Quantitative measurement of resistance force and subsequent attenuation during passive isokinetic extension of the wrist in patients with mild to moderate spasticity after stroke

DOI: https://doi.org/10.21203/rs.3.rs-1491027/v1


Background: Spasticity is evaluated by measuring the increased resistance to passive movement, primarily by manual methods. Few options are available to measure spasticity in the wrist more objectively. Furthermore, no studies have investigated the force attenuation following increased resistance. The aim of this study was to conduct a safe quantitative evaluation of wrist passive extension stiffness in stroke survivors with mild to moderate spastic paresis using a custom motor-controlled device. Furthermore, we wanted to clarify whether the changes in the measured values could quantitatively reflect the spastic state of the flexor muscles involved in the wrist stiffness of the patients.

Materials and Methods: Resistance forces were measured in 18 patients during repetitive passive extension of the wrist at velocities of 30, 60, and 90 deg/s. The Modified Ashworth Scale (MAS) in the wrist and finger flexors was also assessed by two skilled therapists and their scores were summed (i.e. , total MAS) for analysis. Of the fluctuation of resistance, we focused on the damping just after the peak forces and used these for our analysis. A repeated measures analysis of variance was conducted to assess velocity-dependence. Correlations between MAS and damping parameters were analyzed using Spearman’s rank correlation.

Results: The damping force and normalized value calculated from damping part showed significant velocity-dependent increases.

There were significant correlations (ρ=0.49–0.60) between total MAS and the normalized value of the damping part at 60 deg/s and 90 deg/s. The correlations became stronger when the MAS for finger flexors was added to that for wrist flexors (ρ=0.54–0.72).

Conclusions: This custom-made isokinetic device could quantitatively evaluate spastic changes in the wrist and finger flexors simultaneously by focusing on the damping part, which may reflect the decrease in resistance we perceive when manually assessing wrist spasticity using MAS.

Trial registration: UMIN Clinical Trial Registry, as UMIN000030672, on July 4, 2018. 


Spasticity is a common complication of various neurological diseases and lesions in the central nervous system1-3. It occurs in 17-46% of stroke patients4 (17% / 1year5, 42% / 6 months6, 46% / 1 year7) within 12 months after onset. Spasticity is primarily observed in the elbow (79% of patients), wrist (66%), and ankle (66%)8

Lance9 defined spasticity as “a motor disorder characterized by a velocity-dependent increase in tonic stretch reflexes with exaggerated tendon jerks, resulting from hyperexcitability of the stretch reflex” that causes increased muscle tone and, subsequently, increased stiffness to restrict movement. Spastic symptoms can induce pain, contractures, abnormal posture, decreased range of joint motion, tendon retraction, and muscle weakness in patients, which may also impair the patient’s quality of life and limit the potential success of rehabilitation10-12. Accordingly, spasticity management is an essential concept in neurological rehabilitation, and spasticity needs to be measured accurately.

The Modified Ashworth Scale (MAS) measures the level of resistance to passive movement. It is most widely used for evaluating spasticity in a clinical setting and has been investigated in many studies13, in which the assessor subjectively graded the resistance to manual passive stretch. The MAS is easy to use in clinical practice because it takes little time and no equipment is needed to assess muscle tone14,15

While there have been reports that the MAS shows poor reliability between raters16-18, several other studies have reported good intra- and inter-rater reliability, mostly for the upper extremities19-21, and better reliability for evaluations of the wrist flexor compared to those in the proximal elbow flexor or shoulder adductor22

To measure and evaluate spasticity more objectively, various quantitative approaches have been tested using different methodologies23. Several motor-driven or manually driven devices have been used in patients with stroke, and passive resistance forces have been measured in the ankle 24-28, elbow29-32 and wrist33-36 joints. Several studies have shown a significant correlation between the MAS and increased resistance to passive movement in the wrist joint34,35. However, no studies have investigated the correlation between the MAS and force attenuation following increased resistance in the wrist joint when measuring spasticity in patients with stroke.

Since the wrist joint of paralyzed patients tends to experience pain, which is likely to persist, we have developed a device that can measure passive resistance at low angular velocities and reduces excessive resistance to the wrist joint due to extension. We also focused on and analyzed the characteristic damping force observed after the maximum resistance with extension, which could reflect the decrease in resistance we sense while measuring MAS. 

