Abstract
People with lower-limb hemiparesis have impaired function on one side of the body that affects their walking ability. Wearable robotic assistance has been investigated to treat hemiparetic gait by applying assistance to the paretic limb. In this exploratory case series, we sought to compare the effects of bilateral vs. paretic-limb-only ankle exoskeleton assistance on walking performance in a case series of three heterogeneous presentations of lower-limb hemiparesis. A secondary goal was to validate the use of a real-time ankle-moment-adaptive exoskeleton control system for effectively assisting hemiparetic gait; the ankle moment controller accuracy ranged from 72 – 90% across all conditions and participants. Compared to walking without the device, both paretic-limb-only and bilateral assistance resulted in greater average total ankle power (up to 72%), improved treadmill walking efficiency (up to 28%), and increased over-ground walking distance (up to 41%). All participants achieved a more symmetrical, efficient gait pattern with bilateral assistance, indicating that assisting both limbs may be more beneficial than assisting only the paretic side in people with hemiparetic gait. The results of this case series are intended to inform future clinical studies and exoskeleton designs in a wide range of patient populations.
Keywords: Adaptive Control, Prosthetics and Exoskeletons Rehabilitation Robotics
I. Introduction
Hemiparesis is a condition caused by insult to the brain or spinal cord that leads to impairment on one side of the body [1], [2]. As a result, patients with hemiparesis often exhibit unilateral muscle weakness, stiffness, and poor motor control that causes asymmetrical and inefficient walking patterns [3], [4]. Increased energy cost of walking can limit engagement in the community and negatively impact quality of life [5]. Wearable robotic systems have emerged as promising tools to improve walking efficiency and mobility for individuals with hemiparesis from stroke, spinal cord injury (SCI), or rare conditions like Guillain-Barré (GB) syndrome [6], [7].
The ankle joint provides 80% of positive “push-off” power in unimpaired walking [8]. To manage gait abnormality, ankle orthoses and assistive devices are frequently prescribed to patients with hemiparesis [9], [10]. For example, ankle-foot-orthoses (AFOs) can reduce drop foot in stroke survivors and people with cerebral palsy [11], [12]. However, most AFOs also limit ankle plantar-flexion, which reduces ankle push-off and may lead to long-term weakness and stiffness [13], [14]. In contrast, powered ankle exoskeletons can provide assistance that delivers positive joint power during push-off without restricting plantar-flexion or dorsiflexion range of motion [15]–[17].
Ankle exoskeletons have been found to reduce the metabolic cost of walking in unimpaired individuals and improve gait mechanics and energetics for individuals with neuromotor disabilities [15], [16], [18]–[20]. To date, studies have focused on the effects of either unilateral or bilateral assistance, with one exception of a unilateral vs. bilateral ankle assistance comparison completed in unimpaired individuals that found greater energy reduction when assistance was evenly distributed across both legs versus assisting only one leg [21]. Surprisingly, we are not aware of any studies that have made a comparison between unilateral vs. bilateral assistance in adults with hemiparesis, with existing studies reporting the results of assisting the paretic lower-limb alone [15], [16], [19]. In theory, the potential benefits of providing bilateral vs. unilateral assistance include greater improvements in energy efficiency and gait symmetry, for which the latter remains an ongoing challenge in the use of unilateral ankle devices [16], [19].
Our long-term objectives are to design effective powered ankle assistive devices for anyone with walking impairment from hemiparetic ankle dysfunction. As an initial foray towards this objective, the first goal of this exploratory case series was to validate the safety and efficacy of a real-time ankle-moment-adaptive exoskeleton control system for assisting hemiparetic gait, and demonstrate effectiveness across purposefully diverse presentations of lower-limb hemiparesis from stroke, Guillain-Barré (GB) syndrome, and spinal cord injury (SCI). For the first time in these patient populations, this study tested the premise that torque provided proportional to the biological moment can be effective for improving treadmill and over-ground gait. Our second goal was to conduct the first exploration of whether bilateral vs. paretic-limb-only adaptive ankle exoskeleton assistance can be more effective at improving walking performance, efficiency, and ankle function in the same purposefully diverse cohort. We expected that bilateral assistance would reduce steady-state energy cost of walking, increase 6-minute-walk-test distance, and improve gait symmetry more than paretic-limb-only assistance. We purposely sought to conduct comprehensive biomechanical and clinical evaluations in a small but diverse cohort of individuals with hemiparetic gait to lay the groundwork for future, population-specific intervention studies, and inform exoskeleton designs and clinical trials.
