Lowering of Sensory, Motor, and Pain-Tolerance Thresholds With Burst Duration Using Kilohertz-Frequency Alternating Current Electric Stimulation: Part II

Article Outline

• Abstract
• Gildemeister Effect
• Sensory, Motor, and Pain-Tolerance Thresholds
• Discomfort and Kilohertz-Frequency AC Stimulation
• Present Study
• Methods
  • Statistical Analysis
• Results
  • Further Analysis
• Discussion
• Conclusions
• References
• Copyright

Abstract 

Ward AR, Lee Hung Chuen WL. Lowering of sensory, motor, and pain-tolerance thresholds with burst duration using kilohertz-frequency alternating current electric stimulation: part II.

Objective

To determine the optimum burst duration for discrimination between sensory, motor, and pain tolerance thresholds using 20-Hz bursts of kilohertz-frequency sinusoidal alternating current (AC) applied transcutaneously to human participants.

Design

A within-subject, repeated-measures trial.

Setting

A research laboratory.

Participants

Healthy young adults (N=20).

Interventions

Bursts of AC electric stimulation at frequencies of 1 and 4kHz. The burst frequency was 20Hz. Burst durations ranged from 250 microseconds (for 1 cycle of 4-kHz AC) and 1 millisecond (for 1 cycle of 1-kHz AC) to 50 milliseconds (continuous AC).

Main Outcome Measures

Measurement of sensory, motor, and pain-tolerance thresholds.

Results

Thresholds decreased to a minimum with increasing burst duration. The minimum threshold identified the utilization time over which summation of subthreshold stimuli occurs. Utilization times were different for sensory (∼20ms), motor (∼30ms), and pain (>50ms) and were much higher than found in a previous study that used a higher burst frequency (50Hz). As with the previous study, relative thresholds were found to vary with burst duration. Despite the very different utilization times, maximum separation between sensory, motor, and pain thresholds was found to occur with bursts in the range of 1 to 4 milliseconds, the same range found in the previous study.

Conclusions

Our conclusions concur with those reported previously and support the contention that short-duration kilohertz-frequency AC bursts (1–4ms) have a more useful role in rehabilitation than the long-duration kilohertz-frequency bursts that characterize Russian and interferential currents.

Key Words: Electric stimulation, Pain threshold, Rehabilitation

List of Abbreviations: AC, alternating current, ANOVA, analysis of variance

TRANSCUTANEOUS ELECTRIC stimulation is commonly used clinically for pain control and for benefits resulting from muscle contraction such as muscle reeducation, prevention of atrophy, and strengthening.¹, ² Two stimulus types are commonly used: short-duration pulsed current and kilohertz-frequency AC (fig 1). Pulsed current used clinically typically has a pulse duration in the range of 50 to 500 microseconds and a pulse frequency between 1 and 120Hz. It may be biphasic (see fig 1A) or monophasic (see fig 1B). AC stimulation uses a symmetric biphasic waveform that may be rectangular (see fig 1C) or sinusoidal (see fig 1D) with frequencies between 1 and 10kHz, applied in bursts with a burst frequency between 1 and 120Hz. The burst duty cycle (“on” time to “off” time of the bursts) is typically 50% (Russian current)¹ or more (interferential).¹, ², ³ Figure 1C shows a stimulus waveform with a burst duty cycle of 50%; that is, the on and off times are equal. Figure 1D shows typical bursts of interferential current where, strictly speaking, there is no off time, but the stimulus will be subthreshold for part of the time so the effective on time to off time is uncertain.¹, ³

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• Fig 1. 

  Stimulus types commonly used in rehabilitation. (A) Biphasic pulsed current. (B) Monophasic pulsed current. (C) Bursts of AC with a duty cycle of 50%. (D) Bursts of AC typical of interferential current.