We considered that a safe and easy-to-use device that can evaluate such resistance may be useful in introducing the objective measurement of spasticity into daily clinical practice. The purpose of this study was to investigate whether a custom-made motor-controlled device could be used to safely measure extension stiffness in a relatively mild spastic wrist joint in a patient with a post-stroke hemiparetic upper limb. Furthermore, we wanted to clarify whether the subsequent damping changes after the peak resistance could quantitatively reflect the spastic state of the wrist flexors and extrinsic finger flexors involved in the wrist stiffness by examining its correlations to the MAS.

Materials And Methods


Eighteen (mean age 61.7 ± 14.8 y; range 17–82; 4 females) subjects with post-stroke hemiparesis for a mean duration of 24.9 ± 39.4 months (range 0–166) participated in the study. Table 1 shows the characteristics of the patients. The patients were recruited from January 2018 to March 2019. These patients were inpatients or outpatients with stroke from Kagoshima University Hospital and Kagoshima University Hospital Kirishima Rehabilitation Center, Japan. The inclusion criteria were as follows: (1) age between 16 and 80 years, (2) the presence of hemiparesis in an upper limb with stroke, and (3) wrist and finger joint spasticity in the range of MAS 0–3 in the hemiparetic upper limb. Participants were excluded if they had pain in the upper limb or could not understand the study or simple commands.

All of the subjects gave their written and oral informed consent to the experimental procedures and the study. The study was approved by the ethics committee of Kagoshima University Hospital (Study Number: 170201) and was performed in accordance with the Declaration of Helsinki.


The device consisted of a custom-designed hand and forearm plate with a force sensor; Tension/Compression load cell (LUR-A-SA1: Kyowa Electronic Instruments Co. Ltd, Tokyo, Japan) and a servo-controlled DC torque motor (RH-14D-3002: Harmonic Drive Systems Inc., Tokyo, Japan). The outputs from the transducers were amplified and displayed on a laptop PC. The position and force data were recorded with a sampling rate of 66Hz. The experimental setup and the equipment are shown in Fig. 1A and 1B. The load cell was fixed to be perpendicular to the hand orthosis attached to the L-shaped angle material. The slide guide on the upper part of the load cell moves horizontally due to the tensile / compressive force from the hand, and the force is transmitted to the load cell to measure the resistance of the wrist joint. By attaching a slide guide to the side of the hand plate (Fig. 1C), it was expected that unnaturally excessive forces would not be applied to the wrist joint. Figure 1D shows an enlarged detailed view of the motor and encoder compartment.

Equipment for safety measures

Excessive force loading on the wrist joint may cause persistent pain, and we took special care to prevent such loading in this study. The device was designed so that rotation of the wrist joint could be stopped by a force of 90 N or more. Furthermore, when the resistant force measured by the load cell exceeded 50 N, the control software was programmed to automatically stop the motion of the rotating part of the device. The upper limit of this force could be arbitrarily changed to a small value depending on the subject. In addition, a safety switch (Fig. 1B) was provided to the subjects during the examination so that the device could be stopped immediately if they felt any discomfort or pain.

Experimental Procedures

Subjects were comfortably seated upright on a chair and evaluated for muscle spasticity using the MAS prior to each experiment by two therapists who had been well trained and had more than several years of experience in MAS evaluation. To ensure the independence of the evaluation, each evaluator assessed spasticity separately so that they would not know each other's findings. The two therapists assessed the spasticity of wrist flexor and finger flexor muscles using MAS, which is classified into six levels19,37. MAS scores of 0–4 (0, 1, 1+, 2, 3, and 4) were assigned numerical values of 0–5 (0, 1, 2, 3, 4, and 5, respectively) for data analysis. These MAS scores obtained by the two therapists were summed for wrist and finger flexors, to give a “total MAS”38; minimum 0 to maximum 20.

