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(Circulation. 1995;92:1291-1299.)
© 1995 American Heart Association, Inc.

Articles

Effect of Rapid Pacing and T-Wave Scanning on the Relation Between the Defibrillation and Upper-Limit-of-Vulnerability Dose-Response Curves

Robert A. Malkin, PhD; Salim F. Idriss, BSE; Robert G. Walker, BS; Raymond E. Ideker, MD, PHD

From the Duke-North Carolina NSF/ERC in Emerging Cardiovascular Technologies, Department of Electrical Engineering, Duke University, and Departments of Pathology and Medicine, Duke University Medical Center, Durham, NC.

Correspondence to Robert A. Malkin, The University of Memphis, Herff College of Engineering, Biomedical Engineering Department, Memphis, TN 38152.

	Abstract

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Background The critical-point and upper-limit-of-vulnerability (ULV) hypotheses predict that the ULV dose-response curve should be steeper and to the right of the defibrillation (DF) curve. Yet, some recent experimental data contradict this prediction. Two studies are presented that test two explanations for the contradiction: (1) Testing at a single point in the T wave underestimates the ULV dose-response curve and (2) ULV testing at normal heart rates does not mimic the mechanical or electrical state of the heart in ventricular fibrillation (VF).

Methods and Results A nonthoracotomy lead system with a biphasic waveform was used throughout. In eight dogs, the dose-response curve widths (a measure of steepness) were compared between DF data and ULV data gathered at the peak (ULV_PK), middownslope (ULV_DWN), midupslope (ULV_UP), and all times (scanning or ULV_SCN) in the T wave. In another eight dogs, ULV data (ULV_RAP) were gathered by scanning the T wave after 15 rapidly paced beats (166- to 198-ms pacing interval). The rapid pacing interval was chosen to more closely mimic the hemodynamics and activation rate of early VF. ULV data (ULV_STD) at normal heart rates were gathered for all animals. In the first study, scanning significantly reduced the ULV curve width (ULV_SCN, 63.5±29.7 V; ULV_PK, 81.9±45.2 V; ULV_DWN, 116±36.5 V; DF, 105±22.0 V; P<.03) and significantly shifted the ULV curve to the right (ULV_{80 SCN}, 410±62.6 V; ULV_{80 PK}, 266±35.3 V; ULV_{80 DWN}, 355±80.4 V; DF₈₀, 427±60.9 V; P<.001). The subscript 80 signifies that the subject was left in normal sinus rhythm 80% of the time after that stimulus strength was delivered. In the second study, the ULV_RAP curve was shifted dramatically to the right, the average ULV_{50 RAP} being greater than the average DF₉₀. Furthermore, 92% of the ULV_RAP VF inductions occurred between 10 ms before and 50 ms after the peak of the T wave, suggesting that scanning of the entire T wave may not be necessary.

Conclusions With a single rapidly paced ULV sequence with limited T-wave scanning, it may be possible to estimate highly effective defibrillation doses with few VF episodes and high-voltage stimuli.

Key Words: defibrillation • electric stimulation • fibrillation • death, sudden

	Introduction

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It is well known that a stimulus delivered in the T wave of a normal cardiac cycle can induce ventricular fibrillation (VF).^{1 2 3} More recently, it was discovered that there is an upper limit to this vulnerability⁴ ; although a weak stimulus will induce VF, a strong stimulus may not. The critical-point and upper-limit-of-vulnerability hypotheses link the upper limit of vulnerability (ULV; see "Definitions") to defibrillation (DF). These hypotheses predict that a stimulus sufficiently strong to rarely induce VF should frequently defibrillate.^{5 6} Furthermore, since the pattern of recovery is much more repeatable during normal cardiac cycles than during VF, the ULV dose-response curve should be steeper (less probabilistic) than the DF dose-response curve. Combining these two ideas, the ULV dose-response curve should be steeper and to the right of the DF dose-response curve. As a result of this relation, the two dose-response curves should intersect at a dose with a high probability of success, suggesting that ULV data could be used as a predictor of highly effective DF doses.⁴ Data from laboratory animals and humans show that the ULV dose-response curve is actually less steep⁷ and to the left^{4 8 9 10} of the DF dose-response curve, which limits its clinical value. Two studies that test two explanations for the lowered ULV dose-response curve are presented here. The first tests the hypothesis that gathering ULV data throughout the T wave (scanning) removes some of the uncertainty, thereby raising and sharpening the ULV dose-response curve. The second suggests that the ULV dose-response cure is lowered relative to the DF dose-response curve because standard ULV testing at normal heart rates does not mimic the mechanical and electrical state of the heart in VF.

	Methods

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The two studies presented here followed the same animal preparation, DF measurement, and scanned ULV measurement methods.