The use of kilohertz-frequency AC in rehabilitation, in the form of interferential current and Russian current, is widespread. Anecdotal evidence suggests that this is because AC stimulation is perceived to be both comfortable and effective.¹ The explanations have, until recently,³, ⁴, ⁵, ⁶, ⁷, ⁸, ⁹ not been questioned, but they do have some historical basis.¹⁰, ¹¹, ¹², ¹³, ¹⁴, ¹⁵, ¹⁶

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Gildemeister Effect 

With kilohertz-frequency AC stimulation there is the possibility of summation of subthreshold depolarizations, a phenomenon first described by Gildemeister.¹³, ¹⁴ Summation occurs when a burst of AC of sufficiently high frequency is used as the stimulus. During each burst, the nerve fiber membrane is pushed closer to threshold with each successive pulse in the wave-train because the nerve does not have time to recover between pulses. Eventually threshold is reached and an action potential is produced. This means that short-duration bursts will allow for little summation so the thresholds will be high. Longer duration bursts allow greater summation so the threshold intensity will be lower. Gildemeister observed that there was a limit to the time over which pulses could summate: a plateau is reached where further increases in burst duration do not result in any further decrease in threshold voltage. He reported this as the “nuttzeit” or “utilization time” over which summation can occur. Gildemeister studied human participants and used transcutaneous application of the electric stimulation. Schwarz and Ehrig¹⁷ used frog and rat nerve trunk preparations and observed the same effect. They found that motor threshold stimulus voltages decreased as the number of cycles per burst increased and observed a nuttzeit, a plateau in the strength/burst duration graph, at about 2 to 4 milliseconds. Later work by Schwarz and Volkmer¹⁸ used single nerve fiber preparations to directly measure the change in membrane potential at a node of Ranvier. They found that with each successive pulse, the measured membrane potential changed until, after several pulses, threshold was reached and the nerve fiber fired. More recently, Ward and Lucas-Toumbourou¹⁹ measured sensory, motor, and pain-tolerance thresholds at different burst durations using 1- and 4-kHz AC applied transcutaneously to human participants. They observed that each of the 3 thresholds decreased to a minimum as the burst duration was increased. The experimental evidence for the Gildemeister effect (ie, summation of subthreshold depolarizations) is thus substantial.

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Sensory, Motor, and Pain-Tolerance Thresholds 

An interesting finding of the Ward and Lucas-Toumbourou¹⁹ study was that sensory, motor, and pain-tolerance thresholds decreased to a minimum, then increased. There was no plateau but rather a minimum, an optimum burst duration where the threshold was lowest. The optimum burst duration was different for each of the 3 thresholds. Sensory thresholds reached a minimum at about 7 milliseconds, motor thresholds at a little over 10 milliseconds, and pain thresholds at 20 milliseconds or more (20ms was the longest burst duration that could be measured).

This raises the question of whether any different physiologic effects of pulsed current and bursts of kilohertz-frequency AC are explicable in terms of summation, which can only occur with kilohertz-frequency AC where there are multiple pulses, close together, in a burst. Any such explanation would also have to encompass a limit to summation, specified by the utilization time, which is different for different nerve fiber types.

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Discomfort and Kilohertz-Frequency AC Stimulation 

A recent study⁹ that assessed discomfort over the frequency range of 0.5 to 20kHz found that discomfort decreased from 0.5kHz to 4 to 5kHz, then increased to 20kHz. The observation that minimum discomfort occurs at a frequency of 4 to 5kHz helps to justify that interferential current stimulation is clinically advantageous in that it is relatively comfortable.

Burst duration is also an important factor determining discomfort. Ozcan et al⁷ reported that continuous 4-kHz AC (as used in interferential current stimulation) was more uncomfortable than 10-millisecond, 50-Hz bursts of 4-kHz AC (a form of premodulated interferential current) and also elicited less muscle torque. Ward et al⁹ examined a range of AC frequencies (0.5–20kHz) at different burst durations and found that a burst duration of about 4 milliseconds resulted in the least discomfort and that maximum muscle torque is elicited using bursts of about 2 milliseconds.

