The fundamental law of electrostimulation and its application to defibrillation

Estimations of Charge Deposition Onto Convoluted Axon Surfaces Within Extracellular Electric Fields

OBJECTIVE

Biophysical models of neural stimulation are a valuable approach to explaining the mechanisms of neuronal recruitment via applied extracellular electric fields. Typically, the applied electric field is estimated via a macroscopic finite element method solution and then applied to cable models as an extracellular voltage source. However, the field resolution is limited by the finite element size (typically 10's-100's of times greater than average neuronal cross-section). As a result, induced charges deposited onto anatomically realistic curved membrane interfaces are not taken into consideration. However, these details may alter estimates of the applied electric field and predictions of neural tissue activation.

METHODS

To estimate microscopic variations of the electric field, data for intra-axonal space segmented from 3D scanning electron microscopy of the mouse brain genu of corpus callosum were used. The boundary element fast multipole method was applied to accurately compute the extracellular solution. Neuronal recruitment was then estimated via an activating function.

RESULTS

Taking the physical structure of the arbor into account generally predicts higher values of the activating function. The relative integral 2-norm difference is 90% on average when the entire axonal arbor is present. A large fraction of this difference might be due to the axonal body itself. When an isolated physical axon is considered with all other axons removed, the relative integral 2-norm difference between the single-axon solution and the complete solution is 25% on average.

CONCLUSION

Our result may provide an explanation as to why Deep Brain Stimulation experiments typically predict lower activation thresholds than commonly used FEM/Cable model approaches to predicting neuronal responses to extracellular electrical stimulation.

SIGNIFICANCE

These results may change methods for bi-domain neural modeling and neural excitation.

Research study on the efficiency of a defibrillating biphasic pulse of various durations based on mathematical modeling and simulation of a cardiomyocyte

The paper presents the results of our research study on the impact of different durations of a biphasic rectangular pulse on the efficiency of the defibrillating action based on modeling and simulation of a cardiomyocyte in the framework of Cell Electrophysiology Simulation Environment. We used Luo-Rudy Mammalian Ventricular Model II (dynamic) as the mathematical model of the biochemical processes, which occur both on the surface and inside a cardiomyocyte in a guinea pig. An analysis of the obtained results allowed us to determine the optimal time of the defibrillating pulse. It has been shown that a pulse of 4 ms duration has the highest efficiency. The research has been carried out directly based on the mathematical model and simulation of the cardiomyocyte that makes it possible to minimize errors which may occur in experiments on animals

Evaluation of a virtual neurophysiology laboratory as a new pedagogical tool for medical undergraduate students in China

This study compared the effect of a virtual laboratory, a living tissue laboratory, and a blended laboratory on student learning about the generation and conduction of neural action potentials and perceptions about life science. Sixty-three second-year medical students were randomly assigned to one of three groups (living tissue laboratory, virtual laboratory, and blended group). The students conducted the practical activity, and then they were given a postlaboratory quiz and an attitude survey. The blended group euthanized fewer animals and spent less time to finish the animal experiment than the living tissue group did. In the postlaboratory quiz, students who performed the virtual laboratory alone got significantly lower scores than students in the other two groups, and the blended group did not get better scores than the living tissue group. The attitude surveys showed that the virtual laboratory group had a lower perceived value of the science research and activity in which they participated than the other two groups did. Here, 77.8% of all students chose the blended style as the ideal teaching method for experiments. Our findings led us to believe that isolated use of the virtual laboratory in China is not the best practice: the virtual laboratory serves as an effective preparation tool, and the blended laboratories may become the best laboratory teaching practice, provided that the software design for the virtual laboratory is further improved.

A Model of Electrostimulation Based on the Membrane Capacitance as Electromechanical Transducer for Pore Gating

BACKGROUND

Electrostimulation has gained enormous importance in modern medicine, for example, in implantable pacemakers and defibrillators, pain stimulators, and cochlear implants. Most electrostimulation macromodels use the electrical current as the primary parameter to describe the conventional strength-duration relationship of the output of a generator. These models normally assume that the stimulation pulse charges up the passive cell membrane capacitance, and then the increased (less-negative) transmembrane potential activates voltage-gated sodium channels. However, this model has mechanistic and accuracy limitations.

NOVEL CONCEPT

Our model assumes that the membrane capacitance is an electromechanical transducer and that the membrane is compressed by the endogenous electric field. The pressure is quadratically correlated with the transmembrane voltage. If the pressure is reduced by an exogenous field, the compression is released and, thus, opening the pores for Na(+) influx initiates excitation.

RESULTS

The exogenous electric field must always be equal to or greater than the rheobase field strength (rheobase condition). This concept yields a final result that the voltage-pulse-content produced by the exogenous field between the two ends of a cell is a linear function of the pulse duration at threshold level. Thus, the model yields mathematical formulations that can describe and explain the characteristic features of electrostimulation.

CONCLUSIONS

Our model of electrostimulation can describe and explain electrostimulation at cellular level. The model's predictions are consistent with published experimental studies. Practical applications in cardiology are discussed in the light of this model of electrostimulation.

Easy method to examine single nerve fiber excitability and conduction parameters using intact nonanesthetized earthworms

The generation and conduction of neuronal action potentials (APs) were the subjects of a cell physiology exercise for first-year medical students. In this activity, students demonstrated the all-or-none nature of AP generation, measured conduction velocity, and examined the dependence of the threshold stimulus amplitude on stimulus duration. For this purpose, they used the median giant nerve fiber (MGF) in the ventral nerve cord of the common earthworm (Lumbricus terrestris). Here, we introduce a specialized stimulation and recording chamber that the nonanesthetized earthworm enters completely unforced. The worm resides in a narrow round duct with silver electrodes on the bottom such that individual APs of the MGF can be elicited and recorded superficially. Our experimental setup combines several advantages: it allows noninvasive single fiber AP measurements taken from a nonanesthetized animal that is yet restrained. Students performed the experiments with a high success rate. According to the data acquired by the students, the mean conduction velocity of the MGF was 30.2 m/s. From the amplitude-duration relationship for threshold stimulation, rheobase and chronaxie were graphically determined by the students according to Lapicque's method. The mean rheobase was 1.01 V, and the mean chronaxie was 0.06 ms. The acquired data and analysis results are of high quality, as deduced from critical examination based on the law of Weiss. In addition, we provide video material, which was also used in the practical course.

