- Email: [email protected]
Results of Bayesian statistical analysis in normal and ALS subjects
Motor Unit Number Estimation (MUNE) and Quantitative EMG (Supplements to Clinical Neurophysiology, Vol. 60) Editors: M.B. Bromberg # 2009 Elsevier B.V. All rights reserved
Chapter 5
Results of Bayesian statistical analysis in normal and ALS subjects R.D. Hendersona,*, P.G. Ridallb,1, A.N. Pettittb and P.A. McCombec a
Department of Neurology, Royal Brisbane and Women’s Hospital, Herston, QLD 4029, Australia
b
Faculty of Science, School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia c University of Queensland, Centre for Clinical Research, Royal Brisbane Hospital, Herston Queensland 4029, Australia 1
Present address: Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster LA1 4YF, UK
1. Introduction There is a need for a broadly applicable motor unit number estimation (MUNE) method to allow research into possible therapies for amyotrophic lateral sclerosis (ALS) (Shefner, 2001). An ideal MUNE method needs to be applicable to all stages of ALS, to avoid the problems associated with sampling motor units, to allow for motor unit variability (Jillapalli and Shefner, 2004), and to have simple data collection methods so that it can be widely applied in different centers. Knowledge obtained from study of the stimulus–response curve (Henderson et al., 2006), and from existing MUNE methods and their limitations led us to develop a Bayesian statistical approach to MUNE (Ridall et al., 2006,
*
Correspondence to: Dr. Robert D. Henderson, Department of Neurology, Royal Brisbane and Women’s Hospital, Herston, QLD 4029, Australia. E-mail: [email protected]
2007). The biological background and statistical methods for our Bayesian MUNE method based on the whole stimulus–response curve have been presented in the two preceding papers. The results of studies in normal subjects and patients with ALS are presented in this paper. 2. Methods Our MUNE method based on Bayesian statistics used data obtained from the whole stimulus– response curve with a large number stimuli of increasing intensity (Henderson et al., 2006). Standard nerve electrode placements were used on the median, ulnar and peroneal nerves using standard nerve conduction studies, recording from the thenar eminence, hypothenar eminence and extensor digitorum brevis muscles, respectively (Henderson et al., 2003). We used a Viking IV EMG machine with a software modification that allows the collection of a large number of CMAP. The stimulating electrodes were taped in place after carefully identifying the position of
58 the nerve; 1 Hz stimulation frequency was used, along with 0.05–0.1 ms stimulus duration. Careful attention was paid to noise contamination in the recording by increasing the audiometer volume. For the stimulus–response curves, we firstly determined the minimum stimulus intensity as the stimulus value that first elicited a CMAP and the maximum stimulus intensity as the stimulus that elicited the maximal CMAP response. In most subjects, the stimulus intensity was then gradually increased from minimum to maximum and then reduced again. At least 5 stimuli were given for each level of stimulus intensity. At least 500 stimulus responses were obtained from the first study. The number needed for collection for later studies was determined from the first study obtained from each subject. For reproducibility studies in ALS subjects, the electrodes were removed and replaced and the study was repeated. In normal subjects, reproducibility was investigated by repeating the study on different occasions. The size of the CMAP was recorded as area. For data analysis the CMAP was plotted against stimulus intensity (milliamperes, mA). The studies were well tolerated. For serial studies of ALS subjects, the nerve supplying the stronger hand muscle was studied first, until fewer than 5 motor units were present (which could be visually counted) and then a different nerve was studied.
For comparison of the motor unit survival with patient survival, the duration from diagnosis to either death or the date of the last study was used. 3. Results 3.1. Study subjects Forty-nine ALS subjects and 8 normal subjects were studied at least once. Twenty ALS subjects were studied on more than one occasion for longitudinal assessment. Of these ALS subjects, 12 had died by the time of data analysis. 3.2. Stimulus–response curves The stimulus response curves were obtained from each subject. Occasionally, the stimulus–response curve had a different shape depending on whether the stimulus was being increased or decreased (Fig. 1). 3.3. Results of MUNE MUNE analysis can be expressed as a posterior distribution of the probable number of motor units. This distribution can be summarized by a mode and credible interval. Examples of the posterior distributions in 3 subjects are shown in Figs. 5.2–5.4.
