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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/)

Interpolated twitch technique (ITT) is a non-invasive method for assessing the completeness of muscle activation in clinical settings. Voluntary activation level (VA), measured by ITT and estimated by a conventional linear model, was reported to have a non-linear relationship with true voluntary contraction force at higher activation levels. The relationship needs to be further clarified for the correct use by clinicians and researchers. This study was to established a modified voluntary activation (modified VA) and define a valid range by fitting a non-linear logistic growth model. Eight healthy male adults participated in this study. Each subject performed three sets of voluntary isometric ankle plantar flexions at 20, 40, 60, 80 and 100% maximal voluntary contraction (MVC) with real-time feedback on a computer screen. A supramaximal electrical stimulation was applied on tibia nerve at rest and during contractions. The estimated VA was calculated for each contraction. The relationship between the estimated VA and the actual voluntary contraction force was fitted by a logistic growth model. The result showed that according to the upper and lower limit points of the logistic curve, the valid range was between the 95.16% and 10.55% MVC. The modified VA estimated by this logistic growth model demonstrated less error than the conventional model. This study provided a transfer function for the voluntary activation level and defined the valid range which would provide useful information in clinical applications.

Interpolated twitch technique (I.T.T.) is a non-invasive method to study human muscle activation. In clinical rehabilitation, this technique is commonly used for assessing the completeness of muscle activation during voluntary contractions, especially for testing whether a muscle is fully active during a maximal voluntary contraction (MVC) [

The technique is executed with a strong electrical stimulation onto a resting and a contracting muscle. By imposing a supramaximal electrical stimulus on a muscle during a submaximal voluntary contraction, the remaining forces can be evoked. The evoked force is generated from those motor units that have not been recruited [

A potential problem is that the validation of this relationship between VA and true voluntary contraction force has not yet been formally confirmed. The predictive ability of VA to the true voluntary contraction force has only been speculated. The conventional formula, as described previously, for estimating VA was a linear function. One study showed a linear relationship [

For correct use of the I.T.T. and interpretation of the VA without bias, it is important and valuable to develop a new formula to accurately estimate voluntary activation level and to define the appropriate range for clinical use. The purpose of the study was to validate the I.T.T. by finding the transfer function for muscle activation level and determine valid range. The validity of the new developed transfer function was also compared with the conventional function. The conventional linear function is chosen for comparison is due to that this is the most widely used model in clinics and researches.

Eight male adults with no physical disabilities participated in the present study. Their age, height, and weight were 19.2 ± 1.7 yrs, 172 ± 5.36 cm, and 69 ± 8.23 kg, respectively. None of the subjects had any previous history of neuromuscular or skeletal diseases of the lower extremities. Informed consent was obtained from each subject prior to participation in this study.

The plantar flexion torque was measured with a custom-designed ankle torque measurement system [

The force of the plantar flexor muscles was elicited by electrical stimulation on the tibial nerve using a constant-current stimulator (Digitimer DS7A, Digitimer Ltd, Welwyn Court, UK) with a range of 100 to 400 V and a constant current up to 1,000 mA. The tibial nerve was stimulated in the popliteal fossa with the cathode placed over the tibial nerve and the anode placed over the patella. A stimulus intensity of 120% (duration = 1 ms) was used to elicit the supramaximal twitch. The sampling rate of force signal was set at 100 Hz, which is high enough for force sample and was used by previous researches [

During testing, the subject sat on a rigid chair and faced the computer screen. The tested foot was firmly fixed on torque measurement system with the ankle joint kept at a neutral position and the knee flexed to 90 degrees. The subject performed three MVCs of soleus and the force trace was displayed on the computer monitor for real-time feedback. When performing MVCs, the subjects were instructed to fully contract the soleus muscle for five seconds. They were given both verbal encouragement and visual feedback on their force to motivate maximal efforts. The 20, 40, 60, 80 and 100% MVCs were calculated and displayed on the computer monitor. The subject then performed voluntary contractions at 20, 40, 60, 80 and 100% MVCs for three sets. Each of the contraction was sustained for five seconds and a rest period of five seconds was provided between two contractions. The electromyography of tibialis anterior was monitored, but not recorded, to ensure there was no co-contraction of this muscle. The supramaximal stimulus was delivered onto resting soleus muscle and during contractions to elicit the control twitch and the interpolated twitch, respectively.

