Learning Patterns of Pivoting Neuromuscular Control Training– Towards a Learning Model for Therapy Scheduling

Abstract

Objective:

The goal of this study was to investigate the learning patterns in leg pivoting neuromuscular control performance over six-week pivoting neuromuscular control training (POINT) and to estimate how many sessions at beginning are needed to estimate the overall pivoting neuromuscular control learning curve.

Methods:

Twenty subjects (10 females, 10 males) participated in 18 sessions of POINT (three sessions per week for six weeks) program using an off-axis elliptical trainer. Performance measures including pivoting instability and stepping speed were quantified for each study session during a stepping task while subjects were asked to control pivoting movements under a slippery condition. Learning curve relating the pivoting instability to training sessions was quantified by the power law and by the exponential curve as a function of sessions or days with three parameters: the limit of learning, rate of learning, and learning capacity.

Results:

The power and exponential learning models characterized the learning curves similarly with no differences in R². No significant sex differences were found in the limit of learning, rate of learning, and learning capacity. Based on R² and RMSE, data from the first three study sessions might be enough to estimate the pivoting neuromuscular performance over the whole training period.

Conclusion:

The findings showed that subjects’ motor skills to improve pivoting instability followed the learning curve models.

Significance:

The findings and models can potentially be used to develop more effective subject-specific therapy scheduling.

I. Introduction

OVER the last decades, lower limb therapy using locomotion devices has gained popularity in clinics to improve lower limb functions with a steady shift of incorporating real-time biofeedback into the lower limb training sessions [1–3]. Specifically, improving lower limb pivoting neuromuscular control is important to reduce injury risks associated with pivoting related injuries and to improve lower limb functions among patients with pivoting related movement disorders such as cerebral palsy, stroke, and incomplete spinal cord injury. Despite of its importance of improving lower limb pivoting neuromuscular performance, only few studies have reported the effects of neuromuscular training to improve pivoting control during functionally relevant stepping tasks with real-time biofeedback [4, 5]. However, from these studies, how the learning patterns over the course of a long-term training program change is unknown. More detailed information about learning patterns in pivoting neuromuscular control over the training program may help us to design more effective and economical gait therapy protocols for improving pivoting neuromuscular control.

Studies to understand learning patterns were mainly conducted in upper limb within few sessions. From the upper limb studies, it has been found that once a motor skill is obtained, subjects start to perform a motor task rapidly, smoothly, effortlessly with less attention [6, 7]. As task performance is improved through motor skill acquisition, motor task error or task completion time is reduced [6, 7]. The relationships between either motor task error or task completion time and either trial numbers or training sessions can be characterized by a power law of learning [6, 8–11]. However, since more task variability and day-to-day variability can influence on motor task, it is unknown whether the power law is also governed in lower limb tasks in a longer period like 6 weeks. Applying the learning curve to quantify the relationship between a motor task and a long-term training program may provide us an insight into determining which subjects may benefit from the pivoting stepping training, and determining the number of training sessions to show improvements in neuromuscular performance. The gained knowledge and approach also help us to assess modification of therapy protocols for developing effective and targeted subject-specific gait training strategies.

The purpose of this study was to investigate the learning patterns in leg pivoting neuromuscular control performance over a six-week pivoting off-axis intensity adjustable neuromuscular training (POINT) program on a novel off-axis elliptical trainer [4] using three different ways of estimating a learning curve, and to estimate how many sessions are needed to estimate pivoting neuromuscular control. We hypothesize that

1. There are no significant differences in R² among three different ways of estimating a learning curve, namely, power law function in terms of number of sessions, exponential curve function in terms of number of sessions, and exponential curve function in terms of number of days.

2. 1) pivoting instability over the course of six-week POINT in the male and female group will follow the learning curve, and that 2) sex differences will not be seen in learning parameters (limit of learning, learning capability, and rate of learning) since females may show more deficits in neuromuscular control performance that can improve with neuromuscular training[12].

3. There is a certain number of study sessions required to estimate a learning curve model.

II. Methods

A. Subjects

Twenty healthy subjects, 10 males and 10 females without any lower-limb musculoskeletal injury completed our 6-week 18-session study. The age, weight, height, and BMI (mean ± SD) of the males were 25.1±3.8 years, 76.0±5.9 kg, 180.6±7.6 cm, and 23.3±1.3 kg/m², respectively. The age, weight, height, and BMI of the females were 24.5±4.1 years, 60.8±7.1 kg, 166.5±7.5 cm, and 21.9±2.2 kg/m², respectively. All the subjects gave informed consent approved by the Institutional Review Board at Northwestern University. Exclusion criteria included any known gait abnormality including neurological injury, history of orthopedic injury or surgery, or lower limb pain that could bias the results of the study, cardiac arrhythmia, and hypertension.