Fig. 5.1 The stimulus–response curves obtained with increasing then decreasing the stimulus intensity showing that in this subject the curves do not overlap but the levels are similarly located in the upper portion of the curve (Henderson et al., 2006).
CMAP area (yt)
3
CMAP area (yt)
2
0.2 p(Nly)
CMAP area (yt)
2
MUN
1 0 10
40 20 30 Stimulus (St) (mA)
0 15
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30 N
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20
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0.1 0 15
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⫻ 104
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0.2
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30 N
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20
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⫻ 104
2
0
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15 20 25 Stimulus (St) (mA)
0.1 0 15
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10.3.06 0.2
15000 p(Nly)
CMAP area (yt)
Ulnar nerve with lower limb onset disease -12 months
Data 29.4.05
⫻ 104
10000 5000 0 10
15
20
25
30
0.1 0 15
35
Stimulus (St) (mA)
N
Fig. 5.3
Data 2.12.05
MUN 0.2 p(Nly)
2
⫻ 104
1 0 10
⫻ 104
⫻ 104
20 25 Stimulus (St) (mA)
⫻ 104
30
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24.2.06 0.4
15 20 Stimulus (St) (mA)
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2 1 0 10
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0.2 0
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3
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0.4
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p(Nly)
3
15
10
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1 0
0.1 0
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p(Nly)
2
15 20 25 Stimulus (St) (mA)
p(Nly)
CMAP area (yt) CMAP area (yt) CMAP area (yt) CMAP area (yt)
Ulnar nerve with upper limb onset − 5 months
Fig. 5.2 Studies from the ulnar nerve of an ALS subject with lower limb onset disease studied over 12 months.
15 20 Stimulus (St) (mA)
0.2 0
10
15
20 N
Serial studies from the ulnar nerve of an ALS patient with upper limb onset disease studied over 5 months.
60 loss of a motor unit) plotted against the patient survival. There is a broad correlation of motor unit survival with patient survival.
MUN
50 0
0.2
p(Nly)
100
0.1 0
20 40 60 Stimulus (St) (mA)
40
60 N
80
4.6.04 p(Nly)
100 50 0 40 20 Stimulus (St) (mA)
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60 N
80
2.7.04 p(Nly)
100 50 0
40 50 20 30 Stimulus (St) (mA)
0.1 0.05 0
p(Nly)
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30 20 Stimulus (St) (mA)
0.1 0.05 0
40
60 N
80
40
60 N
80
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60 N
80
22.10.04 100 50 0
0.1 0.05 0
30 40 50 20 Stimulus (St) (mA)
3.5. Reproducibility An example of the stimulus–response curve and posterior distribution is shown in Fig. 5.7, where the reproducibility is shown for two ALS subjects. There was good reproducibility of the technique. 4. Discussion
9.8.04
p(Nly)
CMAP area (yt) CMAP area (yt) CMAP area (yt) CMAP area (yt)
Bulbar onset disease studied over 12 months
CMAP area (yt)
Data 17.10.03
Fig. 5.4 Serial studies from an ALS patient with bulbar onset disease studied over 12 months.
In these subjects the MUNE was repeated at intervals with the dates shown above the stimulus– response curves. In normal subjects, the calculated modal value and credible interval for the MUNE in hand muscles was 85 (70–108) and a smaller value obtained from the peroneal nerve — mean 48 (40–58). 3.4. Rate of loss of motor units Fig. 5.5 shows the results expressed as the modal value of the number of motor units with associated credible interval, which is plotted against time. In this patient, there is progressive loss of motor units with a half-life of the nerve of 117 days. In Fig. 5.6, for subjects with ALS, we show the motor unit survival in days (or time taken for the
A Bayesian application to MUNE using the whole stimulus–response curve has many attractive features. The knowledge from 30 years of MUNE and axon excitability research (Brown and Milner-Brown, 1976; Kadrie et al., 1976; Stein and Yang, 1990; Daube, 1995; Slawnych et al., 1996; Blok et al., 2005) can be applied in a model that gives an answer that reflects the uncertainty of the estimate. In particular, the issue of motor unit instability is an important issue in ALS subjects that has recently emerged in MUNE research and needs to be considered (Jillapalli and Shefner, 2004). The use of the whole stimulus–response curve avoids issues of sampling and the order of activation of motor units (Thomas et al., 2002). The variation in sizes of motor units in progressive denervating diseases can also be incorporated in the model. Our simple data collection protocol will allow the collection of data by neurophysiologists or technicians. There remain issues to be resolved. The minimum size of a true surface-recorded motor unit was considered to be 25 mV ms at the 2003 Symposium on MUNE (Bromberg, 2003). Recent work on motor unit instability has defined 100 mV ms (40 mV) as a minimum size of a motor unit that can be distinguished from noise (Shefner et al., 2004; Henderson et al., 2006). We have used this in our model. We have also used a repulsion (or spacing) factor which also restricts the number of small motor units.