For force measurements, subjects were comfortably seated beside a servo-controlled DC torque motor. Each subject’s forearm was fixed in an adjustable arm support and the hand with all fingers extended was strapped to the hand plate coupled to a Tension/Compression load cell. The initial posture of the subjects was set so that the shoulder was in the neutral position, the elbow was flexed at 90°, the forearm was in the neutral position, and the hand and wrist were initially positioned at a relative angle of 180° (Fig. 1B). The rotation axis of the device was aligned to the anatomical axis of the wrist joint by sliding the hand plate and forearm holder. The forearm and fingers were fastened to the device by using Velcro straps, and the examiner checked to ensure that the participants felt no pain or discomfort in the neutral fastened position. The overall experimental procedure consisted of two steps. In the first step, the examiner manually moved the hand plate to slowly extend the wrist joint from the 20° palmar flexed position to the position of extreme dorsiflexion. Ninety percent of extreme dorsiflexion was set as the maximum range of extension so as not to induce pain. In the procedure, the laptop PC sampled and displayed the angular position of the wrist joint. In the second step, 11 cycles of passive extension were performed for force measurements at three angular velocities in the following order, 30 deg/s, 60 deg/s, and 90 deg/s. A stretch cycle was defined as from 20° flexion (palmar flexion) to maximum extension (dorsiflexion) at the previously mentioned velocity, and then back to 20° flexion at a velocity of 15 deg/s. Measurements at each extension velocity were obtained for 11 cycles of passive extension and flexion with 2-second pauses at the end of each movement. Each cycle (with different angular velocities) was performed with a 1- to 2-minute rest period between the cycles.

Data analysis and statistics

Of the 18 subjects, most (16 cases) had a peak resistance force during wrist extension as a negative value. The other two cases had positive peak resistance forces. We considered that the resistance force transmitted to the load cell changed to the proximal side (minus) or the distal side (plus) of the load cell axis due to the sliding mechanism of the hand fixture. Typical examples of 11 cycles of resistance force-time curves with repetitive angular displacement of wrist extension and flexion at each angular velocity obtained with the device are shown in Fig. 2a. The first recording of each of 11 repetitive measurements was excluded from the analysis to avoid bias from startle reflexes.

An example of an enlarged force-time curve with angle data extracted from repetitive measurements is shown in Fig. 2b and 2c. For each curve, the resistance force in the change from wrist flexion to extension was defined as the maximum resistance force (maximum RF) (“A” in Fig. 2b). On the other hand, after the peak resistance force (negative peak)was reached just after the maximum angle, a notable decrease in resistance force (in the positive direction) was observed (“B” in Fig. 2b); namely, the force-gap between the peak resistance force and the subsequent most strongly decreased resistance force was defined as the “damping force” (B). Furthermore, the impulses from the timing of the peak resistance to the timing of the most attenuated resistance were calculated. We defined the area of only the changed part from the peak force as the pure damping impulse (“D” in Fig. 2c), and that of the entire damping area under the curve (including the area of the pure damping impulse) as the total damping impulse (“C” in Fig. 2c). The trapezoidal integration rule was used to approximate the definite integral for calculating impulses.

In previous reports (on the ankle joint), some normalization processes were used to highlight differences25,26. In these reports, normalized values were obtained by expressing passive resistance as a percent of the torque values measured at an extremely low velocity (10deg/s)26, or of the torque values evoked with supramaximal stimulation of the tibial nerve25. With reference to these previous studies, we applied normalization to the obtained values. We defined the ratio of the damping force (B) to the maximum RF (A) as the damping force ratio (B / A) (Fig. 2b) and the ratio of the pure damping impulse (D) to the total damping impulse (C) as the damping impulse ratio (D / C) (Fig. 2c). The absolute value was obtained, and the mean values of repetitions were used for subsequent data analysis.

Since tests with the isokinetic device and force measurements were supervised by one rater, the intra-rater reliabilities of 10 repetitive force measurements were computed with an intraclass correlation coefficient (ICC) for each angular velocity. The reliability calculated with ICC is considered to be excellent for values from 0.75 to 0.90, fair to good for values between 0.40 and 0.75, and poor for values less than 0.4039.

The normality and equality of variance were checked by the Shapiro-Wilk and Levene statistical test. According to the normality analysis, a two-sample t test, Welch’s t test, or Wilcoxon-Mann-Whitney test was performed to compare the differences between mild and moderate spastic groups. A repeated measures analysis of variance (ANOVA) was conducted to assess velocity-dependent differences. Friedman’s test followed by Wilcoxon signed-rank test with Holm’s correction was conducted to evaluate differences for angular speeds of 30 deg/s, 60 deg/s, and 90 deg/s. Correlations between MAS and maximum RF and damping parameters were analyzed using Spearman’s rank correlation. All statistical analyses were performed using R Commander software 2.7-0 (R4.0.2; CRAN, freeware). The significance level for all statistical tests was set to 0.05.



