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Gait Analysis Using a Support Vector Machine for Lumbar Spinal Stenosis

Hiroyuki Hayashi, MD; Yasumitsu Toribatake, MD; Hideki Murakami, MD; Takeshi Yoneyama, PhD; Tetsuyou Watanabe, PhD; Hiroyuki Tsuchiya, MD

Abstract

Lumbar spinal canal stenosis (LSS) is diagnosed based on physical examination and radiological documentation of lumbar spinal canal narrowing. Differential diagnosis of the level of lumbar radiculopathy is difficult in multilevel spinal stenosis. Therefore, the authors focused on gait analysis as a classification method to improve diagnostic accuracy. The goal of this study was to identify gait characteristics of L4 and L5 radiculopathy in patients with LSS and to classify L4 and L5 radiculopathy using a support vector machine (SVM). The study group comprised 13 healthy volunteers (control group), 11 patients with L4 radiculopathy (L4 group), and 22 patients with L5 radiculopathy (L5 group). Light-emitting diode markers were attached at 5 sites on the affected side, and walking motion was analyzed using video recordings and the authors' development program. Potential gait characteristics of each group were identified to use as SVM parameters. In the knee joint of the L4 group, the waveform was similar to that of normal gait, but knee extension at initial contact was slightly greater than that of the other groups. In the ankle joint of the L5 group, the one-peak waveform pattern with disappearance of the second peak was present in 10 (45.5%) of 22 cases. The total classification accuracy was 80.4% using the SVM. The highest and lowest classification accuracies were obtained in the control group (84.6%) and the L4 group (72.7%), respectively. The authors' walking motion analysis system identified several useful factors for differentiating between healthy individuals and patients with L4 and L5 radiculopathy, with a high accuracy rate. [Orthopedics. 2015; 38(11):e959–e964.]

Lumbar spinal canal stenosis (LSS) is the most common cause of lumbar spinal surgery in patients older than 65 years.1–4 Lumbar spinal canal stenosis is diagnosed based on physical examination and radiological documentation of lumbar spinal canal narrowing.5,6 The differential diagnosis of the level of lumbar radiculopathy is difficult in multilevel spinal stenosis. Therefore, the current authors focused on gait analysis as a classification method to improve diagnostic accuracy.

Several studies have reported gait analysis in patients with LSS.7–9 However, almost all studies used specialized equipment, such as a ground reaction force plate. This equipment is expensive and is only available at a few medical facilities. Furthermore, it is difficult to assess the walking motion of patients using a ground reaction force plate. The current authors aimed to use a simple examination method for motion analysis and to identify and quantify gait characteristics in patients with LSS. Using the gait characteristics identified with their method, the authors constructed a classification for differentiating between healthy individuals and patients with L4 and L5 radiculopathy using a support vector machine (SVM). This machine is a learning tool originating from modern statistical learning theory. Recently, SVM learning has been widely used for solving classification problems in the medical field.10–15

This study was performed in 2 phases. In phase 1, gait characteristics of L4 and L5 radiculopathy in LSS patients were identified. In phase 2, L4 and L5 radiculopathy was classified using an SVM.

Phase 1

Materials and Methods

This study was approved by the ethics committee of Kouseiren Takaoka Hospital. Written informed consent was obtained from all participants.

The study group comprised 13 healthy volunteers (control group) and 33 patients with neurological intermittent claudication due to LSS. The healthy volunteers (5 men and 8 women; mean age, 40.2 years [range, 22–55 years]) had no neurological or arthritic diseases causing gait disturbance. Patients with LSS were categorized into 2 groups: those with L4 radiculopathy (L4 group) and those with L5 radiculopathy (L5 group) based on the findings of physical examination, magnetic resonance imaging (MRI), computed tomography (CT), myelography, and selective nerve root block. The L4 group comprised 7 men and 4 women (mean age, 70.2 years [range, 56–80 years]), and the L5 group comprised 9 men and 13 women (mean age, 73.8 years [range, 57–86 years]).

Handmade light-emitting diode markers were attached at 5 sites (acromion, anterior superior iliac spine, fibular head, lateral malleolus of the ankle joint, and fifth metatarsal head) on the affected side (Figure 1). Furthermore, all participants underwent examination of load walk on a treadmill in a dim room. The experiment was performed with the treadmill at 0° of ramp incline. Walking speed was free (ie, each participant's preferred walking speed). The authors stopped performing measurements if a participant could not walk due to lower limb pain. If a participant did not feel pain, he or she walked for 5 minutes. Commercially available digital cameras recorded the walking motion (Figure 2). The authors performed the motion analysis for 10 seconds just before the walking stopped using their development program. The accuracy of this system depends on the resolution of the camera. The distance between the treadmill and camera was from 0.007 to 0.04 rad for the authors' set-up.

Positioning of light-emitting diode markers on the participant. The markers were attached at the following sites: acromion, anterior superior iliac spine, fibular head, lateral malleolus of the ankle joint, and fifth metatarsal head.

Figure 1:

Positioning of light-emitting diode markers on the participant. The markers were attached at the following sites: acromion, anterior superior iliac spine, fibular head, lateral malleolus of the ankle joint, and fifth metatarsal head.

Walking measurement system. Walking was assessed on a treadmill, and a digital camera recorded the motion.

Figure 2:

Walking measurement system. Walking was assessed on a treadmill, and a digital camera recorded the motion.

Joint movement was visualized as a waveform. The waveforms were compared between the 3 groups. The authors mainly focused on lower limb motion and examined the joint angle. Unlike the clinical joint angle, the authors defined each joint angle as shown in Figure 3. In addition, the authors focused on the gastrocnemius and quadriceps muscles because these were considered to be the problem areas. Individual differences in body size made direct comparison of muscle lengths illogical; therefore, a reference model based on the bone lengths of an actual human skeleton model were used. The authors based the sites of attachment of the muscles to the bones in the reference model on anatomical data.16 Using this model and these angle data, the authors calculated normalized maximum expanded muscle length (normalized maximum length), normalized maximum contracted muscle length (normalized minimum length), and normalized motion range.

Sagittal plane view. The angle of each joint is defined in the schema.

Figure 3:

Sagittal plane view. The angle of each joint is defined in the schema.

Statistical evaluation was performed using one-way analysis of variance (ANOVA). Post-hoc tests performed were indicated by ANOVA results using Tukey's test for multiple comparisons. A P value less than .05 was considered statistically significant.

Results

Eighteen participants were able to walk for 5 minutes (13, 3, and 2 participants in the control, L4, and L5 groups, respectively).

