Gait Training for Hemiplegic Stroke Patients: Employing an Automatic Neural Development Treatment Trainer with Real Time Detection

Featured Application: This paper investigates the effectiveness of using an automatic NDT trainer for the clinical rehabilitation of stroke patients. Abstract: This paper presents a clinical rehabilitation protocol for stroke patients using a movable trainer, which can automatically execute a neurodevelopmental treatment (NDT) intervention based on key gait events. The trainer consists of gait detection and motor control systems. The gait detection system applied recurrent neural networks (RNNs) to recognize important gait events in real time to trigger the motor control system to repeat the NDT intervention. This paper proposes a modiﬁed intervention method that simultaneously improves the user’s gait symmetry and pelvic rotation. We recruited ten healthy subjects and had them wear a rehabilitation gaiter on one knee joint to mimic stroke gaits for veriﬁcation of the effectiveness of the trainer. We used the RNN model and a modiﬁed intervention method to increase the trainer’s effectiveness in improving gait symmetry and pelvic rotation. We then invited ten stroke patients to participate in the experiments, and we found improvement in gait symmetry in 80% and 90% of the patients during and after the training, respectively. Similarly, pelvic rotation improved in 80% of the patients during and after the training. These ﬁndings conﬁrmed that the movable NDT trainer could improve gait performance for the rehabilitation of stroke patients. of clinical stroke rehabilitation using a movable trainer employed during NDT intervention. The trainer consisted of a gait detection system and a motor control system. We implemented an RNN model in the gait detection system and a modiﬁed NDT intervention in the motor control system. The RNN model can recognize the HS events in real time to activate the NDT intervention at critical moments. The users can feel walking and intentionally drive their body to regain gait control by motor training. The aim of using the modiﬁed NDT intervention method was to simultaneously improve the user’s gait symmetry and pelvic rotation. We recruited ten healthy subjects to verify the effectiveness of the trainer. The results showed that the trainer could simultaneously improve the subjects’ gait symmetry and pelvic rotation. The ﬁndings from 10 stroke patients invited to participate in the experiments showed that gait symmetry improved in 80% of the patients during the training and 90% after the training. The pelvic rotation was improved in 80% both during and after the training. Based on these results, we conclude that the NDT trainer can potentially help stroke patients’ rehabilitation. Some patients did not show improvements, possibly due to difﬁculty in holding handrails with the paretic hand or variations in the participants’ heights that affected accurate pelvic rotation force and limited induction force options (we only included 100% and 150%). Therefore, in future studies, we plan to fasten the participants’ hands onto the handrails for the participants’ hands to decrease asymmetry during the intervention. We will also modify the trainer design, for example, by applying a suitable mechanism to automatically adjust the intervention positions for patients with different heights and body weights or by adding motor wheels to reduce the burden of pushing the trainer.


Introduction
Stroke has been reported as the second leading cause of death in the last 15 years [1]. The most common disorder caused by stroke is motor impairment, which typically affects the control of movement on one side of the body and is seen in about 80% of patients [2]. Although 65% to 85% of stroke survivors could recover independent walking by six months post-stroke, gait abnormalities persist through the chronic stages [3]. Only 30-50% of stroke survivors achieve community mobility, which is an essential indicator of the activities and participation domains according to the International Classification of Functioning, Disability, and Health [4]. People with stroke may have an impaired ability to adapt to environmental challenges. They have trouble walking across obstacles, increasing the risk of tripping or navigating around more significant obstacles (e.g., another person approaching in the opposite direction). Long-term rehabilitation is usually required for these patients to help them recover their ability to live independently and walk on their own. As stroke recovery progresses, stroke survivors usually develop better gross motor skills in trunk The currently available NDT trainer can repeat the therapist's intervention pattern by cuing the subject's ASIS when observing the HS on the opposite side. However, we noted that the present intervention method improves the subject's longitudinal symmetry but does not improve pelvic rotation. The locomotion of the pelvis is closely related to walking stability [25,26]. For example, Wagenaar et al. [27] showed the contribution of pelvic rotation to lengthening the stride, especially when walking at fast speeds. Energy conservation is crucial during gait, and the vertical displacement of the body is minimized by a number of factors known as the determinants of gaits. These determinants operate independently and simultaneously to produce a smooth sinusoidal vertical and horizontal path, which has one vertical peak and trough for each step. One of the determinants of gait is the rotation of the pelvis, which reduces center of mass (COM) movement, thereby conserving energy [28,29]. Therefore, we analyzed the subjects' pelvic motions and the therapists' interventions during clinical NDT rehabilitation and proposed a modified method to improve the pelvic rotation. We implemented the modified intervention method and recruited 10 healthy subjects who wore a rehabilitation gaiter to mimic stoke gaits to verify the effectiveness of the trainer in improving gait performance and pelvic rotation. We also invited 10 stroke patients to participate in the experiments, and their results confirmed that the proposed intervention method simultaneously improved both pelvic rotation and gait symmetry.
