- Research
- Open Access
A multivariate relationship between the kinematic and clinical parameters of knee osteoarthritis population
- Fatima Bensalma^{1, 2}Email authorView ORCID ID profile,
- Neila Mezghani^{1, 2},
- Youssef Ouakrim^{1, 2},
- Alexandre Fuentes^{2},
- Manon Choinière^{3, 5},
- Nathalie J. Bureau^{3, 6},
- Madelaine Durand^{3, 7} and
- Nicola Hagemeister^{2, 4}
- Received: 25 October 2018
- Accepted: 30 April 2019
- Published: 15 May 2019
Abstract
Background
Biomechanical and clinical parameters contribute very closely to functional evaluations of the knee joint. To better understand knee osteoarthritis joint function, the association between a set of knee biomechanical data and a set of clinical parameters of an osteoarthritis population (OA) is investigated in this study.
Methods
The biomechanical data used here are a set of characteristics derived from 3D knee kinematic patterns: flexion/extension, abduction/adduction, and tibial internal/external rotation measurements, all determined during gait recording. The clinical parameters include a KOOS questionnaire and the patient’s demographic characteristics. Canonical correlation analysis (CCA) is used (1) to evaluate the multivariate relationship between biomechanical data and clinical parameter sets, and (2) to cluster the most correlated parameters. Multivariate models were created within the identified clusters to determine the effect of each parameter’s subset on the other. The analyses were performed on a large database containing 166 OA patients.
Results
The CCA results showed meaningful correlations that gave rise to three different clusters. Multivariate linear models were found explaining the subjective clinical parameters by evaluating the biomechanical data contained within each cluster.
Conclusion
The results showed that a multivariate analysis of the clinical symptoms and the biomechanical characteristics of knee joint function allowed a better understanding of their relationships.
Keywords
- Biomechanics
- Canonical correlation
- Multivariate analysis
- Multiple regression
- Kinematic gait analysis
- Knee osteoarthritis (OA)
Background
Biomechanical knee assessment is increasingly used in gait analysis as a tool for characterizing the knee function [1], understanding pathological knee alterations [2], and assessing the progression of knee pathologies and their impact on gait [3]. It has already been suggested that the type and severity of biomechanical changes should be assessed since they can impact treatment outcomes [4]. Mechanical factors linked to the progression of osteoarthritis (OA) [5] and its treatment [6] have also been identified. Still, the relationship between the kinematic and clinical parameters of knee OA populations has not been sufficiently explained and remains incompletely understood. Only a few studies have investigated the relationship between 3D knee kinematic parameters and clinical data [7, 8]. These studies have been limited to a univariate analysis implying the correlation between one kinematic parameter and one specific clinical parameter. Such analysis is not adapted to the complexity of biomechanical data [9] and can even mask several strong relationships if the parameters are considered independently.
The objective of this study is (1) to evaluate the multivariate relationship (compared to the univariate approach) between a set of biomechanical data and a set of clinical parameters of an osteoarthritis population, and (2) to cluster the most correlated parameter. The biomechanical data are a set of characteristics extracted from 3D knee kinematic patterns during gait recording: flexion/extension, abduction/adduction, and tibial internal/external rotation measurements. The clinical parameters were acquired via the Knee Osteoarthritis Outcome Score (KOOS) questionnaire. Through this questionnaire, the patient provides a valid and reliable assessment of his/her health status relative to the pathology [10]. Our hypothesis is that these subjective clinical measures may complement objective biomechanical measures for a better understanding of knee joint function.
This study utilizes a canonical correlation analysis (CCA) to evaluate the relationship between a set of biomechanical data and a set of clinical parameters of an osteoarthritis population. CCA is a method for exploring the relationship between two multivariate sets of variables all measured on the same individual. Although the CCA has already been successfully applied to several applications in image processing [11] and in the domain of ecology [12], its use remains almost limited in the biomedical field. This situation could be due to the difficulty of interpreting results. To our knowledge, this study is the first to consider such a multivariate analysis combined with multivariate modeling in the biomechanical domain.
Methods
Biomechanical and clinical data collection
Participants were also asked to answer the KOOS questionnaires. The KOOS is a valid and reliable instrument which assesses the impact of knee OA on five domains: symptoms, pain, activities of daily living (ADL), sports and recreation (Sports/Rec), and quality of life (QoL). Scores on the subscales range from 0 (extreme symptoms) to 100 (no symptoms) [10].