II. Methods
A. Ankle Exoskeleton
An untethered, lightweight ankle exoskeleton, weighing 2.6 kg with a 2Ah Li-ion battery, was used in this exploratory case series. The mechanical and electrical design detail of the device can be found in our prior work [22]. Briefly, plantar- and dorsi-flexor ankle assistance was provided by brushless DC motors (Maxon), located in a waist assembly, via Bowden cable transmission. The waist assembly also held a custom PCB with motor drivers, a microcontroller, signal processing components, and a Bluetooth transceiver. The ankle assembly included a carbon fiber footplate with an embedded pressure sensor, a shank cuff, an ankle pulley assembly, and a custom torque transducer (Fig. 1A). The custom torque transducer was made of machined 7075 aluminum and instrumented with strain gauges to measure the bending moment generated between the pulley and footplate. The strain gauge configuration negated out-of-plane bending and twisting loads, isolating the sagittal-plane torque applied to the user’s ankle joint. The Wheatstone bridge voltages were measured, summed, and amplified to estimate torque based on a validated model [22]. Carbon fiber footplates were attached or detached, as needed, for testing unilateral vs. bilateral assistance.
Figure 1.

A) Pictures of the ankle exoskeleton and components. B) Schematic of the real-time ankle-moment-adaptive control system.
B. Adaptive Control Strategy
We implemented a real-time exoskeleton control strategy that had been previously validated to provide assistance proportional to the biological ankle joint moment (estimation model accuracy of 90% in unimpaired level walking) [23]. Custom embedded forefoot pressure sensors (A502, Tekscan, South Boston, MA)) were used to estimate real-time biological ankle moment of the user and to identify the stance and swing phase of a gait cycle. During stance phase, the device provided adaptive plantar-flexor torque proportional to the real-time estimated biological ankle moment, which was unique for each person. The control signal adapted instantaneously to changes in each user’s walking pattern and walking speed because the ankle moment was estimated in real-time. To maximize the accuracy of biological ankle moment estimation, we administrated a calibration immediately after the device began delivering torque. In this way, the influence of device actuation on the user’s interaction with the force sensor was minimized. During swing phase, we provided dorsiflexor assistance as needed to address foot drop (0.03 – 0.11 Nm/kg for our cohort). The magnitude of dorsiflexor assistance was determined by sequentially increasing and decreasing the magnitude until two criteria were met: 1) the research team observed sufficient toe-clearance (i.e., the absence of any toe drag) and 2) the participant felt safe and comfortable to walk with the level of assistance. Torque sensors mounted to the ankle assembly provided feedback to a low-level PID motor controller to track the desired torque profile (Fig. 1B).
C. Participants and Experimental Protocol
The study was approved by the Institutional Review Board of Northern Arizona University (NAU) under protocol #986744-27. Three participants with primarily unilateral gait deficits due to hemiparesis caused by stroke (n = 1, impairment level: B), GB syndrome (n = 1, disability scale: 2), and SCI (n = 1, American Spinal Injury Association (ASIA) classification: Grade C) were recruited from the neurological therapy clinic within the physical therapy department at NAU (Table 1). Inclusion criteria included the diagnosis of any neurological disease or injury that primarily affected one side of the lower limbs; the ability to walk on a treadmill and over-ground with or without a walking aid for at least 6 minutes; at least 20° of passive ankle plantar-flexion range of motion; no knee extension or ankle dorsiflexion contractures greater than 15°; and no orthopedic surgery completed in the prior 6-month.
Table I.
