IntroductionOsteoarthritis is a degenerative joint disease that affects the articular cartilage and surrounding tissues1. The common symptoms of osteoarthritis are joint pain, stiffness, locking, or sticking during the movements, which result in a reduced range of motion, functional limitation, and activity reduction1,2. The most commonly affected joints in osteoarthritis are knee and hip, respectively3. Unfortunately, from 1990 to 2019, the incidence rate of hip osteoarthritis (HOA) increased from 0.74 to 1.58 million worldwide4, and the global prevalence of HOA increased about 127%5. Despite the growing number of HOA cases and the importance of hip joint in gait stability, musculoskeletal biomechanics, and flexibility of lower limb movements6, compared to the knee osteoarthritis, the studies on HOA are quite limited7.General risk factors for osteoarthritis include older age, obesity, sex, sedentary lifestyle, genetics, manual labor, etc.; see 2,8,9,10,11. In addition to the general risk factors, studies have shown that specific gait abnormalities can increase the probability of osteoarthritis development; see 12 as a remarkable systematic review. In other words, the gait abnormality and osteoarthritis are related as cause and effect. Moreover, individuals with high probability of osteoarthritis development do not necessarily present radiographic evidence of osteoarthritis13,14, while gait analysis can detect subtle changes in movement patterns and reveal key information about the progression of musculoskeletal diseases like hip osteoarthritis15,16. Therefore, rapid gait monitoring is essential for diagnosing osteoarthritis in its early stages, controlling its development, and monitoring the medical treatments in individuals with high risk factors; see17,18. Accordingly, the common methods for HOA diagnosis such as conventional radiograph (X-ray), which is limited to clinical environments and associated radiation exposure, cannot be used for rapid monitoring of osteoarthritis development.The growing number of osteoarthritis cases and rapid development of machine learning (ML) methods have motivated researchers to focus on osteoarthritis diagnosis, severity grades detection, and the affected-unaffected leg analysis using ML models trained by kinematic19,20,21, kinetic22,23,24,25,26, and both27,28,29,30,31,32 datasets. In addition to the gait analysis using kinematic and kinetic features, other sensory information such as muscle activity (i.e., electromyography signal) can also be considered/beneficial for ML model development33,34. However, extracting kinetic and muscle information often requires sophisticated equipment, such as force plates and myoelectric sensors, which are expensive and limited to clinical environments. Accordingly, due to the availability and cost-efficiency of kinematic sensors, kinematic-based ML models are more practical for rapid osteoarthritis monitoring. In addition, some of the aforementioned studies have utilized spatiotemporal gait features for their analysis20,24,27,32, however, the analysis of such features is beyond the scope of this paper.Several ML studies attempted to diagnose osteoarthritis and classify its severity grades by mapping gait characteristics to clinical scores. For instance,35,36 utilized the Western Ontario and McMaster Universities Arthritis (WOMAC) index for detecting knee joint osteoarthritis. Moreover, the Kellgren-Lawrence (KL) scale was also used for grading knee37 and hip38,39 osteoarthritis. For additional examples, we refer to the Hip Osteoarthritis Outcome Score (HOOS)40, Knee Osteoarthritis Outcome Score (KOOS)41, and both HOOS and KOOS42.Due to gait variability within the same severity grade, similarities among different grades of osteoarthritis, and the subjectivity of HOA assessment based on clinicians’ decisions which can be influenced by various factors and potentially lead to misclassifications43, severity grades classification approaches for osteoarthritis assessment has been a failure44,45. Additionally, such categorical perspective cannot be used to monitor the effectiveness of physical treatments. Given the degenerative nature of osteoarthritis, rapid gait quality assessment requires a continuous index24. However, only a few studies have tried to present a continuous index to assess the gait quality in individuals with osteoarthritis; see24,27,31. Beynon et al.27 proposed the classifier belief level as an index for severity rating, while24,31 considered the linear regression probability as a continuous index for severity rating. Nevertheless, these continuous indexes lack clinical or physical interpretability, are sensitive to the model’s architecture, parameters, and training data, and consequently, their generalizability and robustness are questionable.In this