WO1998009226A1 - Methods for detecting propensity for fibrillation using an electrical restitution curve - Google Patents

Abstract

A method for detecting a heart disorder comprises examination of a phase-plane plot (PPP) of a patient electrocardiogram (EKG). The PPP's degree of deterministic chaos may be measured by a processor. Analysis of the PPP may indicate a propensity for fibrillation, that is, indicate both the risk of fibrillation and its actual onset (cases where risk is 100 percent). A second method for detecting a heart disorder comprises examination of a frequency-domain transform (such as an FFT) of a patient EKG. An automatic defibrillating device may comprise means for delivering a variable shock, the size of which is determined at least in part by the FFT's peak energy. A method for detecting drug toxicity comprises examination of a parameter time constant for an action-potential duration (APD) restitution curve which is constructed for the patient.

Description

DESCRIPTION

Methods for Detecting Propensity for Fibrillation Using an Electrical Restitution Curve

Field of the Invention

This invention relates to heart disorders. More specifically, this invention relates to detecting and evaluating arrhythmia, fibrillation and related disorders by manipulation of an electrocardiogram signal.

Description of Related Art

Despite major advances in the diagnosis and treatment of ischemic heart disease over the past decade, a substantial number of patients each year may suffer sudden cardiac death as a consequence of ventricular fibrillation

(VF) . To date, no reliable predictive or preventive measures have been developed. By all outward appearances,

VF is a highly complex, seemingly random phenomenon. So are other related heart disorders, including those stages in heart behavior which typically precede VF (onset of VF) . Accordingly, it is difficult for automated devices to determine with any reliability that a patient is undergoing VF or onset of VF . Moreover, onset of VF may also be difficult to determine with any reliability, even for skilled medical personnel.

A method and device for detecting and evaluating heart disorders would therefore find wide applicability and utility. Patient monitoring devices may summon medical personnel if the patient is undergoing VF or onset of VF . Automatic devices which attempt to counter VF, e.g. automatic implantable cardiac defibrillators (AICDs) may vary their operation based on evaluation of the severity of the patient's condition. Methods and devices reliably evaluating the risk of VF may also have important utility in monitoring patients undergoing surgery or other critical therapy. It has been found that some anti -arrhythmic drugs may also have a pro-arrhythmic effect in excess concentrations. For example, quinidme has been known to be toxic in this manner. A method of detecting and evaluating heart disorders would also have wide applicability and utility in determining if a patient has been subjected to a toxic (or partially toxic) dosage of a drug relating to heart condition.

Chaos theory is a recently developed field relating to phenomena which appear to be highly complex and seemingly random, but which may be described as the deterministic result of relatively simple systems. Chaos theory may have potentially wide applications m biologic and other systems involving ambiguity and uncertainty. For example, it has been conjectured that chaos theory may be valuable for describing certain natural processes, including electroencephalogram (EEG) and electrocardiogram

(EKG) signals. Techniques for detecting and evaluating aspects of deterministic chaos are known in the field of chaos theory, but have found little application m the medical field.

Accordingly, there is a need for improved methods and devices for detecting and evaluating heart disorders, including ventricular fibrillation (VF) and the onset of VF .

Summary of the Invention

A first aspect of the invention provides a device and method for detecting a heart disorder, by examination of a phase-plane plot (PPP) of a patient electrocardiogram (EKG) . A normal patient will have a PPP which is relatively smooth; a patient at risk of developing ventricular fibrillation (VF) onset will have a PPP which exhibits features of a chaotic process, such as multiple bands, "forbidden zones", periodicity with period-doubling and phase locking; a patient exhibiting VF will have a PPP which appears noisy and irregular. Differing PPPs may be readily recognized, thus detecting patients with heart disorders .

In a preferred embodiment, the PPP's degree of deterministic chaos may be measured by a processor, such as by graphic and numeric analysis. (1) The processor may measure a Lyapunov exponent or a fractal dimension of the PPP. (2) The processor may determine a Poincare section of the PPP and examine that Poincare section for indicators of deterministic chaos. Also, the processed PPP and Poincare sections may be reviewed by a human operator The processed PPP and Poincare sections may indicate the propensity for fibrillation.

A second aspect of the invention provides a method for detecting a heart disorder, by examination of a frequency-domain transform (such as an FFT) of a patient EKG. A normal patient will have an FFT with a discrete spectrum, while a patient exhibiting VF will have an FFT with a relatively continuous spectrum and a peak energy at a relatively low frequency (e.g., about 5-6 Hz) . A patient exhibiting VF which is difficult to revert with shock will have an FFT with a peak energy at a relatively high frequency (e.g., about 10 Hz or more).

In a preferred embodiment, an automatic defibril- lating device may comprise means for delivering a variable shock, the size of which is determined at least in part by the FFT's peak energy. The defibrillating device may also comprise means for signalling an alarm if the FFT's peak energy is at a relatively high frequency.

A third aspect of the invention provides a method for detecting drug toxicity, based on particulars of an action potential duration (APD) restitution curve, or an action- potential amplitude (APA) curve, which is constructed for the patient, such as fitting an exponential relation to that curve or such as a parameter time constant for that curve. The slope of the fitted curve will indicate the patient's possibility of predisposition to arrhythmia. Differences m the parameters of the fitted curve allow one to distinguish between normal and abnormal patients, e.g. those at risk of arrhythmia or ischemia. A normal patient will have a relatively low parameter time constant; a patient who is exhibiting drug toxicity will have a relatively high parameter time constant. A PPP of APD or APA data may also be generated, and the analytical techniques described herein may be utilized to interpret that PPP, to determine and evaluate drug toxicity.

A fourth aspect of the invention is a method and apparatus for detecting a patient's propensity for ventricular fibrillation based on the particulars of an electrocardiogram restitution curve. The particulars may be obtained from a surface ECG or by an mtracardiac electrogram. For example, the electrocardiogram curve may be constructed using a non- invasive procedure by taking the patient's EKG and plotting the patient's T-wave duration against the time it takes from the end of the patient's T-wave to the onset of the patient's Q-wave. Alternatively, the mtracardiac electrogram may be taken mvasively and analyzed as before using the single cell or monophasic action potential restitution curve. In both embodiments, the slope of the constructed electrocardiogram restitution curve indicates a patient's propensity for fibrillation when the subject's curve slope is greater than a normal patient's curve slope. The apparatus can take the form of a cardiac monitor, or cardiac defibrillator .

Brief Description of the Drawings Figure 1 shows a patient monitoring system. Figure 2 shows a set of sample EKG signals. Figure 3 shows a set of corresponding PPPs for the sample EKG signals of figure 2.

Figure 3A shows a detail of the "funnel" area of the PPP corresponding to the third EKG of F g 2, taken from a patient exhibiting VF . Figure 4 shows an example PPP and a corresponding Poincare section.

Figure 5 shows an example PPP and a corresponding time-lapse Poincare section. Figure 6a shows the frequency-domain fast Fourier transform of an EKG from a normal patient.

Figure 6b shows the frequency-domain fast Fourier transform of an EKG from a patient experiencing VF .

Figure 7 shows an improved automatic implantable cardiac defibrillator ("AICD").

Figure 8 shows a signal response of an individual heart muscle cell to a stimulus, known m the art as "action potential".

Figure 9 shows the correspondence between an EKG and the action potential. Figure 9 shows a flow chart for a method of registering a propensity for fibrillation by calculating a fractal dimension using a box counting method .

Figure 10 shows an electrocardiogram restitution curve for a patient with a propensity for fibrillation and for a normal patient. Figure 10 shows a flow chart for a method of registering a propensity for fibrillation by determining correlation dimension convergence.

Figure 11 is a flow chart depicting the method of detecting the propensity for fibrillation by measuring the slope of an action potential duration restitution curve and comparing it to the slope of a normal patient's curve.

Figure 12 is a flow chart depicting the method of detecting the propensity for fibrillation by numerically comparing the time parameter constant for the patient's fitted action potential duration restitution curve and the value of the time parameter for a normal patient's curve

Figure 13 is a flow chart depicting a method of detecting propensity for fibrillation by comparing the slope of the patient's fitted action potential duration restitution curve with the slope of a normal patient's curve . Figure 14a is a normal patient's EKG signal with TQ and ST intervals indicated.

Figure 14b is a plot of ST versus TQ (the electrical restitution curve) for a normal patient and for a patient with a propensity for fibrillation.

Description of the Preferred Embodiment

A first aspect of the invention relates to detection and evaluation of heart disorders by examination of a phase-plane plot (PPP) of a patient electrocardiogram (EKG) .

Figure 1 shows a patient monitoring system A patient 101 is coupled to an electrocardiogram (EKG) device 102, which acquires EKG signals and transmits them to a processor 103. The processor 103 may display the EKG signals on a monitor 104 (as is well-known m the art) , or it may process the EKG signals and display any results of processing on the monitor 104.

EKG signals are well-known in the art, as are methods of acquiring them. As used herein, an EKG refers to a surface electrocardiogram, but other forms of electrocardiogram would also work with the methods disclosed herein, and are within the scope and spirit of the invention. For example, the EKG shown herein may comprise a surface EKG, an epicardial EKG, an endocardial EKG, or another related signal (or set of signals) measured in or near the heart. Moreover, the signal which is manipulated may be a voltage signal, a current signal, or another related electromagnetic values (or set of values) Figure 2 shows a set of sample EKG signals. A first EKG signal 201 shows a normal patient. A second EKG signal 202 shows a patient in transition to VF. A third EKG signal 203 shows a patient with VF .