B. Experimental Setup

An off-axis elliptical trainer (ET) (Fig. 1) [13, 14] was used to provide and control multi-axis movements including off-axis movements such as axial plane pivoting, frontal plane sliding, or pivoting and sliding with sagittal stepping. Because the focus of the study was to investigate whether pivoting neuromuscular control can be learned during the course of POINT sessions, the sliding mechanisms for frontal plane movements were locked. The off-axis ET provided audio-visual biofeedback of subjects’ task performance as pivoting angle in real-time and subjects’ frontal lower limb alignment through a web camera. The ET provided different sensory stimuli to each foot via servo-motor controls to allow various levels of exercises including tasks under low friction, assistive, and resistive conditions [13]. The subjects were asked to wear a safety harness and each foot was secured to the footplate of the ET, while their tibial long axis was aligned with the center of the pivoting axis on the footplate through a pair of toe and heel straps [13]. The foot and the footplate pivoted together.

Fig. 1.

The off-axis elliptical training system. It allows pivoting movements of the left and right legs simultaneously or independently via cable driven pivoting mechanisms including footplates, torque sensors, servomotors, cables and encoders. Real-time audiovisual feedback helps guide the pivoting position and lower limb alignment in the frontal plane during training.

C. Experimental Protocol

Each subject came to the laboratory three sessions per week for six weeks consisting of total of 18 study sessions (i.e. 15 training sessions and 3 evaluation sessions). Each training session consisted of a total of approximately 30-minute stepping tasks at their comfortable speed. Subjects received real-time audio-visual feedback of their performance as pivoting angle and visual feedback of their frontal lower limb alignment (Fig.1). If subjects’ pivoting angle was beyond the range of ±30°, they would hear a beeping sound [4]. At the beginning and end of each training session, subjects stepped with the locked pivoting and sliding components of the footplates to prepare POINT and to cool down from the training about 2 minutes each [4]. At each task, the subjects were asked to maintain the second toe pointing forward (shown as the middle target in Fig. 1) during sagittal stepping when the footplates were able to pivot under different sensory stimuli (i.e. slippery footplate, spring footplate, and sinusoidal perturbations) representing different foot-floor contacts. Subjects performed 4 minutes of each task in the sequence of the free pivoting task (FPT), assistive spring torque task (ASTT), motor internal perturbation task (MIPT), motor external perturbation task (MEPT), the same ASTT, and the same FPT with adequate rest between tasks if needed [4]. The perturbation intensities were adjusted for subjects’ tolerance and creating challenging tasks but within a torque limit of 10 Nm. Evaluations were performed at 1^st, 9^th, and 18^th study sessions. At each evaluation session, the FPT was performed for a minute. Pivoting angle and potentiometer data were collected at 1000Hz (National Instruments™, Austin, TX).

D. Data Processing

Stepping speed and Pivoting instability.

Based on the time intervals of successive events at the most anterior positions of the same footplate, an averaged stepping speed during the FPT was computed in revolution per minute (RPM) for each person at each session [4, 14]. As away of investigating subjects’ task performance, pivoting instability, defined as standard deviation of pivoting angles [4, 13], was computed during the FPT for each person at each session. If subjects are able to maintain their target position during stepping all the time, pivoting instability should be zero. Thus, lower pivoting instability indicates better task performance. Pivoting instability from the left and right side were quantified at each study session. It should be noted that there were four missing data points, namely subject S6 in 4^th session, S12 in 12^th session, S15 in 16^th session, and S19 in 17^th session due to a problem in the data acquisition channels during the study session.

Learning curve (The law of practice).

Learning curve characterized by the power law quantifies learning patterns that 1) practice can speed up task completion and reduce variability of a motor task, and that 2) the learned motor tasks can be performed effortlessly and the learned motor skills are independent from intention and attention [6, 11]. Based on the power law equation (1), it can be determined whether the relationship between the motor performance error and the training sessions can be characterized by the power law [6, 9–11, 15]. The interpretation of each coefficient was adapted to our study based on [6, 15].

$$I(N)=a_p+b_p{N}^{-c}{}^{{}_p}$$ (1)

Specifically, I denotes the pivoting instability; N denotes the session number; a_p denotes the asymptote, which is the limit of learning determined by the minimum instability the subjects can perform; b_p denotes the amount to be learned (learning capability), which is the difference between the initial performance and asymptotic performance; and C_p denotes the rate of learning. The coefficients were estimated using curve fitting by minimizing error between the estimated I and the I from the empirical data of pivoting instability at each session from each subject to test hypothesis that pivoting instability from each group over multiple sessions can be estimated using the power law. R² was also computed based on the estimated I from the model and the I from the aforementioned empirical data.