paper, we introduce a linear, continuous, and physically interpretable Hip Osteoarthritis Index (HOI) for rating HOA based on gait kinematic data with minimal number of joints using a recently published clinical dataset46. To develop the HOI, we first define a set of gait features for the hip and knee. Then, we select the optimal pair of features using a linear support vector machine (SVM) model to maximize classification rates for healthy-patient, affected-unaffected leg, and severity grades. This optimal pair of features is used to design the HOI. To evaluate the generalization and effectiveness of our linear model, we compare its performance with two powerful machine learning models: a multi-layer perceptron (MLP) and a deep recurrent neural network (RNN). The results demonstrate the efficacy and applicability of the proposed linear model and HOI for HOA assessment.MethodsData descriptionThis study used the dataset collected by Bertaux et al.46, which includes 80 healthy individuals (45 female and 35 male) and 106 patients (55 female and 51 male) with end-stage unilateral HOA. The participants had an average age, mass, height, and body mass index (BMI) of \(63.4 \pm 12.9\) years, \(74.1 \pm 16.1\) kg, \(165.0 \pm 8.8\) cm, and \(27.1 \pm 4.9\,\hbox{kg}/\hbox{m}^2\), respectively.All participants were equipped with 35 reflective markers following the Plug-In-Gait model47. They were asked to walk a straight distance of 6 meters at a self-selected pace; For each participant, at least ten trials with one-step data were reported, resulting in a total of 4622 trials in the dataset. The kinematic data were collected using eight optoelectronic cameras (Vicon MXT40, Vicon, UK) sampled at 100 Hz. Two force plates sampled at 1000 Hz (OR6-5, AMTI, USA) were used to record three-dimensional (3D) ground reaction forces and moments. Video recording was performed on both the sagittal and frontal planes, and the data were processed using Vicon Nexus software.The data were collected once for healthy individuals and twice for individuals with HOA; before and 6–7 months after total hip arthroplasty surgery. Before surgery, a radiographic analysis was performed on each patient to diagnose the affected leg and determine the severity grade using the KL grading scale. The participants were classified into four groups: Healthy, Grade 2, Grade 3, and Grade 4 with 80, 18, 47, and 37 participants for each group, respectively. However, as reported in46, the severity grades could not be determined for 4 participants based on the radiographic images.Data cleaning and data availabilityDue to the focus of this study on proposing a kinematic index for gait quality assessment, only the kinematic data were used for our entire gait analysis. Additionally, in accordance with the suggestion provided in the dataset46, only the angles in the sagittal plane were utilized for this study, i.e., ankle, knee, and hip angles in the sagittal plane. Based on our initial analysis and comparison of joint average trajectories pre- and post-surgery, along with the observation that the knee joint is more affected by HOA than the ankle in the sagittal plane48, we concluded that hip and knee kinematics are sufficient for HOA diagnosis, severity grade detection, and rating. Accordingly, the ankle joint trajectories are not considered in our analysis, but the cleaned ankle joint trajectories are available in our online dataset.Prior to cleaning, we performed pre-processing on the trials, which included shifting the trajectories in time to ensure the joint trajectories start from the heel strike event and adjusting the knee angle to correct hyperextensions. The rationale for correcting hyperextensions was that patients with HOA show reduced knee extension during the stance phase and tend to maintain their knee more flexed rather than extending it beyond normal ranges49. Therefore, hyperextensions in the knee joint could result from marker misalignment during data collection. To apply a consistent systematic strategy across all trials, we corrected hyperextensions for all participants and trials. However, we performed our analysis even without this correction and notably the results of our analysis in the rest of the paper remained nearly unchanged, showing on average 0.03% difference with a maximum change of 4%.In the cleaning process, a total of 1358 trials, including 36 participants, were excluded from our gait analysis; for Healthy, Grade 2, Grade 3, and Grade 4 1, 1, 14, and 16 participants were excluded, respectively. The exclusion criteria included the following procedures in order: (1) trials involving patients without a determined KL score, (2) trials that exceeded 2.5 standard deviations of average of knee and hip joint trajectories across all participants, (3) distorted or incomplete