Waveform of the Knee Joint in Normal Gait. The waveform of the knee joint looks like the letter M (ie, there are 2 waves). The first wave peaks at the time of heel contact on the treadmill (Figure 4). Then, small knee flexion occurs at the transition between the loading response and mid-stance, contributing to controlled shock absorption at the knee; the local minimum knee flexion was recorded as a notch (Figure 4). After the limb advances over the stationary foot, the knee completes its extension during the terminal stance (Figure 4). The latter large wave of flexion occurs during the swing phase and assists with foot clearance (Figure 4).

The waveform of the knee joint in normal gait. Circles indicate positions at which light-emitting diode markers were attached.

Figure 4:

The waveform of the knee joint in normal gait. Circles indicate positions at which light-emitting diode markers were attached.

Waveform of the Ankle Joint in Normal Gait. The ankle joint takes on the position of maximum plantar flexion for strong kicking when the leg leaves the treadmill (Figure 5). Subsequently, the walking motion goes into the swing phase. Then, the heel makes contact with the treadmill with dorsiflexion of the ankle joint (Figure 5), and the wave of plantar flexion occurs when the foot is flat on the treadmill (Figure 5). Then, as the foot goes backward due to the treadmill motion, dorsiflexion of the ankle joint occurs (Figure 5). As a result, the waveform of the ankle joint has bimodal peaks.

The waveform of the ankle joint in normal gait. Circles indicate positions at which light-emitting diode markers were attached.

Figure 5:

The waveform of the ankle joint in normal gait. Circles indicate positions at which light-emitting diode markers were attached.

Gait Characteristics.Figure 6 shows the waveform of a representative case in each group. In the knee joint of the L4 group, the waveform was similar to that of participants with normal gait, but knee extension at initial contact was slightly greater than that of the other groups. The waveform of the ankle joint was also similar to the pattern of normal gait. In the ankle joint of the L5 group, the one-peak waveform pattern with disappearance of the second peak was observed in 10 (45.5%) of 22 cases. This was not observed in the control group and was observed in only 1 patient in the L4 group.

The waveform of representative cases in each group. Waveform of the knee joint: solid line=22-year-old man in the control group; dotted line=56-year-old man in the L4 group; perforated line=81-year-old man in the L5 group (A). Waveform of the ankle joint: solid line=48-year-old man in the control group; dotted line=56-year-old man in the L4 group; perforated line=82-year-old woman in the L5 group (B).

Figure 6:

The waveform of representative cases in each group. Waveform of the knee joint: solid line=22-year-old man in the control group; dotted line=56-year-old man in the L4 group; perforated line=81-year-old man in the L5 group (A). Waveform of the ankle joint: solid line=48-year-old man in the control group; dotted line=56-year-old man in the L4 group; perforated line=82-year-old woman in the L5 group (B).

The authors identified the following 10 potential gait characteristics of each group to use as the parameters of the SVM: amplitude of the ankle angle during the swing phase, average angle of the ankle joint during the swing phase, angle of the knee joint at initial contact in the stance phase, amplitude of the hip angle, normalized maximum length of the gastrocnemius, normalized minimum length of the gastrocnemius, normalized motion range of the gastrocnemius, normalized maximum length of the quadriceps, normalized minimum length of the quadriceps and normalized motion range of the quadriceps. Table 1 shows the results of Tukey's multiple comparison tests. Although several factors showed no significant difference between the groups, all factors were used in the SVM for classification of L4 and L5 radiculopathy in phase 2.

Potential Factors of Gait Characteristics

Table 1:

Potential Factors of Gait Characteristics

Phase 2

Materials and Methods

An SVM classifier was used for data analysis.17 The SVM is originally a binary classifier; however, given the goal of the differentiation in this data set, the authors were able to appropriately judge which group (normal, L4, or L5 group) the data belong to. Therefore, the “one-versus-the-rest” method was used. In this method, 3 binary SVM classifiers were applied, to allow classification of the normal and the others, the L4 and the others, and the L5 and the others. Finally, the group with maximum possibility was chosen. Radial basis function was chosen as the kernel function. The previous 10 factors were normalized and used as SVM parameters. Appropriate parameters were selected for each binary classifier based on the significant differences detected in the phase 1 study.

Results

Table 2 shows the classification results as a confusion matrix. The total classification accuracy was 80.4%, supporting the efficacy of the presented approach. The highest classification accuracy was obtained in the control group and the lowest in the L4 group. In the control group, 2 cases were mistaken for the L4 group. In the L4 group, 2 cases were mistaken for the L5 group and 1 case was mistaken for the control group. In the L5 group, 2 cases were mistaken for the control group and 2 cases were mistaken for the L4 group.

Results of the Classification

Table 2:

Results of the Classification

Discussion

Many studies have performed gait analysis using large ground reaction force plates. Those studies determined the gait speed, stride, pitch, sway, and rhythm. However, the authors wanted to visualize and quantify the gait characteristics in patients with LSS based on the kinematic and morphologic standpoint, focusing on lower limb motion. The optimal classification method would consist of an examination using a simple instrument; this examination could be easily performed even by nonspecialists. Therefore, the authors aimed to develop a simple examination method for walking motion analysis.

The authors' method can be used to analyze walking motion without special equipment such as a force plate and 3-dimensional motion analysis. Compared with walking on the ground, walking on a treadmill is a nonphysiologic condition. However, treadmills offer many advantages in human locomotion analysis.18 Space requirements are constrained, environmental factors can be controlled, steady-state locomotion speeds are selectable, and successive repetitive strides can be documented expeditiously. Thus, use of a treadmill could circumvent some problems inherent in overground locomotion studies. The findings of normal gait in the current study were generally consistent with the results of other overground locomotion studies and indicated the validity of the authors' method.19–21

When gait characteristics of neurogenic disease are evaluated from the kinematic and morphologic aspects, 2 mechanisms should be considered. The first mechanism is that spastic and flaccid paralysis affects the joint motion through muscles; this is an essential finding that strongly reflects the nature of the disease. Another mechanism is the secondary finding of unconsciously performed gait strategy, such as avoidance reaction for pain and compensatory reaction for paralysis. Abnormalities in gait style have been noted soon after patients began to walk,7 suggesting that patients acquire a walking style that precludes the appearance of symptoms.

