Measuring surface potential components necessary for transmembrane current computation using microfabricated arrays

Impact of electrode orientation, myocardial wall thickness, and myofiber direction on intracardiac electrograms: numerical modeling and analytical solutions

Intracardiac electrograms (iEGMs) are time traces of the electrical potential recorded close to the heart muscle. We calculate unipolar and bipolar iEGMs analytically for a myocardial slab with parallel myofibers and validate them against numerical bidomain simulations. The analytical solution obtained via the method of mirrors is an infinite series of arctangents. It goes beyond the solid angle theory and is in good agreement with the simulations, even though bath loading effects were not accounted for in the analytical calculation. At a large distance from the myocardium, iEGMs decay as 1/R (unipolar), 1/R ² (bipolar and parallel), and 1/R ³ (bipolar and perpendicular to the endocardium). At the endocardial surface, there is a mathematical branch cut. Here, we show how a thicker myocardium generates iEGMs with larger amplitudes and how anisotropy affects the iEGM width and amplitude. If only the leading-order term of our expansion is retained, it can be determined how the conductivities of the bath, torso, myocardium, and myofiber direction together determine the iEGM amplitude. Our results will be useful in the quantitative interpretation of iEGMs, the selection of thresholds to characterize viable tissues, and for future inferences of tissue parameters.

Analyzing the effect of electrode size on electrogram and activation map properties

BACKGROUND

Atrial electrograms recorded from the epicardium provide an important tool for studying the initiation, perpetuation, and treatment of AF. However, the properties of these electrograms depend largely on the properties of the electrode arrays that are used for recording these signals.

METHOD

In this study, we use the electrode's transfer function to model and analyze the effect of electrode size on the properties of measured electrograms. To do so, we use both simulated as well as clinical data. To simulate electrogram arrays we use a two-dimensional (2D) electrogram model as well as an action propagation model. For clinical data, however, we first estimate the trans-membrane current for a higher resolution 2D modeled cell grid and later use these values to interpolate and model electrograms with different electrode sizes.

RESULTS

We simulate electrogram arrays for 2D tissues with 3 different levels of heterogeneity in the conduction and stimulation pattern to model the inhomogeneous wave propagation observed during atrial fibrillation. Four measures are used to characterize the properties of the simulated electrogram arrays of different electrode sizes. The results show that increasing the electrode size increases the error in LAT estimation and decreases the length of conduction block lines. Moreover, visual inspection also shows that the activation maps generated by larger electrodes are more homogeneous with a lower number of observed wavelets. The increase in electrode size also increases the low voltage areas in the tissue while decreasing the slopes and the number of detected deflections. The effect is more pronounced for a tissue with a higher level of heterogeneity in the conduction pattern. Similar conclusions hold for the measurements performed on clinical data.

CONCLUSION

The electrode size affects the properties of recorded electrogram arrays which can respectively complicate our understanding of atrial fibrillation. This needs to be considered while performing any analysis on the electrograms or comparing the results of different electrogram arrays.

Excitability and propagation of the electrical impulse in Venus flytrap; a comparative electrophysiological study of unipolar electrograms with myocardial tissue

Mammalian heart cells and cells of leaves of Dionaea muscipula share the ability to generate propagated action potentials, because the excitable cells are electrically coupled. In the heart the propagated action potential causes synchronized contraction of the heart muscle after automatic generation of the impulse in the sinus node. In Dionaea propagation results in closure of the trap after activation of trigger hairs by an insect. The electrical activity can be recorded in the extracellular space as an extracellular electrogram, resulting from transmembrane currents. Although the underlying physiological mechanism that causes the electrogram is similar for heart and Dionaea cells, the contribution of the various ions to the transmembrane current is different. We recorded extracellular electrograms from Dionaea leaves and compared the recorded signals with those known from the heart. The morphology of the electrograms differed considerably. In comparison to activation in mammalian myocardium, electrograms of Dionaea are more temporally and spatially variable. Whereas electrograms in healthy myocardium recorded at some distance from the site of activation reveal a simple biphasic pattern, Dionaea activation showed positive, negative or biphasic deflections. Comparison of patch clamp data from plant cells and cardiomyocytes suggests a role of temperature and ion concentrations in extracellular space for the diversity of morphologies of the Dionaea electrograms.

Electrogram recording and analyzing techniques to optimize selection of target sites for ablation of cardiac arrhythmias

The extracellular electrogram is caused by transmembrane currents that flow into extracellular space during propagation of the electrical impulse. Electrograms are usually recorded in unipolar or bipolar mode that have different characteristics, but provide complementary information. Both recording modes have specific advantages, but also suffer from disadvantages. Techniques to circumvent some of the weaknesses are reviewed. The origin of remote and fractionated deflections and their relation with electrode characteristics are discussed. Epicardial and endocardial sites of origin and breakthrough sites as well as the effect of fatty tissue on extracellular electrograms are presented. Induction of tachycardia to assess the arrhythmogenic area is not always possible because of hemodynamic instability of the patient. Techniques to assess sites with high reentry vulnerability without induction of arrhythmias are outlined such as activation‐repolarization mapping and decremental stimulation. Pitfalls of substrate mapping and techniques to avoid them as omnipolar mapping and characterization of complex electrograms by entropy are presented. Technical aspects that influence electrogram morphology as electrode size, filtering, contact force, and catheter position are delineated. Data from the various publications suggest that a combination of unipolar and bipolar electrogram analysis techniques is helpful to optimize determination of target sites for ablation.