N in the form of the law of practice is based on a monotone decreasing function of session number; however, therapy schedule such as number of days between session numbers might be different between subjects and the learning patterns might be affected by the day when the therapy is received. Thereby, it might be necessary to understand the effects of time scale in terms of session numbers and days on the learning curve estimation. Besides the power law quantifying the relationship between the number of sessions (N) and task performance, the exponential curve (equation (2)) has also been used to quantify a relationship between the number of sessions or the number of days (t) and task performance[16].

$$I(x)=a_e+b_e{e}^{-c_{e}x}$$ (2)

x can be either a number of sessions (N) or a number of days (t). Similar to the power law, a_e denotes the asymptote, the limit of learning; b_e denotes the amount to be learned; C_e denotes the rate of learning. Thereby, aforementioned three types of learnings curves from the left and right side were investigated to understand long-term learning patterns.

Furthermore, empirical pivoting instability data of the left and right side from 3 to 18 sessions were used to investigate how many sessions were needed to estimate pivoting instability using the power law equation. Three sessions were the minimum number of data point required to fit the model. R² and Root Mean Square Error (RMSE) between the empirical pivoting instability and the estimated pivoting instability using the power law at each simulated session were computed.

E. Statistical Analysis

Jarque-Bera normality test was performed in the learning parameters from three types of learning curve models. Because the data distribution of the learning parameters was not normal, Friedman test (non-parametric version of repeated measure) was conducted to compare averaged R² between the left and right side among three types of learning curves. Independent variable was the type of learning curve. Mann-Whitney U tests (non-parametric version of independent t-test) were performed to compare gender differences in the asymptote, learning capability and rate of learning with higher R² values between the left and right side at each learning model. Pearson correlation coefficient was used to evaluate the correlation between the empirical values of pivoting instability obtained from the study and the estimated values of pivoting instability using the power law equation at the first study session. Generalized Estimating Equation (GEE) analysis was performed to investigate the effect of number of sessions to estimate the learning curve. Independent variable was side (left, right) and number of sessions. Dependent variables were R² and RMSE between the empirical pivoting instability and the estimated pivoting instability using the power law. Bonferroni correction was used to reduce potential type I error raised from the multiple comparisons. SPSS (IBM, Chicago, IL) was used for all statistical analysis and the alpha level was set at 0.05.

III. RESULTS

As seen from Fig. 2, pivoting instability across subjects became smaller and stepping speed increased as the study sessions were proceeded. Pivoting instability of a representative subject among different training tasks at a typical training session can be also seen in the left side of Fig. 2 (a).

Fig. 2.

(a) Pivoting instability among different training tasks (the FPT, ASTT, MIPT, MEPT, second ASST indicated as ASST R, second FPT indicated as FPT R respectively) at a session 2 from a representative subject, and averaged pivoting instability from the left and right side respectively, and (b) stepping speed. Each filled black square dot with error bar indicates the mean pivoting instability with ±1SD during the FPT from 20 subjects.

A. Hypothesis 1.

A learning curve using the power law function from a representative subject was shown in Fig. 3(a) with description of each learning parameter. Regarding R², there was no significant difference among three types of learning curves (see Fig. 3(b)). As seen in Fig. 3(c), the empirical pivoting instability and the estimated pivoting instability using the power law equation at the first study session was significantly correlated (p<0.0001, r=0.98).

Fig.3.

(a) learning curve of a representative subject characterizing the pivoting instability of the left side using a power law function in session, exponential curve in session, and exponential curve in days. Each filled black square dot indicates the pivoting instability at a session, a denotes the asymptote; b denotes the learning capability; c denotes the rate of learning. Relationship between the empirical and estimated pivoting instability at the first study session, (b) Boxplot of R² from the power law model, exponential curve in session, and exponential curve in day. In the boxplot, three lines indicate 25 (Ql), 50 (Q2), and 75 (Q3) percentile of the data. The whisker indicates Q3+1.5*(Q3-Q1), and Q1–1.5*(Q3-Q1) and the red cruciate points indicate the value outside of this range, (c) Relationship between the empirical and estimated pivoting instability at the first study session from the left and right side.