In the current study, the gait characteristic of the L4 group was knee extension at initial contact. In cases with quadriceps weakness, knee hyperextension occurs to reduce the demand on a weak quadriceps at initial contact. In the current study, no patients showed changes in the manual muscle test before and after the walking test. However, in the L4 group, the authors considered that even if patients had no obvious muscle weakness, they acquired walking motion to avoid a broken knee as gait strategy. The gait characteristic of the L5 group was the one-peak waveform pattern in the ankle joint. Because the toe and heel make contact with the ground simultaneously by foot drop, the second peak caused by the time lag between the toe and heel making contact with the ground disappears, and the waveform shows a one-peak pattern. Therefore, this finding can be explained by the weakness of the tibialis anterior muscle innervated by the L5 nerve root. The authors focused on the lower limb motion and identified the 10 factors that had the potential to be gait characteristics of each group. However, there may have been more effective classification factors that were not identified.

Several studies have reported gait analysis in patients with LSS.7–9 Suda et al7 evaluated gait improvement after surgery in patients with neurogenic intermittent claudication. Papadakis et al8 compared the gait patterns of healthy people with those of patients with LSS; they also evaluated the postoperative progression of the gait pattern of patients with LSS and showed that gait variability decreased relative to the preoperative gait pattern.9 In contrast, the current study examined walking motion with regard to the gait characteristics of each level of lumbar radiculopathy and classified it among the control, L4, and L5 groups using the SVM. The SVM was first proposed by Vapnik22 and has since attracted a high degree of interest in the machine learning research community. Support vector machine methods have the feasibility and superior ability to extract higher-order statistics and have become extremely popular for classification and prediction. Children with cerebral palsy–related gait have been identified and classified via an SVM-based method.23 The total classification accuracy was greater than 80% using the SVM. The authors consider that identification of other factors for differentiating between the L4 group and the other groups may further improve the classification performance of the SVM.

The current study has some limitations, including small sample size and different participant backgrounds in each group. There are several differences in walking motion associated with sex and age, and it is necessary to match patient backgrounds in future studies.

Conclusion

The authors developed a new and simple examination method for walking motion analysis and identified several factors useful for differentiating between normal healthy people and patients with L4 and L5 radiculopathy. In addition, the derived factors were used to construct an SVM-based differentiation method, with a high accuracy rate. The authors' future work will focus on improving the classification accuracy of this diagnostic method.

References

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Potential Factors of Gait Characteristics

FactorMeanSDPa

Control–L4Control–L5L4–L5
Amplitude of ankle angle during swing phase
  Control group14.865.42
  L4 group12.944.88.520.002b.066
  L5 group9.313.02
Average angle of ankle joint during swing phase
  Control group126.338.59
  L4 group121.058.02.337.001b.129
  L5 group114.429.75
Angle of knee joint at stance phase start time
  Control group164.459.42
  L4 group169.557.23.344.938.154
  L5 group163.409.13
Amplitude of hip angle
  Control group35.376.27
  L4 group28.076.30.009b<.001b.053
  L5 group22.965.16
Normalized maximum length of gastrocnemius
  Control group1.0560.020
  L4 group1.0630.023.744.052.317
  L5 group1.0750.023
Normalized minimum length of gastrocnemius
  Control group0.9660.019
  L4 group0.9940.022.023b<.001b.012b
  L5 group1.0210.029
Normalized motion range of gastrocnemius
  Control group0.0910.016
  L4 group0.0690.026.035b<.001b.105
  L5 group0.0540.018
Normalized maximum length of quadriceps
  Control group1.3140.004
  L4 group1.3040.007.025b<.001.219
  L5 group1.2990.011
Normalized minimum length of quadriceps
  Control group1.2640.007
  L4 group1.2550.010.092.855.157
  L5 group1.2620.011
Normalized motion range of quadriceps
  Control group0.0500.006
  L4 group0.0490.006.949<.001b<.001b
  L5 group0.0370.007

Results of the Classification

Actual Class/Predicted ClassGroup, No.Accuracy

ControlL4L5
Control group (n=13)112084.6%
L4 group (n=11)18272.7%
L5 group (n=22)221881.8%
All (n=46)14122080.4%
Authors

The authors are from the Department of Orthopedic Surgery (HH, HM, HT), Graduate School of Medical Science, and the School of Mechanical Engineering (TY, TW), Kanazawa University, Kanazawa; and the Department of Orthopedic Surgery (YT), Kouseiren Takaoka Hospital, Takaoka, Japan.

The authors have no relevant financial relationships to disclose.

The authors thank Ms Sano, Mr Habe, Mr Kawagishi, and Mr Kobayashi for helping with the analysis of gait pattern data.

Correspondence should be addressed to: Hiroyuki Hayashi, MD, Department of Orthopedic Surgery, Graduate School of Medical Science, Kanazawa University, 13-1 Takara-machi, Kanazawa 920-8641, Japan ( snoopeanuts27@hotmail.com).

Received: October 02, 2014
Accepted: February 23, 2015

10.3928/01477447-20151020-02

Lumbar spinal canal stenosis (LSS) is diagnosed based on physical examination and radiological documentation of lumbar spinal canal narrowing. Differential diagnosis of the level of lumbar radiculopathy is difficult in multilevel spinal stenosis. Therefore, the authors focused on gait analysis as a classification method to improve diagnostic accuracy. The goal of this study was to identify gait characteristics of L4 and L5 radiculopathy in patients with LSS and to classify L4 and L5 radiculopathy using a support vector machine (SVM). The study group comprised 13 healthy volunteers (control group), 11 patients with L4 radiculopathy (L4 group), and 22 patients with L5 radiculopathy (L5 group). Light-emitting diode markers were attached at 5 sites on the affected side, and walking motion was analyzed using video recordings and the authors' development program. Potential gait characteristics of each group were identified to use as SVM parameters. In the knee joint of the L4 group, the waveform was similar to that of normal gait, but knee extension at initial contact was slightly greater than that of the other groups. In the ankle joint of the L5 group, the one-peak waveform pattern with disappearance of the second peak was present in 10 (45.5%) of 22 cases. The total classification accuracy was 80.4% using the SVM. The highest and lowest classification accuracies were obtained in the control group (84.6%) and the L4 group (72.7%), respectively. The authors' walking motion analysis system identified several useful factors for differentiating between healthy individuals and patients with L4 and L5 radiculopathy, with a high accuracy rate. [Orthopedics. 2015; 38(11):e959–e964.]

The authors are from the Department of Orthopedic Surgery (HH, HM, HT), Graduate School of Medical Science, and the School of Mechanical Engineering (TY, TW), Kanazawa University, Kanazawa; and the Department of Orthopedic Surgery (YT), Kouseiren Takaoka Hospital, Takaoka, Japan.

The authors have no relevant financial relationships to disclose.