Occupational exposure in MRI

This article reviews occupational exposure in clinical MRI; it specifically considers units of exposure, basic physical interactions, health effects, guideline limits, dosimetry, results of exposure surveys, calculation of induced fields and the status of the European Physical Agents Directive. Electromagnetic field exposure in MRI from the static field B(0), imaging gradients and radiofrequency transmission fields induces electric fields and currents in tissue, which are responsible for various acute sensory effects. The underlying theory and its application to the formulation of incident and induced field limits are presented. The recent International Commission on Non-Ionizing Radiation Protection (ICNIRP) Bundesministerium für Arbeit und Soziales and Institute of Electrical and Electronics Engineers limits for incident field exposure are interpreted in a manner applicable to MRI. Field measurements show that exposure from movement within the B(0) fringe field can exceed ICNIRP reference levels within 0.5 m of the bore entrance. Rate of change of field dB/dt from the imaging gradients is unlikely to exceed the new limits, although incident field limits can be exceeded for radiofrequency (RF) exposure within 0.2-0.5 m of the bore entrance. Dosimetric surveys of routine clinical practice show that staff are exposed to peak values of 42 ± 24% of B(0), with time-averaged exposures of 5.2 ± 2.8 mT for magnets in the range 0.6-4 T. Exposure to time-varying fields arising from movement within the B(0) fringe resulted in peak dB/dt of approximately 2 T s(-1). Modelling of induced electric fields from the imaging gradients shows that ICNIRP-induced field limits are unlikely to be exceeded in most situations; however, movement through the static field may still present a problem. The likely application of the limits is discussed with respect to the reformulation of the European Union (EU) directive and its possible implications for MRI.

Waveform optimization for internal cardioversion of atrial fibrillation

INTRODUCTION

A novel atrial defibrillator was developed at the Royal Victoria Hospital in collaboration with the Nanotechnology and Integrated Bio-Engineering Centre, University of Ulster. This device is powered by an external pulse of radiofrequency energy and designed to cardiovert using low-tilt monophasic waveform (LTMW) and low-tilt biphasic waveform (LTBW), 12 milliseconds pulse width. This study compared the safety and efficacy of LTMW with LTBW for transvenous cardioversion of atrial fibrillation (AF).

METHODS

Patients were anticoagulated with warfarin to maintain International Normalized Ratio between 2 and 3 for 4 weeks prior cardioversion. Warfarin international normalized ratio level was maintained in between 2 and 3 for 4 weeks prior cardioversion. St Jude's defibrillating catheter was positioned in the distal coronary sinus and right atrium and connected to the defibrillator via a junction box. After a test shock using a dummy load, the patient was cardioverted in a step-up progression from 50 to 300 V. Shock success was defined as return of sinus rhythm for 30 seconds or more. If cardioversion was unsuccessful at peak voltage, the patient was crossed over to the other arm of the waveform type and cardioverted at peak voltage.

RESULTS

Thirty patients were randomized equally to LTBW and LTMW (15 each). Seven out of 15 patients (46%) cardioverted to sinus rhythm with LTBW, and 1 (6%) of 15, with LTMW (P = .035). Including crossover patients, 14 patients (46%) converted to sinus rhythm. After crossover, 4 patients were cardioverted with LTBW and 2 with LTMW. Overall mean voltage, current, and energy used for cardioversion were 270.53 ± 35.96 V, 3.68 ± 0.80 A, and 9.12 ± 3.73 J, respectively, and intracardiac impedance was 70.82 ± 13.46 Ω. For patients who were successfully cardioverted, mean voltage, current, energy, and intracardiac impedance were 268.28 ± 42.41 V, 3.52 ± 0.63 A, 8.51 ± 3.16 J, and 73.92 ± 12.01 Ω. There were no major adverse complications during the study. Cardiac markers measured postcardioversion were unremarkable.

CONCLUSION

Low-tilt biphasic waveform was more efficacious for low-energy transvenous cardioversion of AF. A significant proportion of patients were successfully cardioverted to sinus rhythm with low energy. Radiofrequency-powered defibrillation can be safely used for transvenous cardioversion of AF.

Comparison between two defibrillation waveforms

Two defibrillation waveforms, the chopped biphasic pulses and the constant current pulses, were assessed and compared. Two indices are introduced. The first one is the ratio between the delivered energy W and the energy W(0) of a rectangular pulse with the same duration and electric charge. The second index η(C) = W(0)/W(C0) stands for the level of utilizing the initially loaded capacitor energy W(C0). Some design considerations are also discussed. Another aspect of the study is the choice of appropriate capacitor for pulse generation. The results obtained show that there is no outstanding optimal waveform. The W/W(0) ratio is higher for the known constant current shapes but specifically with a patient resistance lower than 80 Ω. On the other hand, the implementation of these shapes would face several difficulties. The chopped biphasic waveforms are obtained by relatively simple technical solutions leading to very small in size and weight portable instruments.

From defibrillation theory to clinical implications

BACKGROUND

Our defibrillation theory claims that the mean voltage threshold is a hyperbolic function of pulse duration and that voltages below rheobase should be avoided as being counterproductive. Truncation of the pulse just at rheobase level yields minimal stored energy thresholds. To verify or falsify this theory, animal experiments were carried out.

MATERIAL AND METHODS

In two animal experiments, 212 defibrillation thresholds in 22 swine were determined with different biphasic pulses of which 92 were optimally truncated in phase 1. Step-up test procedure was used with the first successful shock defined as "threshold."

RESULTS

Experimental proof is gained that truncation according to "rheobase condition" shows lowest stored energy. A ranking order of stored energy thresholds demonstrates that (1) lower output capacitances reduce needed energy, and (2) pulse durations shorter or longer than optimal increase needed energy. The voltage-pulse-content threshold is linearly correlated with pulse duration.

CONCLUSIONS

Truncation above or below rheobase increases the stored energy threshold. Voltage averaged during pulse duration is a hyperbolic function of pulse duration. The stored energy is reduced with decreasing output capacitance. The experimental results do not only fully verify our theory, they also suggest clinical implications: (1) the current usage of the "constant tilt concept" in implantable cardioverter defibrillator (ICD) should be abandoned in favor of "optimal truncation concept," (2) an algorithm developed for calculating optimal truncation proved to be useful so that incorporation into ICD for automatic adjustment is recommended, and (3) the output capacitance should be reduced from about 100 microF to 60 to 70 microF.

Stimulation threshold comparison of time-varying magnetic pulses with different waveforms

PURPOSE

To clarify whether sinusoidal pulses possess lower thresholds than rectangular ones at perception threshold, a statement often made that contradicts the theory of stimulation.

MATERIALS AND METHODS

The results of a nerve stimulation study with 65 volunteers and with trapezoidal and sinusoidal gradient pulses were used to apply the combination of the electric field, induced in the tissue of the human body, with the "Fundamental Law of Electrostimulation." This law claims that the waveshape of a pulse is not essential as long as the amplitude of the pulse does not decrease below rheobase (rheobase condition).