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Present Study 

A possible explanation for the observation that short burst durations are associated with the greatest torque production and the least discomfort is that the different nerve fiber types associated with sensory stimulation, motor activation, and discomfort respond differently to AC burst stimulation because of their different electrophysiologic properties.³, ¹⁹ Different nerve fiber types have different refractory periods, different periods of hypoexcitability and hyperexcitability, and different recovery times.²⁰, ²¹, ²² This means that sensory, motor, and pain fibers are likely to respond differently to stimuli with varying burst durations. In particular, the rate and effectiveness of summation of subthreshold stimuli would be expected to vary between fiber types, as would the utilization time.³, ¹⁹

In a previous study, Ward and Lucas-Toumbourou¹⁹ measured sensory, motor, and pain-tolerance thresholds, using bursts of 1- and 4-kHz AC with burst durations in the range of .25 to 20 milliseconds.¹⁹ The burst frequency was fixed at 50Hz, so the maximum burst duration was 20 milliseconds. With a 20-millisecond burst duration, the interburst interval is zero so the stimulus waveform is continuous AC. With burst durations less than 20 milliseconds, there is an interburst interval equal to (20 – x) milliseconds, where x is the burst duration.^{19(fig 1)}

An interesting finding of the previous study was that the thresholds did not simply decrease to a plateau as found by Gildemeister and later workers.¹³, ¹⁴, ¹⁵, ¹⁶, ¹⁷, ¹⁸ Rather, at least in the case of sensory and motor thresholds, a minimum was reached, but with further increases in the burst duration, thresholds increased. This finding corroborates and extends the findings of Kantor et al,²³ who used 2.5-kHz AC and measured sensory and motor thresholds with bursts of 4 different durations (0.4, 4, 10, and 20ms) and found minimum sensory and motor thresholds at intermediate burst durations (4 and 10ms). A possible explanation is that the interburst interval is important. In earlier studies,¹³, ¹⁴, ¹⁵, ¹⁶, ¹⁷, ¹⁸ the bursts were applied infrequently, with a time between bursts of at least 1 second. Ward and Lucas-Toumbourou¹⁹ and Kantor²³ used a burst frequency of 50Hz, so that stimulation was more akin to that used clinically, but this means that the time between bursts was very short. This means that when the burst duration is long, the interburst interval will be short, and successive bursts may occur before the nerve fiber has fully recovered. It was hypothesized that when this occurs, an increase in the threshold might be expected.¹⁹ The present study was designed to test this hypothesis. Instead of using a 50-Hz burst frequency, a frequency of 20Hz was used. This meant that the time between bursts could approach 50 milliseconds rather than the 20-millisecond maximum of previous studies. If the interburst interval is important, because of the recovery time needed to restore ion concentrations to normal resting values, it would be expected that the minimum in the threshold versus burst-duration graphs would occur at longer burst durations when a burst frequency of 20Hz rather than 50Hz was used because much longer burst durations would be needed to produce a sufficiently short interburst interval.

A second and perhaps more clinically important reason for the present study was that the previous study¹⁹ found that because minimum thresholds occurred at different burst durations, relative thresholds (ie, motor/sensory, pain/sensory, and pain/motor) varied, and there was an optimal burst duration where maximum discrimination (ie, maximum separation between thresholds) was achieved. This is particularly important because the burst duration that is optimal for discrimination between motor and pain responses might be expected to result in maximum muscle torque production with minimum discomfort. In the previous study,¹⁹ the optimum burst duration was found to be in the range 1 to 4 milliseconds. This is much shorter than the burst durations commonly used clinically (interferential and Russian current stimulation) but is consistent with earlier findings¹⁵, ¹⁶ that shorter burst durations result in less discomfort and greater torque production. An important aim of the present study was to determine whether short burst durations (1–4ms) are still optimal if the burst frequency is varied. We chose a burst frequency of 20Hz for comparison because (1) this is within the range likely to be useful in rehabilitation and corresponds to the maximum physiologic firing rates of slow, fatigue-resistant motor units,¹, ² and (2) it allowed us to examine the effect of longer burst durations without unduly compromising the interburst interval.

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Methods 

The 20 participants in this study were volunteers who met the inclusion criteria. That is, they did not have a pacemaker (or indwelling stimulator), any breaks in the skin under the area where the electrodes were to be placed, and had no known neurologic or musculoskeletal pathologic conditions affecting the upper limb to be tested. The group of participants (7 men, 13 women) were undergraduate students of the university (age range, 20–36y; mean age, 23.5y). Approval for this study was obtained from the Ethics Committee of the Faculty of Health Sciences of La Trobe University before the commencement of this study.