The intra-rater reliability for the maximum RF measurements with this isokinetic device was excellent for all of the angular velocities tested: 30 deg/s; ICC (1,1) [95%CI] = 0.995 (0.991–0.998), 60 deg/s; ICC (1,1) [95%CI] = 0.995 (0.991–0.998), 90 deg/s; ICC (1,1) [95%CI] = 0. 993 (0.987–0.997).

Timing of peak resistance

In this study, there was a 2-sec pause from reaching the maximum extension angle to the start of subsequent flexion. Since the average duration from the peak resistance to the start of the next flexion was 1.813 ± 0.169 sec at an angular velocity of 30 deg/s, 1.78 ± 0.167 sec at 60 deg/s, and 1.996 ± 0.129 sec at 90 deg/s, the peak resistance force was observed after the extension angle reached the target (maximum) angle.

Velocity-dependence of various parameters

The median of the maximum RF at the 3 different velocities was 9.03 N at 30 deg/s, 8.75 N at 60 deg/s, and 8.30 N at 90 deg/s. Although there was no significant difference between the maximum RF at different velocities, these values tended to decrease as the velocities increased (Friedman χ2 = 5.78, df = 2, p-value = 0.056) (Fig. 3). The damping force showed a significant increase (χ2 = 12, df = 2, p-value < 0.01) as the velocities increased, except between 30 deg/s and 60 deg/s, and there was no significant difference in the damping impulse (χ2 = 1.4, df = 2, p-value = 0.49) (Fig. 3). The damping force ratio (B / A) showed a significant velocity-dependent increase (χ2 = 15.75, df = 2, p-value < 0.01) except between 30 deg/s and 60 deg/s, and the damping impulse ratio (D / C) tended to increase with velocity (χ2 = 5.44, df = 2, p-value = 0.066), as shown in Fig. 3.

Correlation between each parameter and the total MAS

We investigated the correlations of the maximum RF, the damping force, the damping impulse, the damping force ratio, and the damping impulse ratio with the clinically scored muscle spasticity according to the total MAS (the summed scores of the MAS obtained by two therapists only for the wrist flexors and for the wrist and finger flexors combined). No significant correlations were found between the maximum RF, the damping force, or the damping impulse and the total MAS. On the other hand, there were significant (p < 0.05) correlations between the damping force ratio and the damping impulse ratio and both the total MAS for wrist flexors (ρ = 0.49–0.60), and the total MAS for wrist and finger flexors (ρ = 0.54–0.72) at velocities of 60 deg/s and 90 deg/s, respectively. However, neither the damping force ratio nor the damping impulse ratio was significantly correlated with the total MAS at 30 deg/s (Table 2). Since the total MAS showed higher correlations with both ratio parameter at 90 deg/s compared to at 60 deg/s, the correlation coefficient ρ tended to increase in a velocity-dependent manner. Furthermore, if we compare the correlations between these ratio parameters and the total MAS scores for wrist flexors to those for both wrist and finger flexors, the latter tended to be more relevant (Table 2).

Differences depending on the severity of spasticity

The differences in each parameter were investigated when the patients were divided into two groups based on the total MAS scores in the wrist and finger flexors assessed by the two evaluators, where a score of 4 or less was considered mild spasticity and 5 or more was considered moderate spasticity. While no significant difference in maximum RF was seen between the two groups at each velocity, both the damping force ratio and the damping impulse ratio were significantly higher in the moderate spasticity group than in the mild group (Fig. 4).


In the present study, we applied mechanical passive stretch with a custom-made motor-controlled device to the hemiparetic wrist in 18 participants with spasticity following stoke. The isokinetic passive extensive displacement of wrist flexor muscles with the device induced resistant reflex forces and subsequent depression of these forces. The indices obtained from maximum RF and the subsequent force reduction after maximum extension (damping force ratio and damping impulse ratio) increased in a velocity-dependent manner and showed significant velocity-dependent correlations with total MAS scores. When the MAS evaluation for the finger flexors was added to the MAS for the wrist flexors, the correlations became stronger. Furthermore, when the patients were divided into a mild group (total MAS 4 or less) and a moderate group (total MAS 5 or more), both the damping force ratio and the damping impulse ratio showed significantly higher values in the moderate group at angular velocities of 60 deg/s and 90 deg/s. Although MAS shows poor reliability at the lower end of the scale40 and all of the patients in this study had MAS scores of 2 or less in both fingers and wrist flexors, significant differences were detected between the mild and moderate groups at 60 deg/s and 90 deg/s. Measurements of the resistance to wrist extension with the current custom device may have detected changes similar to those felt in evaluating stiffness with MAS in a daily clinical setting, and may also overcome the low reliability of MAS, especially in patients with comparatively mild spasticity.

