Dependence of anisotropic myocardial electrical resistivity on cardiac phase and excitation frequency

Determination of lethal electric field threshold for pulsed field ablation in ex vivo perfused porcine and human hearts

Introduction

Pulsed field ablation is an emerging modality for catheter-based cardiac ablation. The main mechanism of action is irreversible electroporation (IRE), a threshold-based phenomenon in which cells die after exposure to intense pulsed electric fields. Lethal electric field threshold for IRE is a tissue property that determines treatment feasibility and enables the development of new devices and therapeutic applications, but it is greatly dependent on the number of pulses and their duration.

Methods

In the study, lesions were generated by applying IRE in porcine and human left ventricles using a pair of parallel needle electrodes at different voltages (500-1500 V) and two different pulse waveforms: a proprietary biphasic waveform (Medtronic) and monophasic 48 × 100 μs pulses. The lethal electric field threshold, anisotropy ratio, and conductivity increase by electroporation were determined by numerical modeling, comparing the model outputs with segmented lesion images.

Results

The median threshold was 535 V/cm in porcine ((N = 51 lesions in n = 6 hearts) and 416 V/cm in the human donor hearts ((N = 21 lesions in n = 3 hearts) for the biphasic waveform. The median threshold value was 368 V/cm in porcine hearts ((N = 35 lesions in n = 9 hearts) cm for 48 × 100 μs pulses.

Discussion

The values obtained are compared with an extensive literature review of published lethal electric field thresholds in other tissues and were found to be lower than most other tissues, except for skeletal muscle. These findings, albeit preliminary, from a limited number of hearts suggest that treatments in humans with parameters optimized in pigs should result in equal or greater lesions.

Modelling the interaction between stem cells derived cardiomyocytes patches and host myocardium to aid non-arrhythmic engineered heart tissue design

Application of epicardial patches constructed from human-induced pluripotent stem cell- derived cardiomyocytes (hiPSC-CMs) has been proposed as a long-term therapy to treat scarred hearts post myocardial infarction (MI). Understanding electrical interaction between engineered heart tissue patches (EHT) and host myocardium represents a key step toward a successful patch engraftment. EHT retain different electrical properties with respect to the host heart tissue due to the hiPSC-CMs immature phenotype, which may lead to increased arrhythmia risk. We developed a modelling framework to examine the influence of patch design on electrical activation at the engraftment site. We performed an in silico investigation of different patch design approaches to restore pre-MI activation properties and evaluated the associated arrhythmic risk. We developed an in silico cardiac electrophysiology model of a transmural cross section of host myocardium. The model featured an infarct region, an epicardial patch spanning the infarct region and a bath region. The patch is modelled as a layer of hiPSC-CM, combined with a layer of conductive polymer (CP). Tissue and patch geometrical dimensions and conductivities were incorporated through 10 modifiable model parameters. We validated our model against 4 independent experimental studies and showed that it can qualitatively reproduce their findings. We performed a global sensitivity analysis (GSA) to isolate the most important parameters, showing that the stimulus propagation is mainly governed by the scar depth, radius and conductivity when the scar is not transmural, and by the EHT patch conductivity when the scar is transmural. We assessed the relevance of small animal studies to humans by comparing simulations of rat, rabbit and human myocardium. We found that stimulus propagation paths and GSA sensitivity indices are consistent across species. We explored which EHT design variables have the potential to restore physiological propagation. Simulations predict that increasing EHT conductivity from 0.28 to 1-1.1 S/m recovered physiological activation in rat, rabbit and human. Finally, we assessed arrhythmia risk related to increasing EHT conductivity and tested increasing the EHT Na+ channel density as an alternative strategy to match healthy activation. Our results revealed a greater arrhythmia risk linked to increased EHT conductivity compared to increased Na+ channel density. We demonstrated that our modeling framework could capture the interaction between host and EHT patches observed in in vitro experiments. We showed that large (patch and tissue dimensions) and small (cardiac myocyte electrophysiology) scale differences between small animals and humans do not alter EHT patch effect on infarcted tissue. Our model revealed that only when the scar is transmural do EHT properties impact activation times and isolated the EHT conductivity as the main parameter influencing propagation. We predicted that restoring physiological activation by tuning EHT conductivity is possible but may promote arrhythmic behavior. Finally, our model suggests that acting on hiPSC-CMs low action potential upstroke velocity and lack of IK1 may restore pre-MI activation while not promoting arrhythmia.