This paper is organized as follows. Section 2 describes the movable trainer, which can automatically conduct NDT rehabilitation intervention. The trainer consists of a gait detection system and a motor control system. The gait detection system employs an RNN model to identify HS events in real time, so that the motor system can be activated for NDT intervention at the key time. Section 3 introduces a modified intervention method that can simultaneously improve the subjects' gait symmetry and pelvic rotation. We recruited 10 healthy subjects and had them wear a rehabilitation gaiter to imitate stroke gaits to test the trainer. The results confirmed the effectiveness of the trainer. Section 4 presents the results for 10 stroke patients invited to participate the experiments and shows that the NDT trainer can improve both gait symmetry and pelvic rotation in stroke patients. Finally, we draw conclusions in Section 5.

The Movable NDT Trainer: Experimental Design and Data Collection
This section describes the movable trainer [16], which automatically repeats the NDT intervention. The trainer consists of a gait detection system and a motor control system, as shown in Figure 1, which equips with an adjustable handle for safety. The gait detection system analyzed the gait information obtained from two IMUs attached to the user's shanks. It could automatically recognize the HS events and send triggering signals to the motor control system to imitate the therapists' intervention. The motor control system could repeat the therapists' intervention patterns by stimulating the users through ropes. The ropes connected the motors and the user's pelvis to cue the user as the traditional NDT training. Load cells were implemented between the ropes and the motors to measure the applied forces for feedback control. Previous studies [14][15][16] showed that the therapists tended to cue the subject's right (left) pelvis when the subject's left (right) foot struck the ground. Therefore, an RNN model [24] was applied to the gait detection system, which detects the HS in real time to activate the motor control system. The motor control system then repeats the NDT intervention after receiving the triggering signals from the gait detection system [14][15][16]. Appl. Sci. 2022, 12, x FOR PEER REVIEW 4 of 16 Stroke patients tend to have uneven gaits due to hemiparesis, and stroke patients have their own individual walking patterns and speeds. Therefore, we developed an RNN model to detect HS events for subjects who might have varied walking patterns and speeds [24]. We applied the APDM OPAL system [30] to measure each subject's kinematic data with a sampling rate of 25 Hz. Two IMUs were attached to the subject's legs, as shown in Figure 2, to measure gait data. The specifications of the IMU are illustrated in Table 1.   Stroke patients tend to have uneven gaits due to hemiparesis, and stroke patients have their own individual walking patterns and speeds. Therefore, we developed an RNN model to detect HS events for subjects who might have varied walking patterns and speeds [24]. We applied the APDM OPAL system [30] to measure each subject's kinematic data with a sampling rate of 25 Hz. Two IMUs were attached to the subject's legs, as shown in Figure 2, to measure gait data. The specifications of the IMU are illustrated in Table 1. Stroke patients tend to have uneven gaits due to hemiparesis, and stroke patients have their own individual walking patterns and speeds. Therefore, we developed an RNN model to detect HS events for subjects who might have varied walking patterns and speeds [24]. We applied the APDM OPAL system [30] to measure each subject's kinematic data with a sampling rate of 25 Hz. Two IMUs were attached to the subject's legs, as shown in Figure 2, to measure gait data. The specifications of the IMU are illustrated in Table 1.    