Participant Information
| Diagnosis | Age (Years) | Sex | Mass (kg) | Height (m) | Paretic Side | Years Since Injury (Years) | Walking Speed (m/s) | Paretic Step Length (m) | Non-paretic Step Length (m) | ||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Baseline | Uni | Bi | Baseline | Uni | Bi | ||||||||
| Stroke | 43 | Male | 86.2 | 1.71 | Right | 8 | 0.35 | 0.42 | 0.38 | 0.36 | 0.37 | 0.36 | 0.38 |
| GB | 65 | Male | 93.5 | 1.73 | Left | 5 | 0.80 | 0.59 | 0.59 | 0.59 | 0.55 | 0.56 | 0.58 |
| SCI | 33 | Male | 68.0 | 1.83 | Right | 1.3 | 0.55 | 0.44 | 0.47 | 0.46 | 0.46 | 0.46 | 0.47 |
GB: Guillain-Barré syndrome, SCI : spinal cord injury; Uni : paretic-limb-only assistance; Bi : bilateral assistance
Following the consent process, we determined each participant’s preferred treadmill walking speeds by sequentially increasing and decreasing belt velocity until the participant indicated their preference for comfortably walking at that speed for 6 minutes. Treadmill and over-ground walking sessions were completed on separate days. During each session, participants started by walking with paretic-limb-only and bilateral assistance for 3 minutes each to acclimate to the device and each condition. This was followed by a >20-minute rest before formal walking comparisons. During formal data collection, participants completed three 6-minute walking conditions in a randomized order: Baseline – walking wearing shoes without the device, Paretic-limb-only – walking with the exoskeleton with detached footplate on the non-paretic side and with assistance on the paretic side, and Bilateral – walking with the exoskeleton as it assisted both paretic and non-paretic sides. Participants took 15-minute rest between conditions.
During treadmill walking, we collected kinematic data using ten infrared motion capture cameras (120Hz; Vicon Motion Systems, Oxford, UK) that recorded the trajectory of markers placed on the torso, pelvis, and lower-extremity [24]. We collected kinetic data from an instrumented treadmill (960 Hz; Bertec, Columbus, OH). Motion and force data were collected for 20 seconds starting at the third minute of each 6-minute trial and synchronized with exoskeleton data (100 Hz). Additionally, we used a portable metabolic system (K5, Cosmed, Italy) to collect O2 and CO2 volume data throughout the 6-minute trials. Before the start of each condition, we asked participants to stand without moving or talking for 5 minutes while we collected standing baseline spirometry data.
At the start of the over-ground session, we instructed participants on standard 6-minute-walk-test guidelines [25]. Next, participants completed 6-minute-walk-test trials along a 25-m hallway under the three conditions (randomized order) while we measured the distance traveled using a distance measuring wheel (ML1212, Komelon, Waukesha, WI) and recorded heart rate using a heart rate monitor (HRM-Dual Heart Rate Monitor, Garmin, Olathe, KS). Using direct questions, we asked each participant their exoskeleton condition preference immediately after they completed the treadmill protocol and again after the over-ground protocol.
D. Data Analysis
We identified gait events (heel strike and toe-off) in Vicon Nexus and derived joint kinematics and kinetics in OpenSim 3.3 [26]. We first scaled a generic musculoskeletal model [24] for each participant, and then computed ankle angles and moments using the inverse kinematics and inverse dynamics analyses, respectively. Ankle power (W) was calculated as the product of the ankle moment (Nm) and the respective ankle angular velocity (rad/s). We calculated stance-phase average positive ankle power by integrating the positive area of the ankle power curve and dividing by stance time. To evaluate gait symmetry, we calculated the absolute step length difference between paretic and non-paretic limbs. At least 7, 12, and 10 steps were analyzed to calculate gait symmetry for the participants with stroke, GB, SCI, respectively. We removed crossover steps for ankle moment and power calculations. Based on the number of available qualified steps for each person, at least 7, 7, and 8 steps were analyzed for the participants with stroke, GB, SCI, respectively.
Metabolic data were analyzed for the last 3 minutes of each treadmill trial and during standing baseline [27]. Metabolic power was calculated from flow rates using Brockway’s standard equation [28]. We subtracted the standing metabolic power from the average metabolic power of each condition [29] and then divided it by body mass to obtain net metabolic power. The Total Heart Beat Index was calculated by dividing the total number of heart beats during the over-ground 6-minute-walk-test by the total distance traveled in that period [30].
To evaluate the accuracy of the adaptive joint-moment controller, we computed the average stance-phase root mean square error (RMSE) between the desired torque profile and the biological ankle moment. To evaluate torque tracking, we computed the average stance-phase RMSE between the desired and measured torque profiles. Group-level results were reported as mean ± standard deviation (SD). We used linear regression to assess the relationship between change in energy cost and walking speed.