RESULTS

If the rheobase condition is applied to sinusoidal waveforms and the pulse duration and amplitude is corrected accordingly, both trapezoidal and sinusoidal gradient pulses have identical threshold amplitudes as a function of pulse duration.

CONCLUSION

The "Fundamental Law of Electrostimulation," including the "rheobase condition," proved to be a good basis for describing magnetic field stimulation (magnetostimulation) and that application of it to magnetostimulation is suitable as the basis for describing magnetic field stimulation with various waveforms. For nonrectangular pulses, pulse durations and pulse amplitudes must be corrected according to the "rheobase condition." The exponential Blair Equation is less suited to be applied in magnetostimulation.

A comparison of chronaxies for ventricular fibrillation induction, defibrillation, and cardiac stimulation: unexpected findings and their implications

INTRODUCTION

A low-energy (<or= 4 J) cardioversion shock (LEC) either terminates reentrant ventricular tachycardia (VT) or accelerates it to ventricular fibrillation (VF). Optimization of the duration and amplitude of LEC shocks could improve the success rate of VT termination without VF induction.

METHODS AND RESULTS

In order to learn how LEC shocks may be optimized, we used an animal model to compare the strength-duration curve for VF induction and the strength-duration curve for cardiac stimulation via the shock coil. Conventional implantable cardioverter-defibrillator (ICD) leads were implanted in 12 narcotized pigs from 20 kg to 25 kg in weight. Stimulation, VF induction, and defibrillation pulses were delivered by custom-designed stimulators at preset pulse durations and amplitudes. The corresponding hyperbolic strength-duration curves were constructed using the least-squares fit method and averaged for all the animals. The mean chronaxie for stimulation via the shock coil of 0.23 ms was significantly shorter than both defibrillation (4.8 ms) and VF induction (3.1 ms) chronaxie values. At a shock duration of 0.3 ms or less, the mean VF-induction threshold amplitude exceeded 300 V.

CONCLUSION

It may be reasonable to study whether LEC pulses from 0.25 ms to 0.30 ms in duration and up to 250 V in amplitude would increase therapeutic yield in VT termination without VF induction in humans. Contrary to the current belief, the discrepancy between defibrillation and stimulation chronaxie is not caused by different electrode size. We postulate that the time constant of the fast sodium channel reactivation may be the underlying reason.

The hyperbolic strength-duration relationship of defibrillation threshold

Defibrillation with square-wave pulses has proved to possess hyperbolic strength-duration relationship. Does such a hyperbolic relation also exist for exponentially decaying pulses as they are commonly used today? This paper hypothesizes that exponentially decaying pulses obey hyperbolic strength-duration relationship, calculates the consequences, and advises of how such thresholds should be investigated. If the strength-duration relationship exists for current, the corresponding charge threshold must be a Weiss' straight threshold line. In analogy, for exponentially decaying pulses, the integral of the amplitude over pulse duration (PD) must be calculated as a function of PD. If this function is linearly correlated, the mean voltage possesses a hyperbolic strength-duration relationship, whereas the peak voltage does not. Peak amplitude curves possess minima shifting to the right with increasing time constant RC limiting the allowed range of useful PDs. To prove that exponentially decaying pulses have a hyperbolic relationship, testing must be done in six steps that are demonstrated with results published in literature. Mean voltages have, indeed, hyperbolic strength-duration relationship. Chronaxie is not calculated correctly as long as peak voltage thresholds are correlated and PDs are greater than allowed.

Can the Direct Cardiac Effects of the Electric Pulses Generated by the TASER X26 Cause Immediate or Delayed Sudden Cardiac Arrest in Normal Adults?

There is only a small amount of experimental data about whether the TASER X26, a nonlethal weapon that delivers a series of brief electrical pulses to cause involuntary muscular contraction to temporarily incapacitate an individual, can initiate ventricular fibrillation to cause sudden cardiac arrest either immediately or sometime after its use. Therefore, this paper uses the fundamental law of electrostimulation and experimental data from the literature to estimate the likelihood of such events. Because of the short duration of the TASER pulses, the large duration of the cardiac cell membrane time constant, the small fraction of current from electrodes on the body surface that passes through the heart, and the resultant high pacing threshold from the body surface, the fundamental law of electrostimulation predicts that the TASER pulses will not stimulate an ectopic beat in the large majority of normal adults. Since the immediate initiation of ventricular fibrillation in a normal heart requires a very premature stimulated ectopic beat and the threshold for such premature beats is higher than less premature beats, it is unlikely that TASER pulses can immediately initiate ventricular fibrillation in such individuals through the direct effect of the electric field generated through the heart by the TASER. In the absence of preexisting heart disease, the delayed development of ventricular fibrillation requires the electrical stimuli to cause electroporation or myocardial necrosis. However, the electrical thresholds for electroporation and necrosis are many times higher than that required to stimulate an ectopic beat. Therefore, it is highly unlikely that the TASER X26 can cause ventricular fibrillation minutes to hours after its use through direct cardiac effects of the electric field generated by the TASER.

Parameters characterizing implantable defibrillator output: a proposal

AIMS

Recently, a discussion was carried out in Heart Rhythm on the specifications that could characterize implantable defibrillators. It is the intention of this paper to participate in this discussion on defibrillation characteristics and to give recommendations on how this problem could be solved. Theoretical considerations and results There are different defibrillation theories, all finding that the defibrillation's efficacy depends on the time constant RC which is output capacitance C times load resistance R. Efficacy decreases with increasing RC. This means that (i) the knowledge of C is of paramount importance, (ii) the energy is 'devalued' with increasing RC and that those parameter settings such as tilt or pulse duration should be adjusted to the time constant, and (iii) the energy values given without further specification are not meaningful. As there is always a voltage drop across an internal resistance within the ICD, the measured voltage across the output differs from the capacitor voltage and is reduced which determines the efficiency of the device. From the data given by Thammanomai et al., one can determine the parameters maximum voltage, capacitance, internal resistance, and tilt. These parameters are adequate and necessary to describe an ICD device and to derive the effective energy for device comparison. Discussion The 'high output devices' with their high nominal energy are reduced in their effective energies to a degree that they are comparable to the best 'standard output devices'. They do not offer that superiority which is promised by the nominal energy. Moreover, if the tilt is fixed and larger than optimal, the energy requirements are still higher or the effective energy will further drop. The term 'delivered energy' is not used by us because the delivered energy increases with increasing tilt. However, today's tilts are too large as judged by theories, which means that high delivered energies can be worse than lower ones. The delivered energy is, therefore, not a meaningful parameter in judging ICDs.