Biomechanical and clinical parameters’ extraction
Description of the 13 biomechanical parameters
Y | Name | Description | Mean (SD) |
---|---|---|---|
\(Y_{1}\) | Rot_RomSw | Range of motion of internal/external rotation during swing | 1.9 (1.2) |
\(Y_{2}\) | Abd_MeanSt | Mean abduction/adduction angle during the stance phase | 4.4 (5.7) |
\(Y_{3}\) | Rot_Init | Internal/external rotation angle at initial contact | 3.0 (3.6) |
\(Y_{4}\) | Flex_Max | Flexion angle maximum | 59.5 (5.7) |
\(Y_{5}\) | Flex_EndSt | Flexion angle at the end of the stance phase | 12.1 (7.2) |
\(Y_{6}\) | Abd_MaxSw | Maximum of the abduction/adduction angle during swing phase | 7.9 (5.6) |
\(Y_{7}\) | Abd_MinLo | Minimum abduction/adduction angle during the loading phase | 4.3 (5.5) |
\(Y_{8}\) | Abd_Init | Abduction/adduction angle at initial contact | 4.8 (5.3) |
\(Y_{9}\) | Abd_Lo | Abduction/adduction angle at the end of the loading phase | 5.6 (5.9) |
\(Y_{10}\) | Abd_Rom | Range of motion of the abduction/adduction angle | 9.3 (3.1) |
\(Y_{11}\) | Rot_InitAbs | Internal/external rotation absolute angle value at initial contact | 3.8 (2.8) |
\(Y_{12}\) | Rot_Rom | Range of motion of the internal/external rotation | 11.3 (3.2) |
\(Y_{13}\) | Abd_RomLo | Range of motion of the abduction/adduction angle during loading phase | −1.3 (2.4) |
The participants in this study were selected if the OA was the main cause of their knee pain. The exclusion criteria were considered for the subjects being on a waiting list for total knee replacement. Patients being pregnant, suffering from rheumatoid arthritis, and active cancer were also excluded. A standardized radiographic examination of both knees was performed after the patient had given written informed consent. Only patients who had a Kellgren–Lawrence (KL) grade ≥ 2 on radiographs were considered and only data from the most painful knee were collected.
Description of the clinical parameters
X | Name | Description | Mean (SD) |
---|---|---|---|
\(X_{1}\) | Grade (1 to 4) | Degree of osteoarthritis severity | 3.0 (0.8) |
\(X_{2}\) | Pain (4 to 10) | Outcome score for pain | 6.6 (1.8) |
\(X_{3}\) | Sex (1: Men, 0: Women) | Gender | Men: n = 68; Women: n = 98 |
\(X_{4}\) | Age | Age (years) | 61.9 (9.2) |
\(X_{5}\) | BMI | Body mass index (kg/m^{2}) | 31.8 (7.3) |
\(X_{6}\) | KOOS_Symptoms | KOOS score for symptoms | 62.7 (17.4) |
\(X_{7}\) | KOOS_Pain | KOOS score for pain | 60.5 (17.3) |
\(X_{8}\) | KOOS_Adl | KOOS score for daily living | 67.4 (18.3) |
\(X_{9}\) | KOOS_Sport | KOOS score for sport and recreation function | 38.7 (25.7) |
\(X_{10}\) | KOOS_Qol | KOOS score for quality of life | 52.3 (22.8) |
\(X_{11}\) | KOOS | Normalized overall KOOS score | 56.3 (17.1) |
Canonical correlation analysis (CCA)
To evaluate the statistical significance of the canonical correlation model, we use the Wilks’ Lambda statistic (\(\lambda \)). This is a multivariate statistic that uses approximations based on the Fisher distribution for the null hypothesis, i.e., all canonical correlations are zero in the population. The small p values for this test \((< 0.05)\) suggest a rejection of the null hypothesis and that the first canonical correlation is significant. In our study, the analysis was conducted using the R software environment for Statistical Computing (R version 3.4.3) [22].
Comparison between the multivariate analysis (CCA) and a univariate analysis
The results of the CCA analysis were compared to those of a univariate analysis based on the pairwise correlation matrix calculated using the Pearson correlation coefficient. The objective of this comparison is to show that the univariate analysis cannot adapt to the complexity of biomechanical data [9] and can even mask several strong relationships if parameters are considered individually.
Clustering via correlation biplot
The results of a CCA are visualized by a correlation biplot graph, which represents the between-set correlation matrix \(R_{\mathbf{X}{} \mathbf{Y}}\) by a joint plot. This format allows for the visualization of the intra-set correlation for the original variables and the corresponding canonical variates and of the correlation between the original variables and the opposite canonical variates. The main features of a correlation biplot are the angles between the variables from sets \(\mathbf{X}\) and \(\mathbf{Y}\) in the biplot, which reflect their correlations [12]. The combined angle and direction of the \(\mathbf{X}\) and \(\mathbf{Y}\) variables indicate the importance of the positive and negative correlations of the two sets. Strongly correlated variables are very close to each other. More specifically, in our case, the correlation biplot graph is used to cluster biomechanical data and clinical parameters. The identified clusters are then used to explain the relationships between the sets of parameters within the clusters.