The processor 103 may construct a phase-plane plot (PPP) from the EKG signal. A first type of PPP comprises a plot of an EKG variable against its first derivative In a preferred embodiment, the EKG variable is voltage, v (itself a function of time) ; its first derivative is dv/dt (also a function of time) .

However, it would be clear to one of ordinary skill in the art, after perusal of the specification, drawings and claims herein, that wide latitude in construction of the PPP is possible. The variable chosen for the PPP may be any one of a variety of different parameters, including EKG voltage, current, or another signal value. The chosen variable (v) may be plotted against its first time deriva- tive (dv/dt), its second time derivative d²v/dt², or another time derivative dⁿv/dtⁿ. Or, an Mth derivative may be plotted against an Nth derivative.

Another type of PPP may comprise a plot of an EKG variable (or an Nth derivative thereof) against a time delayed version of itself, (e.g. v(t) versus v(t-δt)). This type of PPP is sometimes also called a "return map". This type of PPP is led sensitive to EKG signal noise.

Another type of PPP may comprise a plot of three EKG variables (or Nth derivatives thereof) simultaneously (e.g., v, dv/dt, and d²v/dt²) . Such a PPP would be 3- di ensional. Where the PPP is 3 -dimensional , it may be displayed stereoscopically, or a 2-dimensional plane "cut" of the 3 -dimensional display may be displayed on a 2 - dimensional display. It would be clear to one of ordinary skill in the art, that all of these choices described herein, or combinations thereof, would be workable, and are within the scope and spirit of the invention.

Figure 3 shows a set of corresponding PPPs for the sample EKG signals of figure 2. A first PPP 301 corresponds to the first EKG signal 201. A second PPP 302 corresponds to the second EKG signal 202. A third PPP 303 corresponds to the third EKG signal 203. Figure 3A shows a detail of the "funnel" area of the PPP corresponding to the third EKG of Fig. 2, taken from a patient exhibiting VF . The funnel area of the PPP, shown in Fig. 3A, in particular, exhibits an irregular and highly complex pattern, indicative of ventricular fibrillation to even a relatively untrained eye.

Part of this aspect of the invention is the discovery that a normal patient will have a PPP which exhibits the regularity and smoothness of an EKG signal from that normal patient, while a patient undergoing VF will have a PPP which exhibits the irregularity and complexity of an EKG signal which might be deterministic chaos (e.g., aperiodicity, banding and "forbidden zones"). Moreover, a patient in transition from normal into VF (i.e., in VF onset) exhibits a PPP which is consistent with an assessment that the EKG signal for the patient is in transition to deterministic chaos.

A normal patient has a relatively regular beat-to- beat EKG signal. As the patient transitions to VF, the patient's EKG signal at first shows oscillations between pairs of alternant regular beat-to-beat signals. As the transition continues, the patient's EKG signal then shows oscillations between greater and greater numbers of alter- nant regular signals (e. g., four possible alternants, eight possible alternants, etc.), until it is no longer possible to identify alternant regular signals and the EKG signal is irregular and highly complex. At that point, the patient is generally said to be exhibiting VF . In like manner, the patient's PPP will transition from a smooth single-banded display, through a multi - banded display (showing multiple alternants) and finally to an irregular and highly complex display. The display change in the PPP is so striking that even a relatively untrained person can see the difference. This is m contrast with display changes m the EKG, which generally requires a skilled cardiologist to evaluate.

There are several possible factors which might cause a patient to transition from normal to VF . These factors may include drug overdose (especially overdose with an antiarrhythmic which has a pro-arrhythmic effect m over- dosage, e.g., quinidme intoxication), excessive elec- tπcal stimulation, hypothermia, ischemia, and stress. In a preferred embodiment, a patient monitor may examine the patient's PPP so as to determine if the patient is m transition from normal to VF; this could indicate that one of these pro-arrhythmic factors is excessively present.

The processor 103 may further process the PPP so as to measure the PPP's degree of deterministic chaos. Several techniques may be applied for this purpose:

(1) The processor 103 may measure a Lyapunov exponent of the PPP. The Lyapunov exponent of the PPP is a measure of the degree to which nearby paths of the PPP diverge The Lyapunov exponent is well-known m chaos theory and may be measured with available software. See, e.g., Wolf et al . , "Determining Lyapunov exponents from a time series", Physica D 1985;16:285-317.

(2) The processor 103 may measure a fractal dimension of the PPP. The fractal dimension of the PPP is a measure of the degree to which the PPP forms a "space -filling" curve. The fractal dimension is well-known in chaos theory and may be measured with several techniques (e.g. correlation dimension or box-counting methods) , for example as shown below and m Fig. 9:

After the EKG is sensed 901 and the phase-plane plot constructed 902, m order to measure the fractal dimension of the PPP the processor of Fig. 1 superimposes a rectilinear grid (comprising a set of boxes) 903 on the PPP 903 and counts the number of boxes which are cut by the PPP's trace 904. The processor of Fig. 1 then varies the size of the grid and records each grid size and each count 905 The processor of Fig. 1 then computes the constant k m the following relation 906:

In (# of boxes cut) = k * In (# of boxes m grid) The constant k is a measure of the fractal dimension of the PPP. A value of k between about 3 and about 7, especially with a fractional component, implies that the PPP is likely to represent a process based on deterministic chaos, and therefore a patient who is close to (or actually in) VF 907. The propensity for ventricular fibrillation is then registered 908.

The fractal dimension may also be measured with correlation dimension techniques such as shown in Fig. 10 and appendix pp. 29-30. In this process after the EKG is sensed 1001 and the phase-plane plot constructed 1002 the processor of Fig. 1 applies a modified Grassberger- Procaccia algorithm 1003. The correlation dimension is then evaluated for convergence 1004. In the event of convergence the propensity for ventricular fibrillation is registered 1005.

The constant k is a measure of the fractal dimension of the PPP. A value of k between about 3 and about 7, especially with a fractional component, implies that the PPP is likely to represent a process based on deterministic chaos, and therefore a patient who is close to (or actually m) VF. The fractal dimension may also be measured with correlation dimension techniques such as shown in Fig. 10 and appendix pages, 29-30. (3) The processor 103 may determine a Poincare section of the PPP and examine that Poincare section for indicators of deterministic chaos, as described herein. The processed PPP and Poincare sections may also be displayed for review by a human operator, whereupon any visible structure will be readily recognized.

Figure 4 shows an example PPP 401 and a corresponding Poincare section 402. A Poincare section may comprise a line segment drawn across a part of the PPP. In general, such a line segment will be close to perpendicular to the trajectories of the PPP in a region of interest.

The processor 103 may acquire the data points in each Poincare section or PPP and compute a statistical measure of anisotropy or mhomogeneity of those data points. One such measure is based on the mean and standard deviation of those data points (these may be computed by statistical methods which are well-known in the art) . The ratio: r = (standard deviation) / (expected value) (403) is a measure of the degree of clumping in the Poincare section.

A greater value for r implies that the PPP is more likely to represent a process based on deterministic chaos, and therefore a patient who is close to (or actually in) VF. The value for r may be displayed for review by a human operator in comparison with a value for r for a normal patient, together with a set of confidence bands, as is well-known in the art, for indicating a degree of variation from a normal patient.

The processor 103 may also compute other statistical measures of the Poincare section.

The processor 103 may also determine a "time-lapse" Poincare section of the PPP. Figure 5 shows an example PPP 501 and a corresponding time-lapse Poincare section 502. A time-lapse Poincare section may comprise a set of data points selected from the PPP by selecting one data point every t seconds. The time-lapse Poincare section may be analyzed in like manner as the other Poincare section disclosed herein.

A second aspect of the invention relates to detection and evaluation of heart disorders based on a frequency- domain transform of a patient EKG.

Figure 6 shows a set .of corresponding frequency- domain transforms, obtained by performing an FFT on the EKG signal. A first transform 601 corresponds to a first EKG signal (not shown) . A second transform 602 corresponds to a second EKG signal (not shown) .

In the first transform 601 of Fig. 6a, representing a normal patient, the frequency spectrum shows that the energy of the corresponding EKG signal occurs primarily at a discrete set of frequencies. In the second transform 602 of Fig. 6b, representing a patient exhibiting VF, the frequency spectrum shows that the energy of the corresponding EKG signal has a continuous spectrum of frequencies, and has an energy peak 603. Part of this aspect of the invention is the use of both visual and mathematical techniques for analyzing frequency domain transforms, including for example calculation of a harmonic magnitude ratio (HMR) . To determine the HMR, a major peak or a central region of energy distribution m a spectrum of a frequency domain transform (such as an FFT) may be identified, and the HMR calculated as follows: A magnitude of the transform in the region of the identified point is determined (e.g., by summing the magnitude of the transform at the identified point and at surrounding points) , and is summed with the corresponding magnitude in the region of harmonic values of the frequency for the identified point. This sum is divided by a total magnitude of the transform for the entire signal; the ratio is defined as the HMR.

One method which is known for bringing a patient out of VF ( "defibrillating" ) is to administer an electric shock across the patient's heart. This electric shock must generally have a substantial energy, e.g. 10-20 joules, and may often cause tissue damage to the patient even if it is successful m defibrillating the patient. Multiple shocks may be required, generally of increasing energy. Accordingly, it would be advantageous to use a larger shock only when necessary, and it would be advantageous to use as few shocks as possible.

