# Prediction of Wear Rates of UHMWPE Bearing in Hip Joint Prosthesis with Support Vector Model and Grey Wolf Optimization

Authors: Rania E. Hammam; Hani Attar; Ayman Amer; Haitham Issa; Ioannis Vourganas; Ahmed Solyman; P. Venu; Mohammad R. Khosravi; Mohanad A. Deif
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

One of the greatest challenges in joint arthroplasty is to enhance the wear resistance of ultrahigh molecular weight polyethylene (UHMWPE), which is one of the most successful polymers as acetabular bearings for total hip joint prosthesis. In order to improve UHMWPE wear rates, it is necessary to develop efficient methods to predict its wear rates in various conditions and therefore help in improving its wear resistance, mechanical properties, and increasing its life span inside the body. This article presents a support vector machine using a grey wolf optimizer (SVM-GWO) hybrid regression model to predict the wear rates of UHMWPE based on published polyethylene data from pin on disc (PoD) wear experiments typically performed in the field of prosthetic hip implants. The dataset was an aggregate of 29 different PoD UHMWPE datasets collected from Google Scholar and PubMed databases, and it consisted of 129 data points. Shapley additive explanations (SHAP) values were used to interpret the presented model to identify the most important and decisive parameters that affect the wear rates of UHMWPE and, therefore, predict its wear behavior inside the body under different conditions. The results revealed that radiation doses had the highest impact on the model’s prediction, where high values of radiation doses had a negative impact on the model output. The pronounced effect of irradiation doses and surface roughness on the wear rates of polyethylene was clear in the results when average disc surface roughnessRa values were below 0.05 μm, and irradiation doses were above 95 kGy produced 0 mg/MC wear rate. The proposed model proved to be a reliable and robust model for the prediction of wear rates and prioritizing factors that most significantly affect its wear rates. The proposed model can help material engineers to further design polyethylene acetabular linings via improving the wear resistance and minimizing the necessity for wear experiments.


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## Body

## 1. Introduction

The hip joint is one of the most important synovial joints in the human body; so, when it is arthritic or injured, the natural hip joint must be replaced to relieve the related discomfort and to reestablish its functionality. Consequently, the acetabular cartilage and femoral surfaces are removed and then replaced by a hemispherical acetabular component and a spherical femoral head to complete the joint replacement process successfully [1].Since artificial joints functions under sliding and rolling situations [2, 3], particular mechanical wear validation processes are performed over it to testify the replacement joint’s specifications, such as adhesion, abrasion, and fatigue. The adopted verification processes is called ‘the surface degradation validation,’ taking into consideration that increasing the external load and/or the surface roughness of the replacement joint’s contact materials speeds up the wear process. The tribiological system of the joint prosthesis and its deterioration process is defined by the interplay of all of these elements. Consequently, the mechanical qualities and wear resistance of the typical artificial joint’s component materials dictate its expected lifetime.Metallic alloys, including ceramics or cobalt-chromium-molybdenum alloys (CoCrMo), such as alumina composites, agreed to have good functional characteristics, such as hardness, chemical stability, and wear resistance, which allows employing them for the femoral bearings [4].Ultrahigh molecular weight polyethylene (UHMWPE) is also regarded as one of the most successful acetabular bearing materials in total hip prosthesis due to its inimitable mixture of superior wear, fatigue resistance, toughness, chemical stability, as well as a good biocompatibility over other polymers [5, 6]. However, nowadays, UHMWPE produces nanosized and submicron wear debris in large amounts, overwhelming the body’s capability to effectively remove the material. The generated wear debris triggers hostile tissue reactions while articulating with the metallic contact, which leads to osteolysis or bone loss followed by implant loosening and failure [7–9]. The major problem that limits the lifetime of the complete joint prosthesis is the related polyethylene wear-induced osteolysis.Thus, intensified investigations were conducted on increasing the performance and UHMWPE wear resistance in the last 50 years, to provide patients who are youthful and active with long-lasting and effective implants. The studies included methods for enhancing the properties of UHMWPE, such as cross-linking through irradiation [10], surface modification through plasma treatment [11, 12], or reinforcements with particles or fibers [13–15].Recently, cross-linked ultrahigh molecular weight polyethylene has been developed for the use of acetabular cups of hip joint prostheses. A major advantage of cross-linked UHMWPE is that it has lower wear rates compared to the conventional uncross-linked material. Among all cross-linking procedures, Irradiation is the most popular and successful process for cross-linking and/or sterilizing UHMWPE [16–19]. Radiation cross-linking developed by the use of high doses of gamma or electron beam radiation was reported to improve the hardness, lower the ductility of the polymer, and enhance the UHMWPE wear resistance [19–21]. This is because the presence of cross-links prevents UHMWPE from orienting on its surface and thus decreases the production of wear particles caused by shear forces from crossing path motion [22].UHMWPE wear resistance improves when the radiation does increases; however, high dose rates of radiation accelerate the oxidation process as a result of the presence of free radicals that react with oxygen causing brittleness and failure of the implant [23]. Consequently, efforts have been undertaken to reduce the free radicals via thermal treatment, such as gamma-irradiated and melted UHMWPE [24], gamma-irradiated and annealed UHMWPE [25], and vitamin-E blending in UHMWPE as a free radical scavenger. Highly cross-linked polyethylene (HXPE) and vitamin-E-infused/blended cross-linked polyethylene (VEXPE) have shown substantially less wear in vitro [26] and in vivo [27] than the ordinary UHMWPE.To assess the wear behavior of UHMWPE utilized in metal-on-polyethylene (MoP) prosthetic hip implants, several testing configurations such as pin-on-disc (PoD), pin-on-plate, and hip joint simulators have been employed. In a PoD wear measurement coupled to MOP prosthetic hip implants, a polyethylene pin is loaded against a metallic disc, and relative motion between the pin and the disc causes polyethylene wear. PoD wear studies are frequently performed to quantify, compare, and rank the wear of various implant-bearing material combinations as a function of operational factors and environmental conditions. Comparing polyethylene wear results from numerous PoD tests, on the other hand, might be time consuming and complex, potentially leaving information unclear.However, in recent years, researchers have employed machine learning techniques in conjunction with existing datasets to facilitate modeling complex correlations between material structure, constituents, and the corresponding mechanical qualities. These models also help in visualizing and comparing datasets, as well as predicting new results based on the existing knowledge embedded in the model, which would otherwise be difficult or time-consuming to obtain using traditional experimental methods [28].Intelligent prediction and analysis models have been introduced and studied by many researchers in various applications. Gated recurrent unit (GRU) networks have been proposed for point of interest (PoI) category prediction [29] and next PoI recommendation [29]. A long short-term memory (LSTM) model has been studied by Liu et al. [30] for green house climate prediction. Abbasi and Rafiee [31] presented a new analysis framework for predicting the performance of packet classification algorithms on GPU-like highly threaded machines. Nowadays, the internet of things (IoT) has attracted many researchers and academics due to its innovative functions and applications in many fields, such as smart city applications [32] and intelligent transportation systems [33].Due to the complex wear behavior of UHMWPE, it is necessary to find a practical machine learning model to predict the wear rates of polyethylene and therefore supplement time consuming PoD experiments. Hence, this study was aimed at proposing an efficient machine learning algorithm that predicts the wear rates of UHMWPE applied as a bearing material in hip joint prosthesis. The employed dataset was based on published polyethylene data from PoD wear experiments specifically performed in the field of prosthetic hip implants. The proposed model facilitates the understanding and comparison of the data driven from PoD experiments in order to predict the wear performance of UHMWPE inside the body and, therefore, predict its lifetime, which also helps material engineers to further improve the design of polyethylene acetabular linings in order to enhance its performance and mechanical properties and lengthen its lifetime inside the body. The model also assists in identifying and prioritizing factors that most significantly affect polyethylene wear rates. A correlation between the different parameters and wear rates of UHMWPE was also investigated. Another important goal of the proposed research is to investigate the impact of radiation doses and their relation to other factors affecting the wear rates of polyethylene, which helps in determining the optimum radiation doses that produce lower wear rates.The proposed machine learning models presented in this work were Classic SVM, SVM-GWO, SVM using practical swarm optimizer (SVM-PSO), SVM using the genetic algorithm optimizer (SVM-GA). The model’s performance was assessed using the root mean square error (RMSE) and theR2 scores to select the best fit model capable of analyzing and predicting the UHMWPE wear rates based on several operating parameters in PoD experiments. Furthermore, Shapley additive explanations (SHAP) values were used to interpret the model’s prediction accuracy.


