- Research
- Open Access
Modeling and classification of gait patterns between anterior cruciate ligament deficient and intact knees based on phase space reconstruction, Euclidean distance and neural networks
- Wenbao Wu†1,
- Wei Zeng†2Email authorView ORCID ID profile,
- Limin Ma3,
- Chengzhi Yuan4 and
- Yu Zhang†5
https://doi.org/10.1186/s12938-018-0594-1
© The Author(s) 2018
- Received: 6 August 2018
- Accepted: 24 October 2018
- Published: 1 November 2018
Abstract
Background
The anterior cruciate ligament (ACL) plays an important role in stabilizing translation and rotation of the tibia relative to the femur. ACL injury alters knee kinematics and usually links to the alternation of gait patterns. The aim of this study is to develop a new method to distinguish between gait patterns of patients with anterior cruciate ligament deficient (ACL-D) knees and healthy controls with ACL-intact (ACL-I) knees based on nonlinear features and neural networks. Therefore ACL injury will be automatically and objectively detected.
Methods
First knee rotation and translation parameters are extracted and phase space reconstruction (PSR) is employed. The properties associated with the gait system dynamics are preserved in the reconstructed phase space. For the purpose of classification of ACL-D and ACL-I knee gait patterns, three-dimensional (3D) PSR together with Euclidean distance computation has been used. These measured parameters show significant difference in gait dynamics between the two groups and have been utilized to form a feature set. Neural networks are then constructed to identify gait dynamics and are utilized as the classifier to distinguish between ACL-D and ACL-I knee gait patterns based on the difference of gait dynamics between the two groups.
Results
Experiments are carried out on a database containing 18 patients with ACL injury and 28 healthy controls to assess the effectiveness of the proposed method. By using the twofold and leave-one-subject-out cross-validation styles, the correct classification rates for ACL-D and ACL-I knees are reported to be 91.3\(\%\) and 95.65\(\%\), respectively.
Conclusion
Compared with other state-of-the-art methods, the results demonstrate that gait alterations in the presence of ACL deficiency can be detected with superior performance. The proposed method is a potential candidate for the automatic and non-invasive classification between patients with ACL deficiency and healthy subjects.
Keywords
- Gait analysis
- Anterior cruciate ligament
- Movement disorders
- Phase space reconstruction (PSR)
- Euclidean distance (ED)
- Neural networks
Background
Knowledge of spatiotemporal knee motion is important for understanding normal functions as well as addressing clinical problems, including instability after anterior cruciate ligament (ACL) injury. ACL plays an important role in controlling knee joint stability, not only by limiting tibia anterior translation, but also by controlling knee axial rotation and varus movement [1]. Numerous studies have been carried to provide information on biomechanical changes in the ACL-deficient (ACL-D) knees [2–7], which revealed that ACL-D knees would exhibit altered joint kinematics. Currently, the most widely accepted method for assessing joint movement patterns is gait analysis, which offers a unique means of providing insight into mechanisms of ACL-D progression by measuring the kinematic and kinetic parameters [8]. Gait analysis also provides important information concerning motion variability in ACL-D and ACL-intact (ACL-I) knees [9].