Human gaits are regularly periodic. A complete gait cycle, as illustrated in Figure 3, contains three important gait events: mid-swing, HS, and toe-off. We applied the sixaxial IMU data and marked the HS events to build an RNN model [24], as shown in Figure 4. The model was trained by the gait data measured in five healthy subjects who wore a rehabilitation gaiter with a 2 kg mass to limit their joint movement on one knee to increase gait varieties (see Figure 5). We segmented the gait data with a sliding window, as illustrated in Figure 4, which consisted of 50 samples of six-axial IMU data as the model input. The window was then moved by one sample each time, with an overlap of 98%. The model output was marked as 1 for an HS event or 0 for a non-HS event. We applied the leave-one-out cross validation method [31] to train the RNN model. We then applied the model to three groups of subjects: healthy elderly subjects, stroke patients, and patients with PD. The results illustrated in Table 2 confirm that the RNN model successfully recognized the HS events with an average accuracy of 99.65% and an average delay of 0.0256 s. Therefore, we applied the RNN model to detect the HS and to activate the NDT intervention in real time. Human gaits are regularly periodic. A complete gait cycle, as illustrated in Figure 3, contains three important gait events: mid-swing, HS, and toe-off. We applied the six-axial IMU data and marked the HS events to build an RNN model [24], as shown in Figure 4. The model was trained by the gait data measured in five healthy subjects who wore a rehabilitation gaiter with a 2 kg mass to limit their joint movement on one knee to increase gait varieties (see Figure 5). We segmented the gait data with a sliding window, as illustrated in Figure 4, which consisted of 50 samples of six-axial IMU data as the model input. The window was then moved by one sample each time, with an overlap of 98%. The model output was marked as 1 for an HS event or 0 for a non-HS event. We applied the leaveone-out cross validation method [31] to train the RNN model. We then applied the model to three groups of subjects: healthy elderly subjects, stroke patients, and patients with PD. The results illustrated in Table 2 confirm that the RNN model successfully recognized the HS events with an average accuracy of 99.65% and an average delay of 0.0256 s. Therefore, we applied the RNN model to detect the HS and to activate the NDT intervention in real time.   Human gaits are regularly periodic. A complete gait cycle, as illustrated in Figure 3, contains three important gait events: mid-swing, HS, and toe-off. We applied the six-axial IMU data and marked the HS events to build an RNN model [24], as shown in Figure 4. The model was trained by the gait data measured in five healthy subjects who wore a rehabilitation gaiter with a 2 kg mass to limit their joint movement on one knee to increase gait varieties (see Figure 5). We segmented the gait data with a sliding window, as illustrated in Figure 4, which consisted of 50 samples of six-axial IMU data as the model input.
The window was then moved by one sample each time, with an overlap of 98%. The model output was marked as 1 for an HS event or 0 for a non-HS event. We applied the leaveone-out cross validation method [31] to train the RNN model. We then applied the model to three groups of subjects: healthy elderly subjects, stroke patients, and patients with PD. The results illustrated in Table 2 confirm that the RNN model successfully recognized the HS events with an average accuracy of 99.65% and an average delay of 0.0256 s. Therefore, we applied the RNN model to detect the HS and to activate the NDT intervention in real time.