Animal Preparation
The present study followed all applicable institutional guidelines in the care and treatment of laboratory animals. Sixteen dogs (20 to 25 kg) were anesthetized with intravenous pentobarbital (30 to 35 mg/kg initial dose, 0.05 mg · kg^-1 · min^-1 maintenance doses, approximately once per hour, or as indicated). Skeletal muscle paralysis was maintained with intravenous succinylcholine (1 mg/kg initial dose, 0.25 to 0.50 mg/kg maintenance, approximately once per hour, or as indicated). Core body temperature was maintained at 37°C with a hot-water blanket. The dogs were intubated with a cuffed endotracheal tube and ventilated with room air and oxygen through a respirator (Harvard Apparatus). A femoral artery line was inserted for the continuous display of systemic pressure. Arterial blood samples were drawn every 60 minutes to determine pH, partial pressure of oxygen, partial pressure of carbon dioxide, base excess, and sodium bicarbonate, potassium, and calcium contents. Normal saline was continuously infused through a peripheral intravenous line. The saline was supplemented with sodium bicarbonate, potassium chloride, and calcium chloride as indicated to maintain electrolytes within normal values. ECG electrodes for leads I, II, and III were applied, and the ECG was continuously monitored.

The dogs were positioned on their backs. Both external jugular veins were exposed, and a transvenous electrode catheter (2.95 cm² electrode area; CPI) was inserted into each vessel. One electrode was positioned in the superior vena cava (SVC) and one in the distal right ventricle under fluoroscopic guidance. The right ventricular electrode was the cathode for the first phase of a biphasic pulse described below. The anode for ULV and DF shocks was the electrode in the SVC electrically connected to a 113 cm² cutaneous R2 patch (Darox Corp) placed on the left side of the thorax over the point of maximal impulse.

The diastolic pacing threshold and the intrinsic RR interval were measured at the beginning of the study. The pacing stimulus was a unipolar, 5-ms, monophasic pulse delivered from an electrode at the tip of a catheter in the right ventricle to the R2 patch and SVC catheter. The animal was continuously paced until the end of the study at twice the diastolic pacing current threshold at a pacing interval equal to 80% of the intrinsic RR interval. Equipment failure occasionally required resetting the stimulator. In these cases, at least 15 minutes elapsed before a new pacing current threshold was established, and an intrinsic RR interval measurement was made. At least 30 minutes elapsed after the start of continuous pacing (at the beginning of the study or due to a stimulator reset) before the protocol was continued.

All high-voltage shocks were biphasic (6-ms positive first phase, 6-ms negative second phase) truncated exponential waveforms delivered from a Ventritex HVS-02 stimulator (Ventritex Corp). The two phases were separated by 200 µs. To simulate a single capacitor waveform, the leading-edge voltage of the second phase was set equal to the trailing-edge voltage of the first phase. All voltage settings were rounded to the nearest 10 V.

Definitions
Defibrillation testing (DF) delivers the stimulus during VF to determine the DF dose-response curve.

Upper limit of vulnerability testing (ULV) delivers the stimulus during the T wave to determine the ULV dose-response curve. In this article, the ULV is defined only in terms of L_P (see below) on the dose-response curve. No single shock strength is defined as "the ULV."

Upper limit of vulnerability testing at the middownslope (ULV_DWN) delivers the stimulus during the T wave, past the peak, at a time midway between the peak and end of the T wave.

Upper limit of vulnerability testing at the midupslope (ULV_UP) delivers the stimulus during the T wave, before the peak, at a time midway between the peak and beginning of the T wave.

Upper limit of vulnerability testing at the peak (ULV_PK) delivers the stimulus during the T wave, at a time corresponding to the peak of the T wave.

Upper limit of vulnerability testing at all times (ULV_SCN) delivers the stimulus during the T wave, at all times between the beginning and end of the T wave (see "Scanned ULV Measurements" for scanning details).

Upper limit of vulnerability testing at all times (ULV_STD) is the same as ULV_SCN but is applied only to the data for protocol 2.

Upper limit of vulnerability testing at scanned times, rapidly paced (ULV_RAP) delivers the stimulus during the T wave, at all times between the beginning and end of the T wave after pacing at an elevated rate.

The p percent effective dose (L_P) for DF is the shock strength that defibrillates p% of the time. For ULV, it is the T-wave shock strength that does not fibrillate p% of the time.

These symbols may be used alone or in combination. For example, the symbol ULV_{50 PK} refers to the shock strength that does not fibrillate 50% of the time when delivered at the peak of the T wave.

DF Measurements
It has been demonstrated that DF data gathered from ULV-induced VF are not significantly different from other DF data.¹¹ Therefore, DF observations were made 10 seconds after a ULV test shock initiated VF. The DF test shock strengths were selected by use of an up-and-down protocol^{12 13 14 15} with a 40-V step size and a starting shock strength of 370 V. At least 4 minutes elapsed after every DF. More time was permitted, if necessary, to allow the blood pressure to return to normal. The pacing stimuli were delivered throughout the protocol.