The authors thank Ms Sano, Mr Habe, Mr Kawagishi, and Mr Kobayashi for helping with the analysis of gait pattern data.

Correspondence should be addressed to: Hiroyuki Hayashi, MD, Department of Orthopedic Surgery, Graduate School of Medical Science, Kanazawa University, 13-1 Takara-machi, Kanazawa 920-8641, Japan ( snoopeanuts27@hotmail.com).

Received: October 02, 2014
Accepted: February 23, 2015

Lumbar spinal canal stenosis (LSS) is diagnosed based on physical examination and radiological documentation of lumbar spinal canal narrowing. Differential diagnosis of the level of lumbar radiculopathy is difficult in multilevel spinal stenosis. Therefore, the authors focused on gait analysis as a classification method to improve diagnostic accuracy. The goal of this study was to identify gait characteristics of L4 and L5 radiculopathy in patients with LSS and to classify L4 and L5 radiculopathy using a support vector machine (SVM). The study group comprised 13 healthy volunteers (control group), 11 patients with L4 radiculopathy (L4 group), and 22 patients with L5 radiculopathy (L5 group). Light-emitting diode markers were attached at 5 sites on the affected side, and walking motion was analyzed using video recordings and the authors' development program. Potential gait characteristics of each group were identified to use as SVM parameters. In the knee joint of the L4 group, the waveform was similar to that of normal gait, but knee extension at initial contact was slightly greater than that of the other groups. In the ankle joint of the L5 group, the one-peak waveform pattern with disappearance of the second peak was present in 10 (45.5%) of 22 cases. The total classification accuracy was 80.4% using the SVM. The highest and lowest classification accuracies were obtained in the control group (84.6%) and the L4 group (72.7%), respectively. The authors' walking motion analysis system identified several useful factors for differentiating between healthy individuals and patients with L4 and L5 radiculopathy, with a high accuracy rate. [Orthopedics. 2015; 38(11):e959–e964.]

The authors are from the Department of Orthopedic Surgery (HH, HM, HT), Graduate School of Medical Science, and the School of Mechanical Engineering (TY, TW), Kanazawa University, Kanazawa; and the Department of Orthopedic Surgery (YT), Kouseiren Takaoka Hospital, Takaoka, Japan.

The authors have no relevant financial relationships to disclose.

The authors thank Ms Sano, Mr Habe, Mr Kawagishi, and Mr Kobayashi for helping with the analysis of gait pattern data.

Correspondence should be addressed to: Hiroyuki Hayashi, MD, Department of Orthopedic Surgery, Graduate School of Medical Science, Kanazawa University, 13-1 Takara-machi, Kanazawa 920-8641, Japan ( snoopeanuts27@hotmail.com).

Received: October 02, 2014
Accepted: February 23, 2015

Lumbar spinal canal stenosis (LSS) is the most common cause of lumbar spinal surgery in patients older than 65 years.1–4 Lumbar spinal canal stenosis is diagnosed based on physical examination and radiological documentation of lumbar spinal canal narrowing.5,6 The differential diagnosis of the level of lumbar radiculopathy is difficult in multilevel spinal stenosis. Therefore, the current authors focused on gait analysis as a classification method to improve diagnostic accuracy.

Several studies have reported gait analysis in patients with LSS.7–9 However, almost all studies used specialized equipment, such as a ground reaction force plate. This equipment is expensive and is only available at a few medical facilities. Furthermore, it is difficult to assess the walking motion of patients using a ground reaction force plate. The current authors aimed to use a simple examination method for motion analysis and to identify and quantify gait characteristics in patients with LSS. Using the gait characteristics identified with their method, the authors constructed a classification for differentiating between healthy individuals and patients with L4 and L5 radiculopathy using a support vector machine (SVM). This machine is a learning tool originating from modern statistical learning theory. Recently, SVM learning has been widely used for solving classification problems in the medical field.10–15

This study was performed in 2 phases. In phase 1, gait characteristics of L4 and L5 radiculopathy in LSS patients were identified. In phase 2, L4 and L5 radiculopathy was classified using an SVM.

Phase 1

Materials and Methods

This study was approved by the ethics committee of Kouseiren Takaoka Hospital. Written informed consent was obtained from all participants.

The study group comprised 13 healthy volunteers (control group) and 33 patients with neurological intermittent claudication due to LSS. The healthy volunteers (5 men and 8 women; mean age, 40.2 years [range, 22–55 years]) had no neurological or arthritic diseases causing gait disturbance. Patients with LSS were categorized into 2 groups: those with L4 radiculopathy (L4 group) and those with L5 radiculopathy (L5 group) based on the findings of physical examination, magnetic resonance imaging (MRI), computed tomography (CT), myelography, and selective nerve root block. The L4 group comprised 7 men and 4 women (mean age, 70.2 years [range, 56–80 years]), and the L5 group comprised 9 men and 13 women (mean age, 73.8 years [range, 57–86 years]).

Handmade light-emitting diode markers were attached at 5 sites (acromion, anterior superior iliac spine, fibular head, lateral malleolus of the ankle joint, and fifth metatarsal head) on the affected side (Figure 1). Furthermore, all participants underwent examination of load walk on a treadmill in a dim room. The experiment was performed with the treadmill at 0° of ramp incline. Walking speed was free (ie, each participant's preferred walking speed). The authors stopped performing measurements if a participant could not walk due to lower limb pain. If a participant did not feel pain, he or she walked for 5 minutes. Commercially available digital cameras recorded the walking motion (Figure 2). The authors performed the motion analysis for 10 seconds just before the walking stopped using their development program. The accuracy of this system depends on the resolution of the camera. The distance between the treadmill and camera was from 0.007 to 0.04 rad for the authors' set-up.

Positioning of light-emitting diode markers on the participant. The markers were attached at the following sites: acromion, anterior superior iliac spine, fibular head, lateral malleolus of the ankle joint, and fifth metatarsal head.

Figure 1:

Positioning of light-emitting diode markers on the participant. The markers were attached at the following sites: acromion, anterior superior iliac spine, fibular head, lateral malleolus of the ankle joint, and fifth metatarsal head.

Walking measurement system. Walking was assessed on a treadmill, and a digital camera recorded the motion.

Figure 2:

Walking measurement system. Walking was assessed on a treadmill, and a digital camera recorded the motion.