61 LCH.RU 32
number of remaining units (N)
30 28 26 24 22 20 18 16 14 12
0
20
40 60 time in days (t)
80
100
Fig. 5.5 The mode and credible interval over time showing a progressive fall in motor unit number over about 3 months. Motor unit survival 50
motor unit survival (days)
45 40 35 30 25 20 15 10 5 0 0
20
40
60 80 patient survival (months)
100
120
Fig. 5.6 Motor survival plotted against patient survival. The two patients to the far right had predominantly lower motor neuron signs.
Further work is required to determine the full effects of the size of small motor units and the repulsion factor. Phase cancellation of motor units will occur if parts of the CMAP from motor units at lower
stimulus intensities are cancelled by the CMAP from motor units at higher stimulus intensities (Slawnych, 2003). Non-linearity of the contribution of motor units to the total CMAP at different stimulus intensities is a similar issue (Parry et al., 1977).
62 x104
0.2 0.15
2
p(N|y)
CMAP area (y ) t
3
1
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0 10
20 30 Stimulus (St) (mA)
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x104 0.2 0.15
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ALS subject 2.
0.3 p(N|y)
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0 10
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x104
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x104
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0 15
Fig. 5.7 The reproducibility of the method for the ulnar nerve (upper two slides) and peroneal nerve (lower two slides) from two ALS subjects. The different CMAP scans from the paired studies can be seen in the left panel, with calculated MUNE values in the right panels.
63 Further work is needed to consider the significance of these issues, which may lead to an underestimation of the true number of motor units. Without knowledge of the true number of motor units and without a gold-standard, we cannot tell whether our MUNE method gives the true number of motor units. Certainly, the values that we find are smaller than the values found in non-statistical methods (Doherty et al., 1995; Stashuk et al., 2003; Albrecht and Kuntzer, 2004; Boe et al., 2006). However, these non-statistical methods may be an over-estimation, because these methods do not allow for alternation and variable or unstable motor units. A number of technical issues remain with our method. An automated stimulator would allow the widespread applicability of the method to be investigated. The stimulus parameters and the optimal number of data points that need to be collected also require further work.
References Albrecht, E. and Kuntzer, T. (2004) Number of Edb motor units estimated using an adapted multiple point stimulation method: normal values and longitudinal studies in ALS and peripheral neuropathies. Clin. Neurophysiol., 115: 557–563. Blok, J.H., Visser, G.H., De Graaf, S., Zwarts, M.J. and Stegeman, D.F. (2005) Statistical motor number estimation assuming a binomial distribution. Muscle Nerve, 31: 182–191. Boe, S.G. and Stashuk, D.W. et al. (2006) Within-subject reliability of motor unit number estimates and quantitative motor unit analysis in a distal and proximal upper limb muscle. Clin. Neurophysiol., 117: 596–603. Bromberg, M.B. (2003) Consensus. In: M.B. Bromberg (Ed.), Motor Unit Number Estimation (MUNE). Supplements to Clinical Neurophsyiology, Vol. 55, Elsevier, Amsterdam, pp. 335–338. Brown, W.F. and Milner-Brown, H.S. (1976) Some electrical properties of motor units and their effects on the methods of estimating motor unit numbers. J. Neurol. Neurosurg. Psychiatry, 39: 249–257. Daube, J.R. (1995) Estimating the number of motor units in a muscle. J. Clin. Neurophysiol., 12: 585–594. Doherty, T., Simmons, Z., O’Connell, B., Felice, K.J., Conwit, R., Chan, K.M., Komori, T., Brown, T., Stashuk, D.W. and