Scanned ULV Measurements
Both studies required creating dose-response curves from data gathered at multiple times throughout the T wave. These data were called "scanned ULV" data, because the coupling interval between the pacing stimulus and the ULV stimulus was scanned in 10-ms steps through all possible values, ie, from the beginning to the end of the T wave in lead III. However, unlike previous scanning protocols,^{16 17 18} which started scanning the coupling interval from the end or beginning of the T wave, the coupling intervals used here were scanned such that the stimuli started at the peak of the T wave. After the initial stimulus, stimuli were delivered alternately before and after the peak of the T wave, the coupling intervals being selected to move the stimuli away from the peak in 10-ms steps. For example, if the initial coupling interval was 300 ms, then the subsequent coupling intervals would be 310 ms, 290 ms, 320 ms, 280 ms, 330 ms, 270 ms, etc. The same stimulus strength was delivered at all coupling intervals according to the following two rules.

1. If the first ULV stimulus strength induced VF at any coupling interval, then the shock strength was immediately increased 40 V and the coupling interval reset to the peak of the T wave. Thereafter, the shock strength was increased after each VF episode until a shock strength did not induce VF at any coupling interval. This concluded one scanned ULV measurement. The next scanned ULV measurement was started 40 V lower than the shock strength that did not induce VF at any coupling interval.

2. If the first ULV stimulus strength did not induce VF at any coupling interval, then the shock strength was decreased 40 V and the coupling interval reset to the peak of the T wave. Thereafter, successively weaker shocks were delivered at all coupling intervals until VF was induced. This concluded one scanned ULV measurement. The next scanned ULV measurement was started 40 V higher than the shock strength that induced VF.

ULV Measurements
Protocol 1. In eight dogs, four types of ULV dose-response curves were measured: (1) scanned (ULV_SCN), (2) middownslope (ULV_DWN), (3) midupslope (ULV_UP), and (4) peak (ULV_PK) (see "Definitions"). The standard procedure for measuring a variety of dose-response curves in a single animal is to interleave the observations.^{19 20} However, the accuracy of the dose-response curve width (L₈₀-L₂₀) measurements is improved if each dose-response curve is measured without interruption. Interleaving the observations, on the other hand, allows drifts in the dose-response curve caused by physiological changes in the animal to accumulate throughout the experiment. The accumulated drifts increase the curve widths, obscuring the distinction between dose-response curves. If each dose-response curve type is measured without interruption, difference measurements, such as the curve width (L₈₀-L₂₀), are affected only by the small drifts that occur during the relatively short time it takes to measure one dose-response curve type. The result is a more accurate estimate of the curve widths. The order of the curve types followed a randomized Latin square design. This design ensures that the bias in single-point calculations is random between animals and therefore does not affect an ANOVA.

At the beginning of the study, the times to the beginning, peak, and end of the T wave were measured in lead III. The beginning of the T wave was defined as the first dramatic change in slope in the lead III electrogram after the ST segment. Others have reported problems identifying a clear ST segment.⁹ In this study, the ST segment was always easily observed, perhaps because lead III was recorded on a high-resolution digitizing oscilloscope (D6100, Data Precision). The end of the T wave was defined as the dramatic change in slope in the lead III electrogram that preceded the interbeat pause. The peak of the T wave was defined as the maximum observed between the beginning and end of the T wave. Three measurements of the beginning, peak, and end of the T wave were performed and averaged. The time to the middownslope of the T wave was calculated as the sum of the time to the peak and end of the T wave divided by two. The time to the midupslope was calculated as the sum of the time to the peak and the beginning of the T wave divided by two.⁹ A new measurement of the T wave was taken every five DF episodes or when the stimulator was reset. With each new T-wave measurement, scanning times were recalculated.

At least 15 seconds elapsed between a ULV observation that did not induce VF and the next ULV observation. The nonscanned ULV shock strengths were selected by an up-and-down protocol with 40-V steps, starting at 500 V. A total of 15 ULV measurement sequences were made for each of the four ULV dose-response curve types, each sequence consisting of multiple observations: For the peak, middownslope, and midupslope data, a measurement sequence ended at the first reversal, ie, when (1) a ULV shock induced VF, if the first stimulus in the sequence failed to induce VF, or (2) a ULV shock failed to induce VF, if the first stimulus in the sequence induced VF. For the scanned ULV data, a measurement sequence was defined as in "Scanned ULV Measurements."

Protocol 2. In a second set of eight dogs, two ULV dose-response curve types were measured from (1) standard scanned ULV data (ULV_STD) with pacing at 80% of the intrinsic RR interval and (2) scanned ULV data with rapid pacing (ULV_RAP). The standard scanned ULV data were gathered as described above ("Scanned ULV Measurements"). The ULV_RAP data were gathered at a pacing interval short enough to mimic more closely the mechanical and electrical state of the heart during the initial seconds of VF without actually inducing VF. The appropriate ULV_RAP pacing interval is called the target interval.