trajectories, (4) trials with missing knee or hip trajectory data, and (5) trials from patients who lacked pre- or post-surgery data.In this procedure, 4 patients along with 132 trials were excluded due to an undetermined KL score, 811 trials including 7 participants were removed for exceeding 2.5 standard deviations, 147 trials for being distorted or incomplete, 24 trials for lacking hip or knee joint trajectories, and in the remaining data 25 patients along with 244 trials were excluded due to not having pre- or post-surgery data. The average trajectory of each joint in the cleaned dataset for different severity grades, pre- and post-surgery, is illustrated in Fig. 1. The distribution of each group (healthy, grade 2, grade 3, and grade 4) categorized by sex, BMI, and age subgroups after the cleaning process is shown in Table 1. Also, the mean and standard deviation of BMI and age for each group after cleaning are shown in Table 1. The cleaned dataset can be downloaded from here50.Fig. 1Comparison of the joint angle trajectories in the sagittal plane. This figure compares the averaged profiles of joint angles for the cleaned data. The illustrated trajectories are hip (A, D), knee (B, E), and ankle (C, F) joint angles for both healthy individuals and affected leg of patients in different severity grades pre- (A–C) and post-surgery (D–F). As depicted in (A–C), for all three joints, the average trajectories of healthy individuals and patients are separable. In addition, compared to the other joints, hip joint average trajectories provide better discrimination among healthy individuals and patients in different severity grades. Also, the average joint trajectories of patients in grade 3 and grade 4 are very similar, which makes them difficult to separate. Post-surgery, as illustrated in (D–F), still the trajectories of healthy individuals and patients are separable. However, compared to pre-surgery, the post-surgery trajectories of patients are more similar to those of healthy individuals across all three joints.Full size imageTable 1 Distribution of participants in different categories after cleaning.Full size tableFeature extractionFor each participant, 14 linearly independent and physically interpretable features were extracted from the averaged knee and hip joint trajectories of all trials. For healthy participants, the features were extracted once for each leg. For patients, four sets of features were extracted: (1) pre-surgery affected leg, (2) pre-surgery unaffected leg, (3) post-surgery affected leg, and (4) post-surgery unaffected leg.The features can be divided into three main categories: (1) angle-based features extracted from joint angles, (2) velocity-basedFootnote 1 features extracted from the time derivative of joint angles, and (3) velocity-angle-based features extracted from joint limit cycles; see Fig. 2 for an illustration and a detailed description of all features. Some of our suggested features are derived from the gait parameters that were formerly introduced in the lower limb rehabilitation literature, such as gait path: knee-hip angle profile51, limit cycle: hip/knee velocity-angle profile52, and gait speed: Frobenius norm of hip-knee velocity as a function of gait cycle53.Fig. 2The extracted features. This figure illustrates the features extracted from different gait variables. (A) Hip trajectory; (F1) hip maximum extension, and (F2) hip range of motion. (B) Knee trajectory; (F3) knee maximum flexion, and (F4) knee range of motion. (C) Gait path; (F5) area of gait path. (D) Hip velocity; (F6) hip maximum angular velocity, and (F7) hip minimum angular velocity. (E) Knee velocity; (F8) knee maximum angular velocity, and (F9) knee minimum angular velocity. (F) Path speed; (F10) area of path speed. (G) Hip limit cycle; (F11) area of hip limit cycle. (H) knee limit cycle; (F12) area of knee limit cycle during swing (the greater closed curve), and (F13) area of knee limit cycle during stance (the smaller closed curve). (I) Gait speed is computed as Frobenius norm of hip and knee angular velocities, which is a function of gait cycle; (F14) area under gait speed during mid-swing. In all graphs, the zero gait cycle is considered at the heel strike instant.Full size imageMachine learning modelsThree different data-driven models were employed: (1) an SVM model, where we develop our linear index, (2) an MLP as a feature-based ML model, and (3) a deep RNN as a feature-free ML model. For each model, three different classification scenarios were considered for this study: (1) healthy-patient binary classification, (2) affected-unaffected leg binary classification, and (3) severity grades three-class classification. A five-fold cross-validation was employed to analyze classification repeatability and prevent any randomly generated