Modified NDT Intervention
The motor control system can repeat the NDT intervention after receiving the triggering signals from the gait detection system. In previous studies [14][15][16], we concluded that the therapists cued a subject's right (left) pelvis when they observed the subject's left (right) HS during the NDT rehabilitation, as illustrated in Appendix A. Therefore, we designed the motor control system to automatically repeat this pattern. When detecting a HS, the detection system sent a triggering signal to the motor control system on the opposite side, which tracked the following force command: where max F and min F represent the maximum and the minimum forces, respectively, while f is the frequency. Based on previous experiences [14][15][16], we set , and f =1 Hz in the experiments.
Since gait symmetry is critical for walking rehabilitation, we analyzed the asymmetry of the swing phase [32], defined as follows:

Modified NDT Intervention
The motor control system can repeat the NDT intervention after receiving the triggering signals from the gait detection system. In previous studies [14][15][16], we concluded that the therapists cued a subject's right (left) pelvis when they observed the subject's left (right) HS during the NDT rehabilitation, as illustrated in Appendix A. Therefore, we designed the motor control system to automatically repeat this pattern. When detecting a HS, the detection system sent a triggering signal to the motor control system on the opposite side, which tracked the following force command: where F max and F min represent the maximum and the minimum forces, respectively, while f is the frequency. Based on previous experiences [14][15][16], we set F max = 6 lb, F min = 1 lb, and f =1 Hz in the experiments. Since gait symmetry is critical for walking rehabilitation, we analyzed the asymmetry of the swing phase [32], defined as follows: where SP non−paretic and SP paretic represent the proportion of the swing phase on the paretic side and the non-paretic side, respectively. Since stroke patients tend to have hemiparesis and a longer swing time on the paretic side, we applied Asym SP to evaluate the rehabilitation effectiveness and regarded the training as effective if Asym SP approached zero. We recruited 10 healthy subjects for the experiments. The subjects' data are provided in Table 3. A rehabilitation gaiter was attached to one knee joint on each subject to limit the joint movements and to mimic stroke gaits. Each subject received the tests by the A − B − A procedures, where A, B, and A represented the before-treatment, during-treatment, and after-treatment periods, respectively. The subjects first walked on their own once down a 20 m corridor (A). They then received NDT training twice by the trainer on the 20 m corridor (B), and they finally walked on their own down the 20-m corridor once (A). Their gait data were recorded, as illustrated in Appendix B, to evaluate the training effects. The experimental results are shown in Table 4, where imp% represents the percentage improvement of the training compared to before the training (stage A). As shown in Table 4, the asymmetry of the swing phases of 9 of the 10 subjects was improved after the treatment (A stage). A possible reason is that subject H9 had a light body weight and may have had insufficient muscle strength to push the movable trainer. Generally, the NDT intervention is effective in improving Asym SP . Apart from the gait symmetry, the locomotion of the pelvis is also important for maintaining walking stability [25][26][27]. During each step, the pelvis rotates forward on the side of the swinging limb. The axis of this rotation is the hip joint of the stance leg, which undergoes internal rotation. As the pelvis forms a bridge between the two hips, it reduces the angle of intersection of the thighs to reduce the vertical descent of the trunk. As mentioned previously, pelvis rotation conserves energy during the normal gait and allows people to walk at a comfortable pace. Therefore, we further analyzed the subjects' pelvic rotation during the NDT training. The amplitude of pelvic rotation Amp PR is defined as the maximum rotation angle between two consecutive HS events on the paretic side, as follows: where θ max and θ min represent the maximum and minimum pelvic angles during a complete gait cycle, respectively, as shown in Figure 6. Since stroke patients' muscles are usually weakened on the paretic side, their pelvic rotation is limited and less than in healthy persons. Therefore, we can evaluate the effectiveness of the NDT rehabilitation by Amp PR , and we regard the training as effective if Amp PR is increased. We attached an IMU to the subjects' waists (see Figure 5) to record their pelvic rotations. The results are illustrated in Table 5; only 6 of the 10 subjects had an improvement in Amp PR during the treatment (B stage) and after the treatment (A stage). That is, the current intervention method can improve the subjects' gait symmetry but not their pelvic rotation. Therefore, we analyzed the therapists' interventions during the clinical NDT training in [14][15][16], as those interventions were manually conducted by the therapists. The analyses are illustrated in Appendix C and show that the therapist tended to increase the intervention forces on the non-paretic side when the subject's pelvic rotation was small. Based on that analysis, we proposed a modified NDT intervention algorithm that can improve the gait asymmetry and the pelvic rotation simultaneously.