At the beginning of each experiment, before any ULV observations were made, the appropriate target interval was determined. Starting at 80% of the intrinsic RR interval, the pacing interval was decreased in 10-ms steps while the surface ECG (lead III) and the arterial pressure were continuously monitored. The pacing interval was decreased until the arterial pressure dropped abruptly and remained low for at least 15 paced, captured beats (2 to 3 seconds). The surface ECG was carefully monitored (Fig 1) to ensure that every paced beat captured and to ensure that VF was not induced by pacing. The longest pacing interval (slowest pacing rate) that dropped the pressure for 15 beats was taken as the target interval. Once the target interval was found, it was not changed throughout the experiment unless the stimulator was reset. If a reset was required, at least 30 minutes of continuous pacing elapsed before a new target interval was measured.

View larger version (20K): [in this window] [in a new window]   Figure 1. Tracings. All the observations for the ULVRAP analysis were gathered after successful rapid pacing sequences like the one depicted here. The pacing interval for the last 15 beats, called the target interval, was the longest interval that ensured electrical capture but caused an abrupt drop in the arterial pressure. The first beats of a rapid pacing sequence gradually decreased the pacing interval from 80% of the intrinsic RR interval to the target interval in 10-ms steps. For abbreviations, see text.

A preliminary study showed that capture could not be guaranteed when the pacing interval was abruptly decreased to the target interval. Therefore, for the data presented here, the pacing interval was gradually shortened to the target interval in 10-ms steps (Fig 1). A high-voltage ULV_RAP stimulus was delivered after the 15th paced beat at the target interval. Occasionally, a rapid pacing sequence was unsuccessful, either because capture was lost or because the arterial pressure did not drop. In either case, any ULV stimuli delivered after unsuccessful rapid pacing sequences were not included in the determination of the ULV_RAP dose-response curve.

ULV observations for protocol 2 followed the scanning rules described in "Scanned ULV Measurements" except that separate measurements of the T wave were required for rapid pacing and standard pacing intervals. A total of 15 ULV measurement sequences were made for both ULV_RAP and ULV_STD. Because curve width measurements were not the primary focus of protocol 2, the measurement sequences from the two ULV dose-response curve types were randomly interleaved. At least 15 seconds elapsed after each ULV observation that did not induce VF.¹⁶

Statistical Analysis
Protocol 1. All observations from all scan times and measurement sequences were pooled, and dose-response curves were fitted by PROBIT analysis.²¹ The PROBIT procedure²² was used because it not only fits the dose-response curve but also estimates shock strengths for fixed probabilities, such as the L₂₀ and L₈₀. The width of the dose-response curve was estimated as the difference between the L₈₀ and the L₂₀.^{15 23} After the curve width was calculated for each dog, an ANOVA was performed to test for any significant differences in the curve widths between the dose-response curve types. Multiple contrasts with Bonferroni confidence intervals²⁴ were used to individually compare ULV_SCN curve widths with each of the other dose-response curve types. The correlation at both the L₈₀ and L₅₀ voltages was calculated between the DF and the ULV_DWN, ULV_PK, and ULV_SCN, respectively. The significance levels of the correlations were corrected for multiple simultaneous inference based on the Bonferroni inequality.²⁴ Unless otherwise indicated, a lack of statistical significance (P=NS) was considered to be P>.05. For completeness, probability values close to .05 are noted in parentheses.

Protocol 2. For the second study, the PROBIT procedure²² was also used to fit a dose-response curve to each animal for each dose-response curve type. An ANOVA was used to reveal any significant differences between the dose-response curve types at the L₅₀ and the L₈₀. Multiple contrasts with Scheffé confidence intervals²⁵ were used to compare ULV_RAP individually with ULV_STD and DF. The correlation was calculated at both the L₈₀ and L₅₀ voltages between the DF and the ULV_DWN, ULV_PK, and ULV_SCN, respectively. Unless otherwise indicated, a lack of statistical significance (P=NS) was considered to be P>.05. For completeness, probability values close to .05 are noted in parentheses.

	Results

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Protocol 1
In six of the eight dogs, VF could not be induced when the T-wave stimulus was delivered at the midupslope (ULV_UP). At least nine attempts were made in every animal, with at least one attempt at the minimum leading-edge voltage that could be delivered by the defibrillator (100 V). These six animals could not be analyzed for ULV_UP. In the two remaining animals, it was possible to induce VF sporadically at the lowest deliverable leading-edge voltage. However, it is not possible to measure the width of the dose-response curve when VF is induced only at one voltage. Therefore, no analysis could be performed for ULV_UP.

In one dog, VF could be induced only at the lowest voltage setting (100 V) when the stimulus was delivered at the middownslope (ULV_DWN). For this animal, it is possible to state only that the ULV_{DWN 50} and ULV_{DWN 80} are 100 V. Therefore, this animal was dropped from the ULV_DWN curve widths and correlation analyses. For the ANOVA tests, the worst-case value of 100 V was taken. This is worst-case because higher values contradict the data, lower values artificially increase the test significance, and dropping the data eliminates known, valid data points. Binned raw data and the fitted dose-response curves for a typical animal are shown in Fig 2. Table 1 summarizes the dose-response curves for all the animals.