The control mechanisms of heart rate dynamics in a new heart rate nonlinear time series model

The control mechanisms and implications of heart rate variability (HRV) under the sympathetic (SNS) and parasympathetic nervous system (PNS) modulation remain poorly understood. Here, we establish the HR model/HRV responder using a nonlinear process derived from Newton's second law in stochastic self-restoring systems through dynamic analysis of physiological properties. We conduct model validation by testing, predictions, simulations, and sensitivity and time-scale analysis. We confirm that the outputs of the HRV responder can be accepted as the real data-generating process. Empirical studies show that the dynamic control mechanism of heart rate is a stable fixed point, rather than a strange attractor or transitions between a fixed point and a limit cycle; HR slope (amplitude) may depend on the ratio of cardiac disturbance or metabolic demand mean (standard deviation) to myocardial electrical resistance (PNS-SNS activity). For example, when metabolic demands remain unchanged, HR amplitude depends on PNS to SNS activity; when autonomic activity remains unchanged, HR amplitude during resting reflects basal metabolism. HR parameter alterations suggest that age-related decreased HRV, ultrareduced HRV in heart failure, and ultraelevated HRV in ST segment alterations refer to age-related decreased basal metabolism, impaired myocardial metabolism, and SNS hyperactivity triggered by myocardial ischemia, respectively.

Guidelines to electrode positioning for human and animal electrical impedance myography research

The positioning of electrodes in electrical impedance myography (EIM) is critical for accurately assessing disease progression and effectiveness of treatment. In human and animal trials for neuromuscular disorders, inconsistent electrode positioning adds errors to the muscle impedance. Despite its importance, how the reproducibility of resistance and reactance, the two parameters that define EIM, are affected by changes in electrode positioning remains unknown. In this paper, we present a novel approach founded on biophysical principles to study the reproducibility of resistance and reactance to electrode misplacements. The analytical framework presented allows the user to quantify a priori the effect on the muscle resistance and reactance using only one parameter: the uncertainty placing the electrodes. We also provide quantitative data on the precision needed to position the electrodes and the minimum muscle length needed to achieve a pre-specified EIM reproducibility. The results reported here are confirmed with finite element model simulations and measurements on five healthy subjects. Ultimately, our data can serve as normative values to enhance the reliability of EIM as a biomarker and facilitate comparability of future human and animal studies.

Early detection of acute transmural myocardial ischemia by the phasic systolic-diastolic changes of local tissue electrical impedance

Myocardial electrical impedance is influenced by the mechanical activity of the heart. Therefore, the ischemia-induced mechanical dysfunction may cause specific changes in the systolic-diastolic pattern of myocardial impedance, but this is not known. This study aimed to analyze the phasic changes of myocardial resistivity in normal and ischemic conditions. Myocardial resistivity was measured continuously during the cardiac cycle using 26 different simultaneous excitation frequencies (1 kHz-1 MHz) in 7 anesthetized open-chest pigs. Animals were submitted to 30 min regional ischemia by acute left anterior descending coronary artery occlusion. The electrocardiogram, left ventricular (LV) pressure, LV dP/dt, and aortic blood flow were recorded simultaneously. Baseline myocardial resistivity depicted a phasic pattern during the cardiac cycle with higher values at the preejection period (4.19 ± 1.09% increase above the mean, P < 0.001) and lower values during relaxation phase (5.01 ± 0.85% below the mean, P < 0.001). Acute coronary occlusion induced two effects on the phasic resistivity curve: 1) a prompt (5 min ischemia) holosystolic resistivity rise leading to a bell-shaped waveform and to a reduction of the area under the LV pressure-impedance curve (1,427 ± 335 vs. 757 ± 266 Ω·cm·mmHg, P < 0.01, 41 kHz) and 2) a subsequent (5-10 min ischemia) progressive mean resistivity rise (325 ± 23 vs. 438 ± 37 Ω·cm at 30 min, P < 0.01, 1 kHz). The structural and mechanical myocardial dysfunction induced by acute coronary occlusion can be recognized by specific changes in the systolic-diastolic myocardial resistivity curve. Therefore these changes may become a new indicator (surrogate) of evolving acute myocardial ischemia.

Sensor spacing affects the tissue impedance spectra of rabbit ventricular epicardium

This study was designed to test the hypothesis that a complex composite impedance spectra develops when stimulation and recording of cardiac muscle with sufficiently fine spatial resolution in a four-electrode configuration is used. With traditional (millimeter scale) separations, the ratio between the recorded interstitial central potential difference and total supplied interstitial current is constant at all frequencies. This occurs because the fraction of supplied current that redistributes to the intracellular compartment depends on effective membrane resistance between electrodes, which is low, to a much greater extent than effective membrane capacitance. The spectra should therefore change with finer separations at which effective membrane resistance increases, as supplied current will remain primarily interstitial at lower frequencies and redistribute between compartments at higher frequencies. To test this hypothesis, we built arrays with sensors separated (d) by 804 μm, 452 μm, and 252 μm; positioned those arrays across myocyte axes on rabbit ventricular epicardium; and resolved spectra in terms of resistivity (ρt) and reactivity (χt) over the 10 Hz to 4,000 Hz range. With all separations, we measured comparable spectra with predictions from passive membrane simulations that used a three-dimensional structural framework in which intracellular, interstitial, and membrane properties were prescribed based on the limited data available from the literature. At the finest separation, we found mean ρt at 100 Hz and 4,000 Hz that lowered from 395 Ω-cm to 236 Ω-cm, respectively, with maximal mean χt of 160 Ω-cm. This experimental confirmation of spectra development in whole heart experiments is important because such development is central to achieve measurements of intracellular and interstitial passive electrical properties in cardiac electrophysiological experiments using only interstitial access.