usually weakened on the paretic side, their pelvic rotation is limited and less than in healthy persons. Therefore, we can evaluate the effectiveness of the NDT rehabilitation by PR Amp , and we regard the training as effective if PR Amp is increased. We attached an IMU to the subjects' waists (see Figure 5) to record their pelvic rotations. The results are illustrated in Table 5; only 6 of the 10 subjects had an improvement in PR Amp during the treatment (B stage) and after the treatment ( A stage). That is, the current intervention method can improve the subjects' gait symmetry but not their pelvic rotation. Therefore, we analyzed the therapists' interventions during the clinical NDT training in [14][15][16], as those interventions were manually conducted by the therapists. The analyses are illustrated in Appendix C and show that the therapist tended to increase the intervention forces on the non-paretic side when the subject's pelvic rotation was small. Based on that analysis, we proposed a modified NDT intervention algorithm that can improve the gait asymmetry and the pelvic rotation simultaneously.    The modified intervention method is shown in Figure 7, where the maximum intervention forces on the non-paretic side are increased by 50% if the pelvic rotation is less than a given threshold. For example, we applied the rehabilitation gaiter to the subjects' right knee so that the left motor was controlled according to the following procedures: i.
The motor tracked a minimum force of F min to keep the rope straight. ii. The motor was activated to follow the intervention force pattern of (2), when the right HS was detected. iii. The maximum intervention force F max was increased if the pelvic rotation Amp PR was less than a threshold value. right knee so that the left motor was controlled according to the following procedures: i. The motor tracked a minimum force of min F to keep the rope straight.
ii. The motor was activated to follow the intervention force pattern of (2), when the right HS was detected. iii. The maximum intervention force max F was increased if the pelvic rotation PR Amp was less than a threshold value. We implemented the modified intervention method with the movable NDT trainer and repeated the experiments. In this paper, we increased the maximum intervention force max F by 50% when the pelvic rotation  Table 6. First, the modified intervention improved the pelvic rotation in 7 of 10 subjects during the training and in 9 of 10 subjects after the training. That is, the modified method can provide greater improvement in pelvic rotation compared with the original method (see Table 5). Second, the modified method also improved the gait symmetry PR Amp in 7 of 10 subjects during the training and in 9 of 10 subjects after the training. Compared with the data shown in Table 4, the modified method We implemented the modified intervention method with the movable NDT trainer and repeated the experiments. In this paper, we increased the maximum intervention force F max by 50% when the pelvic rotation Amp PR was less than a threshold of 12 • . The analysis results are shown in Table 6. First, the modified intervention improved the pelvic rotation in 7 of 10 subjects during the training and in 9 of 10 subjects after the training. That is, the modified method can provide greater improvement in pelvic rotation compared with the original method (see Table 5). Second, the modified method also improved the gait symmetry Amp PR in 7 of 10 subjects during the training and in 9 of 10 subjects after the training. Compared with the data shown in Table 4, the modified method increased pelvic rotation without sacrificing the improvement in gait symmetry. That is, the modified method can simultaneously improve the subject's pelvic rotation and gait symmetry. However, factors still might limit the improvement in gait symmetry or pelvis rotation. One is that healthy participants still have normal muscle strength to exert a force against external load, so they display a less significant pelvis rotation. By contrast, the paretic side of a stroke patient is relatively weak and less resistant. Another possibility is that the healthy individual's restricted leg can exert more force when extra weight is applied. Therefore, their gait pattern may not be as asymmetric as that of stroke patients before intervention and no improvement may be evident. Therefore, we applied the modified NDT intervention in clinical trials on stroke patients.