## 2. Materials and Methods

### 2.1. Dataset Acquisition

The dataset employed in the proposed study consisted of 129 data points and is adapted from a previous work conducted by Borjali et al. [34]. The dataset was an aggregate of 29 different PoD published UHMWPE datasets performed in the field of prosthetic hip implants. Published datasets collected from Google Scholar and PubMed databases were gathered using keywords including “UHMWPE”, “wear”, “hip” and “Pin-on-Disc”. CoCrMo alloys and ceramics are the two most popular materials for the femoral head in hip joint prostheses, while the acetabular liner is often constructed of ultrahigh molecular weight polyethylene, as discussed earlier in this paper. As a result, this study focused solely on multidirectional motion between a polyethylene pin and a CoCr disc, with flat-on-flat geometry and bovine serum as a lubricant.Additionally, only experiments with properly specified and published operating input parameters as well as polyethylene wear rate statistics were included. UHMWPE wear was assessed using the ASTM F732 standards wear rate (mg/MC), which is measured in terms of material loss per million cycles (MC). The wear rate is calculated by multiplying the normal load, sliding distance, and polyethylene density by the wear factor, which is the wear volume per normal load unit and sliding distance [35]. In cases of missing polyethylene densities, a UHMWPE density of 0.93 mg/mm3 was employed, as reported in previous literature [36]. The UHMWPE materials employed in the dataset were mostly conventional GUR 1020 and 1050. The lubricant temperature range was 25-37°C.


### 2.2. Input Parameters

Several important parameters have a major impact on the UHMWPE wear rates in PoD experiments and, therefore, affect its performance in vivo when applied to the acetabular lining in the hip joint prosthesis. Polyethylene wear has been linked to both the applied stress on the pin and the contact area between the pin and the disc by several researchers [37, 38]. The UHMWPE wear rate is also affected by the disc surface roughness [39] and the lubricant employed in the PoD wear tests. Bovine serum is frequently utilized as a lubricant for PoD wear trials in the setting of prosthetic hip implants [40].The wear aspect ratios and sliding distances are also relevant factors affecting the wear rates of polyethylene. The wear aspect ratio is a metric for determining the shape of motion paths and, as a result, the likelihood of wear between the femoral head and the polyethylene acetabular cup liner. The sliding distance is the overall length of the worn path. The radiation dose (presented in [41]) is another major aspect mentioned in the literature; increasing the radiation dose enhances polyethylene cross-linking, which increases wear resistance.The shapes of the multidirectional wear path employed in the dataset were rectangular, elliptical, circular, and square paths. In the circular and elliptical wear pathways, cross-shear occurs on the surface of the pin throughout the worn route, whereas cross-shear occurs when the pin changes direction along the worn path in the rectangular and square wear paths.Hence, the most relevant operating factors affecting the wear rates of UHMWPE in PoD experiments were selected as input parameters to the proposed models. These parameters included the following: contact area (mm2), wear path aspect ratio, normal load (N), sliding distance per cycle (mm/C), disc average surface roughness (Ra) (μm), polyethylene radiation dose (kGy), frequency (HZ), and test duration in million cycles (MC). The description of the input operating parameters is summarized in Table 1.Table 1
Input parameters.
ParameterDescriptionContact areaContact area between the polyethylene pin and the CoCr disc which in vivo represents the contact area between the CoCr femoral head and UHMWPE acetabular liner in the hip joint prosthesis and it is measured in mm2Wear path aspect ratioThe ratio of the wear path length to the perpendicular width of path, and it provides a way to quantify the shape of motion pathsNormal loadApplied stress on the polyethylene pin and it is measured in Newton which clinically represents the weight of the patient on the artificial hip prosthesisSliding distance per cycleOverall distance of the worn path taken by the polyethylene pin in PoD experiments and it is measured in mm per cycleDisc average surface roughness (Ra)Surface roughness is calculated measuring the average of surface heights and depths across the surface. (Ra) is the arithmetic average of the absolute values of the profile height deviations from the mean line, recorded within the evaluation length. This value summarizes the roughness level of the polyethylene disc employed in PoD experiments. It is measured in micrometer (μm)Polyethylene radiation doseRadiation dose in (kGy) which indicates the level of cross-linking in polyethylene and therefore enhanced wear resistanceFrequencyNumber of cycles per second and measured in Hz. The frequency included in the dataset was around (1.8 Hz) in order to simulate human gait frequencyTest durationDuration of test in MC


### 2.3. Preliminaries

#### 2.3.1. Support Vector Machine (SVM)

SVM is a machine learning model that is commonly employed. It is typically suited for small sample sizes and has a strong statistical base [42–44]. In the disciplines of energy, ecology, hydrology, and economics, SVM has numerous applications [45, 46]. In a regression issue, the training set is defined as [46–48]
(1)xj,yjxj,yj∈Rn,j=1,2,⋯n,wherexj and yj are the input and the output, respectively. The SVM model’s detailed form is
(2)fx=ϖTϕx+c,whereϖ and ϕx are the weighted vector and the nonlinear mapping function, respectively, and c is the deviator. In the SVM model, the two hyperparameters that influence prediction performance are the kernel width and the penalty factor.