Brown, W.F. (1995) Methods for estimating the numbers of motor units in human muscles. J. Clin. Neurophysiol., 12: 565–584. Henderson, R.D., McClelland, R. and Daube, J.R. (2003) Effect of changing data collection parameters on statistical motor unit number estimates. Muscle Nerve, 27: 320–331. Henderson, R.D., Ridall, G.R., McCombe, P.A. and Pettitt, A.N. (2006) The stimulus–response curve and motor unit variability in normal subjects and subjects with amyotrophic lateral sclerosis. Muscle Nerve, 34: 34–43. Jillapalli, D. and Shefner, J.M. (2004) Single motor unit variability with threshold stimulation in patients with amyotrophic lateral sclerosis and normal subjects. Muscle Nerve, 30: 578–584. Kadrie, H.A., Yates, S.K., Milner-Brown, H.S. and Brown, W.F. (1976) Multiple point electrical stimulation of ulnar and median nerves. J. Neurol. Neurosurg. Psychiatry, 39: 973–985. Parry, D.J., Mainwood, G.W. and Chan, T. (1977) The relationship between surface potentials and the number of active motor units. J. Neurol. Sci., 33: 283–296. Ridall, P.G., Pettitt, A.N., Henderson, R.D. and McCombe, P.A. (2006) Motor unit number estimation, a Bayesian approach. Biometrics, doi: 10.1111/j.1541–0420.2006.00577.x. Ridall, P.G., Pettitt, A.N., Friel, N., McCombe, P.A. and Henderson, R.D. (2007) Motor unit number estimation using reversible jump Markov chain Monte Carlo. Appl. Statist., 56: 1–26. Shefner, J.M. (2001) Motor unit number estimation in human neurological diseases and animal models. Clin. Neurophysiol., 112: 955–964. Shefner, J.M., Cudkowicz, M.E., Zhang, H., Schoenfeld, D. and Jillapalli, D. (2004) The use of statistical MUNE in a multicenter clinical trial. Muscle Nerve, 30: 463–469. Slawnych, M., Laszlo, C. and Herschler, C. (1996) Motor unit estimates obtained using the new “MUESA” method. Muscle Nerve, 19: 626–636. Slawnych, M.P. (2003) Issues in motor unit number estimation. In: M.B. Bromberg (Ed.), Motor Unit Number Estimation (MUNE). Supplements to Clinical Neurophysiology, Vol. 55. Elsevier, Amsterdam, pp. 22–28. Stashuk, D.W., Doherty, T.J. and Brown, W.F. (2003) MUNE using decomposition-enhanced spike triggered averaging. In: M.B. Bromberg (Ed.), Motor Unit Number Estimation (MUNE). Supplements to Clinical Neurophysiology, Vol. 55. Elsevier, Amsterdam, pp. 108–121. Stein, R.B. and Yang, J.F. (1990) Methods for estimating the number of motor units in human muscles. Ann. Neurol., 28: 487–495. Thomas, C.K., Nelson, G., Than, L. and Zijdewind, I. (2002) Motor unit activation order during electrically evoked contractions of paralysed or partially paralysed muscles. Muscle Nerve, 25: 797–804.
Chapter 5
Results of Bayesian statistical analysis in normal and ALS subjects R.D. Hendersona,*, P.G. Ridallb,1, A.N. Pettittb and P.A. McCombec a
Department of Neurology, Royal Brisbane and Women’s Hospital, Herston, QLD 4029, Australia
b
Faculty of Science, School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia c University of Queensland, Centre for Clinical Research, Royal Brisbane Hospital, Herston Queensland 4029, Australia 1
Present address: Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster LA1 4YF, UK
1. Introduction There is a need for a broadly applicable motor unit number estimation (MUNE) method to allow research into possible therapies for amyotrophic lateral sclerosis (ALS) (Shefner, 2001). An ideal MUNE method needs to be applicable to all stages of ALS, to avoid the problems associated with sampling motor units, to allow for motor unit variability (Jillapalli and Shefner, 2004), and to have simple data collection methods so that it can be widely applied in different centers. Knowledge obtained from study of the stimulus–response curve (Henderson et al., 2006), and from existing MUNE methods and their limitations led us to develop a Bayesian statistical approach to MUNE (Ridall et al., 2006,
*
Correspondence to: Dr. Robert D. Henderson, Department of Neurology, Royal Brisbane and Women’s Hospital, Herston, QLD 4029, Australia. E-mail: [email protected]