The amplitudes of the interpolated twitch and the control twitch were analyzed and the voluntary activations were then calculated. The voluntary activation level was calculated as the interpolated twitch (

The

In this study, a logistic growth model was used to interpret the curvilinear relationship between true voluntary contraction force and VA. A type of growth form named logistic growth curve is observed to frequently follow an S-shaped or sigmoid pattern when density and time are plotted on arithmetic scales. This model was used not only because it provides non-linear function for sigmoid pattern physiological response but also because the upper and lower limits could be defined for clinical usage in this model. Odum and Barrett [

The equation may be written as follows:

Solving differential Formula (2), we have:
_{e}

The Formula (4) for the logistic function can be expressed as follows:
^{−BX}^{−BX}^{−BX}^{−BX}^{−BX}

To identify the exact meaning of the parameter

Clearing the denominator gives the equation (1 +

The voluntary activation calculated by this logistic growth model was marked as modified VA in order to be distinguished from the VA which was calculated from the conventional function (Formula 1). The functional block diagram was presented in

In order to compare the new model with the conventional model, the difference between the predicted value and the true measured force value were calculated for each model. A paired-t test with p < 0.05 was used to assess if the errors of the two models were different. The root-mean-square errors of both models were also calculated.

The twitch torque evoked by superimposed electrical stimulation diminished with increasing force levels (

The VA and true voluntary contraction force relationship for each individual was somewhat S-shaped or sigmoid (

In Expression (6), the symbol

For comparing the quality of the modified VA to the VA, the difference between the predicted value and the true voluntary contraction force value were calculated. The results showed that the room-mean-square error calculated from the conventional function (VA) was obviously larger than that calculated from the logistic growth model (modified VA) (15.36%

The major finding of this study was that voluntary activation level increased by increasing force levels but in a non-linear manner. The logistic growth model produced less error compared to the conventional model. From the obtained upper and lower limit points of the logistic curve, we found the predictable range of the VA and true voluntary contraction force relationship was between the 95.16% and 10.55% of MVC.

The logistic growth model generated errors compared to the conventional linear model, supporting that the relationship between VA and the voluntary force. Previous studies have shown a curvilinear relationship [

This new model is better than the conventional linera one, not only because it generates less error but also because it provides the lower and upper limits for usage. Therefore, the estimated VA will not be negative value or a value greater than 100%. According to the results of this study, if the data beyond the limits were deleted, the performance of the conventional linear model could be improved. Although most of the studies suggested that the conventional model to calculate the voluntary activation might not be valid, the linear model is widely used in clinics because of easy application and non-complicated mathematical transformation. According to our result, establishing new modified VA models for different muscles are suggested while measuring the voluntary activation level on different muscles. If this procedure is not feasible, using only the range between 95.16% and 10.55% in the conventional model is suggested. The underlying mechanism of a VA and true voluntary contraction force curve at low contraction intensities could be related to the contribution of viscoelastic force loss [

Incomplete voluntary activation is a phenomenon that subjects produce submaximal activation during the maximal effort level. Incomplete voluntary activation may also contribute to the non-linearity relation between the VA and true voluntary contraction force. Any twitch force produced above the voluntary maximum is thought to represent incomplete neural drive to the muscle fibers [

In addition to the effect of the motor unit firing rates, incomplete motor unit recruitment should be noted. According to the investigation by Kendall

The modified VA calculated from the logistic growth model significantly reduced the error in comparison to the conventional model while using the interpolated twitch technique. A valid measure range of muscle activation defined by this new model was between 10.55% and 95.16% MVC. A limitation is that the validation is constrained by muscle type, motor unit recruitment and rate coding properties. If this new model establishing process is not feasible in some clinics or researches on other muscles, using only the range between 95.16% and 10.55% in the conventional model is suggested.

The result of the present study provides a valid range of I.T.T. for clinicians to estimate VA, especially for assessing patients who suffer from muscle weakness and could not generate sufficient force with neural inhibition, such as the subjects with joint injury, arthritis and muscle pain. Establishing activation models for other commonly tested muscles and standardizing the technique application procedures and simplifying the calculations by integrating the sensor system on chips are suggested in the future.

The authors would like to thank the National Science Council of Taiwan, for financially supporting this research under Contract No. NSC-97-2410-H-182-017.

The illustration of I.T.T. at each force level. The

Block diagram illustrating the processing steps of this study. After obtaining

The figure presents the conventional model (A) and the logistic growth model (B) overlaying on the true measured (circles). The conventional model showed a linear relationship between true voluntary contraction force (VF) and the VA. The logistic growth model suggested that VA has a sigmoid relationship with VF. The x axis for both plots is the VA calculated from the conventional model.

Average and standard deviation of voluntary activation across true voluntary contraction force levels (N = 8).

Voluntary activation (%) | 14.23 ± 7.91 | 32.05 ± 10.85 | 54.81 ± 16.04 | 80.44 ± 11.23 | 86.71 ± 12.76 |