#### 2.3.2. Multiobjective Grey Wolf Optimizer

The GWO [49, 50] is the foundation for building a multiobjective GWO. The GWO algorithm is a metaheuristic algorithm based on wolf hunting behavior. Every wolf in the herd has the potential to be a solution to the problem. The ideal, suboptimal, and alternate solutions are represented by the four levels of the wolf swarm. Wolves approach their prey when they find it. Its position equations are
(3)J⟶=M⟶·Lp⟶p−Lw⟶p,Lw⟶p+1=Lp⟶p−N⟶·J⟶,where the separation distance between the prey and the wolf is given byJ⟶, M⟶, and N⟶ are coefficient vectors, the position vectors of the grey wolf and the prey are Lw⟶ and Lp⟶, and the current iteration is given by p.GWO saves the top three solutions and uses Equations (4) and (5) to identify the optimum solution and continuously updates the position of the grey wolf:
(4)Jα⟶=M1⟶·Lα⟶p−Lw⟶p,Jβ⟶⟶=M2¯⟶·Lβp−Lw⟶p⟶,Jγ⟶=M3⟶·Lγ⟶p−Lw⟶p,L1⟶=Lα⟶p−N1⟶Jα⟶,L2⟶=Lβ⟶p−N2⟶Jβ⟶⟶,L3⟶=Lγ⟶p−N3⟶Jγ⟶,(5)Lp⟶p+1=13L1⟶+L2⟶+L3⟶,where α,β, and γ are different levels of grey wolves.The newly created individual is compared to the archived individual after each iteration. Furthermore, all individuals are categorized depending on the distance of the objective function value to avoid an overabundance of similar individuals. The problem of directly selecting three nondominant solutions using the Pareto technique [51] was overcome by using a roulette to choose the archive’s leader wolf. Equation (6) can calculate the probability of each hypercube [52].
(6)Pi=Li−c,where Pi is the probability of the hypercube, Li is the number of Pareto optimal solutions, and c is a constant.


### 2.4. Shapley Values

The SHAP technique is based on the Shapley value principle from the game theory [53, 54]. The Shapley value (SHAP) principle was developed to anticipate the relevance of an individual player in a cooperative team. This concept is based on the relative importance of each player’s participation to the game’s outcome and is meant to distribute the total profit or payment among them. Shapley values produce a distinct result that is distinguished by the following natural features or axioms: consistency (symmetric), local accuracy (additivity), and nonexistence (null effect) [43, 55–57], which offer a solution to each player’s problem of allocating a fair or appropriate reward.Shapley values take into consideration elements of varying magnitudes and signs that contribute to the model’s prediction or forecast. As a result, Shapley values are estimates of the function’s importance (amount of contribution) as well as its direction (sign). Positive SHAP values indicate an increase in the wear rates of polyethylene, whereas negative SHAP values indicate a decrease in the wear rates. The features in the proposed study represent the input operating parameters affecting the wear rates of UHMWPE in PoD experiments. Specifically, the featurei significance is defined by the Shapley value in
(7)∅i=1N!∑SCN\iS!N−S−1!fS∪i−fS,where fS relates to the model output, which can be clarified by the S set of features, and the entire set of all features N. The ultimate impact of the Shapley value of feature i∅i is determined as the middling of its contributions across all possible feature set permutations. Features are then individually applied to the collection, and their importance is exposed by the shift in model performance. Importantly, this approach takes into account feature orderings, which influence reported changes in a model’s performance in the presence of correlated information.


### 2.5. Proposed Approach

The prediction system includes three phases as shown in Figure1: (1) data preprocessing, (2) developing an optimization and prediction system, (3) performance analysis, and (4) interpreting the best fit model using SHAP value.Figure 1
Overall methodology steps.


#### 2.5.1. Data Preprocessing

The main purpose of this step removes the artifacts from the dataset (variables that have missing data points and outlier data) to improve prediction system performance. After that, the dataset was split into two parts. One part is used for training the regression models, while the other part is used for the final evaluation of the models.


#### 2.5.2. Development of the Regression Algorithm

After the preprocessing is complete, the processed data is entered into the SVM-GWO hybrid regression system. This model consists of two operations (training and optimization of the regression model). In the training set, these two procedures are synchronized and executed. That is, both SVM training and optimization are carried out simultaneously. When the optimization is complete, the SVM training is also completed. Academics often create an objective function to reduce the training set’s prediction error in the traditional optimization problem (single-objective optimization). Since the multiobjective optimization used in this article takes into consideration both the precision and the stability of the prediction, two objective functions are defined as(8)m=ObjAcc=RMSEtraining=1St∑kStAk−PkAk,ObjSt=stdAk−Pk,where ObjSt and ObjAcc are the objective stability and prediction precision functions, respectively, RMSEtraining is the training set RMSE, St is the training set’s sample size, Ak and Pk are the actual and at time k predicted values, and std is the population’s standard deviation. Algorithm 1 lists the SVM-GWO global hybrid regression system pseudocode.Algorithm 1: Hybrid regression system in pseudocode.
Algorithm: SVM-GWOInputs: parameters of SVM and GWO (wolf number (x), dimension number (y), search domain (z)), dataset_records[forecast dataset]Output: value of (wear rates of UHMWPE)1: Initialization of variables:Setx⟵random (1, 1)Sety⟵random (1, 1)Setz⟵random (1, 1)2:Initialize training procedure:Set iterations ⟵i3:for each iteration in iterations:SVM (dataset_records[iteration][all],x, y, z)End4:Calculate fitness function:Setl⟵get_length(dataset_records)Set fitness_array []⟵zeros (1,l)5:for counter in range (l):fitness_array[]⟵fitness.calculate(dataset_records)End6:find non_dominant_solution7:initialize archive8:for each iteration in range(iterations):if (true):Output: SVM with hyperparameterselse:search_agent.position ⟵ iterationFitness_array[]⟵fitness.calculate(:)Update: non_dominant_solutionUpdate: archiveEndEnd9:for eachNin range(length(archive)):if (true):pareto_archive_member.remove()else:return: SVM.hyperparamteres.optimal()output: SVM.hyperparameters.optimal()EndEndIn the proposed paper, GWO has been used among other optimization algorithms because the advantages of GWO are as follows: easy to implement due to its simple structure, less storage and computation requirements, faster convergence due to continuous reduction of search space, fewer decision variables, and the ability to avoid local minimums with only two control parameters to adjust the performance of the algorithm, which ensure better stability and avoid complexity.To emphasize the benefits of the proposed model, this paper defines three models as the benchmark models for comparison with our proposed method. The first one of these models is the classic SVM model, and the second and third models are the SVM-PSO and using the genetic algorithm optimizer (SVM-GA). The theory of the benchmark models as well as the reasons for selecting them are previously reported in reference [58].


### 2.6. Model Evaluation

Commonly used metrics are employed in the proposed study to evaluate the performance and prediction errors of the proposed models. These metrics include the square of the correlation coefficientR2 [59, 60] and the RMSE [61]. The values of both metrics yield a good indication of the accuracy and prediction capability of the proposed models and allow us to select the most efficient model for the prediction of wear rates of UHMWPE.RMSE is computed as(9)RMSE=∑i=1nai−pi2n,where ai is the actual value, pi is the predicted value of the ith data point, and n is the dataset’s total number of data points.The value ofR2 is calculated as
(10)R2=1−∑i=1nai−pi2∑i=1nai−a⃐2.