Part of this aspect of the invention is the discovery that when the energy peak 603 of the frequency-domain transform 602 is at a relatively low frequency, a relatively low energy shock will generally suffice to defibπllate the patient When the energy peak 603 of the frequency-domain transform 602 is at a relatively high frequency (also, when a secondary energy peak 604 appears in the frequency-domain transform 602 at a relatively high frequency) , it will require a relatively high energy shock to defibπllate the patient, if it is possible to defib- rillate the patient by means of an electric shock at all. One application of this discovery is in automated implanted cardiac defibrillators (AICDs) , which attempt to automatically detect VF and to automatically administer a shock to defibrillate the patient. Figure 7 shows an improved AICD 701. A patient 702 is coupled to an AICD EKG 703, which acquires EKG signals and transmits them to an AICD processor 704, which controls a shock device 705 for administering a defibrillating shock to the patient 702. The improved AICD 701 also comprises (e.g., as part of the AICD processor 704) software for determining an FFT of the EKG signal and for determining the energy peak in that FFT. If the energy peak in that FFT is relatively low, the AICD processor 704 controls the shock device 705 to administer a relatively small shock to the patient. If the energy peak in that FFT is relatively high, the AICD processor 704 controls the shock device 705 to administer a relatively large shock to the patient, and may also signal an alarm 706 or other indicator that defibrillation may not be successful.

A third aspect of the invention relates to detection and evaluation of drug toxicity based on a parameter time constant for an action-potential duration (APD) restitution curve or an action-potential amplitude (APA) curve which is constructed for the patient.

Figure 8 shows a signal response of an individual heart muscle cell to a stimulus. This individual cell response is known in the art as "action potential".

It is well-known in the art that a time duration for recovery 801 of an individual cell depends on factors including a resting period 802 which the cell has had prior to stimulus. It is also well-known in the art that an APD restitution curve can be constructed for a human patient with the use of an intracardiac catheter. However, the complete relation between the actual time duration for recovery 801 based on the resting period 802 is not known. Part of this aspect of the invention is the discovery that when the time duration for recovery 801 is plotted against the resting period 802 (diastolic interval) , the curve follows an exponential relation: APD = APD_pl - A * exp(-DI/tau) (803) where APD_pl is the plateau APD, A is a proportionality constant, DI is the diastolic interval, and tau is the parameter time constant The nonlinear nature of the APD restitution curve may promote deterministic chaos in response to excessive stimulus of the heart muscle cells. When the APD restitution curve is steeper (i.e., the parameter time constant tau is larger) , there is accordingly a greater predilection for the heart to enter VF . Thus, another part of this aspect of the invention is the discovery that a normal patient will have a relatively low APD restitution parameter time constant, while a patient who is exhibiting drug toxicity

(e.g., quinidine intoxication) will have a relatively high

APD restitution parameter time constant. The restitution parameter time constant may also be used in monitoring cardiac stability, and in evaluating efficacy of anti- arrhythmic drugs. Experimental verification of this aspect of the invention has been achieved by the inventors and is disclosed in Karagueuzian et al . , "Action Potential Alternans and Irregular Dynamics in Quinidine-Intoxicated Ventricular Muscle Cells" (1993), Circulation p. 87:1661 (see p. 24-33) .

In a fourth aspect of the invention, an electrical restitution curve derived from a surface electrocardiogram can be used to detect a susceptibility for fibrillation. In one embodiment, the invention plots the T wave duration (ST) versus its previous recovery period (e.g., end of T wave to onset of the Q wave) . Such a plot is representative of APD versus the diastolic interval since, according to the present invention, the T wave duration (ST) represents the total APD (full repolarization time) and the time from the end of the T wave to the onset of Q wave represents the diastolic interval (recovery time) . See Figs. 14a and 14b Importantly, such a plot reveals the same information as an APD restitution curve but is nonmvasive . Unlike the APD restitution curve, this embodiment does not require mtracardiac recordings. Instead, the electrical restitution curve uses an EKG surface body electrogram recorded with either a standard 12 lead EKG or some variant in order to provide the two end-points necessary for the plot of the electrical restitution curve. As in the earlier discussed mtracardiac APD versus diastolic interval curve, when the electrical restitution curve slope is steeper than normal, i.e., the parameter time constant tau of the curve is larger than normal, the patient has a propensity for VF . See Fig. 14b.

The time constant may be calculated using the exponential equation ST=ST_pl-Ae ^{τo τ} where ST represents the full repolarization time, ST is the plateau of repolarization time, ST is the plateau of repolarization time duration, A is a proportionality constant, TQ represents the previous recovery period. In this manner, the restitution parameter time constant of the electrical restitutions curve may be compared to detect propensity for fibrilla- tion and to monitor cardiac stability, including instability resulting from antiarrhythmia drugs, without requiring an invasive procedure.

Experiment I . A mathematical study used PPPs, return maps, Poincare sections, correlation dimension, and spectral analysis to distinguish periodic, chaotic and random signals. PPPs were useful m distinguishing among all three classes of signals. Periodic signals showed clear, widely separated tra ectories; chaotic signals showed banding, forbidden zones and sensitive dependence on initial conditions, random signals showed no clear internal structure. With the exception of noise effects, the only major difference between the PPPs and the appropriately lagged return map was a 45 degree rotation. Poincare sections were also able to distinguish among the three classes of signals: periodic signals showed isolated points; chaotic signals showed ordered areas of apparent self -similarity; random signals showed a Gaussian distribution of points. Correlation dimension was more able to distinguish between chaotic and random signals than between chaotic and peri- odic signals. Spectral analysis using FFTs and harmonic magnitude ratio (HMR) was able to distinguish periodic signals, but were unable to distinguish between random and chaotic signals: HMRs of periodic signals were greater than 97%; HMRs of chaotic signals varied between 17 and 80%; HMRs of random signals were approximately 40%. PPPs were greatly affected by noise, return maps were less affected, while spectral analysis was relatively immune to noise. It was concluded that PPPs, return maps, Poincare sections, correlation dimension and spectral analysis are all useful determinatives of chaotic systems.

Experiment II.

A mathematical study concentrated specifically on ability of spectral analysis to distinguish chaotic from random signals. In this experiment, two series of random signals were generated. The first series comprised 5000 pseudo-random numbers which were smoothed using a method of least -squares approximation. The second series comprised white noise obtained from an analog-to-digital conversion board. Spectral analysis was performed by applying an FFT to the data, and searching for a broad band spectrum or a change from a narrow band to a broad band, which was presumed to be diagnostic of chaos. It was concluded that spectral analysis by itself was insufficient to unequivocally distinguish chaotic signals from random signals, and that additional tests such as PPPs and return maps were necessary for this purpose. Experiment III.

An experiment examined spectral analysis, visualization of PPPs and correlation dimension analysis, for usefulness in distinguishing between normal sinus rhythm and VF in dogs. Ischemia and re-perfusion were used as stress factors m closed-chest anesthetized dogs. Spectral analysis of the dogs having normal sinus rhythm revealed narrow-band spectra with fundamental frequencies at the sinus rate and harmonics extending beyond 50 Hz. PPPs were consistent with periodic dynamics, and dimension analysis revealed low dimensional behavior (1--2.5) In contrast, spectral analysis of the dogs having VF, revealed broad-band behavior with most of the energy at 6 Hz, and with energy at all frequencies between 1 and 25 Hz. PPPs showed constrained aperiodic behavior, and the dimensional analysis revealed higher dimensions (4-6) than that observed for the normal sinus rhythm dogs. Thus, all three techniques proved useful m distinguishing normal sinus rhythm from VF.

Experiment IV.

An experiment examined spectral analysis, visualization of PPPs, visualization of return maps, and correlation dimension analysis, for their usefulness in identifying VF m humans. These analytical techniques were applied to data from eight hypothermic patients undergoing spontaneous VF, and also to data from three normothermic patients with VF induced during electrophysiology testing. All patients had a broad band frequency spectrum (0-12 Hz) , a low dimension (range 2-5) , and banding and forbidden zones on PPPs and return maps. It was concluded that spectral analysis, visualization of PPPs, visualization of return maps, and correlation dimension analysis are useful m detecting and evaluating VF. Experiment V.

An experiment examined spectral analysis, visualization of PPPs and correlation dimension analysis for their usefulness in distinguishing between normal sinus rhythm and VF in humans. VF eight hypothermic human patients undergoing open-heart surgery was studied. In all patients, first and second order PPPs showed forbidden zones and banding, and an FFT revealed a relatively continuous power spectrum at all frequencies from zero to 25 Hz, with a majority of the power below 12 Hz. In contrast, correlation dimension in all cases was less than 4. It was concluded that multiphasic analysis of the data is preferable to reliance on a single analytical technique such as correlation dimension.

Experiment VI .

An experiment utilized spectral analysis and visualization of PPPs to elucidate the heterogenous nature of atrial fibrillation. In the experiment, the researchers induced acute fibrillation by a rapid tra of stimuli to the atria of seven closed-chested dogs. PPPs based on the EKG data often inscribed well defined structures, and an FFT of the digitized EKGs showed peaks mostly below 15 Hz that were either discrete with clear harmonic components, or had continuous spectra that changed m a time- and site-dependent manner. It was concluded that both spectral analysis and visualization of PPPs are useful techniques for analyzing atrial as well as ventricular fibrillation.