After the procedure was explained to each participant, and informed consent obtained, the skin of the posterior surface of the left forearm was cleaned using an alcohol swab, and conductive rubber electrodes, measuring 37 × 45mm, were attached using conductive, adhesive skin mounts.^a The electrodes were positioned so as to efficiently stimulate the wrist extensors: on a line from the head of the radius to the distal radioulnar joint with the proximal electrode 1cm distal to the head of the radius and the distal electrode 5cm distal to the proximal electrode along this line. The electrode leads were attached, ensuring that the cathode was the distal electrode (ie, the distal electrode was the negative terminal for the initial half-cycle of the sinewave burst).

The stimulator was a purpose-built device designed to produce constant voltage stimuli consisting of bursts of sinewaves with user selection of the sinewave frequency, burst frequency, and number of sinewaves per burst.

Participants experienced stimuli at 2 sinewave frequencies (1 and 4kHz), applied in bursts at a burst frequency of 20Hz. Stimulus waveforms had a predetermined number of sinewave cycles per burst. At 1kHz; 1, 2, 3, 4, 6, 8, 10, 12, 15, 20, 30, 40, and 50 cycles per burst were used (50 cycles meaning continuous stimulation). At 4kHz; 1, 2, 4, 8, 12, 16, 24, 32, 40, 48, 60, 80, 120, 160, and 200 cycles per burst were used (200 cycles being continuous stimulation). The 28 different combinations of AC frequency and cycles per burst were applied in a randomized order for each participant. Randomization was achieved by creating a column of random numbers in a Microsoft Office Excel^b spreadsheet that listed the combinations of frequency and number of sinewaves, then sorting the list by the random number column.

Once the randomized order was determined, it was used to determine sensory thresholds. Participants were asked to manually increase the stimulus intensity until the first perception of cutaneous sensation was reached. The experimenter recorded this threshold (in volts from the stimulator) for 3 measurements at each particular frequency and number of cycles per burst, for each of the 28 combinations of sinewave frequency and burst duration. Once all sensory measurements had been obtained, motor thresholds were determined in the same sequence as used for sensory thresholds. The motor threshold was taken as the first overt indication of muscle activity: visible contraction under the electrodes or wrist or finger extension. Finally, pain-tolerance thresholds were measured. Participants increased the intensity to a value where they felt that any further increase would be too painful.

Before measurements at each threshold, participants experimented with the intensity control to familiarize themselves with the stimulus and establish the criterion that they would use to determine each threshold. The researchers monitored motor thresholds to ensure that the participants were consistent in applying the threshold criterion.

Statistical Analysis 

Data were analyzed with the SPSS version 14 software package^c using repeated-measures ANOVAs. Mauchly's test of sphericity was used and, where appropriate, the results were adjusted using a Huynh-Feldt Epsilon correction factor to reduce the degrees of freedom.

Post hoc t tests were not performed because we were measuring outcomes that were functions of a continuous variable (burst duration), and multiple variable values (13 or 15) were used. Were multiple post hoc t tests to be used, then the needed Bonferroni correction would be unacceptably large, and the likelihood of a type II statistical error would, consequently, be unacceptably high. Rather, trend analysis data, provided as part of the ANOVAs, were used to assess the significance of the apparent variations.²⁴

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Results 

The 3 measurements of each threshold (at each particular frequency and number of cycles per burst) were averaged for each participant, then averaged over the group of participants. Figure 2 shows the group-averaged variation in sensory, motor, and pain-tolerance thresholds with burst duration (in milliseconds) at 1 and 4kHz. Values obtained in a previous study¹⁹ are also plotted for comparison. Note that the scales used differ between the 1- and 4-kHz graphs. This is because skin impedance is lower at 4kHz so less electric energy is dissipated in the skin and more is available to stimulate nerves in the underlying tissue.¹, ³

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• Fig 2. 