View larger version (24K): [in this window] [in a new window]   Figure 2. This animal's dose-response curves were typical of the dose-response curves seen in protocol 1. The raw data have been binned (open symbols) and fitted (solid symbols) by PROBIT analysis. Scanning significantly shifts the dose-response curve to the right and reduces the curve width (L80-L20). For the fitted curves, the placement of the solid symbols is intended only to distinguish among the testing methods and does not indicate data points. NSR indicates normal sinus rhythm. For other abbreviations, see text.

View this table: [in this window] [in a new window]   Table 1. Summary of the Data From Protocol 1

Scanning shifts the dose-response curve significantly back to the right (P<.001 for L₈₀ and L₅₀). The shift is great enough that there is no longer any significant difference between the ULV_{80 SCN} and DF₈₀ (17-V average difference, P<NS) or between the ULV_{50 SCN} and DF₅₀ (4-V average difference, P<NS). On the other hand, the average ULV_{80 DWN} and ULV_{80 PK} are 72 and 161 V below the average DF₈₀ (P<.06). Not only are the averages shifted, but also, in every dog, the ULV_{80 DWN} and the ULV_{80 PK} are below the corresponding DF₈₀. The ULV_{80 SCN} is a considerably better linear predictor of the DF₈₀ than either ULV_{80 DWN} or ULV_{80 PK} (r=.93, P<.05 versus r=.66, P<NS and r=.38, P<NS).

Scanning significantly reduces the dose-response curve width (P<.03). The average curve width, as estimated by the L₈₀-L₂₀, is 63.5 V for ULV_SCN but is significantly higher (P<.03) for ULV_PK (81.9 V), ULV_DWN (116 V), and DF (105 V). The ULV_SCN curve width is also smaller than the DF curve width on an animal-by-animal basis, often by a factor of two or more.

Protocol 2
In all eight dogs combined, the average measured target interval is 179±13 ms (Table 2). Table 3 shows the L₅₀ and L₈₀ voltages from the dose-response curves for ULV_STD, ULV_RAP, and DF. To compare the dose-response curves qualitatively, Fig 3 shows composite logistic dose-response curves that pass directly through the population-averaged L₅₀ and L₈₀. The ULV_RAP dose-response curve is shifted dramatically to the right of the DF and ULV_STD dose-response curves (P<.06 for L₅₀). This shift is of such great magnitude that the average ULV_{50 RAP} is greater than the average DF₉₀. If we examine the mean values in pairs (but correct for multiple comparisons), the average ULV_{50 RAP} is about 100 V above the average DF₅₀ (P<.06) or ULV_{50 STD} (P<.06), but there is no statistically significant difference between the ULV_{50 STD} and the DF₅₀ (P<NS). The average ULV_{80 RAP} is also about 100 V above the ULV_{80 STD} (P<.06) and DF₈₀ (P<.06), but there is no statistically significant difference between the ULV_{80 STD} and the DF₈₀ (P<NS). There is also no statistically significant difference between the ULV_RAP and ULV_STD curve widths, approximated with 2(L₈₀-L₅₀) (P<NS).

View this table: [in this window] [in a new window]   Table 2. T-Wave, Target, and Pacing Times for Protocol 2

View this table: [in this window] [in a new window]   Table 3. Summary of the Data From Protocol 2

View larger version (20K): [in this window] [in a new window]   Figure 3. These composite dose-response curves pass directly through the population-averaged (n=8) L50 and L80. The dose-response curve based on rapidly paced ULV measurements () was significantly different from the dose-response curves for defibrillation () and standard ULV measurements (). The shift is so great that the average ULV50 RAP is greater than the average DF90. NSR indicates normal sinus rhythm. For other abbreviations, see text.

Fig 4 shows the VF induction times for the strongest shocks that still induced VF (stepping up according to rule 1 under "Scanned ULV Measurements") and the strongest shock that just induced VF (stepping down according to rule 2). For ULV_STD, 87% of these VF inductions occurred between 10 ms before and 20 ms after the peak of the T wave. In this study, 92% of these ULV_RAP inductions occurred in a window between 10 ms before and 50 ms after the peak of the T wave. The average time at which VF was induced was 16.6 ms after the peak of the T wave for ULV_RAP and 9.20 ms after the peak for ULV_STD. By ² test,²⁶ there was a highly significant difference between the distribution of the coupling intervals for ULV_STD and ULV_RAP (P<.001) due primarily to the last three bins. The times for ULV_RAP appear to show a bimodal tendency that is absent in the ULV_STD times.

View larger version (30K): [in this window] [in a new window]   Figure 4. Bar graph showing the number of scanning sequences that terminated in each time interval for protocol 2. Scanning sequences were terminated according to rules 1 and 2 described in "Scanned ULV Measurements." Briefly, the bottom of each bar (stippled) represents the first shock that induced VF when stepping down in shock strength, and the top half of each bar (solid) represents the last shock that still induced VF when stepping up. More than 90% of these ULVRAP fibrillation inductions occurred between 10 ms before and 50 ms after the peak of the T wave. This suggests that limited scanning of the T wave may be equivalent to scanning the entire T wave, significantly reducing the number of high-voltage stimuli required for ULV testing. For abbreviations, see text.