A structural framework for interpretation of four-electrode microimpedance spectra in cardiac tissue

Renewed interest in the four-electrode method for identification of passive electrical properties in cardiac tissue has been sparked by a recognition that measurements made with sensors in close proximity are frequency dependent. Therefore, resolution of four-electrode microimpedance spectra (4EMS) may provide an opportunity for routine identification of passive electrical properties for the interstitial and intracellular compartments using only interstitial access. The present study documents a structural framework in which the tissue resistivity (ρt) and reactivity (xt) that comprise spectra are computed using interstitial and intracellular microimpedance distributions that account for differences in compartment size, anisotropic electrical properties in each compartment and electrode separations. We used this framework to consider 4EMS development with relatively wide (d=1 mm) and fine (d=250 μm) electrode separations and sensors oriented along myocyte axes, across myocyte axes and intermediate between those axes.

A new approach for resolution of complex tissue impedance spectra in hearts

This study was designed to test the feasibility of using sinusoidal approximation in combination with a new instrumentation approach to resolve complex impedance (uCI) spectra from heart preparations. To assess that feasibility, we applied stimuli in the 10-4000 Hz range and recorded potential differences (uPDs) in a four-electrode configuration that allowed identification of probe constants (Kp) during calibration that were in turn used to measure total tissue resistivity ρt from rabbit ventricular epicardium. Simultaneous acquisition of a signal proportional to the supplied current (Vstim) with uPD allowed identification of the V- I ratio needed for ρt measurement, as well as the phase shift from Vstim to uPD needed for uCI spectra resolution. Performance with components integrated to reduce noise in cardiac electrophysiologic experiments, in particular, and provide accurate electrometer-based measurements, in general, was first characterized in tests using passive loads. Load tests showed accurate uCI recovery with mean uPD SNRs between 10 (1) and 10 (3) measured with supplied currents as low as 10 nA. Comparable performance characteristics were identified during calibration of nine arrays built with 250 μm Ag/AgCl electrodes, with uCIs that matched analytic predictions and no apparent effect of frequency ( F = 0.12, P = 0.99). The potential ability of parasitic capacitance in the presence of the electrode-electrolyte interface associated with the small sensors to influence the uCI spectra was therefore limited by the instrumentation. Resolution of uCI spectra in rabbit ventricle allowed measurement of ρt = 134 ± 53 Ω· cm. The rapid identification available with this strategy provides an opportunity for new interpretations of the uCI spectra to improve quantification of disease-, region-, tissue-, and species-dependent intercellular uncoupling in hearts.

Implications of complex anatomical junctions on conductance catheter measurements of coronary arteries

In vivo, the position of the conductance catheter to measure vessel lumen cross-sectional area may vary depending on where the conductance catheter is deployed in the complex anatomical geometry of arteries, including branches, bifurcations, or curvatures. The objective here is to determine how such geometric variations affect the cross-sectional area (CSA) estimates obtained using the cylindrical model. Computer simulations and in vitro and in vivo experiments were used to assess how the electric field and associated CSA measurement accuracy are affected by three typical in vivo conditions: 1) a vessel with abrupt change in lumen diameter (e.g., transition from aorta to coronary ostia); 2) a vessel with a T-bifurcation or a Y-bifurcation; and 3) a vessel curvature, such as in the right coronary artery, aorta, or pulmonary artery. The error in diameter from simulation results was shown to be relatively small (<7%), unless the detection electrodes were placed near the junction between two different lumen diameters or at a bifurcation junction. Furthermore, the present findings show that the effect of misaligned catheter-vessel geometrical configuration and vessel curvature on measurement accuracy is negligible. Collectively, the findings support the accuracy of the conductance method for sizing blood vessels, despite the geometric complexities of the cardiovascular system, as long as the detection electrodes are not placed at a large discontinuity in diameter or at bifurcation junctions.

A new measuring and identification approach for time-varying bioimpedance using multisine electrical impedance spectroscopy