### 2.7. Using the SHAP Values to Interpret the Model Prediction

In the proposed work, the SHAP technique was employed to understand the importance of the several parameters that affect the model’s prediction of the wear rates of UHMWPE and therefore help in predicting its in vivo wear performance. Prioritizing factors that affect the UHMWPE wear performance in hip joint prosthesis can assist material engineers to further improve the design of polyethylene acetabular linings and hence improve its wear resistance and expand its lifetime inside the body. A main benefit of the associated SHAP values is that they add interpretability to complicated models. The model interpretability was evaluated both locally and globally by looking at the relative importance of the variables and their impact on the model’s prediction. Global interpretability helps to understand the entire structure of the model, and it can be obtained through summary plots and bar plots that demonstrate the significance of the overall features. The SHAP summary map depicts how much each predictor contributes to the target outcome variable (wear rates of UHMWPE) either positively or negatively. Features are organized by the sum of the magnitudes of the SHAP values in all the samples, i.e., by their global impact∑j=1N∅ij. SHAP values ∅ij are drawn horizontally.


## 2.1. Dataset Acquisition

The dataset employed in the proposed study consisted of 129 data points and is adapted from a previous work conducted by Borjali et al. [34]. The dataset was an aggregate of 29 different PoD published UHMWPE datasets performed in the field of prosthetic hip implants. Published datasets collected from Google Scholar and PubMed databases were gathered using keywords including “UHMWPE”, “wear”, “hip” and “Pin-on-Disc”. CoCrMo alloys and ceramics are the two most popular materials for the femoral head in hip joint prostheses, while the acetabular liner is often constructed of ultrahigh molecular weight polyethylene, as discussed earlier in this paper. As a result, this study focused solely on multidirectional motion between a polyethylene pin and a CoCr disc, with flat-on-flat geometry and bovine serum as a lubricant.Additionally, only experiments with properly specified and published operating input parameters as well as polyethylene wear rate statistics were included. UHMWPE wear was assessed using the ASTM F732 standards wear rate (mg/MC), which is measured in terms of material loss per million cycles (MC). The wear rate is calculated by multiplying the normal load, sliding distance, and polyethylene density by the wear factor, which is the wear volume per normal load unit and sliding distance [35]. In cases of missing polyethylene densities, a UHMWPE density of 0.93 mg/mm3 was employed, as reported in previous literature [36]. The UHMWPE materials employed in the dataset were mostly conventional GUR 1020 and 1050. The lubricant temperature range was 25-37°C.


## 2.2. Input Parameters

Several important parameters have a major impact on the UHMWPE wear rates in PoD experiments and, therefore, affect its performance in vivo when applied to the acetabular lining in the hip joint prosthesis. Polyethylene wear has been linked to both the applied stress on the pin and the contact area between the pin and the disc by several researchers [37, 38]. The UHMWPE wear rate is also affected by the disc surface roughness [39] and the lubricant employed in the PoD wear tests. Bovine serum is frequently utilized as a lubricant for PoD wear trials in the setting of prosthetic hip implants [40].The wear aspect ratios and sliding distances are also relevant factors affecting the wear rates of polyethylene. The wear aspect ratio is a metric for determining the shape of motion paths and, as a result, the likelihood of wear between the femoral head and the polyethylene acetabular cup liner. The sliding distance is the overall length of the worn path. The radiation dose (presented in [41]) is another major aspect mentioned in the literature; increasing the radiation dose enhances polyethylene cross-linking, which increases wear resistance.The shapes of the multidirectional wear path employed in the dataset were rectangular, elliptical, circular, and square paths. In the circular and elliptical wear pathways, cross-shear occurs on the surface of the pin throughout the worn route, whereas cross-shear occurs when the pin changes direction along the worn path in the rectangular and square wear paths.Hence, the most relevant operating factors affecting the wear rates of UHMWPE in PoD experiments were selected as input parameters to the proposed models. These parameters included the following: contact area (mm2), wear path aspect ratio, normal load (N), sliding distance per cycle (mm/C), disc average surface roughness (Ra) (μm), polyethylene radiation dose (kGy), frequency (HZ), and test duration in million cycles (MC). The description of the input operating parameters is summarized in Table 1.Table 1
Input parameters.
ParameterDescriptionContact areaContact area between the polyethylene pin and the CoCr disc which in vivo represents the contact area between the CoCr femoral head and UHMWPE acetabular liner in the hip joint prosthesis and it is measured in mm2Wear path aspect ratioThe ratio of the wear path length to the perpendicular width of path, and it provides a way to quantify the shape of motion pathsNormal loadApplied stress on the polyethylene pin and it is measured in Newton which clinically represents the weight of the patient on the artificial hip prosthesisSliding distance per cycleOverall distance of the worn path taken by the polyethylene pin in PoD experiments and it is measured in mm per cycleDisc average surface roughness (Ra)Surface roughness is calculated measuring the average of surface heights and depths across the surface. (Ra) is the arithmetic average of the absolute values of the profile height deviations from the mean line, recorded within the evaluation length. This value summarizes the roughness level of the polyethylene disc employed in PoD experiments. It is measured in micrometer (μm)Polyethylene radiation doseRadiation dose in (kGy) which indicates the level of cross-linking in polyethylene and therefore enhanced wear resistanceFrequencyNumber of cycles per second and measured in Hz. The frequency included in the dataset was around (1.8 Hz) in order to simulate human gait frequencyTest durationDuration of test in MC


## 2.3. Preliminaries

### 2.3.1. Support Vector Machine (SVM)

SVM is a machine learning model that is commonly employed. It is typically suited for small sample sizes and has a strong statistical base [42–44]. In the disciplines of energy, ecology, hydrology, and economics, SVM has numerous applications [45, 46]. In a regression issue, the training set is defined as [46–48]
(1)xj,yjxj,yj∈Rn,j=1,2,⋯n,wherexj and yj are the input and the output, respectively. The SVM model’s detailed form is
(2)fx=ϖTϕx+c,whereϖ and ϕx are the weighted vector and the nonlinear mapping function, respectively, and c is the deviator. In the SVM model, the two hyperparameters that influence prediction performance are the kernel width and the penalty factor.