Joint movement was visualized as a waveform. The waveforms were compared between the 3 groups. The authors mainly focused on lower limb motion and examined the joint angle. Unlike the clinical joint angle, the authors defined each joint angle as shown in Figure 3. In addition, the authors focused on the gastrocnemius and quadriceps muscles because these were considered to be the problem areas. Individual differences in body size made direct comparison of muscle lengths illogical; therefore, a reference model based on the bone lengths of an actual human skeleton model were used. The authors based the sites of attachment of the muscles to the bones in the reference model on anatomical data.16 Using this model and these angle data, the authors calculated normalized maximum expanded muscle length (normalized maximum length), normalized maximum contracted muscle length (normalized minimum length), and normalized motion range.

Sagittal plane view. The angle of each joint is defined in the schema.

Figure 3:

Sagittal plane view. The angle of each joint is defined in the schema.

Statistical evaluation was performed using one-way analysis of variance (ANOVA). Post-hoc tests performed were indicated by ANOVA results using Tukey's test for multiple comparisons. A P value less than .05 was considered statistically significant.

Results

Eighteen participants were able to walk for 5 minutes (13, 3, and 2 participants in the control, L4, and L5 groups, respectively).

Waveform of the Knee Joint in Normal Gait. The waveform of the knee joint looks like the letter M (ie, there are 2 waves). The first wave peaks at the time of heel contact on the treadmill (Figure 4). Then, small knee flexion occurs at the transition between the loading response and mid-stance, contributing to controlled shock absorption at the knee; the local minimum knee flexion was recorded as a notch (Figure 4). After the limb advances over the stationary foot, the knee completes its extension during the terminal stance (Figure 4). The latter large wave of flexion occurs during the swing phase and assists with foot clearance (Figure 4).

The waveform of the knee joint in normal gait. Circles indicate positions at which light-emitting diode markers were attached.

Figure 4:

The waveform of the knee joint in normal gait. Circles indicate positions at which light-emitting diode markers were attached.

Waveform of the Ankle Joint in Normal Gait. The ankle joint takes on the position of maximum plantar flexion for strong kicking when the leg leaves the treadmill (Figure 5). Subsequently, the walking motion goes into the swing phase. Then, the heel makes contact with the treadmill with dorsiflexion of the ankle joint (Figure 5), and the wave of plantar flexion occurs when the foot is flat on the treadmill (Figure 5). Then, as the foot goes backward due to the treadmill motion, dorsiflexion of the ankle joint occurs (Figure 5). As a result, the waveform of the ankle joint has bimodal peaks.

The waveform of the ankle joint in normal gait. Circles indicate positions at which light-emitting diode markers were attached.

Figure 5:

The waveform of the ankle joint in normal gait. Circles indicate positions at which light-emitting diode markers were attached.

Gait Characteristics.Figure 6 shows the waveform of a representative case in each group. In the knee joint of the L4 group, the waveform was similar to that of participants with normal gait, but knee extension at initial contact was slightly greater than that of the other groups. The waveform of the ankle joint was also similar to the pattern of normal gait. In the ankle joint of the L5 group, the one-peak waveform pattern with disappearance of the second peak was observed in 10 (45.5%) of 22 cases. This was not observed in the control group and was observed in only 1 patient in the L4 group.

The waveform of representative cases in each group. Waveform of the knee joint: solid line=22-year-old man in the control group; dotted line=56-year-old man in the L4 group; perforated line=81-year-old man in the L5 group (A). Waveform of the ankle joint: solid line=48-year-old man in the control group; dotted line=56-year-old man in the L4 group; perforated line=82-year-old woman in the L5 group (B).

Figure 6:

The waveform of representative cases in each group. Waveform of the knee joint: solid line=22-year-old man in the control group; dotted line=56-year-old man in the L4 group; perforated line=81-year-old man in the L5 group (A). Waveform of the ankle joint: solid line=48-year-old man in the control group; dotted line=56-year-old man in the L4 group; perforated line=82-year-old woman in the L5 group (B).

The authors identified the following 10 potential gait characteristics of each group to use as the parameters of the SVM: amplitude of the ankle angle during the swing phase, average angle of the ankle joint during the swing phase, angle of the knee joint at initial contact in the stance phase, amplitude of the hip angle, normalized maximum length of the gastrocnemius, normalized minimum length of the gastrocnemius, normalized motion range of the gastrocnemius, normalized maximum length of the quadriceps, normalized minimum length of the quadriceps and normalized motion range of the quadriceps. Table 1 shows the results of Tukey's multiple comparison tests. Although several factors showed no significant difference between the groups, all factors were used in the SVM for classification of L4 and L5 radiculopathy in phase 2.

Potential Factors of Gait Characteristics

Table 1:

Potential Factors of Gait Characteristics

Phase 2

Materials and Methods

An SVM classifier was used for data analysis.17 The SVM is originally a binary classifier; however, given the goal of the differentiation in this data set, the authors were able to appropriately judge which group (normal, L4, or L5 group) the data belong to. Therefore, the “one-versus-the-rest” method was used. In this method, 3 binary SVM classifiers were applied, to allow classification of the normal and the others, the L4 and the others, and the L5 and the others. Finally, the group with maximum possibility was chosen. Radial basis function was chosen as the kernel function. The previous 10 factors were normalized and used as SVM parameters. Appropriate parameters were selected for each binary classifier based on the significant differences detected in the phase 1 study.

Results

Table 2 shows the classification results as a confusion matrix. The total classification accuracy was 80.4%, supporting the efficacy of the presented approach. The highest classification accuracy was obtained in the control group and the lowest in the L4 group. In the control group, 2 cases were mistaken for the L4 group. In the L4 group, 2 cases were mistaken for the L5 group and 1 case was mistaken for the control group. In the L5 group, 2 cases were mistaken for the control group and 2 cases were mistaken for the L4 group.

Results of the Classification

Table 2:

Results of the Classification

Discussion

Many studies have performed gait analysis using large ground reaction force plates. Those studies determined the gait speed, stride, pitch, sway, and rhythm. However, the authors wanted to visualize and quantify the gait characteristics in patients with LSS based on the kinematic and morphologic standpoint, focusing on lower limb motion. The optimal classification method would consist of an examination using a simple instrument; this examination could be easily performed even by nonspecialists. Therefore, the authors aimed to develop a simple examination method for walking motion analysis.