III. Results
A. Controller Performance
There were no adverse events or falls during walking with the adaptive controller. For the paretic side, the accuracy (1 - RMSE) of prescribed exoskeleton plantar-flexor assistance relative to the biological ankle moment ranged from 72.1 – 89.6% during walking with bilateral assistance and from 81.6 – 89.8% during walking with paretic-limb-only assistance (Fig. 2); the average torque tracking accuracy ranged from 69.8 – 93.3% while walking with bilateral assistance and from 89.3 – 93.4% with paretic-limb-only assistance.
Figure 2.

Top: profiles of the stance-phase biological ankle moment, desired exoskeleton torque, and measured exoskeleton torque for the paretic side during walking with paretic-limb-only ankle assistance for each participant. Root mean square error (RMSE) was reported between biological ankle moment profile and desired exoskeleton torque profile (RMSE1) and between desired and measured exoskeleton torque profiles (RMSE2). Bottom: profiles of the paretic ankle angle across a gait cycle during baseline, paretic-limb-only ankle assistance, and bilateral ankle assistance walking conditions for each participant.
B. Treadmill Walking Mechanics and Efficiency
Compared to baseline (no device), the total peak paretic-limb ankle moment increased by 19.1 – 27.9% with paretic-limb-only assistance and by 13.7 – 23.8% with bilateral assistance; the average positive ankle power increased by 31.7 – 108.2% with paretic-limb-only assistance and 35.3 – 115.4% with bilateral assistance on the paretic side. Improvement in ankle power between paretic-limb-only and bilateral assistance was variable across participants (Fig. 3).
Figure 3.

Ankle moment and power across the gait cycle and peak ankle moment and average positive ankle power of the paretic limb during walking without the device (baseline, gray), with paretic-limb-only ankle assistance (unilateral, green), and with bilateral ankle assistance (bilateral, red) for each participant. GB: Guillain-Barré syndrome; SCI: spinal cord injury. Error bars indicate standard deviation (SD); shading depicts mean ± SD.
Bilateral assistance was equally or more beneficial than paretic-limb-only assistance in reducing the metabolic cost of walking for all participants (Fig. 4). Compared to baseline (no device), metabolic power was reduced by −0.1 – 27.6% during the paretic-limb-only assistance condition and 12.7 – 27.6% during the bilateral assistance condition. There was a relationship between treadmill walking speed and metabolic reduction: participants with slower treadmill walking speeds had greater efficiency improvements from both paretic-limb-only (R2 = 0.99, p = 0.065) and bilateral (R2 = 0.84, p = 0.262) ankle exoskeleton assistance (Fig. 5).
Figure 4.

Net metabolic power and step length difference between the paretic and non-paretic limbs from the treadmill trials, and walking distance and total heart beat index from the 6-minute-walk-tests during walking without the device (baseline), with paretic ankle assistance (paretic-limb-only), and with bilateral ankle assistance (bilateral). GB: Guillain-Barré syndrome; SCI: spinal cord injury.
Figure 5.

Relationship between treadmill walking speed and the percent reduction in metabolic power in assistance conditions relative to baseline. GB: Guillain-Barré syndrome; SCI: spinal cord injury.
Paretic-limb-only assistance improved step-length symmetry by 7.9 – 63.4%, and bilateral assistance improved symmetry by 24.1 – 66.3%, compared to baseline. All participants received benefits from bilateral assistance, which resulted in 8 – 44.2% improvement in gait symmetry compared to paretic-limb-only assistance; ankle assistance decreased paretic limb step length in Stroke, increased non-paretic limb step length in GB, and increased bilateral step length in SCI.
For treadmill walking, the participant with stroke did not have a preference for paretic-limb-only or bilateral assistance, the participant with GB preferred receiving assistance on only the paretic side over both sides, and the participant with SCI preferred receiving assistance on both sides over only the paretic side (Table II).
Table II.