  Sensory threshold versus burst duration at: (A) 1kHz and (B) 4kHz; (C) 1-kHz and (D) 4-kHz motor thresholds; (E) 1-kHz and (F) 4-kHz pain-tolerance thresholds. (⧫) are values in volts (V), measured at a burst frequency of 20Hz, and (⊡) are values at 50Hz previously reported by Ward and Lucas-Toumbourou.¹⁹

As found in the earlier study, the sensory and motor threshold graphs show a minimum threshold rather than simply decreasing to a plateau, and it is evident that at 20Hz, minimum thresholds are all reached at longer burst durations than at 50Hz. The minimum 20-Hz sensory threshold occurs at about 20 milliseconds, but at 50Hz, the minimum is at less than 10 milliseconds (see fig 2A and B). The minimum 20-Hz motor threshold occurs at about 30 milliseconds, but at 50Hz, the minimum is at about 10 milliseconds (see fig 2C and D). No minimum pain-tolerance threshold is discernible in the 20-Hz results (see fig 2E and F), although there appears to be a minimum in the 50-Hz results at 10 to 20 milliseconds (see fig 2E and F). As found in the previous study,¹⁹ the AC frequency appears to make little difference; the variation in thresholds with burst duration is similar at 1 and 4kHz.

To establish whether the apparent minima were real, trend analysis data from the ANOVAs were examined (table 1). Trend analysis partitions the overall sum of squares into linear, quadratic, and residual components and calculates the associated F statistic and P value. A significant quadratic component indicates that the variation is nonlinear, and thus the graph of threshold versus burst duration has a minimum (or maximum). A nonsignificant quadratic component indicates that the variation may be linear or simply nonexistent, as indicated by the linear component F statistic.

Table 1. ANOVA Results Including Trend Analysis of the Sensory, Motor, and Pain-Tolerance Threshold Data

1-kHz Sensory Thresholds					4-kHz Sensory Thresholds
Source	df	SS	F	P	Source	df	SS	F	P
Burst duration	12	1776	11.9	.000	Burst duration	14	2780	17.3	.000
Linear	1	1411	18.5	.000	Linear	1	1832	22.4	.000
Quadratic	1	197	17.6	.000	Quadratic	1	828	36.4	.000
Residual	10	138			Residual	12	120
Error	228	2839			Error	266	3048
Between subject	1	181,484	48.4	.000	Between subject	1	120,744	49.1	.000
Error	19	3752			Error	19	2460

1-kHz Motor Thresholds					4-kHz Motor Thresholds
Source	df	SS	F	P	Source	df	SS	F	P
Burst duration	12	2721	10.2	.000	Burst duration	14	4166	35.0	.000
Linear	1	2512	39.5	.000	Linear	1	3386	118.6	.000
Quadratic	1	134	5.0	.037	Quadratic	1	616	48.8	.000
Residual	10	75			Residual	12	164
Error	228	5083			Error	266	2259
Between subject	1	415,539	121.8	.000	Between subject	1	259,065	146.1	.000
Error	19	3752			Error	19	1774

1-kHz Pain-Tolerance Thresholds					4-kHz Pain-Tolerance Thresholds
Source	df	SS	F	P	Source	df	SS	F	P
Burst duration	12	13,301	19.5	.000	Burst duration	14	16,151	25.8	.000
Linear	1	12,035	28.7	.000	Linear	1	14,684	44.2	.000
Quadratic	1	991	17.8	.000	Quadratic	1	1034	59.1	.000
Residual	10	275			Residual	12	433
Error	228	12,944			Error	266	11,879
Between subject	1	955,056	104.3	.000	Between subject	1	658,508	106.8	.000
Error	19	9156			Error	19	6168

Abbreviation: SS, sum of squares.

As can be seen in table 1, all graphs have a significant quadratic component (1 at the .05 level, the remaining 5 at the .001 level), so the existence of an “optimum” burst duration, where the stimulus voltage is a minimum, is firmly indicated. A conclusion based on visual inspection of figure 2E and F is that pain thresholds probably have a minimum at or near the maximum burst durations.

The F values for the between-subject components of the statistical analysis (see table 1) are all much larger than the F values for the variation with burst duration. This indicates that between-subject differences contribute most to the observed variance and that the error bars, which are SDs across the group, are more a reflection of between-subject variance than actual (random) error. This also explains why the variation in thresholds with burst duration is found to be statistically significant despite the large SDs in each of the graphs.