	Discussion

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Background
A stimulus delivered in the T wave of the normal cardiac cycle can initiate VF.^{2 27} The critical-point hypothesis^{28 29} explains this behavior by defining a critical value of electric field strength and refractoriness. If, in some cardiac region, the degree of refractoriness spans the critical value of refractoriness and the electric field strength spans the critical value of field strength, then a "critical point" will be created at the intersection of the critical value of the electric field strength and refractoriness. A reentrant pathway will form around this critical point, and VF will result.

The ULV hypothesis^{5 6} extends the critical-point hypothesis to state that the same mechanism that causes some T-wave stimuli to induce VF causes weak shocks to fail to defibrillate. Shocks strong enough to raise all of the myocardium above the critical value of electric field strength cannot form a critical point and will leave a subject in normal sinus rhythm whether delivered in the T wave or during VF. In other words, a stimulus strength with a high probability of successfully defibrillating should have a high probability of success (of not inducing VF) when delivered in the T wave. Thus, the ULV and DF dose-response curves should overlap at a stimulus strength with a very high probability of success.

Since the pattern of refractoriness is more repeatable during the T wave than during VF, the critical point and ULV hypotheses also suggest that the ULV dose-response curve should be steeper (less probabilistic) than the DF dose-response curve. T-wave scanning further increases the steepness by systematically probing the repeatable pattern of the refractoriness to find the strongest shock that can still induce VF. If two lines are drawn tangent to the dose-response curves, descending from their point of intersection, the ULV line must intersect any lower probability to the right of the DF line, since the ULV dose-response curve has the greater slope. Thus, the ULV dose-response curve can be said to be to the right of the DF curve.

When the ideas presented in the last two paragraphs are combined, the ULV and critical-point hypotheses predict that the ULV dose-response curve should be steeper and to the right of the DF dose-response curve. However, laboratory data contradict this prediction.^{4 7} Furthermore, if the ULV and DF dose-response curves intersect at a shock strength with a very high probability of success and the ULV curve is steeper, then the ULV₅₀ should be greater than the DF₅₀. Although a strong correlation is seen between the DF₅₀ and the ULV₅₀ both in laboratory animals^{7 8 9 30} and in humans,^{10 17 18 31 32} with the exception of the studies described in References 16, 31, and 32, the data have consistently shown the ULV₅₀ to be significantly below the DF₅₀.

In three reported cases, the population-averaged ULV₅₀ was not significantly below the DF₅₀.^{16 31 32} However, direct comparison is difficult for any study that defines a single shock strength as "the ULV,"^{7 8 9 10 16 17 18 30 31 32} because the value of "the ULV" is sensitive to the subtle changes in the definition or testing protocol.³² Our use of a dose-response curve to describe ULV testing, instead of a single shock strength, should reduce the sensitivity of our results to the specific testing protocol. Comparison is also difficult because some of the previous work used monophasic ULV and DF waveforms.^{8 10} We used biphasic stimulation because there is increasing evidence that it will dominate future clinical practice.³³

T-Wave Scanning
The first portion of this study suggests that some investigators may have observed the ULV₅₀ significantly below the DF₅₀^{4 7 9 10} because they did not scan the T wave (ULV_SCN) but rather followed a simplified ULV measurement sequence, such as ULV_UP or ULV_PK. The effect of scanning can be viewed in terms of the critical-point and ULV hypotheses. If the electric field strength attains the critical value in some region of the heart, then a point of reentry (a critical point) can be formed during that portion of the T wave when the region is in the critical degree of refractoriness. Therefore, the time at which VF can be induced in the T wave by any shock strength is influenced by two factors: (1) the strength and geometry of the electric field, which determines which region is exposed to the critical electric field, and (2) the myocardial recovery sequence during the T wave, which determines the state of recovery in the critical region. Both the geometry and the recovery sequence can change radically between patients and subtly between beats.³⁴ Thus, the critical-point and ULV hypotheses predict that the most reliable way to measure the upper end of the ULV dose-response curve is to scan the vulnerable period, thereby ensuring that shocks are given when the region in which the electric field strength is weakest is in the critical stage of refractoriness. Measuring at a single point in the T wave, on the other hand, may find the critical degree of refractoriness in a region in which the electric field is not weakest. This will lower the ULV dose-response curve, because a lower-strength shock will suffice, at this single point in the T wave, to exceed the critical value of field strength in the region with the critical degree of refractoriness. Since a lower-strength shock is needed to prevent the induction of VF, the ULV dose-response curve is shifted to the left of the ULV curve that would result from scanning. The data shown in Table 1 and those given by Hwang et al³² support this assertion. Here, the average ULV₈₀ measured at a single point in the T wave was as much as 144 V to the left (below) the average ULV_SCN. Hwang et al showed that increasing the number of scanning times in the T wave increased the average ULV by 4 J.

