theoretical results were verified experimentally using a tank, enlarged models of the probes, and a specially developed electronic circuit. It follows from this study that the probe developed by Schafer et al. is characterized by positive and negative sensitivity. This can lead to misinterpretation of the measurements obtained. In contrast, the sensitivity of our probe is dominantly positive. An example of the in vivo result obtained during experimentally induced ischemia in a swine heart is included.

Effects of sample geometry and electrode configuration on measured electrical resistivity of skeletal muscle

Over the past 40 years, researchers from a variety of scientific backgrounds have been using Rush's equations to analyze results of their electrophysiological studies. A lack of understanding of the constraints and the domain in which these equations are valid, often results in situations in which it is challenging to evaluate and compare results obtained by different investigators. In this paper, we reanalyzed the conditions for which Rush's equations were derived, and using mathematical modeling, computer simulation and in vitro measurements, we delineated areas of their appropriate application. Our studies showed that both sample geometry and test electrode configuration affect the measured tissue electrical resistivities: 1) The sample can be considered semi-infinite only if its dimensions are > 50 inter-electrode separation distances (IESD), and thickness > 2.5 IESD, 2) smaller sample sizes increase the transversally measured resistivity, 3) semi-infinite samples thinner than 2.5 IESD, and samples tested with needle electrodes demonstrate reduced anisotropy, and 4) when surface-spot electrodes are longitudinally aligned, as the IESD/tissue thickness ratio decreases, the measured resistivity increases. Our conclusion is that in most experimental situations, it is necessary to use modeling techniques to decouple the electrode configuration/sample geometry influence from the measured tissue resistivity.

Anisotropy of human muscle via non-invasive impedance measurements

Combining non-invasive 50 kHz impedance measurements with a mathematical model for the underlying structure, we obtain in vivo values for the transverse and longitudinal conductivities of the muscles of the human thigh and for the (isotropic) conductivity of the covering skin-fat layer. Results for a healthy male subject are in acceptably good agreement with those obtained elsewhere on surgically exposed or freshly excised animal tissue and with 'global' measurements on humans. Also, measurements using rotatable probes reveal orientations of underlying muscle fibres via minima in resistance versus angle curves. The results suggest potentially useful methods for studying muscle properties in clinical and physiological research.

In vivo measurement of the low-frequency dielectric spectra of frog skeletal muscle

Capacitance, conductance and dielectric loss spectra are obtained, in vivo, for a number of electrode separations in the gastrocnemius muscle of a frog. At each frequency the reciprocals of these parameters are plotted versus electrode separation. From the slopes of the resulting lines the complex permittivity and the conductivity of the muscle can be determined, with electrode effects eliminated. The sequence of power-law responses which is found is consistent with the fractal model proposed by Dissado. The electrical properties measured in vivo with needle electrodes are similar to those measured with surface electrodes for frequencies between 1 kHz and 1 MHz.

The bioelectrical source in computing single muscle fiber action potentials

Generally, single muscle fiber action potentials (SFAPs) are modeled as a convolution of the bioelectrical source (being the transmembrane current) with a weighting or transfer function, representing the electrical volume conduction. In practice, the intracellular action potential (IAP) rather than the transmembrane current is often used as the source, because the IAP is relatively easy to obtain under experimental conditions. Using a core conductor assumption, the transmembrane current equals the second derivative of the IAP. In previous articles, discrepancies were found between experimental and simulated SFAPs. Adaptations in the volume conductor slightly altered the simulation results. Another origin of discrepancy might be an erroneous description of the source. Therefore, in the present article, different sources were studied. First, an analytical description of the IAP was used. Furthermore, an experimental IAP, a special experimental SFAP, and a measured transmembrane current scaled to our experimental situation were applied. The results for the experimental IAP were comparable to those with the analytical IAP. The best agreement between experimental and simulated data was found for a measured transmembrane current as source, but differences are still apparent.

Potential distribution and single-fibre action potentials in a radially bounded muscle model

In modelling the electrical behaviour of muscle tissue, we used to employ a frequency-dependent volume conductor network model, which was infinitely extended in all directions. Equations in this model could be solved using a finite-difference approach. The most important restriction of this model was the fact that no boundary effects could be incorporated. Analytical models of muscle tissue normally do not have this disadvantage, but in those models the microscopic structure of muscle tissue cannot be taken into account. In the paper, we present a combined numerical/analytical approach, which enables the study of potential distributions and SFAPs in simulated microscopic muscle tissue in which the influence of the muscle boundary has been considered. We considered muscle models with radii of 1.5 mm and 10 mm. Both models were compared with an unbounded network model. In the model with a radius of 1.5 mm we varied the position of the active fibre relative to the muscle surface. It appeared that in most cases the presence of a boundary had a considerable effect on the potential distribution. An increase in the peak-to-peak value of the SFAP amplitude up to 300 per cent was noticed when the active fibre was positioned 500 microns beneath the muscle surface in a model with a radius of 1.5 mm.