Transmembrane current imaging in the heart during pacing and fibrillation

Recently, we described a method to quantify the time course of total transmembrane current (Im) and the relative role of its two components, a capacitive current (Ic) and a resistive current (Iion), corresponding to the cardiac action potential during stable propagation. That approach involved recording high-fidelity (200 kHz) transmembrane potential (Vm) signals with glass microelectrodes at one site using a spatiotemporal coordinate transformation via measured conduction velocity. Here we extend our method to compute these transmembrane currents during stable and unstable propagation from fluorescence signals of Vm at thousands of sites (3 kHz), thereby introducing transmembrane current imaging. In contrast to commonly used linear Laplacians of extracellular potential (Ve) to compute Im, we utilized nonlinear image processing to compute the required second spatial derivatives of Vm. We quantified the dynamic spatial patterns of current density of Im and Iion for both depolarization and repolarization during pacing (including nonplanar patterns) by calibrating data with the microelectrode signals. Compared to planar propagation, we found that the magnitude of Iion was significantly reduced at sites of wave collision during depolarization but not repolarization. Finally, we present uncalibrated dynamic patterns of Im during ventricular fibrillation and show that Im at singularity sites was monophasic and positive with a significant nonzero charge (Im integrated over 10 ms) in contrast with nonsingularity sites. Our approach should greatly enhance the understanding of the relative roles of functional (e.g., rate-dependent membrane dynamics and propagation patterns) and static spatial heterogeneities (e.g., spatial differences in tissue resistance) via recordings during normal and compromised propagation, including arrhythmias.

Quantification of transmembrane currents during action potential propagation in the heart

The measurement, quantitative analysis, theory, and mathematical modeling of transmembrane potential and currents have been an integral part of the field of electrophysiology since its inception. Biophysical modeling of action potential propagation begins with detailed ionic current models for a patch of membrane within a distributed cable model. Voltage-clamp techniques have revolutionized clinical electrophysiology via the characterization of the transmembrane current gating variables; however, this kinetic information alone is insufficient to accurately represent propagation. Other factors, including channel density, membrane area, surface/volume ratio, axial conductivities, etc., are also crucial determinants of transmembrane currents in multicellular tissue but are extremely difficult to measure. Here, we provide, to our knowledge, a novel analytical approach to compute transmembrane currents directly from experimental data, which involves high-temporal (200 kHz) recordings of intra- and extracellular potential with glass microelectrodes from the epicardial surface of isolated rabbit hearts during propagation. We show for the first time, to our knowledge, that during stable planar propagation the biphasic total transmembrane current (I(m)) dipole density during depolarization was ∼0.25 ms in duration and asymmetric in amplitude (peak outward current was ∼95 μA/cm(2) and peak inward current was ∼140 μA/cm(2)), and the peak inward ionic current (I(ion)) during depolarization was ∼260 μA/cm(2) with duration of ∼1.0 ms. Simulations of stable propagation using the ionic current versus transmembrane potential relationship fit from the experimental data reproduced these values better than traditional ionic models. During ventricular fibrillation, peak I(m) was decreased by 50% and peak I(ion) was decreased by 70%. Our results provide, to our knowledge, novel quantitative information that complements voltage- and patch-clamp data.

Orthogonal field calibration analysis for myocardial electrode arrays used in defibrillation studies

Mapping the myocardial electric field during a defibrillation pulse requires the recording of potential differences between electrodes. The field is then calculated from these quantities and the corresponding calibration matrix. One straightforward calibration technique involves alignment of a known electric field along each of the orthogonal axes of an electrode array and recording the resulting potential differences. However, no results have been reported to support the efficacy of this technique. This study performs a detailed error analysis including a one-to-one comparison to a precision calibration technique, and quantitatively establishes the efficacy of the orthogonal field technique.