B. Hypothesis 2

The median, 25% and 75% percentile asymptote, amount of learning, rate of learning, and R² in the male and female group were presented in Table I. There were no significant gender differences in the asymptote, amount of learning, rate ol learning, and R².

TABLE I.

Estimated Learning parameters

	Male	Female
Power law
Asymptote a (°)	0 (0,0.63)	0(0, 1.38)
Learning capability b(°)	4.52 (3.89,5.98)	4.46 (2.20,5.55)
Rate of learning c	0.55 (0.49,0.69)	0.91 (0.47,1.24)
R2	0.80 (0.68,0.92)	0.78 (0.52,0.87)
Exponential curve in session
Asymptote a (°)	1.41(0, 1.52)	1.14(0.38,1.39)
Learning capability b(°)	5.44 (3.70,6.07)	4.75(3.50,7.65)
Rate of learning c	0.31(0.18,0.45)	0.45 (0.26,0.69)
R2	0.83(0.81,0.90)	0.82(0.60,0.90)
Exponential curve in day
Asymptote a (°)	1.44(0,1.54)	1.37(0.65,1.61)
Learning capability b(°)	3.69(3.27,3.89)	2.81(1.95,4.57)
Rate of learning c R2	0.16(0.08,0.19) 0.86(0.81,0.90)	0.22(0.11,0.61) 0.82(0.60,0.87)

Estimated asymptote a, learning capability b, and rate of learning c based on the power law in session, and exponential curve in session and in day using each pivoting instability during the FPT at each session. Values are median with (25, 75 percentile) in 10 males and 10 females.

C. Hypothesis 3.

There was a significant effect of the number of sessions of the training data to estimate the pivoting neuromuscular performance under a slippery condition in terms of R² and RMSE between the empirical pivoting instability and the estimated pivoting instability using the power law curve (p<0.001), but no effect in side. Post hoc analysis with a Bonferroni correction revealed that there were no significant R² differences between various numbers of study sessions. The result may indicate that minimum 3 sessions of empirical data are required to estimate the learning curve in pivoting neuromuscular control under a slippery condition. It is important to understand the meaning of model error with a unit, which was expressed as RMSE. Mean values (1SD) of RMSE in the left and right side using the three sessions of empirical data to estimate the learning curve were small as 1.40 (1.43)° and 0.91 (0.46)°, respectively (see Fig. 4). Thereby, in our case, 3 sessions of data might be enough to estimate subject’s a long-term pivoting control task performance under a slippery condition. Furthermore, a representative case of estimating pivoting instability using the power law with the empirical data was reported in Fig. 5.

Fig. 4.

R² and RMSE between the empirical pivoting instability and estimated pivoting instability when 3 to 18 sessions of pivoting instability data was used to estimate a learning curve (in this case, use the power law curve in terms of session). Each filled black square dot with error bar indicates the mean RMSE with ±1SD during the FPT from 20 subjects.

Fig. 5.

A representative case of estimated instability (red color) with the real empirical pivoting instability data (black filled square) obtained during the experiment when each 3 to 18 session data was used (in this case, pivoting instability from the right side). Each number represents the pivoting instability from the respective number of sessions used for the simulation to estimate the learning curve.

IV. DISCUSSION

Understanding learning patterns over multiple sessions may help us develop efficient training strategies for lower limb injury prevention and rehabilitation. This is the first study reporting learning patterns of lower limb pivoting neuromuscular control performance over a 6-week 18 session training program and simulate how many therapy sessions are necessary to obtain a learning curve model. The findings support the hypotheses that 1) there were no significant differences in R² among three different ways of estimating a learning curve, 2) pivoting instability over the course of six-week POINT in the male and female group followed the learning curve, and there were no sex differences in the learning parameters (limit of learning, learning capability, and rate of learning), and 3) there was a certain number of study sessions used to estimate a learning curve.