CONCLUSION

ICD devices should be characterized by: (i) voltage, (ii) capacitance, (iii) tilt or pulse duration (if not programmable), and (iv) internal resistance. All other parameters can be derived from them by simple calculations. Introduction of a 'devaluation factor' characterizes the decreasing efficacy with increasing time constant and renders the output characteristics transparent and comparable.

Novel rectangular biphasic and monophasic waveforms delivered by a radiofrequency-powered defibrillator compared with conventional capacitor-based waveforms in transvenous cardioversion of atrial fibrillation

AIMS

To investigate the feasibility and efficacy of novel low-tilt biphasic waveforms in transvenous cardioversion of atrial fibrillation (AF), delivered by a radiofrequency-powered defibrillator.

METHODS AND RESULTS

The investigation was performed in three phases in an animal model of AF: a feasibility and efficacy study (in 10 adult Large White Landrace swine), comparison with low-tilt monophasic and standard capacitor-based waveforms, and an assessment of sequential shocks delivered over several pathways (in 15 adult Suffolk sheep). Defibrillation electrodes were positioned transvenously under fluoroscopic control in the high lateral right atrium and distal coronary sinus. When multiple defibrillation pathways were tested, a third electrode was also attached to the lower interatrial septum. The electrodes were then connected to a radiofrequency (RF)-powered defibrillator or a standard defibrillator. After confirmation of successful induction of sustained AF, defibrillation was attempted. Percentage success was calculated from the effects of all shocks delivered to all the animals within each set of experiments. Of the low-tilt (RF) biphasic waveforms delivered during internal atrial cardioversion, 100% success was achieved with a 6/6 ms 100/-50 V waveform (1.45+/-0.01 J). This waveform was similar in efficacy to low-tilt (RF) monophasic waveforms (88 vs. 92% success, 1.58+/-0.01 vs. 2.67+/-0.03 J; P=NS; delivered energy 41% lower) and superior to equivalent voltage standard monophasic (50% success, 0.67+/-0.00 J; P<0.001) and biphasic waveforms (72% success, 0.69+/-0.00 J; P=0.03). Sequential shocks delivered over dual pathways did not improve the efficacy of low-tilt biphasic waveforms.

CONCLUSION

A low-tilt biphasic waveform from a RF-powered defibrillator (6/6 ms 100/-50 V) is more efficacious than standard monophasic or biphasic waveforms (equivalent voltage) and is similar in efficacy to low-tilt monophasic waveforms.

Determinants and Effects of Electrical Stimulation of the Inferior Interatrial Parasympathetic Plexus During Atrial Fibrillation

INTRODUCTION

Catheter stimulation of the inferior interatrial ganglionated parasympathetic plexus decreases the ventricular rate during atrial fibrillation (AF) in humans. However, the relatively high stimulation voltages might prevent implementation of neurostimulation in chronic implantable devices. From myocardial electrostimulation it is known that the required impulse energy and charge is lowest at the chronaxie time. In order to lower energy requirements for cardiac neurostimulation, the present study evaluates the impulse-strength versus impulse-duration relationship for a neurostimulation lead that was implanted into the inferior interatrial ganglionated plexus.

METHODS AND RESULTS

In nine dogs, permanent epicardial bipolar screw-in electrodes were fixed in the inferior interatrial ganglionated plexus. AF was maintained via rapid atrial pacing. During AF, neural stimulation was performed at various frequencies (1-100 Hz), impulse durations (0.05-2 msec), and voltages (0.02-11.5 V). There was a linear correlation between R-R interval lengthening and stimulus voltage (R = 0.99; P < 0.001) and a bell-shaped relationship between stimulation frequency and negative dromotropic effect with maximum rate slowing at 30-50 Hz. The rheobase for a 50% R-R interval prolongation during AF was 1.81 V and 2.72 V for high-grade AVB yielding a chronaxie time of 0.14 msec and 0.18 msec, respectively. The impulse energy (charge) at the chronaxie time was 4-6 microJ (6-8 microC).

CONCLUSIONS

Cardiac neurostimulation follows a chronaxie/rheobase behavior. Energy, charge, and voltage values needed to achieve significant negative dromotropic effects are within the limits of conventional cardiac pacemaker outputs, which may allow implementation of neurostimulation capabilities in current pacemaker technology.

Threshold measurements: ten rules for good measuring practice

The following rules for professionally measuring thresholds are derived and discussed: RULE 1: Thresholds should be expressed as voltage averaged over pulse duration to get reproducible and comparable results! RULE 2: Pacing threshold measurements with exponentially decaying pulses should not be extended beyond 1.4 ms as that portion of the pulse below rheobase does not contribute to the stimulation effect! RULE 3: Threshold measurements are best carried out with fixed pulse duration and variable voltage! RULE 4: If threshold measurements are carried out in discrete steps, the steps should be chosen such that the relative step size is as equal as possible! RULE 5: Accuracy of threshold measurements is highly increased if the arithmetically averaged value of the last effective and the first ineffective pulse is defined as threshold! RULE 6: To determine strength-duration-curves, a linear regression of the quantity versus pulse duration should be calculated which yields simply the numerical values of the chronaxie and rheobase! RULE 7: To reach representative strength-duration-curves, measurements with at least four pairs of values must be carried out! RULE 8: Measuring defibrillation thresholds, the relative voltage step size should be chosen equally to have equal accuracy for all steps. RULE 9: If the result of a defibrillation threshold investigation does not reach significance, a too large voltage step size could be an explanation! RULE 10: Comparing intraindividually the threshold of two different defibrillation systems or parameter settings, the threshold ratios should be formed and averaged! Obeying these rules guaranties professional threshold measurements expressed as "rheobase" and "chronaxie" even with devices with discrete steps in parameter programming.

How to program pulse duration or tilt in implantable cardioverter defibrillators

Implantable cardioverter defibrillators (ICDs) are available with independently programmable duration and tilt of the shock pulse waveform. Manufacturers do not, however, commonly advise how these parameters can be programmed for optimal clinical benefit. From theoretical considerations, the author recommends programming both parameters based on the measured lead system resistance R into which the shock is delivered. Assuming that the defibrillation pulse decline below the defibrillation threshold rheobase is undesirable because of the possibility of refibrillation. Mathematical relationships expressing optimal pulse duration and tilt as functions of the output time constant can be derived that are valid for monophasic pulses and the first phase of biphasic pulses. Two ICD manufacturers provide for programmable tilt (Medtronic GEM III, atrial channel) or both tilt T and pulse duration PD. (St. Jude Medical newest devices). Considering its output capacitance, it is recommended that the Medtronic Gem III should be programmed for T = 50% when R < 75 omega and 65% when R < 38 omega. The author considers programming tilt to 30% or 40% useless in clinical conditions. By the same reasoning, he recommends that the newer St. Jude Medical ICDs should be programmed to T = 50% if R < 75 omega and 60% if R < 41 omega, and PD = 5.5, 5.0, 4.5, 4.0, 3.5, and 3.0 ms for R < 75, 73, 62, 51, 40, and 32 omega, respectively. PD = 6 ms was considered clinically unrealistic. Programmable shock pulse duration and tilt are useful in optimizing defibrillation, but it is suggested that this can best be accomplished by programming these parameters with the guidance of theory as described in this discussion.