Canonical prediction model and regression within clusters
Once the clusters are identified, we can explain the relationship between the parameters within the clusters using a regression analysis. This analysis aims at estimating the coefficients of the linear equation, involving one or more independent variables (clinical parameters) that best predict the value of the dependent variables (biomechanical data). The purpose of regression is to predict \(\mathbf{X}\) on the basis of \(\mathbf{Y}\) within the clusters.
In order to determine which variable should be considered as dependent and which as independent, we performed a redundancy analysis. This analysis measures the proportion of variance of one original variable explained by the canonical variate of the other set. The original variables of one set are well represented by the canonical variate of the other set when the redundancy index is higher. A relational model is then proposed to determine which of the variables best explains the other. A redundancy coefficient close to 1 is considered to be the highest, and shows that the amount of the dependent (original) variable’s variance shared with the independent (canonical) variable is significant, and vice versa; a coefficient close to zero means that there is no significance in the shared variance.
Results
Univariate correlation analysis
Canonical correlations and multivariate statistic
The Wilks’ Lambda statistics of the canonical correlation model was \(\lambda =0.32\), p = 0.04. This confirms that canonical correlations are worthy of consideration and the between-set correlations are significant. The two first higher canonical correlations are \(\rho _{1}=0.52\) and \(\rho _{2}=0.44\).
Correlation clustering via biplot
Description of the retained correlation clusters between \(\mathbf{X}\) and \(\mathbf{Y}\)
Cluster | \(\mathbf{X}\) | \(\longleftrightarrow \) | \(\mathbf{Y}\) |
---|---|---|---|
\(\mathbf{C_{1}}\) | \(X_{4}\), \(X_{2}\) | \(\longleftrightarrow \) | \(Y_{6}\), \(Y_{8}\), \(Y_{13}\) |
\(\mathbf{C_{2}}\) | \(X_{7}\) | \(\longleftrightarrow \) | \(Y_{5}\), \(Y_{12}\) |
\(\mathbf{C_{3}}\) | \(X_{5}\), \(X_{9}\) | \(\longleftrightarrow \) | \(Y_{3}\), \(Y_{11}\) |
Canonical correlation model
Redundancy coefficients
The total redundancy corresponds to \(8.98\%\) of the variance of \(\mathbf{X}\) explained by the opposite canonical variate \(\mathbf{V}\), and to \(8.71\%\) of the variance of \(\mathbf{Y}\) explained by the opposite canonical variate \(\mathbf{U}\). We can therefore affirm the equality of the indices of shared variances; more specifically, both clinical and biomechanical parameters may be considered as dependent or independent.
Regression within the clusters
Multiple linear regression models
Cluster | Variables | Coefficient (Std. error) | P value | Residual Std. rrror | Adjusted \(R^{2}\) | P value of F statistic |
---|---|---|---|---|---|---|
\(\mathbf{C_{1}}\) | \(X_{2}{:}\; \text{Pain~regression~model}\) | 0.68 | 0.70 | < 0.01 | ||
\(Y_{6}\): Abd_MaxSw | 0.19 (0.02) | < 0.01 | ||||
\(Y_{8}\): Abd_Init | − 0.33 (0.08) | < 0.01 | ||||
\(Y_{13}\): Abd_RomLo | − 0.14 (0.06) | 0.035 | ||||
\(\mathbf{C_{2}}\) | \(X_{7}{:}\; \text{KOOS\_Pain~regression~model}\) | 0.63 | 0.89 | < 0.01 | ||
\(Y_{12}\): Rot_Rom | 0.26 (0.02) | < 0.01 | ||||
\(Y_{5}\): Flex_EndSt | 0.06 (0.01) | < 0.01 | ||||
\(\mathbf{C_{3}}\) | \(X_{9}{:}\; \text{KOOS\_Sport~regression~model}\) | 1.05 | 0.68 | < 0.01 | ||
\(Y_{3}\): Rot_Init | 0.12 (0.05) | 0.02 | ||||
\(X_{5}\): BMI | 1.39 (0.11) | < 0.01 |
Discussion
Cluster 1 analysis
The cluster \(\mathbf{C}_{1}\) regroups biomechanical data corresponding to kinematic parameters in the frontal plane (abduction/adduction) (\(Y_6\): Abd_MaxSw, \(Y_8\): Abd_Init and \(Y_{13}\): Abd_ROMLo) and the level of pain (\(X_2\)) as described in Tables 1, 2, and 3. The results of the multivariate regression of pain as a function of three parameters of the abduction/adduction movement (the \(X_{2}\): Pain regression model in Table 4) indicate that the pain felt is negatively correlated with \(Y_8\) and \(Y_{13}\), while positively correlated with \(Y_6\).