Experiment VII.

In an experiment, visual analysis of PPPs and the slope of an APD restitution curve were found to be useful for detecting and evaluating quimdme-mduced VF in in vivo hearts. Qu idme was administered at 30 minute intervals over five hours, until either a total of 90-100 mg/kg was administered or until ventricular tachycardia or VF occurred, whichever came first. PPPs of the quinidine intoxicated cells demonstrated sensitive dependence on initial conditions and the presence of forbidden zones, and the corresponding FFTs showed continuous spectra. In contrast, PPPs of cells in a control dog were uniform and densely packed, and the corresponding FFTs showed discrete spectra. The initial slope of the APD restitution curve of quinidine intoxicated cells was much steeper, by at least an order of magnitude, than the slope of normal cells. It was concluded that quinidine toxicity correlates with the slope of the APD restitution curves.

Experiment VIII.

An experiment compared the slope of the APD and APA restitution curves with quinidine intoxication. Quinidine was administered (90-100 mg/kg) to eight dogs over a five hour period. Three untreated dogs served as controls. Ventricular and Purkinje cells from both treated and untreated dogs were then subjected to electrical sti ula- tion with cycles from 900 to below 600 msec. Shortening of the cycle length to 600 msec resulted in irregular dynamics of both APD and APA, including electrical alternants and bifurcation. The slope of an APD restitution curve was calculated, and found to be steeper in quinidine-intoxicated cells for both Purkinje fibers and ventricular muscle cells than the slope during quinidine washout or in normal untreated cells. The curve could be fit by the exponential equation given herein. APA changes were almost always correlated with the APD changes . In the three normal tissue preparations neither ventricular muscle cells nor Purkinje cells showed bifurcative behavior with respect to APD or AA. It was concluded that quinidine toxicity, and presumably other drug- induced pro- arrhythmic effects, correlate with the slope of both APD and APA restitution curves. Experiment IX.

In an experiment, quinidine-induced ventricular tachycardia and VF in dogs was analyzed using PPPs generated from action potential duration (APD) and action potential amplitude (APA) data. Both PPPs showed forbidden zones and sensitive dependence on initial conditions which are indicative of chaos. It was concluded that PPPs based on either APD or APA are useful in detecting and evaluating quinidine toxicity.

Experiment X.

In an experiment, EKGs of quinidine intoxicated dogs were analyzed by frequency spectra, phase plane plots, Poincare sections, return maps and Lyapunov exponents. In the control state and at therapeutic doses, PPPs were uniformly thick and showed no gaps, indicating that cycle- to-cycle variation was due to normal biological "noise" . But as the quinidine dose was increased to intermediate levels (40-50 mg/kg) , PPPs showed clear non-uniform thick- ening, indicating sensitive dependence on initial conditions, and also showed marked banding (densely filled regions separated by divisions or gaps) . At these intermediate doses, Lyapunov exponents became positive and Poincare return maps also indicated nonrandom chaos. At still higher doses, PPPs became more complex. In two dogs that did exhibit VF (and not in another) there was a significant change in the PPP at the last pre-fibrillatory dose: the development of a "funnel", a classic mechanism of chaos. Frequency spectra at all pre- fibrillatory doses were discrete, with peaks at a fundamental frequency and multiple harmonics. It was concluded that chaos does occur during progressive quinidine intoxication, and that PPPs, and graphic and numeric analysis based on the PPPs, are better indicators of chaos than frequency spectra. Experiment XI .

In an experiment, quinidine toxicity in dogs was analyzed using PPPs generated from APA and APD data EKG recordings were made at various driving rates from 1000 to 500 msec. Increase in the driving rate from 1000 to 500 msec caused the progressive appearance of higher order periodicities (period 3 and 4) . Phase locking was seen with a stimulus (S) response (R) pattern repeating periodically all 4 preparations at S:R ratios of 2:1, 5:3, 3:2. At faster drive rates aperiodic variations in APA and APD were observed. A number of intermediate stages that presage chaos were also seen m the quinidine intoxicated fibers. These results further demonstrate the usefulness of the methods of the present invention to detect both quinidine intoxication and precursor stages to intoxication.

Experiment XII .

In an experiment, quinidine toxicity dogs was analyzed using PPPs generated from APA and APD data. Electrical stimuli were used to drive cardiac tissue at various rates from 2000 to under 300 msec. These stimuli caused steady alternants (bifurcation) in APD and APA of 108 ± 36 msec and 12 ± 9 millivolts respectively. Further increase m driving rates gave rise to irregular dynamics. This transition was preceded by various repeating stimulus-response ratios (phase-locking) for up to fifty consecutive beats. No such dynamics could be induced three non treated (control) tissues. The APD restitution curve had significantly (p < 0.05) steeper slope than six control fibers. Stimulus-response latency remained constant at 6 - 9 msec. PPPs of the APDs during the irregular dynamics showed sensitive dependence on initial conditions and forbidden zones consistent with chaos theory. These results further demonstrate the usefulness of the methods of the present invention to detect both quinidine intoxication and precursor stages to intoxication. Experiment XIII.

An experiment used spectral analysis, PPPs, Poincare sections, Lyapunov Exponents and dimension analysis to analyze computer simulated waveforms including sine waves, modulated sine waves, square waves, saw toothed waves, and triangular waves. The researchers added random noise to the waveforms at 1%, 10% and 20%. The experiment further used the same analytical techniques on EKG data from anesthetized dogs which VF was precipitated by five different interventions: qumidme intoxication; premature electrical stimulation followed by qu idme intoxication, coronary occlusion; reperfusion of acutely lschemic myocardium; and global hypothermia. The preliminary results showed that PPPs and Poincare sections in dogs undergoing ventricular fibrillation were consistent with chaos, while spectral analysis was not suggestive of chaos. The researchers concluded part that VF can be described as chaotic electrophysiological behavior, but that single methods of analysis are not sufficient to detect such behavior.

One conclusion which may be drawn from the research cited herein is that the analytical value of each of the aspects of the invention may be enhanced through combination with one or more of the other aspects of the mven- tion. A preferred embodiment of the present invention may include a combination of the aspects of the invention described herein. One preferred embodiment may comprise multiphasic analysis of a PPP (e.g , visually with a display, graphically with Poincare sections, and numerically with Lyapunov exponents and correlation dimension) , frequency spectral analysis, and mathematical analysis of an APD restitution curve.

Alternative Embodiments While preferred embodiments are disclosed herein, many variations are possible which remain within the concept and scope of the invention, and these variations would become clear to one of ordinary skill in the art after perusal of the specification, drawings and claims herein.

It would also become clear to one of ordinary skill in the art that embodiments of the invention may comprise means for continuous monitoring of drug toxicity, atrial fibrillation, ischemia or other heart conditions, such as during surgery or patient recovery from surgery. Moreover, embodiments of the invention may comprise means for indicating heart conditions which are detected to attending medical personnel or to the patient . In one preferred embodiment of the invention, means may be provided for directing the patient (when a heart disorder is detected) to contact a physician or to proceed to a nearby hospital for treatment.

1661

24

Action Potential Alternans and Irregular

Dynamics in Quinidine-Intoxicated

Ventricular Muscle Cells

Implications for Ventricular Proarrhythmia

Hrayr S Karagucuztan. PhD, Steven S Khan. MD, Kichol Hong. MD. Yoshinoπ Kobavasm MD. Timothv Demon, MD. William J Mandel. MD, and Georee A Diamond. MD

Background Cardiac cells display rate-dependent beat-to-beat variations in action -patentul duration (APD). action potential amplitude (ΛPΛ). and excitability during periodic stimulation. We hypothesized that quinidine causes a marked increase in the variability or APD. APA. and excitability of ventricular cells isolated from quiπidine-toxic. arrhvthmic ventricles.

Methods and Results. Action potentials were recorded from πght veπtπcular endocardial tissues ( 1 cm, <2 mm thick) isolated from dogs in which ventricular tachvcardia and ventricular fibrillation (VT/VFl were induced with intravenous quinidine (80-100 mg/kg) over a 5-hour period in >no in = 71. As the basic cycle length (BCD of stimulation was progressively shortened, rate-dependent variations in APD and AP\ occurred. The initial dynamic change was alternans of APD and APA that could be either in or out of phase between two cells. The magnitude of alternans was a function of the BCL and the strength of the stimulation current. At critically short BCLs. irregular APD and APA behavior emerged in the quinidine-intoxicated cells. In control cells (π = 16) isolated from three nontreated dogs, APD and APA remained constant at all BCLs tested (2.000-300 msec). Quinidine increased the slope of the APD restitution curve compared with control. The observed quinidine APD restitution curve was tilled with a biexponencial equation, and computer simulation using the fitted restitution curve reproduced the aperiodic APD seen in the quinidine touc cells dunng peπodic stimulation. Thus, the observed irregular APD behavior was predictable from the restitution curve.