Participant Preference
| Diagnosis | Treadmill | Over-Ground |
|---|---|---|
| Stroke | Same | Bilateral |
| Guillain-Barré Syndrome | Paretic-limb-only | Same |
| Spinal Cord Injury | Bilateral | Same |
C. Over-ground Walking Performance
Over-ground 6-minute-walk-test distance increased by 1.2 – 24.8% during the paretic-limb-only assistance condition and 1.9 – 40.6% during the bilateral assistance condition compared to baseline. Bilateral assistance nearly doubled the improvement in 6-minute-walk test distance for the participant with hemiparesis from stroke; distances were within 3% across paretic-limb-only vs. bilateral assistance conditions for the other participants. The total heart beat index decreased by 1.2 – 27.4% with paretic-limb-only ankle assistance and by 3.8 – 36.4% with bilateral assistance compared to baseline (Fig. 5).
For over-ground walking, the participant with stroke preferred receiving assistance on both sides over only the paretic side, and the other two participants did not show a preference (Table II).
IV. Discussion
The two main goals of this exploratory study were to evaluate the effectiveness of a real-time ankle-moment-adaptive exoskeleton control system across diverse lower-limb hemiparetic walking impairments and compare untethered bilateral vs. paretic-limb-only ankle assistance for improving treadmill and over-ground walking performance in individuals with hemiparesis. We achieved our controller-validation goal, as the adaptive system proved safe for both treadmill and over-ground walking trials and contributed to improved total ankle function, reduced energy cost, increased walking distance, and decreased gait asymmetry compared to walking without the device. Exoskeleton controller accuracy ranged from 72 – 90% and torque tracking accuracy ranged from 70 – 93% for paretic-limb assistance. Both controller accuracy (ankle moment estimation) and torque tracking were slightly more accurate when assisting only the paretic limb compared to assisting both limbs. The small increase in torque tracking error for the bilateral configuration was potentially caused by the current limit (5 A) of the battery used in this study, as there may have been periods during the gait cycle when it was unable to sufficiently source current for both motors. In fulfillment of our second goal, we found that bilateral assistance improved treadmill steady-state walking efficiency and symmetry more than paretic-limb-only assistance, while improvement in over-ground walking distance was mixed; these findings partially supported our a priori hypothesis. Both paretic-limb-only and bilateral assistance increased total (biological contribution + device contribution) ankle function, while paretic-limb-only assistance resulted in a slightly greater paretic-limb peak total ankle moment compared to bilateral assistance.
To the best of our knowledge, this is the first study to compare unilateral vs. bilateral ankle exoskeleton assistance among people with lower-limb hemiparesis. Our findings indicate that bilateral assistance can result in a greater reduction in metabolic cost during steady-state treadmill walking compared to paretic-limb-only assistance. The average group-level difference between bilateral and paretic-limb-only conditions (5.5% more reduction in bilateral vs. paretic-limb-only) was similar to what was reported in unimpaired individuals (5% more reduction in bilateral vs. unilateral) [21]. As expected, bilateral assistance resulted in more energy reduction than paretic-only-assistance because users received more assistance from the device overall. In calculating the metabolic reduction normalized by the total amount of assistance, we found that paretic limb assistance was slightly more efficient (~3.6%) at improving energy cost compared to bilateral assistance. Bilateral assistance was slightly better than unilateral assistance in improving other metrics of walking performance. All participants achieved greater gait symmetry compared to baseline on the treadmill (8 – 44%) and two out of three participants walked longer distance over-ground (1 – 13%) with bilateral vs. paretic-limb-only assistance. Each individual’s gait pattern and mobility level likely contributed to the various range of improvement between participants.
To summarize the walking performance results for this case series: the participant with hemiparetic gait impairment from stroke received more benefit from bilateral than paretic-limb-only assistance in terms of improving over-ground walking performance and efficiency, and treadmill walking symmetry; the participant with gait hemiparetic impairment from GB walked more efficiently and symmetrically on the treadmill with bilateral vs. paretic-limb-only assistance; the participant with hemiparetic gait from SCI had more symmetrical gait during treadmill walking and received similar benefits for all other performance measurements (≤ 3% differences) between bilateral and paretic-limb-only conditions. Preference between bilateral or paretic-limb-only assistance configurations was mixed across participants and walking conditions (Table 2).