results. All ML models were built, trained, tested, and evaluated using Python (v3.10), with the TensorFlow (v2.15) and Scikit-learn (v1.2.2) libraries.SVM model, regression line, and linear indexSVM models with linear kernel were utilized to choose the best pair of features and investigate the classification power of our linear model. In all scenarios, the best pair of the extracted features from right and left legs are used as inputs; the best pair of features for linear model are those that maximized the SVM evaluation results. For severity grades three-class classification scenario, we employed one-vs-one strategy. The regression line was fitted based on the best features of healthy individuals and the pre-surgery affected leg of patients. The hip osteoarthritis index (HOI) for an individual was computed as the normalized minimum-distance projection of the individual’s features on the regression line.MLP modelIn all three MLP scenarios, all of the extracted features from the right and left legs (in total, 28 features) are utilized as inputs. In some conditions, the MLP models also used the general risk factors (sex, BMI, and age) as input features. For all MLP layers, the activation functions were ReLU, except for the output layer, which was softmax. The minimum number of parameters among the MLP models was 1.3 K.The MLP models were trained using two approaches: with and without general risk factors. Moreover, to evaluate the MLP model performance under each general risk factor, each model was also trained under different sex, BMI, and age categories, as shown in Table 1. In total, the MLP models were trained, tested, and evaluated in nine different conditions.Deep RNN modelIn all three deep RNN scenarios, the right/left hip/knee trajectories are utilized as four sequential inputs in the long-short-term-memory (LSTM) layer, with no time-related input. In some conditions, the deep RNN models also used the general risk factors as input features. For all deep RNN models, a five-layer neural network was implemented: LSTM as the first layer, feature concatenation as the second layer to add general risk factors (sex, BMI, and age), three fully connected layers with ReLU activation functions, and softmax as the output layer; the minimum number of parameters among the deep RNN models was 124 K.The models were trained using two approaches: with and without general risk factors. Moreover, the trained deep RNN models were also evaluated using unseen and perfect unseen trials of a participant. Unseen trials refer to individual trials removed from the training dataset, while perfectly unseen trials refer to cases where all trials of the test participant were removed from the training dataset. To study the importance of each general risk factor in the performance of the trained deep RNN models, a sensitivity analysis was conducted by eliminating each risk factor in the evaluation process and checking the model performance on perfect unseen trials in terms of classification accuracy. In total, the models were trained, tested, and evaluated in seven different conditions.StatisticsTo select the most effective extracted features, we conducted the Kruskal-Wallis supervised feature selection test (the non-parametric equivalent of the one-way ANOVA test) using pre-surgery data as the dependent variable and healthy-patient label as the independent variable. We ranked features using the \(-log\)(p-value) derived from the test, and selected those with scores higher than \(-log\)(p-value)\(>60\). The linear correlation coefficients between the features, general risk factors, severity grades, and the proposed linear index were evaluated using Pearson’s correlation coefficient.We also employed one-way ANOVA test with a significance level of 0.05 to determine if the means of different groups are statistically significant. one-way ANOVA test assumes that observations are independent, the dependent variable is continuous, and the variances across groups are homogeneous; all these conditions were studied prior to applying the one-way ANOVA test. For paired comparisons, we utilized the independent sample t-test and paired sample t-test, with a significance level of 0.05. These tests assume normality of data, independence of observations, and homogeneity of variances (for the independent sample t-test); all these conditions were studied prior to applying the t-test. Bonferroni correction was also considered to control for Type I error in multiple comparisons. All statistical analyses were conducted, and test assumptions were examined using the Statistical Package for the Social Sciences (SPSS, v26, IBM Corporation) and MATLAB R2023a.ResultsFeature selectionPre-surgery features’ Kruskal-Wallis test and cross-correlation results are presented in Fig. 3A and