Many studies have addressed gait pattern classification and there are several reviews on this subject [10–14]. However, the research work dealing specifically with ACL-D knees is not sufficient [15–18]. Biomechanics plays an important role in the progression of ACL-D knees and many studies have been carried out in gait laboratories to ascertain which parameters are affected by ACL-D knees compared to healthy controls with bilateral ACL-I knees [19–31]. These gait parameters may be adopted as gait features for the classification of gait patterns between ACL-D and ACL-I knees. In the study by Gao et al. [1], spatiotemporal gait and knee joint kinematic variables were calculated and further analyzed. The ACL-D knees exhibited a significant extension deficit compared to the ACL-I knees. A more varus and internally rotated tibial position was also identified in the ACL-D knees during both stair ascent and descent. Knoll et al. [19] revealed a quadriceps-avoidance gait pattern in acute ACL-D patients. Chronic ACL-D individuals demonstrated a significantly different gait pattern. Robinson et al. [32] investigated whether using a direct kinematic or inverse kinematic modeling approach could influence the estimation of knee joint kinematics and kinetics. The similarity between kinematic and kinetic waveforms was evaluated using the root mean square difference and the one-dimensional statistical parametric mapping. Atarod et al. [33] investigated the interactions between different kinematic degree of freedom during normal gait and determined how these interactions would change over time following ACL transection in vivo. They claimed that ACL deficiency would significantly alter the kinematic and kinetic interactions during in vivo gait. Clinical imaging studies of ACL-D individuals versus healthy controls have found greater medial–lateral posterior tibial slope in injured population, with stronger evidence on the lateral plateau slope. To quantify these effects, Marouane et al. [34] used a lower extremity musculoskeletal model which included a detailed finite element model of the knee joint. It was used to compute the role of changes in medial and/or lateral posterior tibial slope on knee joint biomechanics.
The current study has two aims. First, to provide further evidence to support the claim that ACL-D knees demonstrate altered gait patterns compared to ACL-I knees. Second, to provide an automatic and objective method to distinguish between ACL-D and ACL-I knees. Based on the nonlinear and non-stationary nature of knee kinematic signals [35], a popular nonlinear method named phase space reconstruction (PSR), is a valuable tool for the studies of this kind of signals [36–41]. The principle of PSR is to transform the properties of a time series into topological properties of a geometrical object which is embedded in a space, wherein all possible states of the system are represented, each state corresponds to a unique point, and this reconstructed space sharing the same topological properties as the original space. The dynamics in the reconstructed state space is equivalent to the original dynamics. Hence reconstructed phase space is a very useful tool to extract nonlinear dynamics of the signal [36–41]. It is hypothesized that gait dynamics between ACL-D and ACL-I knee gait patterns is significantly different, which implies that PSR offers the potential to compute the difference and classify the two groups.
In this paper, we present a new method using gait analysis to distinguish between ACL-D and ACL-I knees. First knee rotation and translation parameters are extracted and phase space is reconstructed. The properties associated with the gait system dynamics are preserved in the reconstructed phase space. For the purpose of classification of ACL-D and ACL-I knee gait patterns, three-dimensional (3D) PSR together with Euclidean distance (ED) computation has been used. These measured parameters show significant difference in gait dynamics between the two groups and have been utilized to form a feature set. Neural networks are then constructed to identify gait dynamics and are utilized as the classifier, in which the feature set is embedded, to distinguish between ACL-D and ACL-I knee gait patterns based on the difference of gait dynamics between the two groups.
Methods
Block diagram of the proposed method for the classification of gait patterns between ACL-D and ACL-I knees
Data measurement
Descriptive characteristics of the ACL-D and ACL-I subjects
Healthy controls with ACL-I knees | Patients with ACL-D knees | p value | |
---|---|---|---|
Age (years), mean (SD) | 38.6 (5.9) | 40.3 (6.1) | 0.352 |
Height (cm), mean (SD) | 165.4 (9.6) | 164.1 (7.6) | 0.630 |
Weight (kg), mean (SD) | 65.7 (10.5) | 63.5 (9.4) | 0.474 |
Male/female | 14/14 | 11/7 | − |
A portable marker-based motion analysis system [42]: A The instrument for knee kinematics analysis; B Identifying the femoral and tibial anatomical landmarks using a hand-held probe prior to kinematic data capture
Each subject was required to undergo a 3-min treadmill gait training. Then data were collected with the sampling frequency of 60 Hz for 15 s and all the participants were guided to walk at the speed of 3 km/h. The detailed procedure about data extraction can be seen in the study by Zhang et al. [42]. The study was approved by the ethical review board and a written informed consent was obtained from each participant before data collection began.