Clinical NDT Rehabilitation with Stroke Patients
We recruited 10 stroke patients to participate in the experiments. The following restrictions were set on the selection of subjects: (i) the Mini-Mental State Examination (MMSE) score [33] was higher than 24 and the subject could cooperate with orders; (ii) the Brunnstrom Stage (BS) [34] on the paretic lower extremity was stage 3 to 4; (iii) the Functional Ambulation Category (FAC) [35] was stage 3 to 4; (iv) subjects could walk 10 m indoors with or without aid devices; and (v) subjects could stand up on their own using a handrail and aids. The patients' data are provided in Table 7. All subjects signed informed consent forms approved by the Human Subject Research Ethics Committee of the Institutional Review Board (IRB number: (870)110-16, Cheng-Hsin General Hospital, Taipei, Taiwan, ClinicalTrials.gov Identifier: NCT04968418). We attached three IMUs onto each subject's legs and waist and conducted clinical experiments in the hospital, as shown in Figure 8. Each subject underwent the tests by the A − B − A procedures, as demonstrated in Appendix D. The subjects walked forth and back with the trainer on a straight line of about 11 m. At stage A (before treatment), the subjects walked three times (about 66 m) with the motors off. At stage B (during treatment), the trainer's motors were switched on, and the subjects walked six times (about 132 m). Finally, at stage A (after treatment), the subject walked three times (about 66 m) on their own with the motors off. No break was given between the A − B − A procedures, but the subjects were free to rest at any time during the experiments. this device is not customized for patients with different physical characteristics or ambulation functions. Due to these technical limitations, a future study will optimize the device by adding vertical adjustability and providing fasteners for the participants' hands on the handrails to decrease asymmetry during the intervention.
Overall, based on the clinical experimental results, the movable NDT trainer employing the RNN gait detection model and the modified NDT intervention was deemed to help improve stroke patients' rehabilitation effects. The experimental results are shown in Table 8. The gait symmetry Asym SP was improved in 8 of the 10 patients during the training and in 9 of the 10 patients after the training. The average percentage improvements (imp%) were 13.04% and 22.01% during and after the training, respectively. The pelvic rotation Amp PR was improved in 8 of the 10 patients both during and after the training. The average percentage improvements (imp%) were 24.46% and 8.19% during and after the training, respectively. The trainer helped improve the rehabilitation effects in stroke patients in general. However, several factors may have contributed to the lack of improvement during this intervention. One was that patients with poor hand function of the hemiparetic upper limb were able to hold the handrails only with the unaffected hand. Thus, body sway during walking was common and could have limited the effect of pelvis rotation. Second, spasticity of the lower limbs causes an abnormal synergy pattern of movement, including knee extension and ankle plantarflexion and eversion, which may interfere with the coordination of pelvis rotation. Third, in this study, the patients' heights varied. Therefore, not all NDT interventions could precisely induce pelvic rotation since the cuing force would be a projection of the applied force. For example, taller patients may have experienced downward plus forward force rather than forward force alone to induce pelvic rotation due to their higher pelvic position. Last, the current trainer's induction force is only 100% or 150%. Therefore, this device is not customized for patients with different physical characteristics or ambulation functions. Due to these technical limitations, a future study will optimize the device by adding vertical adjustability and providing fasteners for the participants' hands on the handrails to decrease asymmetry during the intervention.  Overall, based on the clinical experimental results, the movable NDT trainer employing the RNN gait detection model and the modified NDT intervention was deemed to help improve stroke patients' rehabilitation effects.