The bioimpedance measurement/identification of time-varying biological systems Z(ω, t) by means of electrical impedance spectroscopy (EIS) is still a challenge today. This paper presents a novel measurement and identification approach, the so-called parametric-in-time approach, valid for time-varying (bio-)impedance systems with a (quasi) periodic character. The technique is based on multisine EIS. Contrary to the widely used nonparametric-in-time strategy, the (bio-)impedance Z(ω, t) is assumed to be time-variant during the measurement interval. Therefore, time-varying spectral analysis tools are required. This new parametric-in-time measuring/identification technique has experimentally been validated through three independent sets of in situ measurements of in vivo myocardial impedance. We show that the time-varying myocardial impedance Z(ω, t) is dominantly periodically time varying (PTV), denoted as ZPTV(ω, t). From the temporal analysis of ZPTV(ω, t), we demonstrate that it is possible to decompose ZPTV(ω, t) into a(n) (in)finite sum of fundamental (bio-)impedance spectra, the so-called harmonic impedance spectra (HIS) Zk(ω)s with [Formula: see text]. This is similar to the well-known Fourier series of a periodic signal, but now understood at the level of a periodic system's frequency response. The HIS Zk(ω)s for [Formula: see text] actually summarize in the bi-frequency (ω, k) domain all the temporal in-cycle information about the periodic changes of Z(ω, t). For the particular case k = 0 (i.e. on the ω-axis), Z0(ω) reflects the mean in-cycle behavior of the time-varying bioimpedance. Finally, the HIS Zk(ω)s are directly identified from noisy current and voltage myocardium measurements at the multisine measurement frequencies (i.e. nonparametric-in-frequency).

Impact of surrounding tissue on conductance measurement of coronary and peripheral lumen area

Parallel conductance (electric current flow through surrounding tissue) is an important determinant of accurate measurements of arterial lumen diameter, using the conductance method. The present study is focused on the role of non-uniform geometrical/electrical configurations of surrounding tissue, which are a primary source of electric current leakage. Computational models were constructed to simulate the conductance catheter measurement with two different excitation electrodes spacings (i.e. 12 and 20 mm for coronary and peripheral sizing, respectively) for different vessel-tissue configurations: (i) blood vessel fully embedded in muscle tissue, (ii) blood vessel superficially embedded in muscle tissue, and (iii) blood vessel superficially embedded in muscle tissue with fat covering half of the arterial vessel (anterior portion). The simulations suggest that the parallel conductance and accuracy of measurement is dependent on the inhomogeneous/anisotropic configuration of surrounding tissue, including the asymmetric dimension and anisotropy in electrical conductivity of surrounding tissue. Specifically, the measurement was shown to be accurate as long as the vessel was superficial, regardless of the considerable total surrounding tissue dimension for coronary or peripheral arteries. Moreover, it was shown that the unfavourable impact of parallel conductance on the accuracy of conductance catheter measurement is decreased by the combination of a lower transverse electrical conductivity of surrounding muscle tissue, a smaller electrode spacing and a larger lumen diameter. The present findings confirm that the conductance catheter technique provides an accurate platform for sizing of clinically relevant (i.e. superficial and diseased) arteries.

Left ventricular epicardial admittance measurement for detection of acute LV dilation

There are two implanted heart failure warning systems incorporated into biventricular pacemakers/automatic implantable cardiac defibrillators and tested in clinical trials: right heart pressures, and lung conductance measurements. However, both warning systems postdate measures of the earliest indicator of impending heart failure: left ventricular (LV) volume. There are currently no proposed implanted technologies that can perform LV blood volume measurements in humans. We propose to solve this problem by incorporating an admittance measurement system onto currently deployed biventricular and automatic implantable cardiac defibrillator leads. This study will demonstrate that an admittance measurement system can detect LV blood conductance from the epicardial position, despite the current generating and sensing electrodes being in constant motion with the heart, and with dynamic removal of the myocardial component of the returning voltage signal. Specifically, in 11 pigs, it will be demonstrated that 1) a physiological LV blood conductance signal can be derived; 2) LV dilation in response to dose-response intravenous neosynephrine can be detected by blood conductance in a similar fashion to the standard of endocardial crystals when admittance is used, but not when only traditional conductance is used; 3) the physiological impact of acute left anterior descending coronary artery occlusion and resultant LV dilation can be detected by blood conductance, before the anticipated secondary rise in right ventricular systolic pressure; and 4) a pleural effusion simulated by placing saline outside the pericardium does not serve as a source of artifact for blood conductance measurements.

Electrical impedance spectroscopy and diagnosis of tendinitis

There have been a number of studies that investigate the usefulness of bioelectric signals in diagnoses and treatment in the medical field. Tendinitis is a musculoskeletal disorder with a very high rate of occurrence. This study attempts to examine whether electrical impedance spectroscopy (EIS) can detect pathological changes in a tendon and find the exact location of the lesion. Experimental tendinitis was induced by injecting collagenase into one side of the patellar tendons in rabbits, while the other side was used as the control. After measuring the impedance in the tendinitis and intact tendon tissue, the dissipation factor was computed. The real component of impedance and the dissipation factor turned out to be lower in tendinitis than in intact tissues. Moreover, the tendinitis dissipation factor spectrum showed a clear difference from that of the intact tendon, indicating its usefulness as a tool for detecting the location of the lesion. Pathologic findings from the tissues that were obtained after measuring the impedance confirmed the presence of characteristics of tendinitis. In conclusion, EIS is a useful method for diagnosing tendinitis and detecting the lesion location in invasive treatment.