Chen et al⁹ were not able to induce VF consistently at the middownslope (ULV_DWN). In the present study, we were unable to induce VF consistently at the midupslope (ULV_UP). Since Chen et al⁹ used a different electrode configuration and pacing site, this supports the notion, presented above, that the ULV dose-response curve depends on the recovery sequence and electric field geometry and therefore on the pacing and shocking electrode configurations. Fan et al³⁰ found that the ULV₅₀ voltage was not dependent on the pacing site. However, Fan et al measured at only two points in the T wave. From data gathered at only two points in the T wave, it is not possible to know whether the ULV_SCN dose-response curve or the ULV_{80 SCN} voltage would have varied with the pacing site, as predicted above.

Not only do the critical-point and ULV hypotheses predict that T-wave scanning will shift the ULV dose-response curve to the right, but they also predict that scanning should reduce the ULV dose-response curve width. Slight changes in the metabolic or autonomic state of the animal may alter the degree of refractoriness for a fixed point in the T wave. These slight changes increase the curve width for any ULV observations made at a single point in the T wave, eg, ULV_PK and ULV_DWN. On the other hand, a dose-response curve based on T-wave scanning should be less sensitive to shifts in the degree of refractoriness, since scanning always finds the time at which the region of the heart exposed to the weakest electric field strength is in the critical degree of refractoriness. Therefore, the ULV_SCN dose-response curve should have a smaller curve width than ULV_PK or ULV_DWN, according to the critical-point and ULV hypotheses. This prediction is supported by the data presented in Table 1. The average curve width of ULV_SCN is 18 V smaller than ULV_PK and 53 V smaller than ULV_DWN.

Although scanning the entire T wave should yield the smallest curve width, knowledge of the electric field and pacing site or simple trial and error may allow the ULV_STD or ULV_RAP dose-response curves to be measured without scanning the entire T wave. Fig 4 suggests that it might be possible to scan through a reduced window around the peak of the T wave. Nearly 90% of the ULV_STD VF inductions occurred in a window between 10 ms before and 20 ms after the peak of the T wave. In this study, >90% of the ULV_RAP VF inductions occurred in a window between 10 ms before and 50 ms after the peak of the T wave. Further investigation will be required to explain why ULV_RAP should require a wider window than ULV_STD. It is not known whether a limited scanning window exists for other pacing sites, electrode configurations, and ULV protocols.

Rapid Pacing
In the first study, the ULV_SCN dose-response curve is shown to be steeper and to the right of the ULV_PK and the ULV_DWN dose-response curves but not enough to make the ULV_{50 SCN} consistently greater than the DF₅₀, as predicted by the ULV and critical-point hypotheses. Rapid pacing, on the other hand, shifts the mean ULV_{50 RAP} above the DF₅₀. If differences in the electrical or mechanical state of the heart between VF and the paced rhythm account for the lowered ULV_{50 SCN}, then rapid pacing may raise the ULV_{50 RAP} by more closely mimicking the heart in VF.

Differences have been observed between the mechanical state of the heart during the T wave, when a ULV_SCN stimulus is delivered, compared with VF, when a DF stimulus is delivered. The right ventricle has been shown to enlarge early in VF.³⁵ This change may result in a weaker electric field in some region of the heart during VF compared with the same region during pacing at normal heart rates.³⁶ In other words, for the same stimulus, some region of the heart may be exposed to a stronger electric field when the stimulus is delivered during the T wave compared with VF. By this mechanism, standard ULV measurements at normal heart rates may shift the ULV dose-response curve to the left. It is possible that rapid ventricular pacing to the point of hemodynamic compromise (ULV_RAP) places the heart in a geometric or volumetric state similar to that which occurs during VF, minimizing any electric field differences and shifting the ULV dose-response curve back to the right.

It is also possible that rapid pacing induces changes in the electrical state of the heart that can account for the increased ULV_{50 RAP}. Pacing at the target interval, compared with 80% of the RR interval, forces the myocardial cells to activate at a rate closer to the VF activation rate. Perhaps the ULV dose-response curve is sensitive to this difference in activation rates.

Any dependence of ULV data on the pacing rate is in direct contradiction to the results of Chen et al.⁹ They reported that there was no effect on the ULV₅₀ when the pacing interval was varied from 150 to 500 ms. There may be several reasons for this contradiction. Only two (of nine) of their dogs could be consistently paced at 150 ms.⁹ For the remaining seven animals, the shortest pacing interval was 200 ms. In our study, the average target interval was 179±13 ms (Table 2). It is possible, therefore, that Chen et al did not see a significant dependence on pacing rate because this dependence occurs only for pacing intervals shorter than 200 ms, for which they had very few data. Another possible explanation is that Chen et al did not scan the T wave. Perhaps scanning is required to observe a pacing dependency in the ULV dose-response curve. Further studies are necessary to determine the exact cause of these contradictory results.