Data description
Mean, SD, significant statistical difference p and effect sizes of the range of motion (ROM) of tibiofemoral rotations and translations for 28 healthy controls with ACL-I knees and 18 patients with ACL-D knees
Parameters | Groups | Difference between groups | Effect size | |
---|---|---|---|---|
ACL-D knees | ACL-I knees | p-value | Cohen’s d | |
ROM of VV (degree) | 13.01 (5.45) | 15.40 (4.17) | 0.1 | 0.51 |
ROM of IE rotation (degree) | 18.87 (5.77) | 22.45 (4.69) | 0.03 | 0.70 |
ROM of FE (degree) | 59.18 (8.49) | 71.76 (6.93) | < 0.001 | 1.66 |
ROM of AP translation (cm) | 2.41 (0.81) | 1.95 (0.52) | 0.02 | − 0.71 |
ROM of PD translation (cm) | 1.94 (0.74) | 2.38 (0.44) | 0.01 | 0.77 |
ROM of ML translation (cm) | 1.84 (0.49) | 1.86 (0.37) | 0.88 | 0.05 |
The 3-D joint rotations and translations during walking of ACL-D and ACL-I knees. Ensemble curves of each subject group were normalized from heel strike to heel strike in a gait cycle. a IE rotation; b FE; c AP translation; d PD translation
Kinematic variations during walking were observed in 3-D rotations and translations between ACL-D and ACL-I knees, as shown in Fig. 3. For each of the rotational or translational kinematic component, 101 discrete points corresponding to 0–100\(\%\) gait cycle at \(1\%\) interval were extracted using one-dimensional interpolation for statistical analysis. Measures of each spatiotemporal variable as well as each discrete kinematic point were compared between ACL-D and ACL-I knees using an independent t-test analysis of variance (SPSS Inc., IL, USA). A p value of \(<0.05\) was considered to indicate statistical significance.
It is observed from Table 2 that: (1) In the sagittal plane patients with ACL-D knees showed less range of flexion–extension than healthy controls with ACL-I knees (59.18 (8.49) and 71.76 (6.93), respectively, \(p<0.001\)). (2) In the frontal plane, patients with ACL-D knees showed less range of internal–external rotation than healthy controls with ACL-I knees (18.87 (5.77) and 22.45 (4.69), respectively, \(p=0.03\)). (3) The range of PD translation was lower in the ACL-D knees group compared to ACL-I knees group while the range of AP translation was higher in the ACL-D knees group compared to ACL-I knees group (Table 2). (4) Whereas statistical tests of significance tell us the likelihood that experimental results differ from chance expectations, effect-size measurements tell us the relative magnitude of the experimental treatment. In essence, an effect size is the difference between two means divided by the standard deviation of the two conditions [46]. Cohen’s d from t-test [47] was used to describe the effect sizes of the ROM of knee kinematic data, which have been shown in Table 2. The effect sizes were traditionally considered small (\(d = 0.2\)), medium (\(d = 0.5\)), and large (\(d = 0.8\)) [48, 49]. It is seen from Table 2 that IE, FE, AP and PD are with nearly large effect sizes compared to VV and ML, which also means there exist significant differences in IE, FE, AP and PD between ACL-deficient patients and healthy controls. The results are in accordance with the p-value analysis.
It is seen from the statistical analysis in Table 2 that IE rotation, FE, AP and PD translations between ACL-D and ACL-I knees are significantly different, which means gait dynamics of the two groups represented by the knee motion are significantly different. Hence these four signals are utilized as reference variables to carry out the following phase space reconstruction.
Phase space reconstruction (PSR)
The behavior of the signal over time can be visualized using PSR (especially when \(d=\) 2 or 3). In this work, we have confined our discussion to the value of embedding dimension \(d=3\), because of their visualization simplicity. For \(\tau\) setting, we either utilized the first-zero crossing of the autocorrelation function for each time series or the average \(\tau\) value obtained from all the time series in the training dataset by using the method depicted in [52]. In the present study we set the values of time lag \(\tau =1\) to test the classification performance. PSR for \(d=3\) has been referred as 3D PSR.