Previous studies measured joint stiffness including spasticity by considering a passive resistance force or torque in the wrist 3336, 41, elbow29,42, and ankle joints2428. However, no studies have shown the correlation between the attenuated resistance force after the resistance peak and the MAS in hemiparetic patients with mild to moderate spasticity. This is the first report that focuses on the damping force after the peak resistance force induced by passive movement with isokinetic and motor-controlled velocity.

We often encounter a rapid rise of resistance in the latter half of the range of motion and subsequent weakening of resistance in patients with mild spasticity, when spastic muscle tone is measured manually in the clinic. In addition, the so-called clasp-knife phenomenon, which refers to the attenuation of resistance after an increase in resistance, has been known for a long time and is considered to reflect the subsidence of electromyogram and resistance force43,44.

Although the force output by our device is probably different from that applied when spasticity is evaluated in the daily clinical setting, the measured changes in damping with isokinetic passive movements using the current device might reflect the mechanical changes that constitute the clasp-knife phenomenon and which we feel when evaluating a patient’s spasticity.

Normalization procedure

We calculated the ratio of the damping force to the maximum RF and that of the pure damping impulse to the total damping impulse, which may contribute to normalize the fluctuation of resistance due to the sliding mechanism, the effect of the setting position, and the difference in mechanical responsiveness to passive movement between individuals. Several studies have investigated the correlation between resistance to passive movement in various joints and the Ashworth Scale and MAS using a similar device24–28,33−35. In addition, several studies have applied some ratio indices for normalized values25,26,34, as we did in the current study. The correlation with MAS was clarified26 and the difference between spastic and non-spastic patients in low-velocity passive movement was verified25 only when the analysis was performed using normalized values.

In this study, normalization of the damping force and impulse through the use of a ratio might contribute to detect the difference at relatively low velocities, and to identify significant correlations with the total MAS. In studies using mechanical resistance, it might sometimes be important to apply some normalization procedures when comparing resistance to clarify the differences between individual subjects.

Velocity-dependent resistance and correlation with the MAS

Spasticity has been defined as a velocity-dependent increase in resistance during passive stretch. Previous studies have reported that the maximum resistance against passive movements increased in a velocity-dependent manner25,26,35,45 and was correlated with the MAS35. However, in the current study, the maximum RF tended to decrease with velocity, while the normalized damping part tended to increase and showed significant correlations with the MAS in a velocity-dependent manner. One of the reasons why the resistance decreased in a speed-dependent manner in this study could be that measurements were performed in the order 30 deg/s, 60 deg/s, and 90 deg/s with a short interval. Previous studies have indicated that repetitive passive movements reduced reflex torque46 in elbow flexors and post-activation depression in the soleus muscle47. In the wrist and finger flexors, the long latency component of the stretch reflex decreases at faster repetition rates48. As in the current study, it has been reported that the resistance decreased in a velocity-dependent manner in patients with mild spasticity after stroke, and was not correlated with MAS44. However, in the current study, we detected a velocity-dependent increasing tendency by focusing on the damping part, which has not been a focus of previous studies, and found significant correlations with MAS.

In previous studies, electromyographical and resistance changes in spastic muscles were investigated at various passive movement velocities from 5 deg/s to 500 deg/s in the wrist joint33,35,36,41,49,50,51. Among these studies, a few found a significant correlation between the velocity-dependent resistance component and MAS at low-velocity joint movements of 50–70 deg/s 35,49, and our study also supports these findings.

In the current study, the correlation between the damping part and the MAS became stronger when the MAS in finger flexors was added to the MAS in wrist flexors. Since the extrinsic finger muscles affect the passive component of wrist joint stiffness51,52, it was considered that the stiffness of the extrinsic flexors of the fingers fixed to the device in the extended position may further affect the resistance to wrist extension. These changes in the correlations may indicate that the measured changes in force in the damping part quantitatively detect the spastic changes in wrist and finger flexors simultaneously and may support the reliability and validity of MAS itself in patients with mild spasticity after stroke.