Further Analysis 

The observation that pain-tolerance thresholds reach a minimum at longer burst durations than sensory or motor thresholds (see fig 2) indicates that long burst durations will result in the greatest discomfort for a given level of sensory or motor stimulation, because pain-tolerance thresholds will be minimal while sensory and motor thresholds will be elevated. More generally, since the minimum thresholds for sensory, motor, and pain-tolerance responses occur at different burst durations (see fig 2), relative thresholds (ie, motor/sensory, pain-tolerance/sensory, and pain-tolerance/motor) will vary, and there will be an optimal burst duration where maximum discrimination between thresholds is achieved. The ratio of pain-tolerance threshold to motor threshold is particularly important because when this is a maximum, it might be expected that the best discrimination between pain and motor responses might be achieved (ie, a maximum motor response with minimum discomfort). Similarly, the ratio of pain-tolerance threshold to sensory threshold might be expected to identify the burst duration that is optimal for producing sensory stimulation with minimum discomfort. Accordingly, relative thresholds (pain-tolerance/motor and pain-tolerance/sensory) were calculated for each participant at each burst duration, then averaged across the group. Figure 3 shows the pain-tolerance/motor threshold results. Values obtained in the previous study,¹⁹ which used a burst frequency of 50Hz, are also plotted for comparison.

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• Fig 3. 

  Relative thresholds at different burst durations with burst frequencies of 50Hz (⊡) and 20Hz (⧫). (A) Pain/motor thresholds using bursts of 1-kHz AC. (B) Pain/motor thresholds using bursts of 4-kHz AC. 50-Hz relative thresholds were previously reported by Ward and Lucas-Toumbourou.¹⁹

The graphs of pain-tolerance/motor threshold show little difference between the 1-kHz (see fig 3A) and 4-kHz (see fig 3B) results. A broad maximum is seen in the 4-kHz results, at a burst duration of about 1 to 2 milliseconds, and there is little difference between the 20- and 50-Hz results. At 1kHz, it is difficult to establish a maximum because the shortest burst duration possible at this frequency is 1 millisecond, but the consistency with the 4-kHz results supports the notion of bursts of about 1 to 2 milliseconds being optimal for discrimination between pain and motor responses at both kilohertz frequencies. It is clear that above 2 milliseconds, all graphs show a downward trend. To test whether the apparent variation was significant, trend analysis data from the ANOVAs were examined (table 2).

Table 2. ANOVA Results Including Trend Analysis of Pain-Tolerance/Motor Threshold Data at Burst Frequencies of 20Hz^⁎ and 50Hz^†

1-kHz Pain-Tolerance/Motor Thresholds (20Hz)					4-kHz Pain-Tolerance/Motor Thresholds (20Hz)
Source	df	SS	F	P	Source	df	SS	F	P
Burst duration	12	.99	1.4	.266	Burst duration	14	1.23	2.4	.028
Linear	1	.38	4.0	.061	Linear	1	.71	6.6	.019
Quadratic	1	.11	1.2	.290	Quadratic	1	.04	1.8	.193
Residual	10	.59			Residual	12	.48
Error	228	13.83			Error	266	9.95
Between subject	1	636	220.2	.000	Between subject	1	785.73	267.2	.000
Error	19	55			Error	19	2.94

1-kHz Pain-Tolerance/Motor Thresholds (50Hz)					4-kHz Pain-Tolerance/Motor Thresholds (50Hz)
Source	df	SS	F	P	Source	df	SS	F	P
Burst duration	9	1.17	2.2	.061	Burst duration	11	1.47	2.9	.021
Linear	1	.75	7.0	.014	Linear	1	.72	22.1	.000
Quadratic	1	.00	0.0	.910	Quadratic	1	.27	9.1	.006
Residual	7	.43			Residual	9	.47
Error	225	13.32			Error	275	12.84
Between subject	1	1012.55	338.5	.000	Between subject	1	1295.94	299.2	.000
Error	25	2.99			Error	25	4.33

Abbreviation: SS, sum of squares.

The 4-kHz results demonstrate a statistically significant variation in pain-tolerance/motor threshold with burst duration. Trend analysis results show that for the 50-Hz data, both the linear and quadratic components are significant (ie, a maximum exists where the separation between pain and motor thresholds is greatest). At 20Hz, the linear component is significant, but the quadratic component is not.