2007). The biological background and statistical methods for our Bayesian MUNE method based on the whole stimulus–response curve have been presented in the two preceding papers. The results of studies in normal subjects and patients with ALS are presented in this paper. 2. Methods Our MUNE method based on Bayesian statistics used data obtained from the whole stimulus– response curve with a large number stimuli of increasing intensity (Henderson et al., 2006). Standard nerve electrode placements were used on the median, ulnar and peroneal nerves using standard nerve conduction studies, recording from the thenar eminence, hypothenar eminence and extensor digitorum brevis muscles, respectively (Henderson et al., 2003). We used a Viking IV EMG machine with a software modification that allows the collection of a large number of CMAP. The stimulating electrodes were taped in place after carefully identifying the position of
58 the nerve; 1 Hz stimulation frequency was used, along with 0.05–0.1 ms stimulus duration. Careful attention was paid to noise contamination in the recording by increasing the audiometer volume. For the stimulus–response curves, we firstly determined the minimum stimulus intensity as the stimulus value that first elicited a CMAP and the maximum stimulus intensity as the stimulus that elicited the maximal CMAP response. In most subjects, the stimulus intensity was then gradually increased from minimum to maximum and then reduced again. At least 5 stimuli were given for each level of stimulus intensity. At least 500 stimulus responses were obtained from the first study. The number needed for collection for later studies was determined from the first study obtained from each subject. For reproducibility studies in ALS subjects, the electrodes were removed and replaced and the study was repeated. In normal subjects, reproducibility was investigated by repeating the study on different occasions. The size of the CMAP was recorded as area. For data analysis the CMAP was plotted against stimulus intensity (milliamperes, mA). The studies were well tolerated. For serial studies of ALS subjects, the nerve supplying the stronger hand muscle was studied first, until fewer than 5 motor units were present (which could be visually counted) and then a different nerve was studied.
For comparison of the motor unit survival with patient survival, the duration from diagnosis to either death or the date of the last study was used. 3. Results 3.1. Study subjects Forty-nine ALS subjects and 8 normal subjects were studied at least once. Twenty ALS subjects were studied on more than one occasion for longitudinal assessment. Of these ALS subjects, 12 had died by the time of data analysis. 3.2. Stimulus–response curves The stimulus response curves were obtained from each subject. Occasionally, the stimulus–response curve had a different shape depending on whether the stimulus was being increased or decreased (Fig. 1). 3.3. Results of MUNE MUNE analysis can be expressed as a posterior distribution of the probable number of motor units. This distribution can be summarized by a mode and credible interval. Examples of the posterior distributions in 3 subjects are shown in Figs. 5.2–5.4.
Fig. 5.1 The stimulus–response curves obtained with increasing then decreasing the stimulus intensity showing that in this subject the curves do not overlap but the levels are similarly located in the upper portion of the curve (Henderson et al., 2006).
CMAP area (yt)
3
CMAP area (yt)
2
0.2 p(Nly)
CMAP area (yt)
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MUN
1 0 10
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Ulnar nerve with lower limb onset disease -12 months
Data 29.4.05
⫻ 104
10000 5000 0 10
15
20
25
30
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35
Stimulus (St) (mA)
N
Fig. 5.3
Data 2.12.05
MUN 0.2 p(Nly)
2
⫻ 104
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⫻ 104
⫻ 104
20 25 Stimulus (St) (mA)
⫻ 104
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15 20 25 Stimulus (St) (mA)
p(Nly)
CMAP area (yt) CMAP area (yt) CMAP area (yt) CMAP area (yt)
Ulnar nerve with upper limb onset − 5 months
Fig. 5.2 Studies from the ulnar nerve of an ALS subject with lower limb onset disease studied over 12 months.
15 20 Stimulus (St) (mA)
0.2 0
10
15
20 N
Serial studies from the ulnar nerve of an ALS patient with upper limb onset disease studied over 5 months.
60 loss of a motor unit) plotted against the patient survival. There is a broad correlation of motor unit survival with patient survival.