### 2.3.2. Multiobjective Grey Wolf Optimizer

The GWO [49, 50] is the foundation for building a multiobjective GWO. The GWO algorithm is a metaheuristic algorithm based on wolf hunting behavior. Every wolf in the herd has the potential to be a solution to the problem. The ideal, suboptimal, and alternate solutions are represented by the four levels of the wolf swarm. Wolves approach their prey when they find it. Its position equations are
(3)J⟶=M⟶·Lp⟶p−Lw⟶p,Lw⟶p+1=Lp⟶p−N⟶·J⟶,where the separation distance between the prey and the wolf is given byJ⟶, M⟶, and N⟶ are coefficient vectors, the position vectors of the grey wolf and the prey are Lw⟶ and Lp⟶, and the current iteration is given by p.GWO saves the top three solutions and uses Equations (4) and (5) to identify the optimum solution and continuously updates the position of the grey wolf:
(4)Jα⟶=M1⟶·Lα⟶p−Lw⟶p,Jβ⟶⟶=M2¯⟶·Lβp−Lw⟶p⟶,Jγ⟶=M3⟶·Lγ⟶p−Lw⟶p,L1⟶=Lα⟶p−N1⟶Jα⟶,L2⟶=Lβ⟶p−N2⟶Jβ⟶⟶,L3⟶=Lγ⟶p−N3⟶Jγ⟶,(5)Lp⟶p+1=13L1⟶+L2⟶+L3⟶,where α,β, and γ are different levels of grey wolves.The newly created individual is compared to the archived individual after each iteration. Furthermore, all individuals are categorized depending on the distance of the objective function value to avoid an overabundance of similar individuals. The problem of directly selecting three nondominant solutions using the Pareto technique [51] was overcome by using a roulette to choose the archive’s leader wolf. Equation (6) can calculate the probability of each hypercube [52].
(6)Pi=Li−c,where Pi is the probability of the hypercube, Li is the number of Pareto optimal solutions, and c is a constant.


## 2.3.1. Support Vector Machine (SVM)

SVM is a machine learning model that is commonly employed. It is typically suited for small sample sizes and has a strong statistical base [42–44]. In the disciplines of energy, ecology, hydrology, and economics, SVM has numerous applications [45, 46]. In a regression issue, the training set is defined as [46–48]
(1)xj,yjxj,yj∈Rn,j=1,2,⋯n,wherexj and yj are the input and the output, respectively. The SVM model’s detailed form is
(2)fx=ϖTϕx+c,whereϖ and ϕx are the weighted vector and the nonlinear mapping function, respectively, and c is the deviator. In the SVM model, the two hyperparameters that influence prediction performance are the kernel width and the penalty factor.


## 2.3.2. Multiobjective Grey Wolf Optimizer

The GWO [49, 50] is the foundation for building a multiobjective GWO. The GWO algorithm is a metaheuristic algorithm based on wolf hunting behavior. Every wolf in the herd has the potential to be a solution to the problem. The ideal, suboptimal, and alternate solutions are represented by the four levels of the wolf swarm. Wolves approach their prey when they find it. Its position equations are
(3)J⟶=M⟶·Lp⟶p−Lw⟶p,Lw⟶p+1=Lp⟶p−N⟶·J⟶,where the separation distance between the prey and the wolf is given byJ⟶, M⟶, and N⟶ are coefficient vectors, the position vectors of the grey wolf and the prey are Lw⟶ and Lp⟶, and the current iteration is given by p.GWO saves the top three solutions and uses Equations (4) and (5) to identify the optimum solution and continuously updates the position of the grey wolf:
(4)Jα⟶=M1⟶·Lα⟶p−Lw⟶p,Jβ⟶⟶=M2¯⟶·Lβp−Lw⟶p⟶,Jγ⟶=M3⟶·Lγ⟶p−Lw⟶p,L1⟶=Lα⟶p−N1⟶Jα⟶,L2⟶=Lβ⟶p−N2⟶Jβ⟶⟶,L3⟶=Lγ⟶p−N3⟶Jγ⟶,(5)Lp⟶p+1=13L1⟶+L2⟶+L3⟶,where α,β, and γ are different levels of grey wolves.The newly created individual is compared to the archived individual after each iteration. Furthermore, all individuals are categorized depending on the distance of the objective function value to avoid an overabundance of similar individuals. The problem of directly selecting three nondominant solutions using the Pareto technique [51] was overcome by using a roulette to choose the archive’s leader wolf. Equation (6) can calculate the probability of each hypercube [52].
(6)Pi=Li−c,where Pi is the probability of the hypercube, Li is the number of Pareto optimal solutions, and c is a constant.


## 2.4. Shapley Values

The SHAP technique is based on the Shapley value principle from the game theory [53, 54]. The Shapley value (SHAP) principle was developed to anticipate the relevance of an individual player in a cooperative team. This concept is based on the relative importance of each player’s participation to the game’s outcome and is meant to distribute the total profit or payment among them. Shapley values produce a distinct result that is distinguished by the following natural features or axioms: consistency (symmetric), local accuracy (additivity), and nonexistence (null effect) [43, 55–57], which offer a solution to each player’s problem of allocating a fair or appropriate reward.Shapley values take into consideration elements of varying magnitudes and signs that contribute to the model’s prediction or forecast. As a result, Shapley values are estimates of the function’s importance (amount of contribution) as well as its direction (sign). Positive SHAP values indicate an increase in the wear rates of polyethylene, whereas negative SHAP values indicate a decrease in the wear rates. The features in the proposed study represent the input operating parameters affecting the wear rates of UHMWPE in PoD experiments. Specifically, the featurei significance is defined by the Shapley value in
(7)∅i=1N!∑SCN\iS!N−S−1!fS∪i−fS,where fS relates to the model output, which can be clarified by the S set of features, and the entire set of all features N. The ultimate impact of the Shapley value of feature i∅i is determined as the middling of its contributions across all possible feature set permutations. Features are then individually applied to the collection, and their importance is exposed by the shift in model performance. Importantly, this approach takes into account feature orderings, which influence reported changes in a model’s performance in the presence of correlated information.


## 2.5. Proposed Approach

The prediction system includes three phases as shown in Figure1: (1) data preprocessing, (2) developing an optimization and prediction system, (3) performance analysis, and (4) interpreting the best fit model using SHAP value.Figure 1
Overall methodology steps.


### 2.5.1. Data Preprocessing

The main purpose of this step removes the artifacts from the dataset (variables that have missing data points and outlier data) to improve prediction system performance. After that, the dataset was split into two parts. One part is used for training the regression models, while the other part is used for the final evaluation of the models.