At 1kHz, the variation is insignificant, although the variance in the 1-kHz pain-tolerance/motor threshold data at 50Hz (P=.061) indicates the likelihood of a type II statistical error (ie, concluding that there is no difference when, in fact, one exists). Trend analysis showed that there was actually a significant (P=.014) linear decrease in relative threshold with a burst duration above 1 millisecond at 50Hz.

Figure 4 shows the pain-tolerance/sensory threshold results.

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• Fig 4. 

  Relative thresholds at different burst durations with burst frequencies of 50Hz (⊡) and 20Hz (⧫). (A) Pain/sensory thresholds using bursts of 1-kHz AC. (B) Pain/sensory thresholds using bursts of 4-kHz AC. 50-Hz relative thresholds were previously reported by Ward and Lucas-Toumbourou.¹⁹

Pain-tolerance/sensory threshold results at 4kHz (fig 4B) show a maximum at about 2 milliseconds at a burst frequency of 50Hz, and at about 3 to 4 milliseconds at 20Hz, as do pain threshold/sensory threshold results at 1kHz (fig 4A). Trend analysis data are shown in table 3.

Table 3. ANOVA Results Including Trend Analysis of Pain-Tolerance/Sensory Threshold Data at Burst Frequencies of 20Hz^⁎ and 50Hz^†

1-kHz Pain-Tolerance/Sensory Thresholds (20Hz)					4-kHz Pain-Tolerance/Sensory Thresholds (20Hz)
Source	df	SS	F	P	Source	df	SS	F	P
Burst duration	12	3.12	2.1	.062	Burst duration	14	8.15	4.2	.000
Linear	1	2.07	4.0	.060	Linear	1	3.62	6.5	.020
Quadratic	1	.00	0.0	.930	Quadratic	1	2.95	21.8	.000
Residual	10	1.06			Residual	12	1.58
Error	228	28.17			Error	266	37.04
Between subject	1	1763.88	146.6	.000	Between subject	1	2106.60	168.1	.000
Error	19	12.04			Error	19	12.53

1-kHz Pain-Tolerance/Sensory Thresholds (50Hz)					4-kHz Pain-Tolerance/Sensory Thresholds (50Hz)
Source	df	SS	F	P	Source	df	SS	F	P
Burst duration	9	18.22	10.0	.000	Burst duration	11	24.01	4.0	.015
Linear	1	15.70	53.9	.000	Linear	1	13.71	13.3	.001
Quadratic	1	.00	0.0	.972	Quadratic	1	6.36	13.4	.001
Residual	7	2.53			Residual	9	3.95
Error	225	45.57			Error	275	150.23
Between subject	1	4278.40	177.4	.000	Between subject	1	4957.72	178.9	.000
Error	25	24.11			Error	25	27.71

Abbreviation: SS, sum of squares.

The 4-kHz data show a highly significant variation in pain-tolerance/sensory threshold with burst duration and a significant variation in both the linear and quadratic components. The 1-kHz data at 50Hz show a significant linear decrease. At 20Hz, the variation approached but did not demonstrate significance (P=.062), suggesting the likelihood of a type II statistical error if we conclude that there is no variation.

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Discussion 

The Gildemeister effect is a well-established phenomenon that occurs when kilohertz-frequency AC is used for electric stimulation. Successive stimulus pulses in a low-intensity AC burst produce subthreshold depolarizations, and the resulting ion concentration changes take time to recover. Extra stimulus pulses occurring before recovery can therefore summate, pushing ion concentrations further from their resting values until threshold is reached and an action potential is produced. Thus, as the burst duration is increased, the threshold intensity decreases. Summation can only occur if additional stimulus pulses are delivered within the recovery time so that the ion concentrations will continue to change away from the normal faster than the recovery mechanisms can restore them. Thus, bursts of AC result in a lower threshold than single pulses because of summation, but summation only occurs for a limited time (the utilization time or nuttzeit), which is determined by the time constants of the recovery process. A previous study,¹⁹ using a burst frequency of 50Hz, found that utilization times were different for sensory, motor, and pain-tolerance thresholds. The present study, using a burst frequency of 20Hz, confirms this finding.