B, respectively. The features with \(-log\)(p-value)\(>60\) are the candidates for the linear index design. Based on the Kruskal-Wallis test results, F5 (area of gait path; see Fig. 3G) provides the highest Kruskal–Wallis feature selection score; i.e., this feature can provide the highest level of healthy-patient classification rate. Besides F5, F6 (hip maximum angular velocity; see Fig. 3H), F10 (area of path speed; see Fig. 3I), and F11 (area of hip limit cycle; see Fig. 3J) are also among the candidate features for linear index design. Nevertheless, healthy-patient classification rate is not the only criterion for feature selection; the best pair of features should also provide a high affected-unaffected leg classification rate, severity grades classification rate, and linear regression goodness of fit; i.e., \(R^2\).Fig. 3Feature selection. (A) Features’ rank based on Kruskal-Wallis supervised feature selection test. (B) The features’ cross-correlation results. (C–F) compare the pairs of candidate features in terms of (C) linear regression \(R^2\), (D) healthy-patient classification rate, (E) affected-unaffected leg classification rate, and (F) severity grades classification rate. In addition, (G–J) illustrate the average profiles of the gait parameters for selected features of healthy individuals and pre-surgery affected leg of patients in different severity grades; (G) shows the area of gait path (F5), (H) depicts the hip maximum angular velocity (F6), (I) illustrates the area of path speed (F10). and (J) shows the area of hip limit cycle (F11).Full size imageThe paired comparison of the candidate features in terms of \(R^2\), healthy-patient, affected-unaffected legs, and severity grades classification rates are presented in Fig. 3C–F, respectively. Comparing all four indicators, it is concluded that F6 (hip maximum angular velocity) and F10 (area of path speed) are the best pair for presenting a linear gait quality index with \(R^2 = 92\%\) reported in Fig. 3C, 84% healthy-patient classification rate presented in Fig. 3D, 91% affected-unaffected leg classification rate reported in Fig. 3E, and 41% severity grades classification accuracy depicted in Fig. 3F.Hip osteoarthritis indexFigure 4 presents the overall results of the proposed linear model and index. The regression line, computed based on the best-selected features (F6 and F10) of healthy participants and affected legs of patients pre-surgery, is used throughout Fig. 4. The normalized projection of the data points on the regression line is considered as HOI, where HOI \(=0\) (HOI \(=1\)) indicates the highest similarity to the normal (grade 4) gait pattern; see Fig. 4A. Figure 4A shows the distribution of data points for healthy individuals and affected legs in different severity grades along the regression line (\(R^2 = 0.92\)), pre-surgery. Also, there is a strong correlation (\(r = 0.76\)) between pre-surgery HOI of affected legs and KL grades, including healthy individuals. This correlation becomes weaker for post-surgery data (\(r = 0.55\)).Fig. 4Hip osteoarthritis index results. (A, B) The scatter plot of area of path speed (F10) versus hip maximum angular velocity (F6) for individuals and affected leg of patients in three different severity grades (i.e., , , and ) (A) pre- and (B) post-surgery. (C) compares the distribution of HOI in healthy individuals with affected legs in different severity grades pre- and post-surgery; the seven-group one-way ANOVA test with \(p^*< 0.0001\). (D, E) The scatter plot of area of path speed (F10) versus hip maximum angular velocity (F6) for the and legs and individuals (D) pre- and (E) post-surgery. (F) compares the distribution of HOI in individuals with and legs pre- and post-surgery; the five-group one-way ANOVA test with \(p^*< 0.0001\). Note that the regression line in all subfigures is identical, computed using the best features from healthy participants and the pre-surgery affected legs of patients.Full size imagePost-surgery, the regression line remains valid (\(R^2 = 89\%\)), and the distribution of data points for affected legs has shifted closer to that of healthy individuals; see Fig. 4B. Accordingly, the HOI difference between affected leg pre- and post-surgery for each severity grade is statistically significant (\(p^*0.16\) for all paired comparisons within each scenario). Although all models were successful for healthy-patient diagnosis (\(86.5\pm 2.5\%\)) and affected and unaffected legs pre-surgery detection (\(89.5\pm 1.5\%\)), all of them failed to properly classify different severity grades (accuracies \(40.5\pm 1.5\%\)). This is also observed in comparing the distribution of HOI for different severity grades pre-surgery, where the multiple comparison of HOI distribution among three different severity grades failed; see