### 2.5.2. Development of the Regression Algorithm

After the preprocessing is complete, the processed data is entered into the SVM-GWO hybrid regression system. This model consists of two operations (training and optimization of the regression model). In the training set, these two procedures are synchronized and executed. That is, both SVM training and optimization are carried out simultaneously. When the optimization is complete, the SVM training is also completed. Academics often create an objective function to reduce the training set’s prediction error in the traditional optimization problem (single-objective optimization). Since the multiobjective optimization used in this article takes into consideration both the precision and the stability of the prediction, two objective functions are defined as(8)m=ObjAcc=RMSEtraining=1St∑kStAk−PkAk,ObjSt=stdAk−Pk,where ObjSt and ObjAcc are the objective stability and prediction precision functions, respectively, RMSEtraining is the training set RMSE, St is the training set’s sample size, Ak and Pk are the actual and at time k predicted values, and std is the population’s standard deviation. Algorithm 1 lists the SVM-GWO global hybrid regression system pseudocode.Algorithm 1: Hybrid regression system in pseudocode.
Algorithm: SVM-GWOInputs: parameters of SVM and GWO (wolf number (x), dimension number (y), search domain (z)), dataset_records[forecast dataset]Output: value of (wear rates of UHMWPE)1: Initialization of variables:Setx⟵random (1, 1)Sety⟵random (1, 1)Setz⟵random (1, 1)2:Initialize training procedure:Set iterations ⟵i3:for each iteration in iterations:SVM (dataset_records[iteration][all],x, y, z)End4:Calculate fitness function:Setl⟵get_length(dataset_records)Set fitness_array []⟵zeros (1,l)5:for counter in range (l):fitness_array[]⟵fitness.calculate(dataset_records)End6:find non_dominant_solution7:initialize archive8:for each iteration in range(iterations):if (true):Output: SVM with hyperparameterselse:search_agent.position ⟵ iterationFitness_array[]⟵fitness.calculate(:)Update: non_dominant_solutionUpdate: archiveEndEnd9:for eachNin range(length(archive)):if (true):pareto_archive_member.remove()else:return: SVM.hyperparamteres.optimal()output: SVM.hyperparameters.optimal()EndEndIn the proposed paper, GWO has been used among other optimization algorithms because the advantages of GWO are as follows: easy to implement due to its simple structure, less storage and computation requirements, faster convergence due to continuous reduction of search space, fewer decision variables, and the ability to avoid local minimums with only two control parameters to adjust the performance of the algorithm, which ensure better stability and avoid complexity.To emphasize the benefits of the proposed model, this paper defines three models as the benchmark models for comparison with our proposed method. The first one of these models is the classic SVM model, and the second and third models are the SVM-PSO and using the genetic algorithm optimizer (SVM-GA). The theory of the benchmark models as well as the reasons for selecting them are previously reported in reference [58].


## 2.5.1. Data Preprocessing

The main purpose of this step removes the artifacts from the dataset (variables that have missing data points and outlier data) to improve prediction system performance. After that, the dataset was split into two parts. One part is used for training the regression models, while the other part is used for the final evaluation of the models.


## 2.5.2. Development of the Regression Algorithm

After the preprocessing is complete, the processed data is entered into the SVM-GWO hybrid regression system. This model consists of two operations (training and optimization of the regression model). In the training set, these two procedures are synchronized and executed. That is, both SVM training and optimization are carried out simultaneously. When the optimization is complete, the SVM training is also completed. Academics often create an objective function to reduce the training set’s prediction error in the traditional optimization problem (single-objective optimization). Since the multiobjective optimization used in this article takes into consideration both the precision and the stability of the prediction, two objective functions are defined as(8)m=ObjAcc=RMSEtraining=1St∑kStAk−PkAk,ObjSt=stdAk−Pk,where ObjSt and ObjAcc are the objective stability and prediction precision functions, respectively, RMSEtraining is the training set RMSE, St is the training set’s sample size, Ak and Pk are the actual and at time k predicted values, and std is the population’s standard deviation. Algorithm 1 lists the SVM-GWO global hybrid regression system pseudocode.Algorithm 1: Hybrid regression system in pseudocode.
Algorithm: SVM-GWOInputs: parameters of SVM and GWO (wolf number (x), dimension number (y), search domain (z)), dataset_records[forecast dataset]Output: value of (wear rates of UHMWPE)1: Initialization of variables:Setx⟵random (1, 1)Sety⟵random (1, 1)Setz⟵random (1, 1)2:Initialize training procedure:Set iterations ⟵i3:for each iteration in iterations:SVM (dataset_records[iteration][all],x, y, z)End4:Calculate fitness function:Setl⟵get_length(dataset_records)Set fitness_array []⟵zeros (1,l)5:for counter in range (l):fitness_array[]⟵fitness.calculate(dataset_records)End6:find non_dominant_solution7:initialize archive8:for each iteration in range(iterations):if (true):Output: SVM with hyperparameterselse:search_agent.position ⟵ iterationFitness_array[]⟵fitness.calculate(:)Update: non_dominant_solutionUpdate: archiveEndEnd9:for eachNin range(length(archive)):if (true):pareto_archive_member.remove()else:return: SVM.hyperparamteres.optimal()output: SVM.hyperparameters.optimal()EndEndIn the proposed paper, GWO has been used among other optimization algorithms because the advantages of GWO are as follows: easy to implement due to its simple structure, less storage and computation requirements, faster convergence due to continuous reduction of search space, fewer decision variables, and the ability to avoid local minimums with only two control parameters to adjust the performance of the algorithm, which ensure better stability and avoid complexity.To emphasize the benefits of the proposed model, this paper defines three models as the benchmark models for comparison with our proposed method. The first one of these models is the classic SVM model, and the second and third models are the SVM-PSO and using the genetic algorithm optimizer (SVM-GA). The theory of the benchmark models as well as the reasons for selecting them are previously reported in reference [58].


## 2.6. Model Evaluation

Commonly used metrics are employed in the proposed study to evaluate the performance and prediction errors of the proposed models. These metrics include the square of the correlation coefficientR2 [59, 60] and the RMSE [61]. The values of both metrics yield a good indication of the accuracy and prediction capability of the proposed models and allow us to select the most efficient model for the prediction of wear rates of UHMWPE.RMSE is computed as(9)RMSE=∑i=1nai−pi2n,where ai is the actual value, pi is the predicted value of the ith data point, and n is the dataset’s total number of data points.The value ofR2 is calculated as
(10)R2=1−∑i=1nai−pi2∑i=1nai−a⃐2.


## 2.7. Using the SHAP Values to Interpret the Model Prediction

In the proposed work, the SHAP technique was employed to understand the importance of the several parameters that affect the model’s prediction of the wear rates of UHMWPE and therefore help in predicting its in vivo wear performance. Prioritizing factors that affect the UHMWPE wear performance in hip joint prosthesis can assist material engineers to further improve the design of polyethylene acetabular linings and hence improve its wear resistance and expand its lifetime inside the body. A main benefit of the associated SHAP values is that they add interpretability to complicated models. The model interpretability was evaluated both locally and globally by looking at the relative importance of the variables and their impact on the model’s prediction. Global interpretability helps to understand the entire structure of the model, and it can be obtained through summary plots and bar plots that demonstrate the significance of the overall features. The SHAP summary map depicts how much each predictor contributes to the target outcome variable (wear rates of UHMWPE) either positively or negatively. Features are organized by the sum of the magnitudes of the SHAP values in all the samples, i.e., by their global impact∑j=1N∅ij. SHAP values ∅ij are drawn horizontally.