The findings from this study support one of motor learning theories including the three stages of motor learning. During the course of acquiring new motor skills, three stages of motor learning involve cognitive, associative, and autonomous stages[7]. During the cognitive stage, subjects try to understand the instruction of task, and during the associative stage, subjects’ performance is less variable and performance error become less frequent and smaller. During the autonomous stage, the acquired skill becomes habitual or automatic [7]. In our study, when subjects were asked to maintain the target pivoting position at subjects’ preferred speed, subjects reduced pivoting instability and increased stepping speed over 6 weeks. The findings suggest that subjects required less attention to control pivoting motions during stepping due to learned motor skills [17]. Furthermore, it has been believed that acquired automatic skills can be quantified using a learning curve model (e.g. a power law equation and an exponential equation) based on performance measures such as minimized endpoint error over repetitive tasks [6, 8, 11, 18]. There were no differences in R² between the power law equation and exponential equation to estimate a learning curve based on the performance measures in this study. From this motor learning point of view, the finding of showing the relationship between pivoting instability and study sessions over the six weeks following the learning curve model suggests the possibility of translating learned motor skills from POINT into pivoting control during strenuous daily activities. Reduced pivoting instability might be related to the altered motor commands to be more specific and efficient sequence over time of training sessions [4, 19, 20]. While the findings from the current study did not investigate the direct links between altered brain activities and reduced pivoting instability following POINT, previous studies reported that as motor skills were obtained, corticospinal excitability and muscle activation patterns were modified [21]. Subjects who were trained to gain their motor skills demonstrated a significant correlation between the changes in corticospinal excitability and motor performance [21].

Our results showed that subjects’ rate of reducing pivoting instability was faster at earlier study sessions than later study sessions. Based on the power law, while the rate of improvement can be small at the later study sessions, the subjects’ performance can continuously improve when subjects receive more training. Indeed, one study monitored cigar wrapping time among cigar factory workers for over seven years and found out that the workers were still getting faster although the amount of improvement was getting smaller [11, 22].

Then, one question is raised. How many sessions are necessary to estimate learning patterns to develop a therapeutic training program at subject-specific need? Our findings suggest that in our case, data from three sessions might be enough to estimate subject’s a long-term pivoting control task performance under a slippery condition. While the result of small estimated RMSE as near 1° between the simulated and empirical data using the first three sessions of data to estimate the learning curve is encouraging, further studies are needed to understand clinical meaning of the small estimated error in terms of neuromuscular control performance in daily life. The well-fitted empirical data with a learning curve model implies that improvement in pivoting neuromuscular control performance might be due to automatized motor skills [23–25]. Significant correlation between the empirical and estimated pivoting instability at the first study session could also provide a guideline for subjects who receive more benefits from POINT than others. In summary, our findings to understand learning patterns and methods can be a basis for further investigation to develop more efficient training methods with shorter training durations and fewer training sessions with other pivoting related functional tasks. In addition, further studies on learning patterns among a larger population, patients with musculoskeletal injuries and with neurological disorders may be necessary to generalize the current findings, and to understand effective schedules for therapeutic neuromuscular training considering that delayed improvement is observed in pathological conditions [26].

No significant gender differences were found in the asymptote, learning capability and rate of learning in this study, based on the samples available. The results suggest that females can improve their task performance similarly to males under injury-related scenarios, and their learning patterns are similar to males although more challenging tasks may demonstrate different learning patterns between males and females. Since this is the first study reporting the application of power law to quantify the relationship between the study sessions and pivoting instability, it is difficult to make comparisons with other previous studies. However, the findings can be supported by evidences of neuromuscular training for lower limb injury prevention programs. For example, neuromuscular training helped female subjects to reduce injury risk factors and incident of having ACL injuries when 2-year follow up studies were performed [27, 28]. While it is still unknown whether gender bias on incidents of musculoskeletal injuries is decreased by the neuromuscular training, the current practice of neuromuscular training on females who are at a higher risk of musculoskeletal injuries can be justified. The current approach can potentially be used to screen subjects who may receive more benefits from POINT and can be expanded to other training regimes to reduce musculoskeletal injuries and assist clinicians to prescribe effective therapy schedule in the future. Of note is that the non-significant differences between males and females were based on the available small sample of healthy subjects. Further studies would be necessary to understand learning patterns between males and females among patients with pivoting-related injuries for developing subject-specific rehabilitation strategies of musculoskeletal injuries.

V. Conclusion

The findings suggest that subjects can obtain motor skill to reduce pivoting instability, which will help them to improve pivoting neuromuscular control during daily activities and reduce potential pi voting-related injuries in real-life situations. The methods to estimate a learning curve based on the neuromuscular performance measures used in this study help us to predict and determine how many sessions of training are needed to improve motor skills to control pivoting on a subject-specific basis. Further studies are needed to generalize the findings to different tasks and develop more effective rehabilitation protocols following injuries.