Fig. 4C. In other words, although there is a high discrimination between gait kinematic of healthy and patients, there is a high similarity between different severity grades, which makes them hardly separable.Table 3 The overall comparison between linear, MLP, and deep RNN models.Full size tableDiscussionIn this paper, we presented the gait analysis of the dataset recorded from 80 healthy and 106 patient individuals with end-stage unilateral HOA. The entire kinematic part of the dataset was cleaned, the joint trajectories were studied, the gait features were extracted, and a gait quality index for HOA rating was proposed.The Kruskal-Wallis test was employed to rank the extracted features as candidates for linear model design; selection criteria: healthy-patient classification rate. The area of gait path, hip maximum angular velocity, area of path speed, and area of hip limit cycle were selected as the candidate features. Interestingly, these candidate features were among our newly suggested features for osteoarthritis gait analysis from lower limb rehabilitation literature. The paired combinations of candidate features were evaluated in terms of goodness of fit, healthy-patient, affected-unaffected leg, and severity grades classification rates. Comparing the evaluation results, the hip maximum angular velocity and area of path speed were selected as the best pair for linear model design. While one might argue that changing the feature selection criteria (e.g., severity grade classification accuracy) could yield different pairs of features with better evaluation results, we tested various combinations and found the presented pair to be the best.HOI evaluation and machine learning model selectionThe proposed linear model was compared with two well-known ML models (MLP and deep RNN) to address two key questions:1.Is the proposed linear model the best linear model that can be designed based on the extracted features? The MLP model was used to answer this question, as it utilizes all extracted features and can derive the best possible (linear and nonlinear) model from them.2.Are the extracted features the best possible features that can be derived from the gait kinematics? The deep RNN model was employed to answer this question, as it effectively handles sequential data such as gait kinematics. Being feature-free, it captures information directly from the joint trajectories, which has been previously used for feature extraction from gait data in the literature54.The comparable average accuracies of linear, MLP, and deep RNN models along with no statistically significant differences between their results indicate that the response to both questions is yes.While our deep RNN and MLP models were sufficient to address these questions, alternative architectures can also be explored. For deep RNNs, models like Quasi-Recurrent Neural Networks (QRNNs)55 and Transformer-based architectures56 could offer potential options. For MLP models, Convolutional Neural Networks (CNNs)57, Gradient Boosting Machines (GBMs)58, and Kolmogorov-Arnold Networks (KANs)59 may provide valuable alternatives. However, using more complex structures, such as those mentioned, may not necessarily improve performance due to the large number of parameters and the lack of sufficient training data. Therefore, we selected more generalized models like RNN and MLP for this study.Advantages of HOIThe high correlation between the HOI and KL grades (including healthy individuals), along with the strong discrimination between healthy individuals and patients, affected and unaffected legs, and pre- and post-surgery of affected legs within each severity grade, confirm the effectiveness of the proposed model and index. In addition, the comparable classification accuracies of our linear model with MLP and deep RNN models further validate the model’s efficacy. Moreover, HOI has some other advantages which cannot be attained by other machine learning models.1.The linear model is physically interpretable. Assuming a healthy participant with degenerating gait quality, an individual after joint surgery, or the unaffected leg of a patient, the output of ML models for such cases is not clear. However, since the linear model is interpretable, its accuracy in such cases is guaranteed; i.e., the higher hip maximum angular velocity and area of path speed result in the lower HOI, the better gait quality, and the lower HOA risk.2.The linear model provides the gait quality rating as HOI. An orthopedic doctor or a physiotherapist can rapidly measure this index during the treatment sessions and assess HOA development; see Fig. 5. This unique property is the advantage of using an interpretable model, which other complex and non-transparent ML models, such as MLP and deep RNN, cannot provide.3.The linear model