## 3. Results and Discussion

The primary target of this study is to develop a model having the highest efficiency and capability of predicting the UHMWPE wear rates based on cross-path motion in the hip joint prosthesis. Cross-shear occurs when the relative motion between the pin and the disc changes direction with regard to the surface of the pin, preventing polymer molecular alignment and resulting in polyethylene wear similar to that found in vivo. It was reported that a combination of multidirectional and a serum-based lubricant is known to be essential requirements for laboratory simulation of clinical wear mechanisms of prosthetic hip joints [21, 62]; therefore, PoD wear experiments employing Bovine serum as lubricants are included in this work.To select the most efficient model, the performance of the implemented models was evaluated using RMSE andR2 scores, and their values were tabulated in Table 2.Table 2
Evaluation metrics of the proposed models.
Model nameRMSER2Classic SVM3.3040.84SVM-PSO3.3740.91SVM-GA2.8280.88SVM-GWO2.3450.96It was clear from Algorithm1 that the SVM-GWO outperformed the other implemented models since it attained the least RMSE and the highest R2 score for prediction of the UHMWPE wear rates. It is known that if the RMSE approaches zero, the model’s performance is regarded as being excellent [63]. As a result, the suggested model’s SVM-GWO RMSE value of 2.345 indicates that the model’s predicted values are inconsistent with the experimental data, and all errors are within acceptable limits. Furthermore, the R2 score having a value of 0.96, which is very close to 1, tells us that all points predicted by the model lie exactly on the experimental or actual data curve with no scatter and the results have the perfect correlation. Since the results showed the high accuracy and reliability of SVM-GWO as compared to the other counterpart models, it was further employed in this study to analyze and predict the UHMWPE wear rates based on different operating parameters.To interpret the SVM-GWO and to show the relative importance of the different variables (input operating parameters) on the predicted wear rates of UHMWPE, an aggregate bar graph was performed and shown in Figure2. The bar graph plots the mean absolute SHAP value for each variable. Moreover, a SHAP summary plot shown in Figure 3 was developed that provided more context than the bar chart and also their range of effects over the dataset. A row of the dataset is represented by each point in the SHAP summary plot. This is similar to a bar plot, except it can illustrate if each variable has a negative or positive relationship with the output target. The significance of the features is ranked in ascending order. In the SHAP summary plot, the horizontal location indicates whether the influence of that value is associated with a higher or lower model prediction. The x-axis points indicate the impact on the model output and whether it is positive or negative. Color refers to either high (red) or low (blue) relative variables. Positive SHAP values indicate an increase in the wear rates of UHMWPE, whereas negative SHAP values indicate a decrease in the wear rates predicted by the model.Figure 2
Bar plot to show the importance of each feature.Figure 3
Model 2 summary plot for SHAP.It was seen from the bar plot in Figure2 that the parameters having a major effect on the prediction models of UHMWPE wear rates are ranked as follows from the most important to the least: radiation dose, average disc surface roughness, contact area, normal load, sliding distance, and wear path shape.The SHAP summary plot in Figure3 revealed that the radiation doses had the maximum impact on the model’s prediction, where high values of radiation doses had a negative impact on the model output wear rate of UHMWPE implying that high doses of radiation decrease the wear rate of UHMWPE, which is similar to previous findings since irradiation increases the cross-linking in polyethylene which in turn improves its wear resistance. The second significant parameter is the disc surface roughness. However, it is not clear from the curve whether low values affect positively or negatively on the model output. Another relevant observation from the SHAP summary plot is that high values of contact area affect positively the model’s prediction, which tells us that as the contact area increases, it leads to an increase of polyethylene wear rates, which is compatible with clinical results, which is because in vivo, the metal on plastic prosthetic hip implants show increasing wear rates with increasing femoral head size which means that large contact areas between femoral head and UHMWPE liner increases the wear rate of UHMWPE liner. Because the dataset covers a short range (1.8 Hz) to simulate human gait frequency, the influence of frequency on polyethylene wear rates had no evident effect on the model’s prediction.To get a deeper understanding of the interactions between different operating parameters, SHAP dependence plots were further developed. They depict the marginal effect that one or two variables have on the predicted outcome of the model. Each dot represents a single row from the dataset. The value of the feature appears on thex-axis and the y-axis is the SHAP value for that feature, which defines how much the feature’s value affects the model output. The color relates to a second feature that may have a combined effect with the feature that has been plotted. The second feature is selected automatically. Figure 4 shows dependence plots between different input parameters and their effect on the model predicted outcome. Figure 4(a) shows the SHAP values of radiation doses, and the contact area was selected to show the interaction between them. It was clear that there were three ranges of radiation doses in the dataset, 0 kGy (nonirradiated polyethylene), 30-50 kGy (conventional polyethylene), and 95-150 kGy highly cross-linked UHMWPE-HXPE. It was noticed that nonirradiated polyethylene (0 kGy) accompanied with large contact areas had the highest wear rates since it showed positive SHAP values. On the other hand, high values of radiation doses higher than 95 kGy accompanied by large contact areas produced the lowest wear rates of UHMWPE since it showed the lowest prediction of the model (negative SHAP values). This conclusion was in agreement with a previous study [64] which employed different wear settings in PoD experiments but the authors also reported that radiation doses of 100 kGy increased the cross-linking density of UHMWPE and thus its wear resistance.Figure 4
(a) Dependence plot that shows SHAP values of radiation dose. (b) Dependence plot that shows SHAP values of contact area. (c). Dependence plot that shows SHAP values of average disc roughness. (d) Dependence plot that shows SHAP values of sliding distance.
(a)(b)(c)(d)Figure4(b) showed that there was a positive trend between the contact area and the target variable (wear rate). The higher the values of contact areas, the more positive the SHAP values, which means higher wear rates which is compatible with clinical results [64]. In addition, low values of contact areas accompanied by a low radiation dose up to 40 kGy caused low wear rates of polyethylene.The SHAP values for the average disc surface roughnessRa and its correlation with radiation doses were plotted in Figure 4(c). It was clear that the wear rates of polyethylene increased with Ra values higher than 0.05 μm, while it decreased below that value. Also, high radiation doses did not decrease the wear rate of UHMWPE with high values of surface roughness, which shows the significant impact of surface roughness on the wear rates. Persson et al. [65] reported that surface roughness affects the contact mechanisms and consequently has a big influence on the wear rate of articulating surfaces of hip and knee prosthesis.Figure4(d) showed the SHAP values for the sliding distance, where it was obvious that sliding distances of 30 mm/cycle had a high impact on the model’s prediction for the wear rates of UHMWPE. This result shows that as the sliding distance increases above 30 mm per cycle associated with low values of loads up to 150 N, this leads to the increase in the wear rates of Polyethylene. The increase in the wear rates with increasing sliding distance per cycle was reported by McKellop et al. [66].The dataset was further classified according to the radiation dose they received for sterilization and/or cross-linking in order to examine the effect of radiation doses on the wear rates of UHMWPE with different input operating parameters. The subgroups were as follows: 0 kGy (nonirradiated polyethylene), 30-50 kGy (conventional polyethylene), and 95-150 kGy (highly cross-linked UHMWPE-HXPE).Scatter diagrams showing the effect of different operating parameters on the wear rates of UHMWPE were plotted in each subgroup and shown in Figures5–8. Figure 5 shows scatter diagrams for the effect of normal load on the wear rates of UHMWPE in the three subgroups. It was noticed that at loads around 70 N, the wear rates were ranging between 1 and 10 mg/MC in the nonirradiated polyethylene while in the second subgroup (30-50 kGy), the wear rates were clustered in the range of 0-6 mg/MC and a few points were from 8 to 12 mg/MC. Wear rates of 0-2 mg/MC were obtained at the same load for the third subgroup (95-150 kGy). At higher loads above 200 N, there was an apparent difference between the nonirradiated and highly irradiated polyethylene (HXPE) where the wear rates of the nonirradiated polyethylene were in the range of 8-11 mg/MC and 1-2 mg/MC for HXPE. The variability of the wear results at the same load is due to the different operating test parameters. The clear difference in the wear rates shows the effect of radiation doses on the wear rates of UHMWPE where radiation doses higher than 95 kGy increased the wear resistance of UHMWPE, especially at high loads.Figure 5
Scatter diagrams showing the effect of normal load on wear rates of UHMWPE. (a) 0 kGy (nonirradiated polyethylene), (b) 30-50 kGy (conventional polyethylene), and (c) 95-150 kGy (highly cross-linked UHMWPE-HXPE).
(a)(b)(c)Figure 6
Scatter diagrams showing the effect of contact area on wear rates of UHMWPE. (a) 0 kGy (nonirradiated polyethylene), (b) 30-50 kGy (conventional polyethylene), and (c) 95-150 kGy (highly cross-linked UHMWPE-HXPE).
(a)(b)(c)Figure 7
Scatter diagrams showing the effect of average disc surface roughnessRa on wear rates of UHMWPE. (a) 0 kGy (nonirradiated polyethylene), (b) 30-50 kGy (conventional polyethylene), and (c) 95-150 kGy (highly cross-linked UHMWPE-HXPE).
(a)(b)(c)Figure 8
Scatter diagrams showing the effect of sliding distance on wear rates of UHMWPE. (a) 0 kGy (nonirradiated polyethylene), (b) 30-50 kGy (conventional polyethylene), and (c) 95-150 kGy (highly cross-linked UHMWPE-HXPE).
(a)(b)(c)Furthermore, scatter diagrams showing the effect of contact area on the wear rates of UHMWPE were plotted in Figure6. It was seen that the wear rates of the nonirradiated polyethylene increased with the increase of the contact area reaching 11 mg/MC at contact areas of approximately 64 mm2 and continues to increase at higher contact areas. The wear rates for conventional polyethylene were ranging between 0 and 14 mg/MC at 64 mm2 for different test parameters. The wear rates of the highly irradiated polyethylene (HXPE) were in the range 0-2 mg/MC at nearly the same contact area (around 64 mm2).Figure7 reveals the impact of average disc surface roughness Ra on the wear rates of polyethylene in the three subgroups. At low values of Ra below 0.05 μm, it was seen that the wear rates of the nonirradiated polyethylene ranged nearly between 0 and 18 mg/MC and 0 and 8 mg/MC for conventional polyethylene. However, the highly irradiated UHMWPE (HXPE) produced a wear rate of 0 mg/MC for values of Ra below 0.05 μm and it increased to 2 mg/MC for Ra values above or equal 0.05 μm. This result reveals the pronounced effect of surface roughness and irradiation dose on the wear rates of polyethylene where Ra values below 0.05 μm and irradiation doses above 95 kGy produced 0 mg/MC wear rates. This finding confirms the results shown in the SHAP summary plot in Figure 4 where the irradiation dose and the average surface roughness were the top most significant factors having the highest impact on the model’s prediction for wear rates of UHMWPE.It was also clear from Figure8 that HXPE had wear rates (0-2 mg/MC) at a sliding distance of 30 mm/cycle which are much lower than the nonirradiated and conventional polyethylenes. Despite the different test circumstances, highly cross-linked UHMWPE can be discriminated from conventional and nonirradiated UHMWPE based on wear rates.Hence, the proposed model was able to predict the wear rates of UHMWPE based on different operating parameters and it had the efficient capability to discriminate between different operating parameters and their effect on the wear rates and also prioritize the most important parameters that affect the model’s prediction. This robust and efficient model can further help in visualizing other datasets and predicting the wear rates of polyethylene based on variable parameters and hence deduce its behavior inside the human body and reduce the number of wear experiments. The model can also facilitate the design of UHMWPE-bearing materials with enhanced mechanical properties and design for applications in hip prosthesis.Since the proposed study included only in vitro wear studies of polyethylene in PoD experiments, thus, future enhancement of the work includes further studies that should be conducted on the design of UHMWPE acetabular liners with improved mechanical properties utilized in metal-on-plastic hip implants. The liner should be made from highly cross-linked UHMWPE that is subjected to irradiation doses higher than 95 kGy which proved to have excellent wear resistance and its further implantation in the hip joints of clinically approved animals for in vivo long-term evaluation.