The authors' method can be used to analyze walking motion without special equipment such as a force plate and 3-dimensional motion analysis. Compared with walking on the ground, walking on a treadmill is a nonphysiologic condition. However, treadmills offer many advantages in human locomotion analysis.18 Space requirements are constrained, environmental factors can be controlled, steady-state locomotion speeds are selectable, and successive repetitive strides can be documented expeditiously. Thus, use of a treadmill could circumvent some problems inherent in overground locomotion studies. The findings of normal gait in the current study were generally consistent with the results of other overground locomotion studies and indicated the validity of the authors' method.19–21

When gait characteristics of neurogenic disease are evaluated from the kinematic and morphologic aspects, 2 mechanisms should be considered. The first mechanism is that spastic and flaccid paralysis affects the joint motion through muscles; this is an essential finding that strongly reflects the nature of the disease. Another mechanism is the secondary finding of unconsciously performed gait strategy, such as avoidance reaction for pain and compensatory reaction for paralysis. Abnormalities in gait style have been noted soon after patients began to walk,7 suggesting that patients acquire a walking style that precludes the appearance of symptoms.

In the current study, the gait characteristic of the L4 group was knee extension at initial contact. In cases with quadriceps weakness, knee hyperextension occurs to reduce the demand on a weak quadriceps at initial contact. In the current study, no patients showed changes in the manual muscle test before and after the walking test. However, in the L4 group, the authors considered that even if patients had no obvious muscle weakness, they acquired walking motion to avoid a broken knee as gait strategy. The gait characteristic of the L5 group was the one-peak waveform pattern in the ankle joint. Because the toe and heel make contact with the ground simultaneously by foot drop, the second peak caused by the time lag between the toe and heel making contact with the ground disappears, and the waveform shows a one-peak pattern. Therefore, this finding can be explained by the weakness of the tibialis anterior muscle innervated by the L5 nerve root. The authors focused on the lower limb motion and identified the 10 factors that had the potential to be gait characteristics of each group. However, there may have been more effective classification factors that were not identified.

Several studies have reported gait analysis in patients with LSS.7–9 Suda et al7 evaluated gait improvement after surgery in patients with neurogenic intermittent claudication. Papadakis et al8 compared the gait patterns of healthy people with those of patients with LSS; they also evaluated the postoperative progression of the gait pattern of patients with LSS and showed that gait variability decreased relative to the preoperative gait pattern.9 In contrast, the current study examined walking motion with regard to the gait characteristics of each level of lumbar radiculopathy and classified it among the control, L4, and L5 groups using the SVM. The SVM was first proposed by Vapnik22 and has since attracted a high degree of interest in the machine learning research community. Support vector machine methods have the feasibility and superior ability to extract higher-order statistics and have become extremely popular for classification and prediction. Children with cerebral palsy–related gait have been identified and classified via an SVM-based method.23 The total classification accuracy was greater than 80% using the SVM. The authors consider that identification of other factors for differentiating between the L4 group and the other groups may further improve the classification performance of the SVM.

The current study has some limitations, including small sample size and different participant backgrounds in each group. There are several differences in walking motion associated with sex and age, and it is necessary to match patient backgrounds in future studies.

Conclusion

The authors developed a new and simple examination method for walking motion analysis and identified several factors useful for differentiating between normal healthy people and patients with L4 and L5 radiculopathy. In addition, the derived factors were used to construct an SVM-based differentiation method, with a high accuracy rate. The authors' future work will focus on improving the classification accuracy of this diagnostic method.

References

  1. Andreisek G, Imhof M, Wertli M, et al. A systematic review of semiquantitative and qualitative radiologic criteria for the diagnosis of lumbar spinal stenosis. AJR Am J Roentgenol. 2013; 201(5):W735–W746. doi:10.2214/AJR.12.10163 [CrossRef]
  2. Athiviraham A, Wali ZA, Yen D. Predictive factors influencing clinical outcome with operative management of lumbar spinal stenosis. Spine J. 2011; 11(7):613–617. doi:10.1016/j.spinee.2011.03.008 [CrossRef]
  3. Ciol MA, Deyo RA, Howell E, Kreif S. An assessment of surgery for spinal stenosis: time trends, geographic variations, complications, and reoperations. J Am Geriatr Soc. 1996; 44(3):285–290. doi:10.1111/j.1532-5415.1996.tb00915.x [CrossRef]
  4. Deyo RA, Gray DT, Kreuter W, Mirza S, Martin BI. United States trends in lumbar fusion surgery for degenerative conditions. Spine (Phila Pa 1976). 2005; 30(12):1441–1445. doi:10.1097/01.brs.0000166503.37969.8a [CrossRef]
  5. Katz JN, Harris MB. Clinical practice: lumbar spinal stenosis. N Engl J Med. 2008; 358(8):818–825. doi:10.1056/NEJMcp0708097 [CrossRef]
  6. Kim YS, Park SJ, Oh IS, Kwan JY. The clinical effect of gait load test in two level lumbar spinal stenosis. Asian Spine J. 2009; 3(2):96–100. doi:10.4184/asj.2009.3.2.96 [CrossRef]
  7. Suda Y, Saitou M, Shibasaki K, Yamazaki N, Chiba K, Toyama Y. Gait analysis of patients with neurogenic intermittent claudication. Spine (Phila Pa 1976). 2002; 27(22):2509–2513. doi:10.1097/00007632-200211150-00016 [CrossRef]
  8. Papadakis NC, Christakis DG, Tzagarakis GN, et al. Gait variability measurements in lumbar spinal stenosis patients: Part A. Comparison with healthy subjects. Physiol Meas. 2009; 30(11):1171–1186. doi:10.1088/0967-3334/30/11/003 [CrossRef]
  9. Papadakis NC, Christakis DG, Tzagarakis GN, et al. Gait variability measurements in lumbar spinal stenosis patients: Part B. Preoperative versus postoperative gait variability. Physiol Meas. 2009; 30(11):1187–1195. doi:10.1088/0967-3334/30/11/004 [CrossRef]
  10. Dukart J, Mueller K, Barthel H, et al. Meta-analysis based SVM classification enables accurate detection of Alzheimer's disease across different clinical centers using FDG-PET and MRI. Psychiatry Res. 2013; 212(3):230–236. doi:10.1016/j.pscychresns.2012.04.007 [CrossRef]
  11. El-Naqa I, Yang Y, Wernick MN, Galatsanos NP, Nishikawa RM. A support vector machine approach for detection of microcalcifications. IEEE Trans Med Imaging. 2002; 21(12):1552–1563. doi:10.1109/TMI.2002.806569 [CrossRef]
  12. Lee Y, Chang Y, Kim N, Lim J, Seo JB, Lee YK. Fast and efficient lung disease classification using hierarchical one-against-all support vector machine and cost-sensitive feature selection. Comput Biol Med. 2012; 42(12):1157–1164. doi:10.1016/j.compbiomed.2012.10.001 [CrossRef]
  13. Ramirez L, Durdle NG, Raso VJ, Hill DL. A support vector machines classifier to assess the severity of idiopathic scoliosis from surface topography. IEEE Trans Inf Technol Biomed. 2006; 10(1):84–91. doi:10.1109/TITB.2005.855526 [CrossRef]
  14. Wang Q, Kang W, Wu C, Wang B. Computer-aided detection of lung nodules by SVM based on 3D matrix patterns. Clin Imaging. 2013; 37(1):62–69. doi:10.1016/j.clinimag.2012.02.003 [CrossRef]
  15. Wu WJ, Lin SW, Moon WK. Combining support vector machine with genetic algorithm to classify ultrasound breast tumor images. Comput Med Imaging Graph. 2012; 36(8):627–633. doi:10.1016/j.compmedimag.2012.07.004 [CrossRef]
  16. Putz R, Pabst R, Weiglein AH, Taylor AN. Sobotta Atlas of Human Anatomy. Philadelphia, PA: Lippincott Williams and Wilkins; 2001.
  17. Chang CC, Lin CJ. LIBSVM: a library for support vector machines. ACM Trans Intell Syst Technol. 2011; 2(3):1–27. doi:10.1145/1961189.1961199 [CrossRef]
  18. White SC, Yack HJ, Tucker CA, Lin HY. Comparison of vertical ground reaction forces during overground and treadmill walking. Med Sci Sports Exerc. 1998; 30(10):1537–1542. doi:10.1097/00005768-199810000-00011 [CrossRef]
  19. Murray MP, Drougt AB, Kory RC. Walking patterns of normal men. J Bone Joint Surg Am. 1964; 46:335–360.
  20. Murray MP, Kory RC, Sepic SB. Walking patterns of normal women. Arch Phys Med Rehabil. 1970; 51(11):637–650.
  21. Pietraszewski B, Winiarski S, Jaroszczuk S. Three-dimensional human gait pattern: reference data for normal men. Acta Bioeng Biomech. 2012; 14(3):9–16.
  22. Vapnik V. The Nature of Statistical Learning Theory. New York, NY: Springer-Verlag; 1995. doi:10.1007/978-1-4757-2440-0 [CrossRef]
  23. Kamruzzaman J, Begg RK. Support vector machines and other pattern recognition approaches to the diagnosis of cerebral palsy gait. IEEE Trans Biomed Eng. 2006; 53(12, pt 1):2479–2490. doi:10.1109/TBME.2006.883697 [CrossRef]