Left ventricular volume measurement in mice by conductance catheter: evaluation and optimization of calibration

The conductance catheter (CC) allows thorough evaluation of cardiac function because it simultaneously provides measurements of pressure and volume. Calibration of the volume signal remains challenging. With different calibration techniques, in vivo left ventricular volumes (VCC) were measured in mice ( n = 52) with a Millar CC (SPR-839) and compared with MRI-derived volumes (VMRI). Significant correlations between VCC and VMRI [end-diastolic volume (EDV): R2 = 0.85, P < 0.01; end-systolic volume (ESV): R2 = 0.88, P < 0.01] were found when injection of hypertonic saline in the pulmonary artery was used to calibrate for parallel conductance and volume conversion was done by individual cylinder calibration. However, a significant underestimation was observed [EDV = −17.3 μl (−22.7 to −11.9 μl); ESV = −8.8 μl (−12.5 to −5.1 μl)]. Intravenous injection of the hypertonic saline bolus was inferior to injection into the pulmonary artery as a calibration method. Calibration with an independent measurement of stroke volume decreased the agreement with VMRI. Correction for an increase in blood conductivity during the in vivo experiments improved estimation of EDV. The dual-frequency method for estimation of parallel conductance failed to produce VCC that correlated with VMRI. We conclude that selection of the calibration procedure for the CC has significant implications for the accuracy and precision of volume estimation and pressure-volume loop-derived variables like myocardial contractility. Although VCC may be underestimated compared with MRI, optimized calibration techniques enable reliable volume estimation with the CC in mice.

Impact of physiological variables and genetic background on myocardial frequency-resistivity relations in the intact beating murine heart

Conductance measurements for generation of an instantaneous left ventricular (LV) volume signal in the mouse are limited, because the volume signal is a combination of blood and LV muscle, and only the blood signal is desired. We have developed a conductance system that operates at two simultaneous frequencies to identify and remove the myocardial contribution to the instantaneous volume signal. This system is based on the observation that myocardial resistivity varies with frequency, whereas blood resistivity does not. For calculation of LV blood volume with the dual-frequency conductance system in mice, in vivo murine myocardial resistivity was measured and combined with an analytic approach. The goals of the present study were to identify and minimize the sources of error in the measurement of myocardial resistivity to enhance the accuracy of the dual-frequency conductance system. We extended these findings to a gene-altered mouse model to determine the impact of measured myocardial resistivity on the calculation of LV pressure-volume relations. We examined the impact of temperature, timing of the measurement during the cardiac cycle, breeding strain, anisotropy, and intrameasurement and interanimal variability on the measurement of intact murine myocardial resistivity. Applying this knowledge to diabetic and nondiabetic 11- and 20- to 24-wk-old mice, we demonstrated differences in myocardial resistivity at low frequencies, enhancement of LV systolic function at 11 wk and LV dilation at 20–24 wk, and histological and electron-microscopic studies demonstrating greater glycogen deposition in the diabetic mice. This study demonstrated the accurate technique of measuring myocardial resistivity and its impact on the determination of LV pressure-volume relations in gene-altered mice.

Estimation of Cardiac Bidomain Parameters from Extracellular Measurement: Two Dimensional Study

Cardiac tissue conductivity measurements can be used to assess the electrical substrate underlying normal and abnormal wavefront propagation. We describe a method of solving the inverse cardiac bidomain model to estimate average longitudinal and transverse intra and extra-cellular conductivities and fiber angle relative to an electrode array placed arbitrarily on the epi- or endocardial surface. A Newton-Raphson reconstruction method and two Tikhonov-type regularizations were able to stably identify conductivities and fiber angles in tissue models having anisotropies similar to those in real cardiac tissue. The reconstruction methods were tested with data from increasingly realistic two dimensional cardiac bidomain models and performed well both when measurement noise was added, and when simulated experimental and forward model matching was diminished. This approach may be a suitable basis for continuous monitoring of myocardial condition in-vivo via a catheter based electrode array.

Early time course of myocardial electrical impedance during acute coronary artery occlusion in pigs, dogs, and humans

Changes in myocardial electrical impedance (MEI) and physiological end points have been correlated during acute ischemia. However, the importance of MEI's early time course is not clear. This study evaluates such significance, by comparing the temporal behavior of MEI during acute total occlusion of the left anterior descending coronary artery in anesthetized humans, dogs, and pigs. Here, interspecies differences in three MEI parameters (baseline, time to plateau onset, and plateau value normalized by baseline) were evaluated using Kruskal-Wallis ANOVA and post hoc tests ( P < 0.05). Noteworthy differences in the MEI time to plateau onset were observed: In dogs, MEI ischemic plateau was reached after 46.3 min (SD 12.9) min of occlusion, a significantly longer period compared with that of pigs and humans [4.7 (SD 1.2) and 4.1 min (SD 1.9), respectively]. However, no differences could be observed between both animal species regarding the normalized MEI ischemic plateau value (15.3% (SD 4.7) in pigs, vs. 19.6% (SD 2.6) in dogs). For all studied MEI parameters, only swine values resembled those of humans. The severity of myocardial supply ischemia, resulting from coronary artery occlusion, is known to be dependent on collateral flow. Thus, because dogs possess a well-developed collateral system (unlike humans or pigs), they have shown superior resistance to occlusion of a coronary artery. Here, the early MEI time course after left anterior descending coronary artery occlusion, represented by the time required to reach ischemic plateau, was proven to reflect such interspecies differences.