Clinical Implications
It has been suggested that ULV data could be used to predict DF efficacy.^{4 9 10 16 17 18 31 32} If results in patients are shown to be similar to our results in dogs, then this study suggests that ULV_RAP may be more reliable or more accurate than ULV_STD for DF efficacy estimation. Accuracy is defined here as the average squared difference between the estimate and the true value. Reliability is defined here as the probability that the estimate is above the true value. By this definition, typical unbiased, accurate estimates achieve only 50% reliability. A highly reliable estimate, on the other hand, may be inaccurate, but not because of underestimation.

Rapidly paced ULV data can be used as a reliable estimator of the DF₈₀. For example, assume that several successively weaker ULV shocks are delivered (possibly with an abbreviated scanning sequence) during pacing at the target interval, reducing the shock strength until VF is induced. We can assume that the lowest delivered ULV shock strength that did not induce VF is above the ULV_{80 RAP}. (This assumption can always be satisfied. A proof of universality can be directly extrapolated from Reference 37 by setting the starting voltage high and the step size small.) Table 4 shows the differences between the ULV_{80 RAP} and the DF₈₀. If the variables in Table 4 are gaussian normal random variables with mean µ and standard deviation , then it is possible to estimate the probability that the ULV_{80 RAP} is above the DF₈₀:

View this table: [in this window] [in a new window]   Table 4. Summary of the Difference Between ULVRAP and DF

where the right side is of the form Pr[y>(-µ/)] and y is a gaussian normal random variable with mean equal to zero and variance equal to one. From a standard table for Pr(y>x),³⁸ the probability that the lowest noninducing ULV_RAP shock strength is greater than the DF₈₀ is .85. By the same logic, the probability that the last noninducing rapid ULV shock strength is greater than the DF₅₀ is .95. Thus, stepping down in ULV_RAP shock strengths until VF is induced is a simple and 85% reliable estimator of the DF₈₀ and a 95% reliable estimator of the DF₅₀ in dogs. It is important to determine whether equally good results can be obtained in patients.

Even a reliable estimate may be more than is clinically necessary. In some cases, it may be sufficient to simply know that the DF₈₀ is below some shock strength, eg, S. This knowledge could be gained with ULV_RAP measurements without inducing VF. The implanting physician would deliver successively lower ULV_RAP stimuli until the shock strength was equal to or just below S. Since VF has not been induced, we can again assume that this shock strength is greater than the ULV_{80 RAP}. By the same analysis as in the previous paragraph and given that the shock strength has been stepped down to S without inducing VF, the probability that the DF₈₀ is less than S is >.85.

Study Limitations
Several points may limit the clinical implications presented above. Although stepping down to S indicates that the DF₈₀ is probably below S, the converse does not hold: Failure to step down to S may not indicate a high DF₈₀. Furthermore, the probability that the DF₈₀ is below S is calculated with the assumption that the starting voltage is high and the step size small. Protocols that deviate widely from this assumption may not attain the predicted reliability. Thus, it is possible that clinically viable ULV_RAP protocols will not attain sufficient reliability to justify the increased morbidity associated with rapid pacing and T-wave scanning. Finally, the dog hearts in this study were normal. It remains to be determined whether it is possible to rapidly pace diseased human hearts without inducing VF.

It is assumed throughout the testing for protocol 2 that rapid pacing more closely mimics the electrical or mechanical state of the heart during VF. Although some evidence supports this assertion, it is not directly proved in this study. It is possible that acute rapid pacing increases the ULV₈₀ via a mechanism unrelated to the state of the heart in VF. However, this would not affect the results of this study, since they are based on the shifted dose-response curves, not on the mechanism responsible for the shifts.

Protocol 1 did not follow the common practice of randomly interleaving the observations to reduce bias errors due to physiological drift. Instead, each curve type was measured in sequence, and the order of the curve types followed a randomized Latin square design. This measurement sequence improves the accuracy of the estimated curve widths but reintroduces the susceptibility to physiological drifts for paired analyses. For this reason, paired analysis was not performed in this study, except in the calculation of the correlation coefficients, in which it cannot be avoided. Since any random factor, including physiological drift, will reduce the correlation, the correlation coefficients presented here may underestimate the true correlation coefficients.

Conclusions
The ULV and critical-point hypotheses predict that the ULV dose-response curve should be steeper and to the right of the DF dose-response curve. Yet experimental data contradict this prediction. The data presented here suggest that this contradiction arises because (1) the width of the dose-response curve is increased by experimental protocols that do not scan the T wave and (2) the ULV measurements are made when the heart is in a different mechanical or electrical state than the DF measurements. A significant clinical implication of this work, which must be confirmed in patients, is that rapidly paced ULV stimuli with limited scanning could be used to reliably estimate the DF₈₀.

	Acknowledgments

 
This work was supported in part by National Science Foundation/Engineering Research Center grant CDR-8622201 and NIH research grants HL-42760 and HL-44066.

Received November 7, 1994; revision received February 15, 1995; accepted February 25, 1995.

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