Potential Factors of Gait Characteristics

FactorMeanSDPa

Control–L4Control–L5L4–L5
Amplitude of ankle angle during swing phase
  Control group14.865.42
  L4 group12.944.88.520.002b.066
  L5 group9.313.02
Average angle of ankle joint during swing phase
  Control group126.338.59
  L4 group121.058.02.337.001b.129
  L5 group114.429.75
Angle of knee joint at stance phase start time
  Control group164.459.42
  L4 group169.557.23.344.938.154
  L5 group163.409.13
Amplitude of hip angle
  Control group35.376.27
  L4 group28.076.30.009b<.001b.053
  L5 group22.965.16
Normalized maximum length of gastrocnemius
  Control group1.0560.020
  L4 group1.0630.023.744.052.317
  L5 group1.0750.023
Normalized minimum length of gastrocnemius
  Control group0.9660.019
  L4 group0.9940.022.023b<.001b.012b
  L5 group1.0210.029
Normalized motion range of gastrocnemius
  Control group0.0910.016
  L4 group0.0690.026.035b<.001b.105
  L5 group0.0540.018
Normalized maximum length of quadriceps
  Control group1.3140.004
  L4 group1.3040.007.025b<.001.219
  L5 group1.2990.011
Normalized minimum length of quadriceps
  Control group1.2640.007
  L4 group1.2550.010.092.855.157
  L5 group1.2620.011
Normalized motion range of quadriceps
  Control group0.0500.006
  L4 group0.0490.006.949<.001b<.001b
  L5 group0.0370.007

Results of the Classification

Actual Class/Predicted ClassGroup, No.Accuracy

ControlL4L5
Control group (n=13)112084.6%
L4 group (n=11)18272.7%
L5 group (n=22)221881.8%
All (n=46)14122080.4%

The authors are from the Department of Orthopedic Surgery (HH, HM, HT), Graduate School of Medical Science, and the School of Mechanical Engineering (TY, TW), Kanazawa University, Kanazawa; and the Department of Orthopedic Surgery (YT), Kouseiren Takaoka Hospital, Takaoka, Japan.

The authors have no relevant financial relationships to disclose.

The authors thank Ms Sano, Mr Habe, Mr Kawagishi, and Mr Kobayashi for helping with the analysis of gait pattern data.

Correspondence should be addressed to: Hiroyuki Hayashi, MD, Department of Orthopedic Surgery, Graduate School of Medical Science, Kanazawa University, 13-1 Takara-machi, Kanazawa 920-8641, Japan ( snoopeanuts27@hotmail.com).

Received: October 02, 2014
Accepted: February 23, 2015
Positioning of light-emitting diode markers on the participant. The markers were attached at the following sites: acromion, anterior superior iliac spine, fibular head, lateral malleolus of the ankle joint, and fifth metatarsal head.

Figure 1:

Positioning of light-emitting diode markers on the participant. The markers were attached at the following sites: acromion, anterior superior iliac spine, fibular head, lateral malleolus of the ankle joint, and fifth metatarsal head.

Walking measurement system. Walking was assessed on a treadmill, and a digital camera recorded the motion.

Figure 2:

Walking measurement system. Walking was assessed on a treadmill, and a digital camera recorded the motion.

Sagittal plane view. The angle of each joint is defined in the schema.

Figure 3:

Sagittal plane view. The angle of each joint is defined in the schema.

The waveform of the knee joint in normal gait. Circles indicate positions at which light-emitting diode markers were attached.

Figure 4:

The waveform of the knee joint in normal gait. Circles indicate positions at which light-emitting diode markers were attached.

The waveform of the ankle joint in normal gait. Circles indicate positions at which light-emitting diode markers were attached.

Figure 5:

The waveform of the ankle joint in normal gait. Circles indicate positions at which light-emitting diode markers were attached.

The waveform of representative cases in each group. Waveform of the knee joint: solid line=22-year-old man in the control group; dotted line=56-year-old man in the L4 group; perforated line=81-year-old man in the L5 group (A). Waveform of the ankle joint: solid line=48-year-old man in the control group; dotted line=56-year-old man in the L4 group; perforated line=82-year-old woman in the L5 group (B).