Electrical impedance along connective tissue planes associated with acupuncture meridians

Background

Acupuncture points and meridians are commonly believed to possess unique electrical properties. The experimental support for this claim is limited given the technical and methodological shortcomings of prior studies. Recent studies indicate a correspondence between acupuncture meridians and connective tissue planes. We hypothesized that segments of acupuncture meridians that are associated with loose connective tissue planes (between muscles or between muscle and bone) visible by ultrasound have greater electrical conductance (less electrical impedance) than non-meridian, parallel control segments.

Methods

We used a four-electrode method to measure the electrical impedance along segments of the Pericardium and Spleen meridians and corresponding parallel control segments in 23 human subjects. Meridian segments were determined by palpation and proportional measurements. Connective tissue planes underlying those segments were imaged with an ultrasound scanner. Along each meridian segment, four gold-plated needles were inserted along a straight line and used as electrodes. A parallel series of four control needles were placed 0.8 cm medial to the meridian needles. For each set of four needles, a 3.3 kHz alternating (AC) constant amplitude current was introduced at three different amplitudes (20, 40, and 80 μAmps) to the outer two needles, while the voltage was measured between the inner two needles. Tissue impedance between the two inner needles was calculated based on Ohm's law (ratio of voltage to current intensity).

Results

At the Pericardium location, mean tissue impedance was significantly lower at meridian segments (70.4 ± 5.7 Ω) compared with control segments (75.0 ± 5.9 Ω) (p = 0.0003). At the Spleen location, mean impedance for meridian (67.8 ± 6.8 Ω) and control segments (68.5 ± 7.5 Ω) were not significantly different (p = 0.70).

Conclusion

Tissue impedance was on average lower along the Pericardium meridian, but not along the Spleen meridian, compared with their respective controls. Ultrasound imaging of meridian and control segments suggested that contact of the needle with connective tissue may explain the decrease in electrical impedance noted at the Pericardium meridian. Further studies are needed to determine whether tissue impedance is lower in (1) connective tissue in general compared with muscle and (2) meridian-associated vs. non meridian-associated connective tissue.

In vitro measurement of myocardial impedivity anisotropy with a miniature rectangular tube

Due to rapid change of fiber orientation, it is difficult to measure myocardial impedivity separately in a longitudinal or transverse fiber direction without mutual influence in the two directions. Previously published values of the longitudinal and the transverse myocardial impedivity were derived indirectly from measurements that mixed the impedivity in all directions. Those values are questionable because the derivations were based on a simplified uniform myocardial fiber model. In this paper, a miniature rectangular tube was devised to facilitate direct measurement of myocardial impedivity in a uniform fiber direction. The average transverse-to-longitudinal ratio of the measured in vitro swine myocardial impedivity was about 1.66 from 1 Hz to 1 kHz and dropped to 1.25 at 1 MHz. The result is important for accurate modeling of the electrical property of myocardium in biomedical research of radio-frequency cardiac catheter ablation.

Convenient automated conductance volumetric system

Conventional conductance volumetric systems require ex-vivo calibrations for blood conductivity and parallel conductance. It is often impractical to repeat blood sampling and hypertonic saline infusion for these calibrations. To overcome these limitations, we developed a useful, self-calibrating conductance volumetric system that does not require ex-vivo calibrations. On a conventional 6-electrode catheter, we added an extra electrode close to one of the recording electrodes to estimate blood conductivity. These two electrodes were placed close (0.5 mm) enough so that conductance between them reflected only blood conductivity regardless of cardiac volume. We estimated parallel conductance by the dual-frequency excitation (2 and 20 kHz) method. In 18 anesthetized rabbits, blood conductivity (sigma(est)) thus estimated agreed well with that (sigma(conv)) measured by the conventional ex-vivo blood sampling method (sigma(est) = 1.04sigma(conv)-0.25, R(2) = 0.98, SEE = 0.01 mS/cm, 1.2% error). Parallel conductance (G(p est)) estimated by dual-frequency excitation also agreed well with that (G(p conv)) estimated by the saline injection method (G(p est) = 0.95G(p conv)+4.25, R(2) = 0.87, SEE = 4.0 mS, 6.0% error). Estimated ventricular volume (V(est)) by our system agreed reasonably well with that (V(conv)) by the conventional method (V(est) = 0.93V(conv)+0.01, R(2) = 0.86, SEE = 0.22 ml, 14.7% error). The fact that this self-calibrating conductance volumetric system drastically simplifies volume measurement makes it an attractive tool for the assessment of cardiac function where significant changes in blood conductivity and parallel conductance are inevitable, such as in cardiac surgery.