is personalized and compares each individual with themselves across the index line, rather than assigning a specific grade to each patient, particularly for those with low gait similarity to others in the same group.4.The proposed linear model and HOI are based on kinematic information; hence, using inertial measurement units (IMUs) or smartphones camera, HOA can be detected, measured, and consequently, the gait quality can be tracked to warn an individual and prevent early stages of HOA.Fig. 5Application flow diagram. This figure illustrates the application flow diagram of the designed linear model and index for HOA diagnosis, affected leg detection, severity grades classification, and computation of HOI. The diagram begins with kinematic data acquisition from a camera or an IMU sensor, followed by HOA diagnosis and the affected leg detection. It then proceeds to severity grade classification and HOI computation. Monitoring the HOI values over time provides physiotherapists with a comprehensive view to assess the development of HOA.Full size imageKinematic measurementThe proposed HOI is built upon gait kinematic measurements. Accordingly, the accuracy of the kinematic measurement device is an important factor that can limit HOI application and impact its performance. Various devices and measurement techniques can be used to assess gait quality and extract HOI such as marker-based, markerless, and inertial motion capture systems. However, regardless of the measurement technique, it is essential to evaluate the robustness of the proposed HOI in the face of measurement error.It is important to note that the proposed HOI is defined based on the average of gait trials rather than a single precise gait measurement. Hence, it is robust to noise in kinematic measurements and Gaussian-type distortions. Additionally, in this dataset, the average (maximum) root mean squared error (RMSE) of patients across trials is \(9.56^\circ\) (\(22.41^\circ\)) for the hip joint and \(6.53^\circ\) (\(15.67^\circ\)) for the knee joint, indicating that regardless of the measurement approach and device, if the measurement error is less than \(6.5^\circ\), HOI can be properly extracted from kinematic data. However, selecting an appropriate measurement method involves a trade-off between accuracy, cost-efficiency, accessibility, ease of use, and time limitations.In addition to device-related errors, inter-rater reliability is a critical factor when evaluating the clinical applicability of HOI. Since HOI is computed from averaged gait kinematics across trials and does not depend on subjective interpretation, it is inherently less sensitive to rater-dependent variability. However, measurement techniques that require extensive calibration procedures or rely heavily on trained operators can introduce rater-related errors. To minimize the subjectivity in HOI computation, it is therefore important to employ measurement methods that are robust to manual annotation and less dependent on operator expertise.Marker-based systems, such as Vicon which are commonly used for clinical gait analysis are considered the standard for human motion capture. Despite their high accuracy, they have limitations, including equipment costs, reliance on laboratory environments, time-consuming preparation and data analysis, and the need for trained operators60,61. In contrast, recent advancements in artificial intelligence and deep learning have led to the development of markerless methods for human gait analysis. One such method is multi-camera systems which estimate the 3D pose from data collected by multiple cameras. Some recently developed multi-camera systems can collect gait data with high accuracy and reliability62,63. While multi-camera systems offer a faster and more time-efficient data collection method compared to marker-based systems, they still come with high costs, are limited to clinical environments, and typically require trained personnel for setup and handle calibration. Inertial motion capture systems can also be used to accurately extract knee and hip joint trajectories by applying IMUs64, making them suitable for determining HOI. However, IMU systems can be expensive, prone to noise and accumulative error in long-term usage, and require time-consuming setup and calibration procedures, necessitating trained operators for proper deployment.60.Alternatively, pose estimation methods, which detect joint landmarks in a video, such as OpenPose65, DeepLabCut66, have demonstrated highly accurate and reliable performance along with high accessibility and cost-time efficiency67,68. Additionally, an open-source gait data collection and analysis platform called OpenCap69 has been developed. This platform utilizes video captured from at least two smartphones to compute 3D joint kinematic