Feature extraction and selection
- (1)
Reconstruct the phase space for the above mentioned reference variables including knee IE rotation, FE, AP and PD translations with selected values of d and \(\tau\) for each gait trial;
- (2)
Compute ED of 3D PSR of knee IE rotation, FE, AP and PD translations as gait features. Concatenate these features to form a feature vector \([ED_j^{IE},ED_j^{FE},ED_j^{AP},ED_j^{PD}]^T\) and the dimension of feature space would be four.
Samples of 3D PSR of the knee kinematic signals from ACL-D and ACL-I gait patterns: a 3D PSR of the IE rotation; b 3D PSR of the FE; c 3D PSR of the AP translation; d 3D PSR of the PD translation
Samples of Euclidian distance of 3D PSR of the knee kinematic signals from ACL-D and ACL-I gait patterns: a Euclidian distance of 3D PSR of the IE rotation; b Euclidian distance of 3D PSR of the FE; c Euclidian distance of 3D PSR of the AP translation; d Euclidian distance of 3D PSR of the PD translation
Training and modeling mechanism based on selected features
In this section, we present a scheme for modeling and identification of gait dynamics of ACL-I and ACL-D knees based on the above mentioned features.
Classification mechanism
In this section, we present a scheme to distinguish between ACL-I and ACL-D knees.
The fundamental idea of the classification between ACL-D and ACL-I knees is that if a test gait pattern generated from a certain ACL-D or ACL-I knee is similar to the trained gait pattern \(s~(s\in \{1,\ldots ,k\})\), the constant RBF network \(\bar{W}_i^{s^T}S_i(x)\) embedded in the matched estimator s will quickly recall the learned knowledge by providing accurate approximation to gait system dynamics. Thus, the corresponding error \(\Vert \tilde{\chi }_i^s(t)\Vert _1\) will become the smallest among all the errors \(\Vert \tilde{\chi }_i^k(t)\Vert _1\). Based on the smallest error principle, the appearing test gait pattern can be classified. We have the following classification scheme.
Classification scheme: If there exists some finite time \(t^s,~s\in \{1,\ldots ,k\}\) and some \(i\in \{1,\ldots ,n\}\) such that \(\Vert \tilde{\chi }_i^s(t)\Vert _1<\Vert \tilde{\chi }_i^k(t)\Vert _1\) for all \(t>t^s\), then the appearing gait pattern can be classified.
Experimental results
The classification results of ACL-D knees will be evaluated in the twofold cross-validation and leave-one-subject-out cross-validation styles, respectively. In the experiment of twofold cross-validation style, we randomly select half of the group of patients with ACL-D knees and half of the group of the healthy controls with ACL-I knees to constitute the training dataset, the rest of the subjects in the two groups are selected as the test dataset. That means there are 9 patients with ACL-D knees and 14 healthy controls with ACL-I knees in the training dataset. In the experiment of leave-one-subject-out cross-validation, each time we select one subject for classification, the rest of the 45 subjects for training. This process is repeated 46 times and the leave-one-subject-out classification accuracy is calculated as the average of the classification accuracy of all of the individually left-out subjects.
In the training phase, the RBF network \(\hat{W}_i^TS_i(x)\) is constructed in a regular lattice, with nodes \(N=83521\), the centers \(\mu _i\) evenly spaced on \([-1.2,1.2]\times [-1.2,1.2]\times [-1.2,1.2]\times [-1.2,1.2]\) so as to cover all the trajectories of the input vectors, and the widths \(\eta =0.15\). The weights of the RBF neural networks are updated according to Eq. (7). The initial weights \(\hat{W}_i(0)=0\). The design parameters for (6) and (7) are \(a_i=0.5, \Gamma =diag\{1.5,1.5,1.5,1.5\}, \sigma _i=10, (i=1,\ldots ,4)\).