Impedance spectroscopy: an accurate method of differentiating between viable and ischaemic or infarcted muscle tissue

The object of the paper is to present results that show that impedance spectroscopy is an accurate method of assessing the condition of muscle tissue. Specimens of muscle tissue were excised from 36 Atlantic salmon and subjected to impedance spectroscopy measurements made at intervals during an 8h period of ischaemia and necrosis. These measurements were conducted for three different temperatures and for both the longitudinal and the transverse orientations of the muscle fibres. The specimens were also subjected to ATP, pH and visco-elastic measurement and analysis to establish the degree of correlation between changes in these quantities and impedance spectroscopy parameters due to ischaemia. It was concluded that the mean relaxation time, tau(c) was the impedance spectroscopy parameter that best described the changes taking place in the muscle tissue during the post-mortem period, decreasing by 60-76% during the 8h. This was the case for all three temperatures and for both orientations. Furthermore, the muscle tissue changes due to ischaemia, as reflected in the decrease in the mean relaxation time tau(c), were highly correlated with changes in the tissue ATP, pH and dynamic shear storage modulus G'.

In-vivo measurement of swine myocardial resistivity

We used a four-terminal plunge probe to measure myocardial resistivity in two directions at three sites from the epicardial surface of eight open-chest pigs in-vivo at eight frequencies ranging from 1 Hz to 1 MHz. We calibrated the plunge probe to minimize the error due to stray capacitance between the measured subject and ground. We calibrated the probe in saline solutions contained in a metal cup situated near the heart that had an electrical connection to the pig's heart. The mean of the measured myocardial resistivity was 319 ohm x cm at 1 Hz down to 166 ohm x cm at 1 MHz. Statistical analysis showed the measured myocardial resistivity of two out of eight pigs was significantly different from that of other pigs. The myocardial resistivity measured with the resistivity probe oriented along and across the epicardial fiber direction was significantly different at only one out of the eight frequencies. There was no significant difference in the myocardial resistivity measured at different sites.

Error analysis of tissue resistivity measurement

We identified the error sources in a system for measuring tissue resistivity at eight frequencies from 1 Hz to 1 MHz using the four-terminal method. We expressed the measured resistivity with an analytical formula containing all error terms. We conducted practical error measurements with in-vivo and bench-top experiments. We averaged errors at all frequencies for all measurements. The standard deviations of error of the quantization error of the 8-bit digital oscilloscope with voltage averaging, the nonideality of the circuit, the in-vivo motion artifact and electrical interference combined to yield an error of +/- 1.19%. The dimension error in measuring the syringe tube for measuring the reference saline resistivity added +/- 1.32% error. The estimation of the working probe constant by interpolating a set of probe constants measured in reference saline solutions added +/- 0.48% error. The difference in the current magnitudes used during the probe calibration and that during the tissue resistivity measurement caused +/- 0.14% error. Variation of the electrode spacing, alignment, and electrode surface property due to the insertion of electrodes into the tissue caused +/- 0.61% error. We combined the above errors to yield an overall standard deviation error of the measured tissue resistivity of +/- 1.96%.

Development of a multifrequency conductance catheter-based system to determine LV function in mice

Transgenic mice offer a valuable way to relate gene products to phenotype, but the ability to assess the cardiovascular phenotype with pressure-volume analysis has lagged. Conductance measurement offers a method to generate an instantaneous left ventricular (LV) volume signal in the mouse but has been limited by the volume signal being a combination of blood and LV muscle. We hypothesized that by developing a mouse conductance system that operates at several simultaneous frequencies, we could identify and correct for the myocardial contribution to the instantaneous volume signal. This hypothesis is based on the assumption that mouse myocardial conductivity will vary with frequency, whereas mouse blood conductivity will not. Consistent with this hypothesis, we demonstrated that at higher excitation frequency, greater end-diastolic and end-systolic conductance are detected, as well as a smaller difference between the two. We then empirically solved for LV blood volume using two frequencies. We combined measured resistivity of mouse myocardium with an analytic approach and extracted an estimate of LV blood volume from the raw conductance signal. Development of a multifrequency catheter-based system to determine LV function could be a tool to assess cardiovascular phenotype in transgenic mice.