analysis via a web-based service. OpenCap has been shown to perform comparably to markerless multi-camera systems, achieving an RMSE of 5.8° in gait kinematic measurement61. The effectiveness of this method has also been evaluated for patients with knee osteoarthritis70. These methods are largely automated and rater-independent, making them suitable for less-equipped clinical settings.Limitations and future worksDespite the presented encouraging results, there are some limitations which should be counted and considered. The utilized dataset does not encompass a full range of demographic data across different age and BMI groups or geographical conditions, which may influence the outcomes. Also, the dataset lacks sufficient clean data for all severity grades, especially grade 2, and contains no data from grade 1 patients. In addition, several trials lacked complete joint trajectory data, and post-surgical data were unavailable for some patients. Moreover, this study focused solely on the kinematic aspects of the dataset to propose an accessible and affordable gait quality index. Based on these limitations, future directions are considered as follows:1.More diverse clinical data collection to enhance the study and validate the reliability and generalizability of HOI across different grades of HOA.2.Exploring additional aspects of gait, including spatiotemporal parameters such as stride time, cadence, stride length, and step length, as well as kinematic features from other joint coordinates, including ankle and pelvic rotation, and upper limb movements.3.Kinetic and other sensory information, such as force and EMG data, could be explored for additional studies on HOA development.4.Since the index uses the angular velocity of the knee in the F10 (area of path speed) feature, the generalizability of HOI could also be investigated in patients with knee osteoarthritis.Data availabilityThe dataset analyzed during the current study is available in the Figshare repository, https://figshare.com/projects/Dataset_of_gait_analysis_data_of_hip_osteoarthritis_patients_before_and_6_month_after_arthroplasty_and_asymptomatic_volunteers/91103. The cleaned dataset is available in the Figshare repository, https://doi.org/10.6084/m9.figshare.26336998.v1. The codes used to clean data and generate results during the current study are available in Figshare repository, https://doi.org/10.6084/m9.figshare.26336812.v1.NotesIn this subsection, the term “velocity” refers to “angular velocity”.ReferencesLespasio, M. J. et al. Hip osteoarthritis: A primer. Perm. J. 22, 17–84 (2018).PubMed PubMed Central Google Scholar Katz, J. N., Arant, K. R. & Loeser, R. F. Diagnosis and treatment of hip and knee osteoarthritis: A review. JAMA 325, 568–578 (2021).PubMed PubMed Central Google Scholar Aresti, N., Kassam, J., Nicholas, N. & Achan, P. Hip osteoarthritis. BMj354 (2016).Fu, M., Zhou, H., Li, Y., Jin, H. & Liu, X. Global, regional, and national burdens of hip osteoarthritis from 1990 to 2019: Estimates from the 2019 global burden of disease study. Arthritis Res. Ther. 24, 1–11 (2022).Google Scholar Long, H. et al. 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Also, authors would like to thank Parsa Sattari and Mostafa Hamidifard for their comments on the first draft of this paper.Author informationAuthors and AffiliationsResearch Institute for Robotics, Artificial Intelligence, and Information Science (RAIIS), School of Electrical and Computer Engineering, University of Tehran, Tehran, IranKamyar Rahmani, Mansour Davoudi, Mohammad Sajjad Alamdar & Rezvan NasiriAuthorsKamyar RahmaniView author publicationsSearch author on:PubMed Google ScholarMansour DavoudiView author publicationsSearch author on:PubMed Google ScholarMohammad Sajjad AlamdarView author publicationsSearch author on:PubMed Google ScholarRezvan NasiriView author publicationsSearch author on:PubMed Google ScholarContributionsKamyar Rahmani: literature review, writing the paper, preparing figures, cleaning dataset, and running machine learning models. Mansour Davoudi: preparing figures, statistical analysis, cleaning dataset, running machine learning codes, and proofreading the text. Mohammad Sajjad Alamdar: cleaning dataset, running machine learning models, and proofreading the text. Rezvan Nasiri: supervision, data analysis, conceptualization, writing the paper, and preparing figures.Corresponding authorCorrespondence to Rezvan Nasiri.Ethics declarationsCompeting interestsThe authors declare no competing interests.Additional informationPublisher’s noteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Kamyar Rahmani and Mansour Davoudi contributed equally to this work.Rights and permissionsOpen Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. 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