Despite the differences between unilateral and bilateral assistance, receiving either paretic-limb-only or bilateral assistance from ankle assistance produced clinically-relevant benefits, especially among participants with poorer mobility (stroke and SCI): ankle assistance increased 6-minute-walk-test by 41 m for the patient with stroke and by 52 m for the patient with SCI; for reference, the Minimal Clinically Important Difference, which reflects a meaningful improvement in disability, ranges from 14.0 to 30.5 m for 6-minute-walk-test across multiple patient groups [31]. The near-immediate improvement in the over-ground 6-minute-walk-test performance from receiving ankle assistance outperformed the outcome (15.5 m increase in 6-minute-walk-test distance) following 6-week gait training with a commercial ankle-knee-hip exoskeleton in people with SCI [32]. During treadmill walking, participants had an average metabolic reduction of 13% with paretic-limb-only assistance and 19% with bilateral assistance; the total paretic-limb plantar-flexion moment increased by 24% and 20% with paretic-limb-only and bilateral assistance, respectively. For comparison, another unilateral ankle assistive device increased paretic plantar-flexion moment by 16% but did not reduce metabolic cost in five participants with stroke [16].
The results of this study were similar to prior findings in children with hemiplegic and diplegic cerebral palsy (CP). As a comparison, children with CP had a 19% improvement in metabolic cost of transport, 44% increase in total ankle power, and 6% faster over-ground walking speed while walking with bilateral ankle exoskeleton assistance compared to without the device [33], [34]. Our previous research in cerebral palsy indicated that baseline walking speed was a simple predictor of the performance benefit from bilateral ankle exoskeleton assistance, accounting for 94% of the variance in the energy reduction during assisted walking [35]. The present study found a similar finding that participants with slower walking speeds had greater efficiency improvements from both paretic-limb-only and bilateral ankle exoskeleton assistance (Fig. 5). A slower self-selected speed is associated with more neuromuscular impairment [36]; our findings suggest that participants with greater impairment may have benefitted more from ankle assistance compared to those with less impairment. Our present and prior results also indicate that ankle assistance can improve not only speed but also the efficiency of over-ground walking, particularly in more impaired individuals (e.g., our stroke and SCI participants; Fig. 4). This corroborates a finding from a study that faster and more symmetric walking is more energetically advantageous in people with stroke [37].
With this exploratory case series, we sought to inform future study design and lay the foundation for larger clinical trials by demonstrating that bilateral vs. paretic-limb-only assistance is an important intervention variable to consider when treating walking disability. While the small sample size was a limitation of this study, we were still able to provide valuable insight by demonstrating that there can be both meaningful and non-meaningful differences in walking performance with bilateral vs. paretic-limb-only ankle exoskeleton assistance in individuals with hemiparetic gait. By confirming that additional benefits are possible for some individuals when assisting both the impaired and unimpaired limbs, our study suggests that it may be necessary to evaluate bilateral vs. paretic-limb-only assistance when seeking to maximize walking performance outcomes with robotic ankle exoskeletons in people with hemiparetic gait. We did not focus on non-paretic performance in the current paper. Future studies should evaluate how bilateral vs. unilateral assistance affects both paretic and non-paretic ankle function.
V. Conclusion
We validated an ankle-moment-adaptive exoskeleton controller in three participants with hemiparetic gait and demonstrated safety and efficacy of both bilateral and paretic-limb-only assistance for improving total ankle function and walking performance on a treadmill and over-ground. In our small, purposefully diverse cohort, bilateral assistance was more reliably effective than unilateral assistance in improving clinically relevant treadmill and over-ground walking performance. However, because each participant responded differently, our results suggest that clinicians should adopt personalized interventions to maximize patient outcomes. Some individuals with hemiparetic gait will likely benefit more from bilateral vs. paretic-limb-only assistance, warranting the added cost of such a device, while other individuals may see no, or only a minor, additional benefit from assisting the unimpaired limb. Our findings support future research on exploring the participant characteristics that influence whether they will benefit more from bilateral or paretic-limb-only ankle assistance.
Acknowledgment
The authors thank Greg Orekhov and Samuel Franklin Maxwell for their assistance with this study. ZFL is a co-founder with shareholder interest of a university start-up company seeking to commercialize the device used in this study. He also holds intellectual property inventorship rights.
This work was supported in part by the Northern Arizona University Foundation, the National Science Foundation under award number 2045966, and the Eunice Kennedy Shriver National Institute of Child Health & Human Development of the National Institutes of Health under award number R44HD104328. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health or National Science Foundation.
Footnotes
This paper was recommended for publication by Dr. Jee-Hwan Ryu upon evaluation of the Associate Editor and Reviewers’ comments.
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