Electromyography in MRI--first recordings of peripheral nerve activation caused by fast magnetic field gradients

Prior studies on the evaluation of stimulation by MRI were based on the subjective feeling of the volunteers. A wide variety of stimulation thresholds between the subjects was observed. In order to exclude subjective perception levels as a cause of this variation, we developed a method to investigate the activation of peripheral nerves after gradient switching by electromyography (EMG) within the MR-imager. Five healthy volunteers were positioned in the MR-scanner with the bridge of the nose at isocenter. The amplitude of sinusoidal pulse trains of the anterior-posterior gradient (rise-times: 200 or 300 micros, various numbers of oscillations) was increased stepwise. Four surface electrodes were placed on the region where a muscle-twitch was reported. Electric activity of the muscle during stimulation experiments was recorded with an MR-compatible electro-physiologic amplifier. Stimulation thresholds were defined by the appearance of an EMG-signal. Thresholds were sharp and consistent with the report of the subjects.

Paradigm shift in lead design

During the past 30 years there has been a tremendous development in electrode technology from bulky (90 mm2) to pin-sized (1.0 mm2) electrodes. Simultaneously, impedance has increased from 110 Ohms to >1 kOhms, which has been termed a "paradigm shift" in lead design. If current is responsible for stimulation, why is its impedance a key factor in saving energy? Further, what mechanism is behind this development based on experimental findings and what conclusion can be drawn from it to optimize electrode size? If it is assumed that there is always a layer of nonexcitable tissue between the electrode surface and excitable myocardium and that the electric field (potential gradient) produced by the electrode at this boundary is reaching threshold level, then a formula can be derived for the voltage threshold that completely describes the electrophysiology and electrophysics of a hemispherical electrode. Assuming that the mean chronic threshold for porous steroid-eluting electrodes is 0.6 V with 0.5-ms pulse duration, thickness of nonexcitable tissue can be estimated to be 1.5 mm. Taking into account this measure and the relationship between chronaxie and electrode area, voltage threshold, impedance, and energy as a function of surface area can be calculated. The lowest voltage for 0.5-ms pulse duration is reached with r(o) = 0.5 d, yielding a surface area of 4 mm2 and a voltage threshold of 0.62 V, an impedance of 1 kOhms, and an energy level of 197 nJ. It can be deduced from our findings that a further reduction of surface areas below 1.6 mm2 will not diminish energy threshold substantially, if pulse duration remains at 0.5 ms. Lowest energy is reached with t = chronaxie, yielding an energy level <100 nJ with surface areas < or =1.5 mm2. It is striking to see how well the theoretically derived results correspond to the experimental findings. It is also surprising that the hemispheric model so accurately approximates experimental results with differently shaped electrodes that it can be concluded that electrode shape seems to play a minor role in electrode efficiency. Further energy reduction can only be achieved by reducing the pulse duration to chronaxie. A real paradigm shift will occur only if the fundamentals of electrostimulation in combination with electrophysics are accepted by the pacing community.

Predicting the relative efficacy of shock waveforms for transthoracic defibrillation in dogs

STUDY OBJECTIVE

Previous work has shown that a passive membrane model using a parallel resistor-capacitor circuit is capable of predicting optimal waveforms for transvenous defibrillation. This study tested the ability of that model to predict optimal waveforms for transthoracic defibrillation.

METHODS

This study was divided into 3 parts, each of which determined transthoracic defibrillation thresholds (DFTs) in 6 dogs for several different waveform shapes and durations. For each part, strength-duration relationships were determined from both experimental and model data and then compared with test model predictions. Part 1 DFTs were determined at various durations for 3 different monophasic waveforms-the ascending ramp, descending ramp, and square waveform. Part 2 DFTs were determined for 3 biphasic waveforms. Phase 1 was a 30-ms ascending ramp, and phase 2 was an ascending ramp, a descending ramp, or a square waveform. Part 3 DFTs were determined for 3 biphasic waveforms with very short second-phase durations. Phase 1 was a 30-ms ascending ramp, and phase 2 was a descending ramp.

RESULTS

For part 1, the model was able to predict the relative defibrillation efficacy of the 3 monophasic waveforms ( P < .05). For parts 2 and 3, the model was able to predict the biphasic waveforms with the lowest DFTs. These predictions were based on the criterion that the model response at the end of the second phase should return to or slightly pass the model response value at the beginning of the first phase.

CONCLUSION

The resistor-capacitor model successfully predicted the relative defibrillation efficacy of several different waveforms delivered transthoracically.

Relationship between efficacy of defibrillation shocks and frequency characteristics of shock waveforms

INTRODUCTION

Using the Fourier transform, it is possible to replace each time domain representation of a defibrillatory shock by a unique frequency domain representation in which the shock waveform is defined in terms of a complex number function of frequency and typically described as an amplitude in amperes per hertz (or, closely related, joules per hertz) and an associated frequency-dependent phase angle.

METHODS AND RESULTS

The present article describes the conceptual basis of the Fourier transform, sketches a simplified mathematical framework for deriving frequency domain parameters, considers properties crucial to interpreting defibrillatory-type shocks when expressed in the frequency domain, and then presents a series of shock waveforms in the frequency domain. Although not definitive, knowledge of the energy distribution with frequency alone, usually presented in joules per hertz, is shown to yield considerable insight into the probable comparable efficacy of uniphasic/biphasic rectangular, untruncated/truncated uniphasic exponential, and various biphasic "single capacitor" waveforms.

CONCLUSION

In general, efficacy in achieving ventricular defibrillation is improved by parameter changes that shift a larger percentage of the delivered energy into a mid-frequency range (very roughly, 40 to 160 Hz). With further study, the frequency domain approach may prove to be a useful tool in the a priori selection of optimal defibrillatory shock waveforms.