Conclusions. Quinidine toxicity increases the temporal and spatial variability of APD and APA in the ventricle that may promote the initiation of reentrant VT/VF in vivo. The slope of the APD restitution curve provides a method to quantitate inhomogeneities in repolarization time and could be a useful marker for proarrhythmia. (Circulation 1993:87:1661-1672)

K£Y WORDS • action potential duration restitution • bifurcation • proarrhvthmid • chaos quinidine

S ir Thomas Lewis observed in 1911 that "heart stances the muscle is either markedlv degenerate or the alternation occurs under two circumstances It is heart shows evidence of embarrassment as a result of seen when the cardiac muscle is not of necessitv poisoning or some other factor ^" altered structurally, as an accompaniment of great Although Lewis'¹ experimental observations were acceleration of the rate of rhythm It is also found when made more than 80 years ago, the importance of the pulse is of normal rate, and under such circum- beat-to-beat changes in cardiac cellular electrical activity became appreciated only recently It was found

From the Division of Cardiology. Cedars-Sinai Medical Re that qu idme could exert qualitatively variable effects search Institute, and the Departmem of Medicine UCLA School on cardiac excuabilrlv during a modest elevation of of Medicine, Los Angeles extracellular potassium ion concentration ([K]„) ^: In

This studv was supported bv the Electrocardiographs Heartfact, it was shown that quinidine could either increase beat Organization Research Foundation, by the Division of Caror decrease the excitability of isolated sheep cardiac diology. Cedars-Sinai Medical Center, and by a generous gift from the Ralph M Parsons Foundation Purkinje fibers ^; This biphasic response is common in

Presented in pan at the 11th Annual Meetings of the North nonlinear dynamical systems³ and mav conceivably American Society of Pacing and Electrophysiologv, San Diego, lead to or be associated with other qualitative electro- Calif . Mav 1990. al the 10th International Symposium of Cardiac physiological changes such as alternations in action Pacing (Cardio-Sli ) Nice. France. June 1990 and ai the 16th potential duration (APD) and/or action potential amAnnual International Society for Computerized Electrocardiologv plitude (APA) '-⁵ The development or such beat-to- Conference. Santa Barbara. Calif April 1991

Address for correspondence Hravr S Karaeueuztan PhD beat alternations is termed a bifurcation ³ It has been Cedars-Sinai Medical Center. Davis Building. Room 6066 8700 hypothesized that such bifurcations could promote Beverlv Blvd . Los Angeles CA 90048 temporal and spatial cardiac electrophvsiological het-

Received July 28 1992 revision accepted January 11 1993 erogeneitv that in turn could facilitate the induction of 1662 Circulation Vol 87, So _^ May 1993 25 reentry"¹ and might be the cellular mechanism of drug- major vessels. Right ventπcular endocardial tissue blocks induced proarrhvthmia -⁵ (1-2 cm. <2 mm thick) were then excised and mounted

Bifurcations and irregular cardiac action potential in a tissue bath. Immediately before removal of the properties including APA, APD. and cardiac excitabilhearts, 10 ml of venous blood was withdrawn from the ity were also observed duπng regular pacing under jugular vein in each dog for piasma qumidme assay by conditions simulating various diseased states.⁵-⁷ These fluorescence polaπzation immunoassay ¹³ experimentally observed irregular cellular electrodynamics were also reproduced using computer simulation In Vitro Microelectrode Studies of realistic cardiac cell models in which the slope of the The isolated tissues were mounted in a bath with the APD restitution curve was increased to specified levpinned endocardial surface upward and were super- els ⁵-^§ Although these isolated tissue studies have fused with Tyrode's solution maintained at 36.5±0.5°C strongly suggested that such irregular cellular dynamics at pH 7 4*0.02. Three similarly prepared tissues were may be potential mechanιsm(s) for reentrant arrhythisolated from control nontreated dogs The Tyrode's mias in the situ heart.'⁴-⁵ there exists no report at present solution was gassed with 95% oxygen and 59c nitrogen that has shown the presence of ιrτegυlar cellular dynamand had the following millimolar (mM) composition ics in cardiac cells isolated from in situ arrhythmic NaCl 135, KCi 4 5, NaH,PO, 1 8. CaCI, 2.7, MgCl, 0.5, ventricles Furthermore, the presence of irregular cardextrose 5 5, NaHCO, 12 in triple-distilled deiomzed diac cellular dynamics duπng drug-induced proarrhythwater " Both the tissue bath and the Tyrode s stock mia also remains undefined. Consequently, the purpose of the present study was to determine whether ventricsolutions were continuously gassed with 959c oxygen ular mvocardial cells isolated from in situ drug-induced and 5^ nitrogen. The preparations were first regularlv arrhythmic ventπcles manifest alternans and beat-to- stimulated at 1,000-msec basic cycle length (BCL) with Dcat irregular action potentials (bifurcation) duπng bipolar silver electrodes that were Teflon coated except periodic stimulation. The results indicate that ventricuat the tip (0.12-mm diameter) lar mvocardial cells isolated from quimdine-induced Transraembrane action potentials were recorded with arrhythmic ventricle do manifest bifurcations and irregmachine-puiled. glass capillary electrodes from the ular action potential dynamics that may predispose to most superficial ventricular muscle cells (I e., two to four ventricular tachyarrhythmias in vivo ceil layers deep) because the most superficial (one to two cell layers) are made of Purkinje cells.^{14 15} Unless

Methods otherwise specified, the stimulus intensity was twice

Surgical Preparation diastolic current threshold with 2-msec duration and

Ten mongrel dogs were anesthetized with intravenous was applied within 1 mm of the microelectrode. The sodium pentobarbital (30-35 mg/kg), inrubated with effects of different BCLs of stimulation (spanning cuffed endotracheal tubing, and ventilated with room air 2.000-250 msec or until block was reached) and in some using a Harvard respirator at 4 cm H_;0 pressure. A cases the effects of increasing stimulus current intensity Teflon catheter (1 d.. 1.58: o d., 3 17) was placed in the on APD. APA. and excitation patterns were then evalright carotid aπerv and advanced to the ascending aoπa uated. In four of the seven quinidine-treated tissues, to monitor aoπic blood pressure, and another catheter rwo simultaneous action potentials from two different «.as inserted in the ri nt jugular vein for systemic drug cells along with an extracellular bipolar electrograms miections A 6F USCI bipolar catheter was mseπed (6USCI) were recorded from the endocardia! surface through the left jugular vein and positioned at the right The two microelectrodes were placed close to the two ventricular aoex under fluoroscopic control for the purpoles of the bipolar electrode The line connecting the pose of pacing the ventricle.' Surface lead ECG signals stimulating electrode, the rwo microelectrodes. and the (I. III. and V,) and aortic blood pressure were continutwo poles of the bipole was parallel to the long axis of ously monitored, hard copy was obtained at 50-100 mm the superficial endocardial fiber orientation The disper second paper speed on a Honeywell VR-16 oscillo- tance between the stimulating electrode and the proxiscopic-photographic recorder In seven dogs, increasing mal recording microelectrode was < 1 mm. cumulative doses of intravenous quinidine (quinidine The protocol of the study consisted of recording gluconate injection USP, Eli Lilly) were administered for sequentially from superficial ventπcular muscle cells at the purpose of inducing ventricular tachycardia and/or ventπcular fibπllation (VT/VF) ¹⁰ This model of sysmultiple sites (seven to 14 cells in each tissue) duπng temic cardiac intoxication was used to ensure that indiprogressive increases in the frequency of stimulation vidual cells subsequently selected for in vitro microeiec- APD restitution curves, i.e., the relation of APD with trode studies would be reasonably representative (see respect to its previous diastolic interval (electπcal resbelow) Each dose of qumidme ( 10 mg/kg) was administitution) of ventricular muscle cells both in control tered intravenously over a 2-mιnute peπod at 30-mιnute nontreated and in quinidine-treated preparations, were intervals until VT/VF was induced. Two minutes after constructed with the extrastimulus method duπng regeach dose, the ventricle in each dog was paced for ular drive at a BCL of 1.500 msec." " Duπng the studies peπods of 5-10 minutes at cycle lengths of 300-500 msec in quinidine-intoxicated tissues, the Tyrode's solution with constant current (2 -msec duration at twice diastolic contained 10 μg/mL quinidine gluconate (Lilly) to threshold) to increase rate-dependent mvocardial uptake maintain toxicity. Action potentials and bipolar electro- and subsequent toxicity of quinidine " ¹² In all seven grams were first recorded on an analog tape recorder treated dogs (after various forms of VT/VF were in(Bell & Howell, 4010 CRP) and then played back on a duced), the hearts were rapidly removed by seveπng the Honeywell (VR-16) for analysis. Karagueuaan et al Quinidine-Intoxicated . entricular Muscle Cells 1663

TAJJ E 1. Sle*dy-suιe Action Potential Properties of ranged between 45 and 74 μg/mL. with a mean of Ventricular Muscle Cells 54*21 μg/mL (mean±SD). When veπtπcular tachyarrhythmias developed, the hearts were rapidly removed and placed in cold (4"C), oxygenated Tyrode^'s solution for isolated in vitro microelectrode studies.