Force components that make up the damping force

The damping part that we focused on might be mainly associated with a neural component that includes spasticity. According to several studies, the resistance generated by passive wrist dorsiflexion consists of inertia, elasticity, viscosity, and neural components caused by muscle stretch reflexes35,42. In post-stroke patients, Lindberg et al. showed that there are individual differences in the magnitude of passive resistance and in the composition of each component. However, for these components, the viscosity and neural components change in a velocity-dependent manner, and the elastic component continues with constant resistance and increases at the end of the range of extension. Additionally, the proportion of neural components in the total resistance is relatively large35. On the other hand, inertia appears and disappears for a short time at the start of the increase in resistance and just before reaching the maximum range of extension26,35. Based on these reports, the resistance damping part that we focused on in the current study could have arisen from both the viscosity and the neural components and the damping part might be mainly associated with the neural component including spasticity, since that part depended on velocity and appeared after the wrist joint reached the maximum range of extension.


In several previous studies that measured torque and force for the assessment of joint stiffness or spasticity, the measurements of passive resistance were conducted only after sufficient time intervals. In the current study, continuous sessions with pauses of only several seconds were performed with a short rest of 1 to 2 minutes in the ascending order of velocities (30 deg/s, 60 deg/s, and 90 deg/s) in all subjects. The resistance forces were considered to be affected by attenuation due to repetition. The measurement intervals could have been longer26,35 and the angular velocities could have been measured randomly25 or in a different order35.

The ingenuity of the sliding mechanism could contribute to cancel out excessive tension on the wrist joint, while the resistance force fluctuated due to movement of the positional relationship of the hand with respect to the pressure-measurement part of the tension/compression load cell. Furthermore, when the hand and forearm were fixed to the device, misalignment of the wrist joint axis could occur, and therefore it would be necessary to address inter-rater reliability and the measurements in healthy controls.


Our custom-made isokinetic device could be used to perform a quantitative evaluation of spasticity by focusing on the damping part following increased resistance. In addition, the damping part might be equivalent to the decrease in resistance we perceive when assessing wrist spasticity manually using MAS.

Especially for patients with mild to moderate spasticity, focusing on the damping part measured with this device may make it possible to objectively, stably and safely detect differences in stiffness including spasticity with isokinetic passive movements at a low angular velocity. In the field of rehabilitation, to improve the ability to control the wrist and fingers of patients with spastic hemiparesis after stroke with a higher dexterity, it is very important to accurately evaluate these stiffnesses and control them by therapeutic intervention. This device, which could simultaneously reflect spastic changes in both the wrist and finger flexors, may be effectively used in diagnosis and treatment for various neurological diseases in a daily clinical setting.


MAS: Modified Ashworth Scale; maximum RF: maximum resistance force; ICC: intraclass correlation coefficient; ANOVA: analysis of variance.



We appreciate all of the subjects and the staff of Department of Rehabilitation Medicine, Kagoshima University Hospital and Graduate School of Science and Engineering, Kagoshima University who contributed to this study. 

Author’s contributions

TN, RH, and YY designed and produced the device used in this study.

SN, YJ, SE, and KK contributed to data collection. SE and KK analyzed data and drafted manuscript. KN supported KK to conduct the statistical analysis. MS critically revised the manuscript and supervised the study. All authors read and approved the final manuscript.


This report was partially supported by JSPS KAKENHI Grant Number JP26350574.

Availability of data and materials

The datasets are available from the corresponding author on reasonable request.

Ethics approval and consent to participate

All of the subjects gave their written and oral informed consent to the experimental procedures and the study. The study was approved by the ethics committee of Kagoshima University Hospital (Study Number: 170201) and was performed in accordance with the Declaration of Helsinki. 

Consent for publication

Not applicable

Competing interests

The author(s) declare that there are no potential competing interests with respect to the research, authorship, and/or publication of this article.

Author details

1Department of Rehabilitation and Physical Medicine, Kagoshima University Graduate School of Medical and Dental Sciences, 8-35-1, Sakuragaoka, Kagoshima City, Kagoshima 890-8520, Japan. 2Department of Rehabilitation, Faculty of Health Science, Nihon Fukushi University, Aichi, Japan. 3Department of Mechanical Systems Engineering, Okayama University of Science, Okayama, Japan. 4Department of Rehabilitation, Kagoshima University Hospital, Kagoshima, Japan.

5Department of Mechanical Engineering, Graduate School of Science and Engineering, Kagoshima University, Kagoshima, Japan


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Tables 1 to 2 are available in the Supplementary Files section