MUN
50 0
0.2
p(Nly)
100
0.1 0
20 40 60 Stimulus (St) (mA)
40
60 N
80
4.6.04 p(Nly)
100 50 0 40 20 Stimulus (St) (mA)
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80
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100 50 0
40 50 20 30 Stimulus (St) (mA)
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3.5. Reproducibility An example of the stimulus–response curve and posterior distribution is shown in Fig. 5.7, where the reproducibility is shown for two ALS subjects. There was good reproducibility of the technique. 4. Discussion
9.8.04
p(Nly)
CMAP area (yt) CMAP area (yt) CMAP area (yt) CMAP area (yt)
Bulbar onset disease studied over 12 months
CMAP area (yt)
Data 17.10.03
Fig. 5.4 Serial studies from an ALS patient with bulbar onset disease studied over 12 months.
In these subjects the MUNE was repeated at intervals with the dates shown above the stimulus– response curves. In normal subjects, the calculated modal value and credible interval for the MUNE in hand muscles was 85 (70–108) and a smaller value obtained from the peroneal nerve — mean 48 (40–58). 3.4. Rate of loss of motor units Fig. 5.5 shows the results expressed as the modal value of the number of motor units with associated credible interval, which is plotted against time. In this patient, there is progressive loss of motor units with a half-life of the nerve of 117 days. In Fig. 5.6, for subjects with ALS, we show the motor unit survival in days (or time taken for the
A Bayesian application to MUNE using the whole stimulus–response curve has many attractive features. The knowledge from 30 years of MUNE and axon excitability research (Brown and Milner-Brown, 1976; Kadrie et al., 1976; Stein and Yang, 1990; Daube, 1995; Slawnych et al., 1996; Blok et al., 2005) can be applied in a model that gives an answer that reflects the uncertainty of the estimate. In particular, the issue of motor unit instability is an important issue in ALS subjects that has recently emerged in MUNE research and needs to be considered (Jillapalli and Shefner, 2004). The use of the whole stimulus–response curve avoids issues of sampling and the order of activation of motor units (Thomas et al., 2002). The variation in sizes of motor units in progressive denervating diseases can also be incorporated in the model. Our simple data collection protocol will allow the collection of data by neurophysiologists or technicians. There remain issues to be resolved. The minimum size of a true surface-recorded motor unit was considered to be 25 mV ms at the 2003 Symposium on MUNE (Bromberg, 2003). Recent work on motor unit instability has defined 100 mV ms (40 mV) as a minimum size of a motor unit that can be distinguished from noise (Shefner et al., 2004; Henderson et al., 2006). We have used this in our model. We have also used a repulsion (or spacing) factor which also restricts the number of small motor units.
61 LCH.RU 32
number of remaining units (N)
30 28 26 24 22 20 18 16 14 12
0
20
40 60 time in days (t)
80
100
Fig. 5.5 The mode and credible interval over time showing a progressive fall in motor unit number over about 3 months. Motor unit survival 50
motor unit survival (days)
45 40 35 30 25 20 15 10 5 0 0
20
40
60 80 patient survival (months)
100
120
Fig. 5.6 Motor survival plotted against patient survival. The two patients to the far right had predominantly lower motor neuron signs.
Further work is required to determine the full effects of the size of small motor units and the repulsion factor. Phase cancellation of motor units will occur if parts of the CMAP from motor units at lower
stimulus intensities are cancelled by the CMAP from motor units at higher stimulus intensities (Slawnych, 2003). Non-linearity of the contribution of motor units to the total CMAP at different stimulus intensities is a similar issue (Parry et al., 1977).
62 x104
0.2 0.15
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ALS subject 2.
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x104
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15 20 25 Stimulus (St) (mA)
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0 15
Fig. 5.7 The reproducibility of the method for the ulnar nerve (upper two slides) and peroneal nerve (lower two slides) from two ALS subjects. The different CMAP scans from the paired studies can be seen in the left panel, with calculated MUNE values in the right panels.
63 Further work is needed to consider the significance of these issues, which may lead to an underestimation of the true number of motor units. Without knowledge of the true number of motor units and without a gold-standard, we cannot tell whether our MUNE method gives the true number of motor units. Certainly, the values that we find are smaller than the values found in non-statistical methods (Doherty et al., 1995; Stashuk et al., 2003; Albrecht and Kuntzer, 2004; Boe et al., 2006). However, these non-statistical methods may be an over-estimation, because these methods do not allow for alternation and variable or unstable motor units. A number of technical issues remain with our method. An automated stimulator would allow the widespread applicability of the method to be investigated. The stimulus parameters and the optimal number of data points that need to be collected also require further work.
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