## 4. Conclusion

The primary aim of the proposed study is to develop a model having the highest efficiency and capability of predicting the wear rates of ultrahigh molecular weight polyethylene (UHMWPE), based on multidirectional motion in hip joint prosthesis and therefore help predict its in vivo wear behavior inside the body. The proposed machine learning model in this work is the support vector machine-grey wolf optimizer (SVM-GWO) hybrid regression system. For purpose of evaluation, the performance of the presented model was compared to other counterpart models including classic support vector machine (SVM), support vector machine using grey wolf optimizer (SVM-GWO), SVM using practical swarm optimizer (SVM-PSO), and SVM using genetic algorithm optimizer (SVM-GA). The results showed that the SVM-GWO outperformed the other implemented models since it attained the least root mean square error (RMSE) and the highestR2 score for prediction of the wear rates of UHMWPE. Shapley additive explanations (SHAP) values were used to interpret the SVM-GWO model and to show the relative importance of the different variables (input operating parameters) on the predicted wear rates of UHMWPE.The findings of this study revealed that the parameters having a significant effect on the model’s prediction of UHMWPE wear rates are radiation doses, average disc surface roughness, contact area, normal load, and sliding distance. Radiation doses had the maximum impact on the model’s prediction, where high values of radiation doses had a negative impact on the model output (wear rate of UHMWPE) which implies that high doses of radiation decreased the wear rates of PE. The pronounced effect of surface roughness and irradiation doses on the wear rates of UHMWPE was seen in the results whereRa values below 0.05 μm and irradiation doses above 95 kGy produced 0 mg/MC wear rates. The high regression ability of the SVM-GWO model proves that it is a useful, efficient, and reliable model that can be utilized for the prediction of wear rates of UHMWPE bearings in hip joint prosthesis and aid in prioritizing the different variables that affect the wear rates of polyethylene.The future work is directed to implement advanced technology to obtain better results, such as signal processing technology to improve the quality in the obtained results such as the technology proposed by the authors in [67–71].



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*Source: 6548800-2022-05-09.xml*