The previous study¹⁹ found that thresholds reached a minimum and then increased. Minima occurred at approximately 7 milliseconds (sensory threshold), 10 milliseconds (motor threshold), and 20 milliseconds or more (pain threshold). It was surmised that the reason for the increase in thresholds at long burst durations was that the interburst interval becomes small and is less than the ion concentration recovery time of the nerve fiber, so there is inadequate recovery between bursts. The present study used 20-Hz bursts of AC, thus allowing for a greater interburst interval, and we found minima at much longer burst durations: approximately 20 milliseconds (sensory threshold), 30 milliseconds (motor threshold), and 50 milliseconds or more (pain threshold). The finding that minima occurred at greater burst durations at 20-Hz burst frequency is consistent with the idea that the time for recovery between bursts is important in determining the minimum threshold.

A possibility is that if minimum thresholds occur at different burst durations when the burst frequency is varied, then relative thresholds, in particular pain/motor and pain/sensory, might also vary. If this were the case, then the previous findings¹⁹ that an optimum burst duration for discrimination between sensory, motor, and pain responses was 1 to 4 milliseconds might only apply at a burst frequency of 50Hz. The most important finding of the present study is that although the absolute thresholds do have minima at very different burst durations, the relative thresholds do not. In the present study, we found that best discrimination between pain and motor thresholds occurs at about 1- to 2-millisecond burst duration, and best discrimination between pain and sensory thresholds possibly occurs at slightly longer burst durations (∼2–4ms).

The 2 major findings of the present study are that for stimulation with bursts of 1- and 4-kHz AC, (1) there is a minimum in the threshold versus burst-duration graphs that is different for sensory, motor, and pain threshold stimulation (see fig 2), and minima occur at different burst durations when the burst frequency is changed from 50 to 20Hz; and (2) relative thresholds (pain/motor and pain/sensory) exhibit a maximum at a burst duration of about 1 to 4 milliseconds (see Fig 3, Fig 4), and this does not differ appreciably between burst frequencies of 50 and 20Hz.

Our finding that at low burst durations (1–4ms) the separation between thresholds is greatest, whether the burst frequency is 20 or 50Hz, suggests that greater sensory stimulation before provoking a pain response and greater motor stimulation before a pain response are possible at shorter burst durations, and that the burst frequency makes little or no difference. This is consistent with earlier findings⁹ that the greatest muscle torque is evoked, and the least discomfort also results, using short-duration bursts. Ward et al⁹ used 50-Hz bursts of AC to compare a range of AC frequencies and duty cycles (burst durations) and found that 1-kHz AC with a low burst duration (1–2ms) was optimal for torque production, while a higher frequency and burst duration (4-kHz AC, 2- to 4-ms bursts) was optimal for minimizing discomfort. These optimal burst durations (1–4ms) are much shorter than those normally used clinically for sensory and motor stimulation¹ where a burst duration of 10 milliseconds or so is more usual. The present findings suggest that short-duration bursts of kilohertz-frequency AC may be more clinically effective than those now commonly used regardless of the particular burst frequency chosen. The risk of evoking unwanted pain is the least if short-duration bursts are used. Further, for motor stimulation with the least discomfort, short-duration bursts would appear to be more effective than the long-duration bursts commonly used clinically. This seems to be true whatever the chosen burst frequency.

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Conclusions 

Earlier findings are that (1) summation occurs when bursts of kilohertz-frequency AC are used for nerve stimulation, and (2) there is a distinct time frame (the nuttzeit or utilization time) over which summation is possible. The present study confirms these earlier findings but also indicates that the burst frequency is important in determining the optimum burst duration where thresholds are a minimum, possibly due to the effect of the interburst interval, which is less at 50Hz than 20Hz.

Despite the fact that optimum burst durations for each threshold differed with burst frequency (20 or 50Hz), relative thresholds (pain/motor and pain/sensory) differed little, indicating that there is an optimal burst duration where separation between thresholds is greatest, and this appears to be independent of the actual burst frequency.

A comparison of relative thresholds at 20 and 50Hz identified the range of 1 to 4 milliseconds as best for sensory, motor, and pain threshold discrimination. This helps to explain and support recent findings⁷, ⁸, ²⁰ that, in terms of muscle torque production⁸ and relative discomfort,⁷, ²⁰ short-duration kilohertz-frequency AC bursts are more effective than the long-duration bursts commonly used clinically.¹

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