Linear electrode arrays for stimulation and recording within cardiac tissue space constants

In this paper, we document a fabrication process that yields linear arrays of rectangular platinum black electrodes spaced 25 mum apart with edge-to-edge separation of 20 microm. The spatial arrangement is therefore sufficiently fine to insure stimulation and recording within cardiac tissue space constants, as six electrodes with dimensions of either 5 x 100 microm2, 5 x 250 microm2, or 5 x 500 microm2 were positioned in a 130-microm2 span in the arrays. Despite the small electrode sizes and available surface areas, favorable impedance characteristics were identifed. Averages ranged from 111 kOmega to 146 kOmega at 0.5 Hz and from 14 kOmega 39 kOmega at 500 Hz. Differences in impedances between the electrode sizes tested were small. Potential differences (deltaphis) recorded using the two central electrodes during stimulation with combinations at separations of only 75 microm, 100 microm, and 125 microm had low signal noise. As a preliminary test of the use of these arrays for possible application to impedance measurements in cardiac tissue, the deltaphis recorded during stimulation were compared to deltaphis obtained from finite-difference simulations using an isotropic volume conductor model. Anticipated decays in deltaphi with widening electrode separation identified in those simulations matched the decays in the recorded deltaphis closely. These findings are significant because they suggest intracellular and interstitial microimpedance mesurements in heart experiments will be straightforward.

Bayesian analysis of fiber impedance measurements

The resistivities of microscale components of excitable tissue include the longitudinal intracellular and interstitial resistivities and the membrane resistivity. Measurements of these tissue micro impedances have rarely been obtained, mainly because of the lack of a satisfactory measurement system. Here we evaluate a possible strategy for obtaining such measurements, and begin with a simulation. In the model, a one-dimensional fiber was stimulated with closely space interstitial electrodes at four frequencies, and the voltage differences that occurred in response were recorded. We then considered the inverse question, asking if tissue micro impedances could be found from the voltage measurements plus additive noise. In so doing, we used a Bayesian interpretation of the measured data to find the probability that each of the longitudinal and transmembrane resistivity sets was their origin. The Bayesian procedure proved better suited for interpreting the measurements than was conventional least-squares analysis. It was better because all known data, including realistic noise specifications and a priori probabilities, were included in the defined procedure. The results show that the micro impedances were found satisfactorily using realistic parameters and noise levels. The overall quantitative evaluation is promising for future experimental measurements.

Analysis of Electrode Configurations for Measuring Cardiac Tissue Conductivities and Fibre Rotation

: This paper describes a multi-electrode grid, which could be used to determine cardiac tissue parameters by direct measurement. A two pass process is used, where potential measurements are made, during the plateau phase of the action potential, on a subset of these electrodes and these measurements are used to determine the bidomain conductivities. In the first pass, the potential measurements are made on a set of 'closely-spaced' electrodes and the parameters are fitted to the potential measurements in an iterative process using a bidomain model and a solver based on a modified Shor's r-algorithm. This first pass yields the extracellular conductivities. The second pass is similar except that a 'widely-spaced' electrode set is used and this time the intracellular conductivities are recovered. In addition, it is possible to determine the fibre rotation throughout the tissue, since the bidomain model used here is able to include the effects of fibre rotation. In the simulation studies presented here, the model is solved with known conductivities, on each of the two subsets of electrodes, to generate two sets of 'measured potentials.' Conductivities are then recovered by solving an inverse problem based on the measured potentials, to which various levels of noise are added. For example, simulations in the first pass are performed using an electrode spacing of 500 mum, for a situation where the longitudinal and transverse space constants are 769 and 308 mum, respectively. These give very accurate average percentage relative errors for the longitudinal and transverse extracellular conductivities, over five simulations with 1% noise added, of 0.3 and 0.2%. Twenty-five second pass simulations, on a 1 mm grid, yield average percentage relative errors of 3.8, 2.6 and 1.4% for the corresponding intracellular values and the fibre rotation angle, respectively.

Cardiac microimpedance measurement in two-dimensional models using multisite interstitial stimulation

We analyzed central interstitial potential differences during multisite stimulation to assess the feasibility of using those recordings to measure cardiac microimpedances in multidimensional preparations. Because interstitial current injected and removed using electrodes with different proximities allows modulation of the portion of current crossing the membrane, we hypothesized that multisite interstitial stimulation would give rise to central interstitial potential differences that depend on intracellular and interstitial microimpedances, allowing measurement of those microimpedances. Simulations of multisite stimulation with fine and wide spacing in two-dimensional models that included dynamic membrane equations for guinea pig ventricular myocytes were performed to generate test data ( partial differentialphio). Isotropic interstitial and intracellular microimpedances were prescribed for one set of simulations, and anisotropic microimpedances with unequal ratios (intracellular to interstitial) along and across fibers were prescribed for another set of simulations. Microimpedance measurements were then obtained by making statistical comparisons between partial differentialphio values and interstitial potential differences from passive bidomain simulations (Deltaphio) in which a wide range of possible microimpedances were considered. Possible microimpedances were selected at 25% increments. After demonstrating the effectiveness of the overall method with microimpedance measurements using one-dimensional test data, we showed microimpedance measurements within 25% of prescribed values in isotropic and anisotropic models. Our findings suggest that development of microfabricated devices to implement the procedure would facilitate routine measurement as a component of cardiac electrophysiological study.