[Influence of waveform and configuration of electrodes on the defibrillation threshold of implantable cardioverter-defibrillators]

The defibrillation threshold (DFT) is no threshold in the true sense. Between energy levels which defibrillate in all cases and energy levels which never defibrillate, a broad range of energies exists which might or might not defibrillate. Thus, the value of the DFT is dependant on the protocol used for its determination. Usually the DFT presents an energy at which the implantable cardioverter-defibrillator (ICD) will defibrillate successfully at a rate of approximately 75%. To achieve a 100% success rate the energy has to be programmed 15 J above the DFT or twice the DFT.Using DFT measurements the energy needed for internal defibrillation could be gradually reduced in the last years. Major break throughs have been the introduction of the biphasic defibrillation waveform and the use of pectorally implanted ICD shells as defibrillation electrodes. The shortening of the defibrillation impulse by the use of lower capacitances could not improve DFTs but allowed to construct ICDs of smaller volume. Addition of a superior vena cava electrode or a subcutaneous array electrode at the left lateral chest to the standard bipolar electrode system (right ventricle, pectoral ICD can) allowed for tri- and quadripolar lead configurations which reduced DFTs on average only slightly but reduced the standard deviation of DFTs significantly and thus helped to avoid high DFTs. Besides building smaller ICDs, reduction of DFTs and thus programming of lower defibrillation ICD energies allows for improved battery longevities and reduced capacitor charging times and thus a lower incidence of syncopes.

Testing different biphasic waveforms and capacitances: effect on atrial defibrillation threshold and pain perception

OBJECTIVES

The goal of this study was to compare the effect of different tilts and capacitances for biphasic shocks on atrial defibrillation efficacy and pain threshold.

BACKGROUND

Although biphasic shocks have been shown to be superior to monophasic shocks, the effect of tilt and capacitance on atrial defibrillation success and pain perception has not been studied in patients.

METHODS

Atrial defibrillation threshold (DFT) testing was performed using a right atrial appendage/coronary sinus lead configuration in 38 patients with a history of paroxysmal atrial fibrillation undergoing an invasive electrophysiologic study. Biphasic waveforms with 40%, 50%, 65%, 80%, 30%/50% and 40%/50% were tested randomly in 22 patients (Group 1). In 16 patients (Group 2), a 65% tilt waveform with 50- and 120-microF capacitance was tested. Before sedation, pain sensation was graded by 15 patients in Group 1 after delivery of a 0.5-J shock and by 10 patients in Group 2 after two 1.5-J shocks with 50- and 120-microF capacitance were delivered.

RESULTS

The DFT energy for the 50% tilt waveform was significantly lower than the 65%, 80% and 30%/50% tilt waveforms. The 40%/50% tilt waveform provided slightly lower energy requirements than the 50% tilt waveform. Nine patients (60%) described the 0.5-J shock as very painful, and four (26.6%) complained of slight pain. The 50-microF capacitor lowered energy requirements compared with the 120-microF capacitor. Six patients (60%) perceived the 1.5-J 50-microF capacitor shock as more painful, whereas three (30%) perceived both shocks as equally painful.

CONCLUSIONS

Biphasic waveforms with 50% tilt in both phases and a smaller tilt in the positive phase than that in the negative phase (40%/50%) provided a decrease in energy requirements at atrial DFT. In addition, stored energy was reduced by biphasic shocks with 50-microF capacitance compared with 120-microF capacitance. Despite the reduction in energy requirements, shocks < 1 J continued to be perceived as painful in the majority of patients.

A conceptual basis for pacing waveforms

A model is developed that allows evaluation of the pacing efficacy of different stimulus waveforms. It treats the heart as having a first order time constant and enables ready visualization of the time course of the effective voltage within the heart. For pacemakers, where the stimulus pulse is produced by the discharge of a capacitor, the voltage within the heart rapidly rises to a peak and then more slowly decays to zero. The time interval at which the peak occurs defines the optimal duration, i.e., the shortest duration with minimal pacing voltage. Characteristics are developed that show the changes in optimal duration and pacing threshold for changes in the pacemaker's output capacitor and for differences in lead impedance and time constant of the heart.

A conceptual basis for defibrillation waveforms

A model is developed for defibrillation that treats the heart as a first order time constant. Such a model allows ready evaluation of different monophasic waveforms. For implantable devices where the voltage is provided by the discharge of a capacitor, it can be seen that the effective voltage within the heart rises rapidly to a peak and then decays to zero. The time interval at which this peak occurs is defined as the optimal duration, and there is no advantage in extending the pulse beyond this point. Characteristics are presented that show how the time course of this voltage within the heart changes with different device capacitors and load impedances. The effect of different heart time constant are also examined. For biphasic waveforms, a contour plot of threshold voltage is presented with phase 1 and phase 2 durations on the two axes. It is seen that there is a region of reliable low threshold defibrillation from 3.5/1.5 ms to 9/6 ms.

Defibrillation using a high-frequency series of monophasic rectangular pulses: observations and model predictions

INTRODUCTION

Capacitor-discharge type waveforms are practical for defibrillation devices but may not be optimum. Discharging a capacitor as a series of high-frequency (HF) pulses may allow effective waveform shaping by modulating the pulses. This approach could lead to improved defibrillation by allowing waveforms that would otherwise be unachievable with a capacitor-discharge approach. However, little is known about defibrillation with HF.

METHODS AND RESULTS

In open chest pentobarbital anesthetized dogs, we measured defibrillation thresholds for continuous rectangular waveforms with 5-, 10-, and 20-msec durations and for 10- and 20-msec long series of HF rectangular pulses. HF series had a 50% "on-time" duty cycle at 100 Hz to 20 kHz. At 1 kHz and above, defibrillation with HF required the same time-averaged current but approximately twice the peak current and energy as defibrillation with continuous waveforms having the same envelope duration. At lower frequencies, defibrillation peak current and energy approached values required for the continuous waveforms. While waveforms were not actually filtered, the heart responded as though the HF series were low-pass filtered. A filtered effective waveform model with a 3.7-msec time constant predicts these HF data and makes reasonable predictions for various continuous waveform shapes.

CONCLUSION

Defibrillation is possible using HF pulses up to 20 kHz and has a frequency response similar to a low-pass filter. A filtered effective waveform model predicts these HF results and may help explain how waveforms influence defibrillation efficacy. While the unmodulated HF pulsing used in this study increased defibrillation requirements, these findings support the concept that HF pulse modulation can be used to change the effective shape of a waveform, which could permit more efficacious waveform shapes and a net reduction of thresholds.