Cluster 2 analysis
From the second cluster \(\mathbf{C_{2}}\), the Flexion angle at the end of the stance phase (\(Y_{5}\) :Flex_EndSt), the Range of motion of the internal/external rotation (\(Y_{12}\) :Rot_Rom), and the pain measured by the score KOOS (\(X_{7}\) :KOOS_Pain) were very directly related. The association between the improvement in KOOS_Pain score and changes in the range of motion (ROM) in the transverse plane was identified by Makovey et al. [23]. The subjective value of KOOS_pain is positively correlated with parameters in the sagittal (flexion/extension) and transverse (internal/external rotation) plane as shown by the \(X_{7}\) :KOOS_Pain regression model in Table 4.
Cluster 3 analysis
From the third cluster \(\mathbf{C_{3}}\), only kinematic parameters in the transverse plane (internal/external rotation) \(Y_{3}\) presented correlations with \(X_{5}\) (BMI) and \(X_{9}\) (KOOS_Sport), more precisely the internal/external rotation angle at initial contact. The improvement in KOOS_Sport score was identified by Makovey et al. [23] as being related to the changes in the range of motion (ROM) in the transverse plane. Therefore, the model explaining the value of KOOS_Sport and recreation score as a function of the kinematic parameters in the transverse plane and the BMI showed (Table 4) positive correlations.
When comparing the multiple regression models in \(\mathbf{C_{1}}\) and \(\mathbf{C_{2}}\) (Table 4), we note that they are both related to pain scores (\(X_{2}\): Pain Numerical Scale and \(X_{7}\): KOOS_Pain) but they are not associated with the same kinematic parameters. Indeed, these two scores, i.e., \(X_{2}\) and \(X_{7}\), are quite different because they are evaluated based on different symptoms: the Pain numerical Scale variable (\(X_{2}\)) was evaluated on a 0–10 pain intensity scale and concerns a general pain felt for knees, whereas KOOS_Pain variable (\(X_{7}\)) was evaluated based on (9) questions, especially relative to the knee injury [10].
Conclusion
The CCA results showed a moderate correlation that gave rise to three clusters of the most closely related parameters. Multivariate linear models were found complementing the subjective clinical parameters by the biomechanical data using the correlation clusters.
Only the age, BMI, pain which is measured based on Pain Numerical Scale (NS), KOOS_Pain, and KOOS_Sport scores were correlated with the kinematic parameters (mechanical biomarkers). Biomechanical data corresponding to kinematic parameters in the frontal plane (abduction/adduction) during swing phase, the kinematic parameters in the sagittal plane (flexion/extension) at the end of the stance phase, and the kinematic parameters in the transverse plane (internal/external rotation) were positively correlated with pain. In other words, pain increased when kinematic parameters in those planes also increased. On the other hand, Biomechanical data corresponding to kinematic parameters in the frontal plane (abduction/adduction) at initial contact and during the loading phase were correlated negatively with pain. This means a decrease in the frontal plane at those phases is related with an increase in pain level. Kinematic parameters in the transverse plane (internal/external rotation) were correlated positively with the KOOS sport and recreation function. This means that KOOS_Sport increased when movement in the transverse plane was more increased in kinematic parameters.
Finally, the results show that a multivariate analysis of the clinical symptoms and the biomechanical characteristics of knee joint function allows a better understanding of their relationships and would help to better understand how biomechanical characteristics can be used in guiding clinical decision making in OA management.
Declarations
Acknowledgements
The authors would like to thank Alix Cagnin for data collection and management.
Funding
This research was supported by the Canada Research Chair on Biomedical Data Mining (950-231214) and FPQIS_Fond de partenariat pour un Québec innovant et en santé.
Authors' contributions
Conceptualization, formal analysis, and methodology: FB. Resources, supervision and project administration: NM. Data curation: YO. Software, validation, and visualization: FB. Writing—original draft preparation: FB. Writing—review and editing: FB and NM. Revising and correcting: NM, AF, MC, NB, MD, and NH. Clinical interpretation: NM, AF, and NH. Discussion of findings and their relevance: NM, AF, MC, NB, and NH. All authors read and approved the final manuscript.
Ethics approval and consent to participate
The data collection was approved by institutional ethics committees of the University of Montreal Hospital Research Center (Reference numbers CE 10.001-BSP and BD 07.001-BSP) and of the École de technologie supérieure (Reference numbers H20100301 and H20170901).
Consent for publication
All authors give their consent for publication.
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Authors’ Affiliations
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