Confusion matrix of gait pattern classification between ACL-D and ACL-I knees by using twofold cross-validation method
ACL-D knees | ACL-I knees | |
---|---|---|
ACL-D knees | 8 | 1 |
ACL-I knees | 1 | 13 |
Confusion matrix of gait pattern classification between ACL-D and ACL-I knees by using leave-one-subject-out cross-validation method
ACL-D knees | ACL-I knees | |
---|---|---|
ACL-D knees | 17 | 1 |
ACL-I knees | 1 | 27 |
Discussion
Comparing the results of accuracy in classifying gait patterns between ACL-I and ACL-D groups using different methods
Different from the methods in the above-mentioned literature, our method focused on modeling the human gait and extracting the disparity of gait system dynamics between ACL-D and ACL-I knees for the discrimination task. It abandoned the traditional and direct comparison of lower extremity motion parameters between ACL-D and ACL-I knees and adopted instead the modeling, identification and classification of gait dynamics based on motion parameters. This may better explain and reveal the motion principle of pathological and healthy gaits hidden underneath the parameters extracted through PSR and ED. The proposed method serves not only as a measure of kinematic variability and discrimination between two groups of patients with ACL deficiency and healthy controls, but also as a non-invasive, objective and assistant technical means to other diagnostic approaches such as X-rays, MRI, arthroscopy, etc.
However, there are some limitations in the present study which need further improvement. Experiments were carried out on a small database and more participants need to be recruited to verify the effectiveness. At current stage, the proposed method is more suitable to be a tool applicable for gait reeducation on previously diagnosed patients. It is not easy for the clinicians to distinguish a deficiency of the ACL from a possible injury of another structure of the knee, such as posterior cruciate ligament or collateral ligaments, since these injuries may also lead to the same gait patterns. Only when the patients were highly suspected to have the ACL injury, can the proposed method be used to diagnose it as an assistant tool. In future work, injury of other structures of the knee, including posterior cruciate ligament or collateral ligaments injury and their related gait patterns, may also be included in our study to assist in diagnosing the knee injury more accurately. In addition, other parameters regarding different knee lessons can be adopted to improve the classification accuracy.
Conclusions
The results of this study indicate that the pattern classification of knee kinematic data can offer an objective and invasive method to assess the gait disparity between ACL-D and ACL-I knees. These results demonstrate the potential of the proposed technique for detecting pathological gait patterns caused by ACL deficiency by analysing and measuring the disparity of gait system dynamics using PSR, ED and neural networks. PSR is one of the most used methods which is the time-delay embedding and fits well with 1-dimensional time series. The d-dimensional space of delay coordinates serves as a pseudo state-space which provides a natural setting to approximate the quantitative aspects of the gait system dynamics. PSR plots gait system dynamics along the gait signal trajectory in a 3D phase space diagram and visualizes the gait system dynamics. ED measures and derives gait features, which are fed into RBF neural networks for the modeling, identification and classification of gait system dynamics between ACL-D and ACL-I knees. However, some limitations such as the small size of the database, the regulation principle of the embedding dimension and time lag, still need to be improved and overcome. Future work will include a clinical validation of the proposed technique with a larger number of patients with ACL deficiency and age-matched healthy controls. In the present study, PSR parameters such as the time lag and embedding dimension are with fixed values. Assessments of the relationship between the embedding dimension, time lag and the classification accuracy can also be considered in future investigations.
Notes
Declarations
Authors' contributions
Study concept and design (WZ); drafting of the manuscript (WZ and WW); critical revision of the manuscript for important intellectual content (WZ, WW and CY); obtained funding (WW, WZ and YZ); administrative, technical, and material support (LM); study supervision (WZ and YZ). WW, WZ and YZ contributed equally. All authors read and approved the final manuscript.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. 61773194, 61304084, 31700880), by the Natural Science Foundation of Fujian Province (Grant No. 2018J01542), by the Program for New Century Excellent Talents in Fujian Province University, by the Science and Technology Planning Project of Guangzhou city (Grant No. 201803010106) and by the Science and Technology Project of Longyan City (Grant No. 2017LY85).
Competing interests
The authors declare that they have no competing interests.
Availability of data and materials
The datasets used and/or analyzed during in current study are available from the corresponding author on reasonable requests.
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