Steady-state Action Potential Properties

Both depressed fast-response (with resting membrane potential [RMP] between -75 mV and -66 mV)

and slow-response (with RMP more positive than -65

RMP, resting membrane potential: APD. action potential dura- mV) ventricular muscle cells were recorded from the lion for 100% repolarization: APA. action potential amplitude, superficial endocardial ventricular muscle cell layers. V„„. maximum slope of phase-zero depolarization. No ventricular muscle cell with RMP more negative

All three compaπsons are significantly different from each other than -79 mV could be recorded from the quinidine- (p<0.01). Basic cycle length of stimulation was 1.500 msec toxic tissues. At relatively long cycle lengths of stimulation ( > 1,000 msec), each stimulus was followed by an

Statistical Analysis action potential that had a fixed morphology in both

The paired ( test was used to test differences in fiber types. Table 1 describes action potential properties parameters between groups of cells. ANOVA was used of the rwo quinidine-toxic cell types and the control for repeated measurements in a given group during the nontreated groups of ventricular muscle cells. comparisons of the various parameters measured at No spontaneous diastolic depolarization or automatic different BCLs. A value of p<0.05 was considered activity either in the form of early or delayed afterde- significant. polarizations could be observed or induced in any of the quinidine-intoxicated cells at all BCLs studied (2,000-

Results 300 msec).

Quinidine-Induced Ventricular Tachyarrhythmias in Intact In Situ Hearts Dynamic Action Potential Properties

Three of the seven quinidine-treated dogs developed Alternans versus frequency of stimulation. As the cycle VF, one spontaneously and two during pacing at 500- length of stimulation was progressively decreased, the msec cycle -iength when the total cumulative dose of constant one-to-one stimulus response pattern (seen at quinidine was 100 mg/kg. Two of the remaining five relatively longer cycle lengths of stimulation) disapdogs developed runs of noπsusta ed and sustained peared, and alternation of APD and APA emerged (>30 seconds) VT when the total dose of quinidine was instead. These alternations depended on the frequency 80 rag/kg. In the remaining two dogs, a slow, wide QRS of stimulation and on the type of ventricular muscle cell "agonal" rhythm (rate, 60 beats per minute) was instudied (i.e., depressed fast-response versus slow-reduced when the total cumulative dose of quinidine was sponse fibers). Figure 1 illustrates the emergence of 100 mg/kg. The systolic aortic blood pressure during such alternans in a fast depressed cell as the stimulation these terminal rhythms was 45 ±5 mm Hg and diastolic frequency is increased. In 30 of 37 fast depressed fibers aortic blood pressure was 30±4 mm Hg. Quinidine and in 11 of 18 slow-response cells, alternans of APD plasma levels at the time of removal of the hearts and APA emerged as the frequency of stimulation was

NORMAL QUINIDINE

FIGURE 1. Comparative effects of progressive shortening of the cycle length (CL) of stimulation in normal (left panels) and quinidine-toxic (right panel) subendocardial ventricular muscle cells. A stable and constant action potential duration (APD) and action potential amplitude (APA) is present at each of the stimulating CLs tested (2.000-300 msec). In contrast, in the cell isolated from a quinidine-intoxicated dog, alternans of both APD and APA occurred when the CL of stimulation decreased from 900 to 750 msec. Further shortening of the CL to 600 msec resulted tn irregular APD and APA dynamics. The horizontal bar is 0.5 seconds for the normal recordings and I second for the qumidme recordings. 1664 Circulation Vol 87, No j May 1993

TABLE 2 Action Potential Duration and Action Potential manifest differing APD and/or APA properties during Amplitude Alternations in Quinidine-Toxic Ventncular the same stimulus, creating spatial and temporal disperMuscle Cells sion of action potential propeπies Figure 3 illustrates

Difference in Difference in one example of out-of-phase APD alternans In-phase A D,™) (msec) AfA (mV) alternation of APD is seen inmallv but evolves over time

BCL (msec) BCL (msec) to an out-of-phase pattern of alternation thus creating temporal and spatial gradient of APD Similar observa¬

1 000 900 800 800 700 600 tions were also seen in three other quinidine-toac

Fast depressed tissues in which both APD and APA alternations be¬

(π-30) 28*7 75 = 26 135 = 40 3 = 1 9 = 4 14 = 6 came out of phase

Slow response Alternans versus current strength of snmulation It has

(n-11) 20=4 48 =5 95 = 20 7 = 3 14 = 4 25 = 6 been suggested⁵ " that stimulus amplitude can odifv

APD_IΠJ action potential duration for 100% repolarization the dvnamic behavior of normal sheep cardiac Purkinje APA action poiennal amplitude BCL basic cvcle length fiber action potentials during repetitive stimulation

BCL dependent changes of APD and APA in both cell types Specifically, a critical stimulus amplitude I e , twice and differences at a given BCL between the two cell tvpes are all diastolic current threshold, was found to be necessarv statistical!* significant (p<005) for the induction of alternans Higher and lower current levels were often unable to induce alternans In three increased Table 2 summarizes these findings A stable quinidine-toxic ventπcular muscle cells, we tested the and steadv RMP was maintained during these episodes effect of changes in stimulation current amplitude on of alternans in APD and APA No alternation could be action potential dynamics Figure 4 illustrates one such induced in anv of the 18 control nontreated ventricular experiment When APD and APA alternation occurred muscle cells at cvcle lengths ranging between 2 000 and at twice diastolic current threshold an increase in the 250 msec (Figure 1) stimulus amplitude caused alternation to disappear

To determine whether alternation of APD and APA However, when the frequency of stimulation was further results from individual cell action potentials and not increased and stimulus amplitude was maintained at from alternate activation (resulting from alternate conthese elevated levels, alternans of APD and APA duction block) we recorded the overall tissue activation reappeared again (Figure 4) This change occurred pattern bv recording two cellular action without changing stimulus response latency, suggesting potentials along with an extracellular bipolar electrodirect excitation bv the stimulus at the proximal site gram Figure 2 illustrates one such experiment The This supports the concept that alternans is caused bv extracellular bipolar electrogram and the rwo cellular intrinsic cellular ionic alterations rather than bv changes action potentials demonstrate simultaneous in-phase in the sequence of activation Furthermore these studalternans of APD and APA at all three recording sites ies indicate that a critical stimulus amplitude, which This suggests that beat-to-beat variability results from depends on the frequency of stimulation, is needed for intrinsic (rhythmic) variability of cellular transmem the induction of alternans Because such a critical level brane ionic currents rather than by alternate sequence of current amplitude (i e , twice diastolic current threshof act ation Similar observations were made in five old) is necessarv to demonstrate irregular dy namics we additional quinidine toxic tissues The influence of the maintained the level of stimulus amplitude at twice sequence o activation with tissue sizes similar to ours threshold to detect potential irregular cellular dvnamics has yielded a maximum of 6-8-msec APD difference in in quinidine toxic cells in subsequent studies canine tissue w hen the direction of propagation was switched from longitudinal to transverse direction ^lβ Dvnamics of Excitabihtv and Frequence

In phase patterns of alternation could however of Stimulation switch to out-of-phase (discordant) alternation patIt was shown in normal sheep cardiac Purkime fibers⁴- terns In some experiments two adjacent cells couid and in aggregates of chick cmbrvoπic ventricles' that as

FIGURE 2 Simultaneous re cordmgs of action potentials

50 mV from two cells (cell 1 and cell 2) 1 cm distant from each other

Cell 1 (upper recordings) along with an extracellular bipolar electrogram (BEG) with 1-cm inter- electrode distance The endocar dial tissue was isolated from an

70mV m vivo quinidine-intoxicated

Cell 2

dog Sole the presence of stmul tanεous -phase action poiennal duration and action poten ttal amplitude alternans at all

BEG ImV three recording sues The prepa

IMC ration was regularly snmulated at 900-msec cvcle length 2B Karagueuzian et al Quinidine-lnioxicated Ventπcular Muscle Cells 1665

FIGURE 3 Simultaneous recordings of action potentials from two cells (cell, and cell.) 1 cm distant from each other in an endocardial tissue isolated from a dog with quinidine intoxication Note the in-phase action potential duration and action potential amplitude alternans (panel A)

BCL = 1000msec which 8 seconds later (panel Bl becomes out of ec phase The dots in panel B show the beats that became out of phase πith respect to both action potential duration and action potential ampli

tude BCL. basic cycle length of stimulation o* .ydJ^y JJ dJJJ U the BCL of stimulation was decreased, there was a locking patterns in eight fast depressed αuinidine-toxic progressive and predictable decrease in the activation ventπcular muscle cells Figure 5 illustrates one such ratio These patterns of activation were considered to be example As the BCL of stimulation was decreased from stable stimulus-response locking when the same se800 to 700 msec, the stimulus-response ratio changed quence of action potentials and dropped beats was from stable 1 1 locking (ac ation ratio 1 ) to stable 3 2 repeated several times, typically four to 10 times ⁵ In the locking (activation ratio 0 661 after transient unstable present study, we observed stable stimulus-response locking patterns of 4 3 and 5 4 The 3 2 locking pattern could be promptly reversed to 1 1 locking upon lengthening of the BCL of stimulation from 700 msec back to

BCL 800 msec Further decrease in the BCL of stimulation

UIAliU IOOO ΓHMC from 800 to 600 msec changed the locking from 1 1 to 2 I

1.2 mA (activation ratio, 0 50), and with fuπher decrease of BCL

is different from the above four recording panels response is obtained 1666 Circulation Vol 87, No 5 May 1993

1st MINUTE 1:1

FIGURE 6 Simultaneous record gs of two

action potentials t upper two recordings) and an extracellular bipolar electrogram (bottom recording on each panel) in a quinidine- intoacaied endocardial preparanon The tissue was stimulatea regularly at a basic cycle