Biphasic defibrillation using a single capacitor with large capacitance: reduction of peak voltages and ICD device size

The volume of current implantable cardioverter defibrillators (ICD) is not convenient for pectoral implantation. One way to reduce the size of the pulse generator is to find a more effective defibrillation pulse waveform generated from smaller volume capacitors. In a prospective randomized crossover study we compared the step-down defibrillation threshold (DFT) of a standard biphasic waveform (STD), delivered by two 250-microF capacitors connected in series with an 80% tilt, to an experimental biphasic waveform delivered by a single 450-microF capacitor with a 60% tilt. The experimental waveform delivered the same energy with a lower peak voltage and a longer duration (LVLD). Intraoperatively, in 25 patients receiving endocardial (n = 12) or endocardial-subcutaneous array (n = 13) defibrillation leads, the DFT was determined for both waveforms. Energy requirements did not differ at DFT for the STD and LVLD waveforms with the low impedance (32 +/- 4 omega) endocardial-subcutaneous array defibrillation lead system (6.4 +/- 4.4 J and 5.9 +/- 4.2 J, respectively) or increased slightly (P = 0.06) with the higher impedance (42 +/- 4 omega) endocardial lead system (10.4 +/- 4.6 J and 12.7 +/- 5.7 J, respectively). However, the voltage needed at DFT was one-third lower with the LVLD waveform than with the STD waveform for both lead systems (256 +/- 85 V vs 154 +/- 51 V and 348 +/- 76 V vs 232 +/- 54 V, respectively). Thus, a single capacitor with a large capacitance can generate a defibrillation pulse with a substantial lower peak voltage requirement without significantly increasing the energy requirements. The volume reduction in using a single capacitor can decrease ICD device size.

Choosing the optimal monophasic and biphasic waveforms for ventricular defibrillation

INTRODUCTION

The truncated exponential waveform from an implantable cardioverter defibrillator can be described by three quantities: the leading edge voltage, the waveform duration, and the waveform time constant (tau s). The goal of this work was to develop and test a mathematical model of defibrillation that predicts the optimal durations for monophasic and the first phase of biphasic waveforms for different tau s values. In 1932, Blair used a parallel resistor-capacitor network as a model of the cell membrane to develop an equation that describes stimulation using square waves. We extended Blair's model of stimulation, using a resistor-capacitor network time constant (tau m), equal to 2.8 msec, to explicitly account for the waveform shape of a truncated exponential waveform. This extended model predicted that for monophasic waveforms with tau s of 1.5 msec, leading edge voltage will be constant for waveforms 2 msec and longer; for tau s of 3 msec, leading edge voltage will be constant for waveforms 3 msec and longer; for tau s of 6 msec, leading edge voltage will be constant for waveforms 4 msec and longer. We hypothesized that the best phase 1 of a biphasic waveform is the best monophasic waveform. Therefore, the optimal first phase of a biphasic waveform for a given tau s is the same as the optimal monophasic waveform.

METHODS AND RESULTS

We tested these hypotheses in two animal experiments. Part I: Defibrillation thresholds were determined for monophasic waveforms in eight dogs. For tau s of 1.5 msec, waveforms were truncated at 1, 1.5, 2, 2.5, 3, 4, 5, and 6 msec. For tau s of 3 msec, waveforms were truncated at 1,2,3,4,5,6, and 8 msec. For tau s of 6 msec, waveforms were truncated at 2,3,4,5,6,8, and 10 msec. For waveforms with tau s of 1.5, leading edge voltage was not significantly different for the waveform durations of 1.5 msec and longer. For waveforms with tau s of 3 msec, leading edge voltage was not significantly different for waveform durations of 2 msec and longer. For waveforms with tau s of 6 msec, there was no significant difference in leading edge voltage for the waveforms tested. Part II: Defibrillation thresholds were determined in another eight dogs for the same three tau s values. For each value of tau s, six biphasic waveforms were tested: 1/1, 2/2, 3/3, 4/4, 5/5, and 6/6 msec. For waveforms with tau s of 1.5 msec, leading edge voltage was a minimum for the 2/2 msec waveform. For waveforms with tau s of 3 msec, leading edge voltage was a minimum for the 3/3 msec waveform. For waveforms with tau s of 6 msec, leading edge voltage was a minimum and not significantly different for the 3/3, 4/4, 5/5, and 6/6 msec waveforms.

CONCLUSIONS

The model predicts the optimal monophasic duration and the first phase of a biphasic waveform to within 1 msec as tau s varies from 1.5 to 6 msec: for tau s equal to 1.5 msec, the optimal monophasic waveform duration and the optimal first phase of a biphasic waveform is 2 msec, for tau s equal to 3.0 msec, the optimal duration is 3 msec, and for tau s equal to 6 msec, the optimal duration is 4 msec. For both monophasic and biphasic waveforms, optimal waveform duration shortens as the waveform time constant shortens.

Magnetostimulation in MRI

In national and international bodies, there is active discussion of appropriate safety regulations of levels of magnetic field strength in MRI. Present limits are usually expressed in terms of the switching rate dB/dt, but the validity of this is open to debate. Application of the fundamental law of electrostimulation is well-established, both on theoretical and experimental grounds. Application of this law, in combination with Maxwell's law, yields a very simple equation that we call the fundamental law of magnetostimulation. This law has the hyperbolic form of a strength-duration curve and allows an estimation of the lowest possible value of the magnetic flux density capable of stimulating nerves and muscles. Calculations prove that the threshold for heart excitation is much higher than those for nerve and muscle stimulations. Experimental results from us and other authors confirm the correctness of the derived laws for magnetostimulation. In light of these findings, proposed safety limits should be reconsidered.

Optimizing defibrillation through improved waveforms

Defibrillation of the heart is achieved if an electrical current depolarizes the majority of the unsynchronized fibrillating myocardial cells. The applied current or the corresponding voltage described as a function of time is called the waveform. In pacing, to stimulate myocardial cells close to the electrode, a relatively low voltage is needed for a relatively brief duration. However, in defibrillation, approximately a 100-fold higher voltage is needed and achieved by the use of capacitors. The exponential voltage decay of a capacitor during its discharge determines the basic waveform for defibrillation. In an attempt to lower the energy needed for defibrillation, the steepness of the decay (different capacitances), the duration (fixed duration waveforms) or tilt (fixed tilt waveforms), or the initial polarity can be changed. Additionally, the polarity of the electrodes can be reversed during the discharge of the capacitor once (biphasic waveform) or twice (triphasic waveform). If two capacitors and defibrillation pathways are available, bidirectional defibrillation pulses can be delivered sequentially. In humans, the original standard waveform used with endocardial leads was a single monophasic pulse delivered by a 125-microF capacitor using the endocardial right ventricular electrode as cathode. It is now known that a reversal of the initial polarity and a reversal of polarity during capacitor discharge may significantly lower the energy needed for defibrillation, thereby preventing formerly frequent failures of defibrillation with endocardial lead systems. The use of sequential pulses showed no or only slight reductions of energy requirements and was abandoned due to the additional electrode needed. The use of a smaller capacitance (60-90 microF reduced maximum energy output but generally did not reduce energy requirements for defibrillation. However, with more efficient electrodes, smaller capacitances that will help to reduce the size of the defibrillator might be used. Thus, today defibrillation is optimized with respect to energy, capacitor size, and ease of implantation if an approximately 90-microF capacitor is used to deliver a biphasic pulse via a bipolar lead system using the right ventricular electrode as anode.