Figure 6:

The waveform of representative cases in each group. Waveform of the knee joint: solid line=22-year-old man in the control group; dotted line=56-year-old man in the L4 group; perforated line=81-year-old man in the L5 group (A). Waveform of the ankle joint: solid line=48-year-old man in the control group; dotted line=56-year-old man in the L4 group; perforated line=82-year-old woman in the L5 group (B).

Potential Factors of Gait Characteristics

Table 1:

Potential Factors of Gait Characteristics

Results of the Classification

Table 2:

Results of the Classification

References

  1. Andreisek G, Imhof M, Wertli M, et al. A systematic review of semiquantitative and qualitative radiologic criteria for the diagnosis of lumbar spinal stenosis. AJR Am J Roentgenol. 2013; 201(5):W735–W746. doi:10.2214/AJR.12.10163 [CrossRef]
  2. Athiviraham A, Wali ZA, Yen D. Predictive factors influencing clinical outcome with operative management of lumbar spinal stenosis. Spine J. 2011; 11(7):613–617. doi:10.1016/j.spinee.2011.03.008 [CrossRef]
  3. Ciol MA, Deyo RA, Howell E, Kreif S. An assessment of surgery for spinal stenosis: time trends, geographic variations, complications, and reoperations. J Am Geriatr Soc. 1996; 44(3):285–290. doi:10.1111/j.1532-5415.1996.tb00915.x [CrossRef]
  4. Deyo RA, Gray DT, Kreuter W, Mirza S, Martin BI. United States trends in lumbar fusion surgery for degenerative conditions. Spine (Phila Pa 1976). 2005; 30(12):1441–1445. doi:10.1097/01.brs.0000166503.37969.8a [CrossRef]
  5. Katz JN, Harris MB. Clinical practice: lumbar spinal stenosis. N Engl J Med. 2008; 358(8):818–825. doi:10.1056/NEJMcp0708097 [CrossRef]
  6. Kim YS, Park SJ, Oh IS, Kwan JY. The clinical effect of gait load test in two level lumbar spinal stenosis. Asian Spine J. 2009; 3(2):96–100. doi:10.4184/asj.2009.3.2.96 [CrossRef]
  7. Suda Y, Saitou M, Shibasaki K, Yamazaki N, Chiba K, Toyama Y. Gait analysis of patients with neurogenic intermittent claudication. Spine (Phila Pa 1976). 2002; 27(22):2509–2513. doi:10.1097/00007632-200211150-00016 [CrossRef]
  8. Papadakis NC, Christakis DG, Tzagarakis GN, et al. Gait variability measurements in lumbar spinal stenosis patients: Part A. Comparison with healthy subjects. Physiol Meas. 2009; 30(11):1171–1186. doi:10.1088/0967-3334/30/11/003 [CrossRef]
  9. Papadakis NC, Christakis DG, Tzagarakis GN, et al. Gait variability measurements in lumbar spinal stenosis patients: Part B. Preoperative versus postoperative gait variability. Physiol Meas. 2009; 30(11):1187–1195. doi:10.1088/0967-3334/30/11/004 [CrossRef]
  10. Dukart J, Mueller K, Barthel H, et al. Meta-analysis based SVM classification enables accurate detection of Alzheimer's disease across different clinical centers using FDG-PET and MRI. Psychiatry Res. 2013; 212(3):230–236. doi:10.1016/j.pscychresns.2012.04.007 [CrossRef]
  11. El-Naqa I, Yang Y, Wernick MN, Galatsanos NP, Nishikawa RM. A support vector machine approach for detection of microcalcifications. IEEE Trans Med Imaging. 2002; 21(12):1552–1563. doi:10.1109/TMI.2002.806569 [CrossRef]
  12. Lee Y, Chang Y, Kim N, Lim J, Seo JB, Lee YK. Fast and efficient lung disease classification using hierarchical one-against-all support vector machine and cost-sensitive feature selection. Comput Biol Med. 2012; 42(12):1157–1164. doi:10.1016/j.compbiomed.2012.10.001 [CrossRef]
  13. Ramirez L, Durdle NG, Raso VJ, Hill DL. A support vector machines classifier to assess the severity of idiopathic scoliosis from surface topography. IEEE Trans Inf Technol Biomed. 2006; 10(1):84–91. doi:10.1109/TITB.2005.855526 [CrossRef]
  14. Wang Q, Kang W, Wu C, Wang B. Computer-aided detection of lung nodules by SVM based on 3D matrix patterns. Clin Imaging. 2013; 37(1):62–69. doi:10.1016/j.clinimag.2012.02.003 [CrossRef]
  15. Wu WJ, Lin SW, Moon WK. Combining support vector machine with genetic algorithm to classify ultrasound breast tumor images. Comput Med Imaging Graph. 2012; 36(8):627–633. doi:10.1016/j.compmedimag.2012.07.004 [CrossRef]
  16. Putz R, Pabst R, Weiglein AH, Taylor AN. Sobotta Atlas of Human Anatomy. Philadelphia, PA: Lippincott Williams and Wilkins; 2001.
  17. Chang CC, Lin CJ. LIBSVM: a library for support vector machines. ACM Trans Intell Syst Technol. 2011; 2(3):1–27. doi:10.1145/1961189.1961199 [CrossRef]
  18. White SC, Yack HJ, Tucker CA, Lin HY. Comparison of vertical ground reaction forces during overground and treadmill walking. Med Sci Sports Exerc. 1998; 30(10):1537–1542. doi:10.1097/00005768-199810000-00011 [CrossRef]
  19. Murray MP, Drougt AB, Kory RC. Walking patterns of normal men. J Bone Joint Surg Am. 1964; 46:335–360.
  20. Murray MP, Kory RC, Sepic SB. Walking patterns of normal women. Arch Phys Med Rehabil. 1970; 51(11):637–650.
  21. Pietraszewski B, Winiarski S, Jaroszczuk S. Three-dimensional human gait pattern: reference data for normal men. Acta Bioeng Biomech. 2012; 14(3):9–16.
  22. Vapnik V. The Nature of Statistical Learning Theory. New York, NY: Springer-Verlag; 1995. doi:10.1007/978-1-4757-2440-0 [CrossRef]
  23. Kamruzzaman J, Begg RK. Support vector machines and other pattern recognition approaches to the diagnosis of cerebral palsy gait. IEEE Trans Biomed Eng. 2006; 53(12, pt 1):2479–2490. doi:10.1109/TBME.2006.883697 [CrossRef]
This Article