\ V _\ \ length (BCL) of 1,000 msec (Dotlom recordings were obtained at a BCL of 720 msec) Note time-dependent changes in the locking

patterns from 2 1 to 3 1 to 4 1 * hile the BCL was maintained at 1.000 msec Al a BCL of 720 msec, 1 0 locking occurred.

of stimulation to 500 msec, a stable locking pattern of 1 0 stimulation frequency was maintained constant, the 1 1 emerged. Earlier studies in non-drug-treated cardiac locking evolved to 2 1, then 3 1. and finally to .1 With ceils demonstrated intermediate locking patterns (Devil's further decreases in the BCL of stimulation to 720 msec, staircasej. which could be reasonably well predicted by phase locking of 1 0 occurred In three preparations Farey s series (despite an inherent noise factor) '•^a) simultaneous recording of rwo cells showed that locking Farey^'s series predicts the order of stimulus-response could occur either in or out of phase, and in-phase patterns that occur as a result of a parameter change, locking could switch over time to out-of-phase locking including changes in the frequency of stimulation, These findings demonstrate that changes in either the changes in the stimulus amplitude, and time-αependent duration or the rate of periodic stimulation can cause recovery processes ⁵ " For example, one can predict the observed locking patterns. This may explain at least through Farev^'s seπes the phase-locking pattern between in part the unexpected and transient unstable locking 1 1 and 3 - 2 by adding the numerators and the denomipatterns observed in our quinidine-toxic ventricular nators of adjacent patterns and obtain in this particular muscle cells. Time-dependent changes in the coupling example the 4 3 phase-locked pattern (i e , 1 -3=4 and pattern have been observed in embrvonic chick heart 1 +2=3) With similar procedures, one can easily comcell aggregates during periodic stimulation.¹¹ Similarly , pute the presence of 5 4 phase locking between rwo incorporation of time-dependent parameters in a model adiacent patterns of 1 1 and 4 3 These rwo lockine describing the complex dynamics of atπoventπcular patterns transiently occurred m our example given tn conduction reflectine recovery of excitability successFigure 5 Theoretically, there exists an infinite number of fully predicted complex patterns of atπoventπcular steps between two adjacent patterns of phase locking that Wenckebach patterns of conduction in humans ^u even the Devil cannot climb (Devil s staircase). However, in normal nontreated ventricular muscle cells, repetit is questionable whether these theoretical patterns can itive stimulation at a BCL of 1.000-300 msec (or until be precisely duplicated in experimental settings because block) induced no locking pattern. The 1 1 response highly controlled progressive change in a parameter pattern was observed in all ventricular muscle cell⁵ value may not be practical. More studies are needed to (ι = 8) studied until failure of capture occurred clarify this issue. It must be noted that in our quinidine- toxic cells, transient rather than stable locking patterns Frequency of Stimulation and Aperiodic often emerged. Tins indicates that changes do occur Cellular Dynamics constantly duπng a single specified condition despite the At a critical BCL of stimulation, quinidine-toxic cells common assumption that the expenmental conditions generated action potentials that had irregular beat-to- are "controlled." For example, the concentration of beat APA and APD dynamics (Figure 1 and Figure 7) sodium channel-bound quinidine may continuously In 20 of 37 depressed fast-response fibers, irregular change because it is known that quinidine exhibits freaction potential dynamics were induced at a mean cycle quency-dependent block of sodium channels " length of stimulation of 625..250 msec (range, 850-280

In addition to frequency-dependent locking patterns, msec). Duπng the irregular activity, no periodic patterr we found that quinidine-toxic ventricular muscle cells m either APD or APA could be detected for up to 20' also manifested time-dependent locking patterns, when consecutive beats. We could see neither the dynamic the BCL of stimulation remains constant. To separate phenomenon of "recurrent fluctuations" between reguthe frequency and time dependency, tn five quinidine- lar and irregular activity nor the behavior of "multi- toxic cells the effect of time on the pattern of phase rhythmicity" with locking previously reported in Purlocking was evaluated while maintaining constant frekinje fibers.⁵ This type of irregular activity that is seen at quency Figure 6 illustrates one such experiment. As fixed cycle lengths of stimulation and at a constani Karagueuzian et al Quinidine-Intoxicated Ventπcular Muscle Cells 1667

BCL = 1000 msec BCL - 800

FIGURE 7 Recordings show induction of irreg ular action potential dynamics m a qumidme

BCL - 600 intoxicated ventricular muscle cell At a basic cycle length (BCL) of 600 msec slight alterna tion of action potennal duration and action potential amplitude occurred which with further decrease to 500 msec caused irregular action potential dynamics to emerge

stimulus amplitude is characterized bv random fluctuacy 3^j s M IS J₀ g_{a an} insight into the cellular mecha tions in stimulus response patterns that have common nism of APD alternans and apeπodicitv, v,e constructed activation ratios (i e , 2 1, 6 3, 18 6, etc ^s) It has been APD restitution curves in eight quinidine-toxic ventπc suggested that multirhvthmicitv has been related to ular muscle cells Figure 9 illustrates one such expeπ supernormal excitability in cardiac Purkinje fibers ment The APD restitution curves obtained were fit bv However, its relevance to other forms of action potenά biexponential equation using a curye-fitting software tial dynamics and evcπtuallv reentrant arrhvthmias repackage (PEAKFΓΓ, Jandel Scientific. Cone Madera. Cal main undefined at the present In slow-response fibers if ) (Figure 9) The slope of the APD restitution curve in however, no aperiodic or irregular action potential six of the eight quinidine-toxic fibers was significantly dynamics could be observed in any of the 18 slow- steeper at short diastolic inter^yals than in control response ventricular muscle cells studied Instead, pronontreated muscle cells (π=6) The fitted curve showed gressive increases in the rate of stimulation caused that the slope of the quinidine-intoxicated APD restivaπous patterns of phase locking to emerge that ultitution curve increased to 1 at a diastolic interval of 270 mately led to inexcitabtlitv msec and increased further at shorter diastolic intervals

We did not observe irregular action potential dynamIn the control preparation, the slope of the restitution ics in the 18 normal nontreated ventricular muscle cells curve was very close to 1 but did not exceed it even at during regular pacing at cvcle lengths of 2,000-280 shorter diastolic intervals msec However, the rate-dependent shortening of APD Superfusion with quinidine-free Tvrode s solution for expected in ventπcular muscle cells was regularly ob3 hours partially reversed the qumidme effect and served in all the normal cells studied (Figure 1) restored the slope of the APD restitution curve to values near normal At this time, stimulation of the

Irregular Action Potennal Dvnamics and Induction of partially recovered tissues failed to induce anv of the Nondnven Responses dynamic behaviors that were observed before quinidine

It has been suggested that asynchronous fiπng and washout repolarization of cells or groups of cells may generate local excitatory currents that can make reexcitation Analytic Solunon possible In rwo qumidme -toxic preparations, nondnven To determine whether the increase in the slope of the action potential-like responses were induced duπng APD restitution curve could cause aperiodic activity of phase three repolarization when the BCL of stimulation the sort observed in the present study, we iterated the reached a critical level within which irregular dynamics biexponential curve using the values obtained from the are expected to occur Figure 8 illustrates one such fitting Figure 10 illustrates one example of a bifurcation example The two sampled cells in this case were diagram obtained by iteration of the following biexposeparated by about 1 cm and showed only a minimal nential equation which is a one-dimensional difference alternans in their APD and APA as the BCL of stimulation was decreased from 600 to 400 msec The rapid equation stimulation and resulting asynchroπy induced nondnven APD₍, ₎=A -(B_l ^,e^|-^c""^,')-(B_: ^,e^|-^D'"-') single responses that were not sustained (they subsided when the stimulation was turned off) These findings are APD,. i is the APD of interest, DI is the diastolic suggestive of a local reexcitation phenomenon caused by interval before the APD of interest, and A, B, , -, , and the mechanism of reflection seen in Purkinje fibers ⁱ²³ τ₂ are the coefficients obtained from the curve-fitting procedure of the APD restitution curve The values of

Action Potennal Duranon Resntunon Curves the constants are presented in Table 3

It has been suggested that an increase in the slope of Alternans of the observed experimental data octhe APD restitution curve may be important in the curred at a longer diastolic interval than the theoretical induction of APD alternans and aperiodic APD dynammodel (Figure 11) This suggests that in addition to the ics during regular stimulation at a critical frequendiastolic interval and the slope factor, other mecha- 1668 Circulation Vol 87, So 5 May 1993

FIGURE 8. Simultaneous recordings of action potentials from two cells (cell #1 and cell #2) in qumidme -intoxicated ventricular cells showing the induction of nondnven action poiennal-like responses when the basic cycle length of stimulation was decreased lo 400 msec (arrows). nisms may be involved in the genesis of rate-dependent stressful stimuli⁴-" and are consistent with behavior APD dynamics. seen in other nonlinear dynamical systems subjected to stress.³ "

Discussion The irregular behavior induced by quinidine adds

Our results demonstrate that antiarrhythmic drug further experimental evidence that cardiac cells behave loxicin increases beat-to-beat vaπability in APD and as "nonlinear dynamical systems.^"" The action potenAPA duπng periodic stimulation and therefore causes tial dynamics induced by quinidine closely resemble the temporal and spatial nonuniformities in action potendynamics observed in cardiac cells exposed to a variety observations are comparable with earlier of stressful conditions including low temperature, the reports using cardiac tissue exposed to electrical uncoupler heptanol. and rapid pacing ³'^5-7