Optimization of cardiac defibrillation by three-dimensional finite element modeling of the human thorax

The goal of this study was to determine the optimal electrode placement and size to minimize myocardial damage during defibrillation while rendering refractory a critical mass of cardiac tissue of 100%. For this purpose, we developed a 3-D finite element model with 55,388 nodes, 50,913 hexahedral elements, and simulated 16 different organs and tissues, as well as the properties of the electrolyte. The model used a nonuniform mesh with an average spatial resolution of 0.8 cm in all three dimensions. To validate this model, we measured the voltage across 3-cm2 Ag-AgCl electrodes when currents of 5 mA at 50 kHz were injected into a human subject's thorax through the same electrodes. For the same electrode placements and sizes and the same injected current, the finite element analysis produced results in good agreement with the experimental data. For the optimization of defibrillation, we tested 12 different electrode placements and seven different electrode sizes. The finite element analyses showed that the anterior-posterior electrode placement and an electrode size of about 90 cm2 offered the least chance of potential myocardial damage and required a shock energy of less than 350 J for 5-ms defibrillation pulses to achieve 100% critical mass. For comparison, the average cross-sectional area of the heart is approximately 48 cm2, about half of the optimal area. A second best electrode placement was with the defibrillation electrodes on the midaxillary lines under the armpits. Although this placement had higher chances of producing cardiac damage, it required less shock energy to achieve 100% critical mass.

A minimal model of the single capacitor biphasic defibrillation waveform

A quantitative model of the single capacitor biphasic defibrillation waveform is proposed. The primary hypothesis of this model is that the first phase leaves a residual charge on the membranes of the unsynchronized cells, which can then reinitiate fibrillation. The second phase diminishes this charge, reducing the potential for refibrillation. To suppress this potential refibrillation, a monophasic shock must be strong enough to synchronize a critical mass of nearly 100% of the myocytes. Since the biphasic waveform performs this protection function by removing the residual charge (with its second phase), its first phase may be of a lower strength than a monophasic shock of equivalent performance. A quantitative model was developed to calculate the residual membrane voltage, Vm, assuming a capacitive membrane being alternately charged and discharged by the first and second phases, respectively. It was further assumed that the amplitude of the first phase would be predicted by a minimum value plus a term proportional to Vm2. The model was evaluated on the pooled data of three relevant published studies comparing biphasic waveforms. The model explained 79% of the variance in the first phase amplitude and predicted optimal durations for various defibrillator capacitances and electrode resistances. Assuming a first phase of optimal duration, the optimal second phase duration appears to be about 2.5 msec for all capacitances and resistances now seen clinically.

CONCLUSION

The effectiveness of the single capacitor biphasic waveform may be explained by the second phase "burping" of the deleterious residual charge of the first phase that, in turn, reduces the synchronization requirement and the amplitude requirements of the first phase.

Effect of capacitor size and pathway resistance on defibrillation threshold for implantable defibrillators

BACKGROUND

The time constant of truncated exponential pulses used with implantable defibrillators is determined by the output capacitor size and defibrillation pathway resistance. The optimal capacitor size is unknown.

METHODS AND RESULTS

This study compared defibrillation threshold (DFT) for standard 120-microF capacitors (DFT120) and smaller 60-microF capacitors (DFT60) at implantation of cardioverter-defibrillators in 67 patients using epicardial electrodes (15 patients) or one of four transvenous electrode configurations (52 patients). Paired comparisons of DFT60 and DFT120 were made for 44 defibrillation pathways using monophasic pulses and for 53 pathways using biphasic pulses. Truncated exponential pulses with 65% tilt were used. Pooled data from all electrode configurations showed a significant inverse correlation between pathway resistance and the ratio of stored energy DFT60 to DFT120 (monophasic pulses: r = .75, P = .0001; biphasic pulses: r = .68, P = .0001). Data from all electrode configurations formed a continuum with 120-microF capacitors superior for low-resistance pathways and 60-microF capacitors superior for high-resistance pathways. For pathways with resistance < or = 40 omega, the modest advantage of 120-microF capacitors applied primarily to pathways with low DFTs: 8.2 +/- 6.1 versus 9.6 +/- 5.4 J (P = .001) for monophasic pulses and 4.1 +/- 2.8 versus 5.1 +/- 3.1 J (P < .02) for biphasic pulses. The greater advantage of 60-microF capacitors for pathways with resistance > or = 61 omega applied to pathways with higher DFTs: 12.4 +/- 4.3 versus 23.1 +/- 6.4 J (P = .0001) for monophasic pulses and 8.5 +/- 4.9 versus 12.5 +/- 6.4 J (P = .0001) for biphasic pulses. For pathways using monophasic 120-microF pulses versus 95% for 60-microF pulses. Similarly, the DFT was < or = 10 J for 48% of pathways using biphasic 120-microF capacitors versus 83% for 60-microF pulses.

CONCLUSIONS

In comparison with conventional 120-microF capacitors, 60-microF capacitors had clinically insignificant higher DFTs for low-resistance pathways and clinically important lower DFTs for high-resistance pathways. Optimal capacitance is inversely related to pathway resistance for clinical defibrillation pathways and waveforms.

Response of a single cell to an external electric field

The response of a cell to an external electric field is investigated using dimensional analysis and singular perturbation. The results demonstrate that the response of a cell is a two-stage process consisting of the initial polarization that proceeds with the cellular time constant (< 1 microseconds), and of the actual change of physiological state that proceeds with the membrane time constant (several milliseconds). The second stage is governed by an ordinary differential equation similar to that of a space-clamped membrane patch but formulated in terms of intracellular rather than transmembrane potential. Therefore, it is meaningful to analyze the physiological state and the dynamics of a cell as a whole instead of the physiological states and the dynamics of the underlying membrane patches. This theoretical result is illustrated with an example of an excitation of a cylindrical cell by a transverse electric field.

A minimal model of the monophasic defibrillation pulse

A minimal model of the defibrillation capability of a monophasic capacitive discharge pulse is derived from the Weiss-Lapicque strength duration model. The model suggests that present, empirically derived values of pulse durations and tilts are close to optimum for presently used values of capacitors and electrode resistances. The model suggests that neither the tilt nor fixed duration specification is universally superior to the other for dealing with electrode resistance changes. A tilt specification would appear to best handle resistance decreases while a fixed duration specification would best handle resistance increases. The model was used to study the effect of capacitance changes. It appears that the optimum tilt and pulse duration vary with the capacitance value. The model further suggests that decreasing the capacitance from presently used values may lower defibrillation thresholds.