Estimation of parallel conductance by dual-frequency conductance catheter in mice

The conductance catheter method has substantially enhanced the characterization of in vivo cardiovascular function in mice. Absolute volume determination requires assessment of parallel conductance (V(p)) offset because of conductivity of structures external to the blood pool. Although such a determination is achievable by hypertonic saline bolus injection, this method poses potential risks to mice because of volume loading and/or contractility changes. We tested another method based on differences between blood and muscle conductances at various catheter excitation frequencies (20 vs. 2 kHz) in 33 open-chest mice. The ratio of mean frequency-dependent signal difference to V(p) derived by hypertonic saline injection was consistent [0.095 +/- 0.01 (SD), n = 11], and both methods were strongly correlated (r(2) = 0.97, P < 0.0001). This correlation persisted when the ratio was prospectively applied to a separate group of animals (n = 12), with a combined regression relation of V(p(DF)) = 1.1 * V(p(Sal)) - 2.5 [where V(p(DF)) is V(p) derived by the dual-frequency method and V(p(Sal)) is V(p) derived by hypertonic saline bolus injection], r(2) = 0.95, standard error of the estimate = 1.1 microl, and mean difference = 0.6 +/- 1.4 microl. Varying V(p(Sal)) in a given animal resulted in parallel changes in V(p(DF)) (multiple regression r(2) = 0.92, P < 0.00001). The dominant source of V(p) in mice was found to be the left ventricular wall itself, since surrounding the heart in the chest with physiological saline or markedly varying right ventricular volumes had a minimal effect on the left ventricular volume signal. On the basis of V(p) and flow probe-derived cardiac output, end-diastolic volume and ejection fraction in normal mice were 28 +/- 3 microl and 81 +/- 6%, respectively, at a heart rate of 622 +/- 28 min(-1). Thus the dual-frequency method and independent flow signal can be used to provide absolute volumes in mice.

Dependence of apparent resistance of four-electrode probes on insertion depth

The apparent resistance of a finite-thickness layer measured with a four-electrode plunge probe depends on the electrode insertion depth, electrode spacing, and layer thickness, as well as the resistivity ratio of an underlying layer. A physical model consisting of air, a saline solution layer, and an agar layer simulates the real situation of resistivity measurement. The saline layer represents the finite-thickness layer whose resistivity is to be measured by a plunge electrode probe, and the agar layer represents an underlying perturbing layer. A micropositioner controls the insertion depth of the four electrodes into the saline solution. With the apparent resistance measured on a semi-infinite-thickness layer of saline solution as standard, measurement results show decreasing apparent resistance and increasing error with increasing electrode insertion depth. This information is important for correct measurement of myocardial resistivity in vivo and in vitro.

The effect of changing excitation frequency on parallel conductance in different sized hearts

OBJECTIVE

An important component of the ventricular volume measured using the conductance catheter technique is due to parallel conductance (Vc), which results from the extension of the electric field beyond the ventricular blood pool. Parallel conductance volume is normally estimated using the saline dilution method (Vc(saline dilution)), in which the conductivity of blood in the ventricle is transiently increased by injection of hypertonic saline. A simpler alternative has been reported by Gawne et al. [12]. Vc(dual frequency) is estimated from the difference in total conductance measured at two exciting frequencies and the method is based on the assumption that parallel conductance is mainly capacitive and hence is negligible at low frequency. The objective of this study was to determine whether the dual frequency technique could be used to substitute the saline dilution method to estimate Vc in different sized hearts.

METHODS

The accuracy and linearity of a custom-built conductance catheter (CC) system was initially assessed in vitro. Subsequently, a CC and micromanometer were inserted into the left ventricle of seven 5 kg pigs (group 1) and six 50 kg pigs (group 2). Cardiac output was determined using thermodilution (group 1) and an ultrasonic flow probe (group 2) from which the slope coefficient (alpha) was determined. Steady state measurements and Vc estimated using saline dilution were performed at frequencies in the range of 5-40 kHz. All measurements were made at end-expiration. Finally, Vc was estimated from the change in end-systolic conductance between 5 kHz and 40 kHz using the dual frequency technique of Gawne et al. [12].

RESULTS

There was no change in measured volume of a simple insulated cylindrical model when the stimulating frequency was varied from 5-40 kHz. Vc(saline dilution) varied significantly with frequency in group 1 (8.63 +/- 2.74 ml at 5 kHz; 11.51 +/- 2.65 ml at 40 kHz) (p = 0.01). Similar results were obtained in group 2 (69.43 +/- 27.76 ml at 5 kHz; 101.24 +/- 15.21 ml at 40 kHz) (p < 0.001). However, the data indicate that the resistive component of the parallel conductance is substantial (Vc at 0 Hz estimated as 8.01 ml in group 1 and 62.3 ml in group 2). There was an increase in alpha with frequency in both groups but this did not reach significance. The correspondence between Vc(dual frequency) and Vc(saline dilution) methods was poor (group 1 R2 = 0.69; group 2 R2 = 0.22).

CONCLUSION

At a lower excitation frequency of 5 kHz a smaller percentage of the electric current extends beyond the blood pool so parallel conductance is reduced. While parallel conductance is frequency dependent, it has a substantial resistive component. The dual frequency method is based on the assumption that parallel conductance is negligible at low frequencies and this is clearly not the case. The results of this study confirm that the dual frequency technique cannot be used to substitute the saline dilution technique.