Arrhythmic Consequences of Cellular Bifurcation Dynamics

The irregular action potential dynamics of quinidine- toxic cells could create spatial and temporal inhomogc- neities in repolarization and conduction in the ventricles. The overall similarity in BCL at which arrhythmias developed in vivo (BCL, 500 msec) and the BCLs at which irregular APD dynamics occurred in vitro (average BCL, 625 msec) suggests a probable link between the occurrence of irregular APD dynamics and arrhythmias in the intact heart. These irregular APD dynamics may facilitate reentry either by the mechanism of reflection^{23 28} or by the mechanism of circus movement resulting from inhomogeneity in conduction.²' Such a

possibility is suggested by our ability to induce non-

FIGURE 9. Action potential duration (APD) restitution driven activity in the isolated tissue during critically curves of a control nontreated ventricular muscle cell (solid rapid BCL of stimulation. At present, we do not know if curvet and that of a ventricular muscle cell isolated from a a similar cellular mechanism is also operative in the quinidine-intoxicated dog (dotted curve). The lines are obintact ventricle or whether or not pacing-induced tained by fining the data by a biexponential equation (see text VT/VF in the quinidine-intoxicated dog resulted from for details). such cellular dynamics. Karagueuzian et al Quinidine-Intoxicated Ventπcular Muscle Cells 1669 nondnven beats could have been caused bv an auto¬

FIGURE 10 Bifurcation diagram obtained bv iteration of a biexponential equation (see text) that fits the experimental data Upper panel shows bifurcation diagram in which the slope of the action potential duration (APD) resntunon curve was similar to that seen in control nontreated cells Note the presence of 2 1 and 3 1 block at basic cvcle lengths of 380 msec and 185 msec, respectively n the bottom panel the slope of the APD restitution curve was made steeper, as seen in the experimental data Note the presence of irregular (chaotic) APD dynamics at basic cycle lengths of 720 msec, 350 msec, 220 msec, and 190 msec

The possibility of an automatic mechanism for the quinidiπe-induced VT/VF in the intact dogs and in the

isolated tissue studies does not seem possible for rwo Cellular Mechanisms of Unstable Action reasons First, in our in vitro studies, we never observed Potential Dynamics spontaneous diastolic depolarization and/or induced In an attempt to determine the possible cellular automatic activity either bv the mechanism of early or mechanisms of APD alternans. we constructed APD delayed afterdeoolaπzations in any of the quinidine- restitution curves It has been suggested that increasing toxic cells We have previously shown³⁰ that low quinithe steepness of the slope of the APD restitution curve dine concentrations (1-2 μg/mL), low extracellular pocould lead to APD alternans and to irregular APD tassium (2 7 mM). and long cycle lengths of stimulation dynamics ⁵-^{824 23} In the present study, we found an were required for the induction of early afterdepolar- increased slope of the APD restitution curve of quini- izations In our vitro studies, induction of nondnven diπe-toxic cells compared with control nontreated cells beats arose in the absence of all these three experimenIteration of the equation descπbing the APD restitution tal conditions, therefore it is unlikely that the induced curve showed that increases in the steepness of the slope ( > 1) was associated with bifurcation and irregular J Values of Ibe Constants of the Biexponential APD dynamics Equation Used for Iteration Alternans in the πumeπcal model occurred at faster rates of stimulation compared wtth the rate at which the

Control Quinidine quinidine-toxic muscle cells showed alternans This in¬

A 303 98 666 24 dicates that in addition to the slope, other factors mav

B, 2.039 47 5.449 37 aiso be operative in the genesis of APD bifurcations and rι 36 43 45 95 irregular APD dynamics This also explains at least in

8903 39899 part why relatively modest increases in the slope (ι e . final values < 1 ) could also cause alternans at a critically

724 86 268 01 high frequency of stimulation " 1670 Circulation Vol 87, So 5 Mav 1913

Z 300 o

<

IT o FIGURE 11 Experimental (dots) and

200 theorencal (curve) bifurcation diagrams Experimental data were derived from a qumidme intoxicated \ entricular muscle

Z LU cell, theoretical curve was constructed by r- iteration of the biexponential equation thai o 100

Ω. fit the observed data isee text for details) The observed data manifests bifurcation

Z g at a shorter pacing cvcle length than the model υ <

300 600 900 1200

PACING CYCLE LENGTH

The ionic mechanιsm(s) of quinidine-induced inSimulation studies using mod-fied Beeler-Reuter carcrease in the slope of APD restitution remain undediac cell models have shown that rate-dependent excifined Voltage-clamp studies on isolated guinea pig tation failure and irregular APA dynamics duπng regventricular mvocvtes have shown that quinidine delayed ular stimulation could also result from delaved recovery the activation of the delaved rectifier outward current of the sodium current and from L-type calcium cur(I ) and reduced us amplitude *° Such an effect could rents *' We do not know which of these potential ionic conceivablv cause an upward shift in the APD restitumechanisms may be responsible for the induction of tion curve with an attendant increase in us slope In a these observed dynamic behaviors because quinidine recent computer simulation of two-dimensional impulse could interact simultaneously with multiple ionic chanpropagation an isolated increase in the slope of the nels and potentially manifest nonspecific ion channel APD restitution facilitated the induction of APD alterblock at hjgh (toxic) concentrations ^2J°^J' nans and the induction of nonstationary double spiral waves ⁴¹ Similar spiral waves have been induced in thin Clinical Relevance sheets of sheep epicardial muscle cells during appropriThe tachyarrhvthmias that occur duπng acute ischemia ate stimulation protocols ⁴² It has been suggested that are often preceded bv depolarization and repolanzation APD alternans during acute ischemia could result from alternans ³²-⁵³ One studv has shown an increased likelialternation of intracellular calcium ([Ca] ) transients hood of VF occurrence duπng discordant (out-of-phase 1 jnd that such APD alternation could promote the repolarization alternans *⁴ More recently, abnormal initiation of sponianeous VF in the intact ventricle ⁴³ monophasic APD (MAPD) restitution curves resulting An important regulatory role of [Ca], on the APD from exaggerated APD shortening were observed in parestitution in canine endocardial ventricular muscle tients with ventricular disease and complicating VT ^!5 The cells has recently been emphasized " MAPD restitution curves were altered in diseased areas in

The ionic mechanism of altered dynamics of APA and these patients, often showing greater steepness compared rate-dependent block of excitation during rapid stimuwith curves obtained from normal zones The greater lation in qu idme toxic cells remains undefined Del- steepness of APD restitution curves in these patient' mar et al⁴⁵ have sho n in isolated guinea pig ventπcular could cause greater temporal and spaual dispersion ol myocyies that the time course of I deactivation kinetics repolarization leading to VT ³⁵ Therefore, MAPD restiwas similar to the time course of growth of subthreshold tution curves³⁴ may allow momtoπng antiarrhvthmic drug depolarizing responses. Such a property of ventricular toxicity (proarrhvthmta) in humans since MAPD restitumvocvtes was shown to cause various patterns of rate- tion curves with the contact electrode closely resemble dependent excitation failure (phase locking). These transmembrane cellular APD restitution " mechanistic suggestions were confirmed by computer simulation bv the same authors ** More recently, Joyner Summary et al⁴⁷ have shown that delayed recovery of excitability We have shown that ventricular muscle cells isolated of ventricular cells could lead to variable degrees of from quinidine-mduced arrhythmic canine ventricle^1; excitation block during a sudden increase in the rate of manifest rate-dependent beat-to-beat changes in APD stimulation These authors suggested that beat-to-beat and APA including phase locking (alternans) and irregaccumulation of lnacuvation can lead to variable deular dynamics The cellular mechanism of the dynamic grees of activation ratios We do not know if quinidine APD changes could be analytically described by quini- can delay the deactivation kinetics of I_κ in canine dme-induced increase of the slope of the restitution ventπcular muscle cells as it does in rabbit nodal cells⁴* curve, whereas the mechanism of quinidine-mduced or delav recovery of excitability, or both. APA dynamics remains undefined.

Claims

Cl aims ;

1. A device for detecting heart data, comprising a) a recording means designed for recording an EKG surface electrocardiogram; b) a first measuring means for measuring a T wave duration of said EKG surface electrocardiogram; c) a second measuring means for measuring the T wave's previous recovery period; d) constructing means for constructing an elec- trical restitution curve by plotting the T wave duration versus its previous recovery period; e) a third measuring means for measuring the slope of said electrical restitution curve; f) a comparator for comparing the slope of said electrical restitution curve with the slope of a normal electrical restitution curve; and g) a register for registering the result obtained by the comparator.

2. The device of claim 1, characterized in that the second measuring means is designed for determining the time from the end of the T wave to the onset of the Q wave .

3. The device of claims 1 or 2 , characterized in that the third measuring means measures the slope of said electrical restitution curve by fitting a curve to said measured values for the T wave duration and its previous recovery period using the exponential equation ST = ST_μι - Ae ^τo/τ where ST represents the full repolarization time, ST_ι is the plateau of repolarization time duration, A is a proportionality constant, TQ i s said previous recovery period, and Ύ is the time constant; and uses the slope of the fitted curve as the approximate slope of said elec- trical restitution curve.

4. The device of one of claims 1 to 3 , characterized m that the device is a cardiac defibrillato .

5. The device of one of claims 1 to 3, characterized in that the device is a cardiac monitor.