Conclusions
This paper demonstrated the results of clinical stroke rehabilitation using a movable trainer employed during NDT intervention. The trainer consisted of a gait detection system and a motor control system. We implemented an RNN model in the gait detection system and a modified NDT intervention in the motor control system. The RNN model can recognize the HS events in real time to activate the NDT intervention at critical moments. The users can feel walking and intentionally drive their body to regain gait control by motor training. The aim of using the modified NDT intervention method was to simultaneously improve the user's gait symmetry and pelvic rotation. We recruited ten healthy subjects to verify the effectiveness of the trainer. The results showed that the trainer could simultaneously improve the subjects' gait symmetry and pelvic rotation. The findings from 10 stroke patients invited to participate in the experiments showed that gait symmetry improved in 80% of the patients during the training and 90% after the training. The pelvic rotation was improved in 80% both during and after the training. Based on these results, we conclude that the NDT trainer can potentially help stroke patients' rehabilitation. Some patients did not show improvements, possibly due to difficulty in holding handrails with the paretic hand or variations in the participants' heights that affected accurate pelvic rotation force and limited induction force options (we only included 100% and 150%). Therefore, in future studies, we plan to fasten the participants' hands onto the handrails for the participants' hands to decrease asymmetry during the intervention. We will also modify the trainer design, for example, by applying a suitable mechanism to automatically adjust the intervention positions for patients with different heights and body weights or by adding motor wheels to reduce the burden of pushing the trainer. remained after the treatment (stage A). Therefore, we analyzed the relationship between the therapists' interventions and the subjects' pelvic rotations in the following three scenarios: (1) the applied forces when the pelvic rotation was better; (2) the pelvic rotation when the applied forces were larger; and (3) the influences of larger forces on the asymmetry of the swing phases. (Figures: 20% forces and 20% pelvic rotation). (1) The applied forces when the pelvic rotation was better: we analyzed the applied forces when the pelvic rotation was better. For example, Figure A2 illustrates the intervention forces when the pelvic rotation Amp PR was the largest (20%). We noted that: (i) the average pelvic rotation is 22.98 • , where the average applied force was F max = 2.79 lb; (ii) for the largest Amp PR (20%), the average pelvic rotation was 28.24 • and the average applied force was F max = 3.07 lb.
That is, the therapists' intervention forces were greater when the pelvic rotation was larger. remained after the treatment (stage A ). Therefore, we analyzed the relationship between the therapists' interventions and the subjects' pelvic rotations in the following three scenarios: (1) the applied forces when the pelvic rotation was better; (2) the pelvic rotation when the applied forces were larger; and (3) the influences of larger forces on the asymmetry of the swing phases. (Figures: 20% forces and 20% pelvic rotation) (1) The applied forces when the pelvic rotation was better: we analyzed the applied forces when the pelvic rotation was better. For example, Figure A2 illustrates the intervention forces when the pelvic rotation (2) The pelvic rotation when the applied forces were larger: we analyzed the impacts of the magnitudes of applied forces on pelvic rotation, as follows: (i) the average applied force was (ii) when the applied forces were the largest (20%), the average applied force was (2) The pelvic rotation when the applied forces were larger: we analyzed the impacts of the magnitudes of applied forces on pelvic rotation, as follows: (i) the average applied force was F max = 2.79 lb, where the average pelvic rotation was 22.98 • ; (ii) when the applied forces were the largest (20%), the average applied force was F max = 3.8 lb and the average pelvic rotation was 23.81 • .
That is, the pelvic rotation was larger when the intervention forces were larger.
(3) The influences of larger forces on the asymmetry of the swing phases: we analyzed the influences of the magnitudes of the applied forces on the gait symmetry Asym SP .
The results shown in Table A2 indicate that the magnitudes of the applied forces had no significant influence on the gait symmetry index Asym SP . That is, the modified intervention method had no significant influence on the gait symmetry. From the above analyses, changing the magnitudes of applied forces can improve the pelvic rotation Amp PR without influencing the gait symmetry Asym SP . Therefore, we propose the modified intervention method as follows: increasing the intervention forces F max when the pelvic rotation Amp PR is less than a threshold of, as illustrated in Figure 7