How much change in pelvic sagittal tilt can result in hip dislocation due to prosthetic impingement? A computer simulation study

1 INTRODUCTION

The importance of the preoperative sagittal pelvic tilt (SPT) assessment and its effect on the risk of total hip arthroplasty (THA) dislocation has been previously shown.1-12 The magnitude of the SPT during different daily activities is personalized based on the patients' functional anatomy.1, 3-5, 10, 13-17 SPT changes with spinal pathologies as well as spinal surgeries, but there is limited evidence regarding the magnitude of SPT change that can increase the risk for postoperative THA dislocation. The criteria that is known is the spinal stiffness (SPT change less than 10°) that can increase the risk of dislocation.17-19 The risk has been assessed by lateral lumbosacral radiographs in standing and sitting positions or advanced functional imaging techniques, such as bi-planer radiography (EOS; EOS imaging).

Computer simulation models that can predict risk are another method to study THA impingement in patients with spinal fusion or spinal pathologies. Computer simulation of hip motion is a research model which makes investigation of THA impingement possible. These models allow us to investigate replicable motion which is not readily available in motion analysis laboratories or clinical studies. These models can accurately predict the anatomical and functional orientation of the THA implants while modifying the simulation variables by only 1° at a time, which permits testing thousands of different scenarios with minimum cost.

Our purpose was to determine the magnitude of the SPT change caused by variable hip-spine positions that could lead to THA prosthetic impingement. We hypothesized that the magnitude of this SPT change is less than 10° but would be variable for different hip motions, different prosthetic femoral head sizes and stems with different femoral neck-shaft angles.

2 METHODS 2.1 Study setting

This study was conducted using a computer simulation of hip motions with THA implants. No human subjects were included in this study and the study was exempt from institutional review board. This project was conducted under National Institution of Health clinical investigator (K08) award.

2.2 Computer model development

We developed our computer model with Matlab 2020a (Simscape—Multibody) (MathWorks). A deidentified pelvis and lower body computed tomography (CT) scan of a patient without previous lower extremity arthroplasty or fracture surgery was used to import the bony anatomy (pelvis, femur, tibia) into the model (Figure 1). The computer aided design models for the THA implant components (a full hemispherical acetabular cup without an elevated rim [best fit diameter = 56 m], polyethylene liner without an elevated rim and a triple-taper cementless stem with three different neck shaft angles [127°, 132°, 135°]) were designed in SolidWorks (Dassault Systèmes SolidWorks Corporation) and imported into the Matlab model. Acetabular cup and liner were placed in the acetabulum and the stem was placed in the proximal femur based on the anatomical orientation as defined below. The hip joint could move at the center of the acetabular cup in all directions (flexion/extension, abduction/adduction and internal/external rotation) and the knee joint could move into flexion and extension.

image This figure shows how the computer simulation model. (A) pelvis computed tomography (CT) scan. (B) Femur CT scan. (C) Acetabular cup computer aided design (CAD) model. (D) Acetabular liner CAD model. (E) Femoral stem and prosthetic head CAD model. (F) Computer simulation of sitting motion [Color figure can be viewed at wileyonlinelibrary.com]

The polar axis (PA) represents the point on the prosthetic head where the line passing through the center of the prosthetic neck exits (Figure 2A). Motions of the femoral head inside the liner will produce a motion map with accurate coordinates and this map can be utilized to study the motions of the hip joint during daily activities. If PA moves closer to the edge of the polyethylene liner, the probability of prosthetic impingement and subsequent dislocation will increase (Figure 2A,B). Figure 3 shows the area inside a 28, 32, 36, and 40 mm liners. The red line shows when the prosthetic impingement between the trapezoidal femoral neck and polyethylene liner occurs. The blue line shows the 90% distance between the center and the edge of the polyethylene liner and represents our more conservative model. In mechanical engineering, the probability of error in calculation of the risk of prosthetic impingement increases when the PA passes the 90% distance line. Also, most dislocations that are due to bone on bone impingement would occur when the hip is closer to the end of the range of motion and PA crosses the blue line rather than at the red line, prosthetic impingement. We did our analysis separately for each of the blue and red lines (Figure 2B). As seen in Figure 3, the distance between the red line and blue line (safety region) increases with larger prosthetic femoral head diameters. This shows how larger femoral prosthetic heads lower the dislocation rate by increasing range of motion to impingement.

image (A) Polar axis (PA) represents the point where the line passing through the center of the prosthetic neck exits the head. (B) Motions of the (B, C) PA inside the cup (D) can be mapped and studied [Color figure can be viewed at wileyonlinelibrary.com] image This figure shows the area inside 28, 32, 36, and 40 mm liners. Red line represents a true prosthetic impingement and blue line represents the 90% distance between the center and the edge of the liner [Color figure can be viewed at wileyonlinelibrary.com] 2.3 Implant orientation measurement

Anatomical acetabular implant anteversion was calculated relative to the anterior pelvic plane (APP) (Figure 4).1, 7, 20 Anatomical acetabular implant abduction was calculated relative to the horizontal plane that connected the hip center of rotation and was vertical to the APP. Anatomical femoral anteversion was calculated relative to the posterior femoral condylar plane. The functional acetabular implant orientation was measured relative to the horizontal (ground) and the vertical planes. If the APP was zero, the APP and vertical planes were parallel and the functional and anatomical cup orientations were similar. Functional femoral orientation was calculated as the angle between the femoral neck and the vertical plane in standing (Figure 5).

image Anterior pelvic plane (APP) [Color figure can be viewed at wileyonlinelibrary.com] image Functional femoral neck anteversion was measured relative to the vertical plane in standing [Color figure can be viewed at wileyonlinelibrary.com] 2.4 Pelvic tilt and lower extremity parameters during simulated activities

In our model, we considered coronal and axial tilt as zero (except for pivoting) to standardize the sagittal measurement. The sagittal pelvic plane was considered zero when the APP was vertical. Posterior pelvic tilt was considered negative and anterior tilt positive. Table 1 shows the SPT in different motions as well as hip flexion, abduction and rotation as well as their range for this simulation. The SPT was then modified by 1° to a maximum of 45° for stand and sit and 35° for the other positions in both anterior and posterior directions. This range matches the extremes of pelvic tilts reported in the literature.5, 21-24

Table 1. Range of pelvic tilt and hip motions for the simulation Hip position Body motion/position Degree of change in SPT Pelvic tilt Hip motion The sagittal tilt in standing and pivoting The sagittal tilt in sitting, sit to stand, squatting and bending forward Coronal Axial Flexion Abduction Extension Standing ±45 0 (−45 to +45) N/A 0 0 5 (±10) 0 Pivoting ±35 −5 (−40 to +30) N/A 0 50 0 (±10) 0 Flexion Sitting ±45 N/A −15 (−60 to +30) 0 0 65 (±10) 0 Sit to stand ±35 N/A 10 (−25 to +45) 0 0 90 (±10) 0 Squatting ±35 N/A 20 (−15 to +55) 0 0 100 (±10) 5 Bend over ±35 N/A 50 (+15 to +85) 0 0 70 (±10) 5 Abbreviation: SPT, sagittal pelvic tilt. 2.5 Motion simulation

The hip implant motion map is presented in Figure 1. The coordinates of the PA at its closest distance to the polyethylene edge during each motion were captured. For example, the colored dot for sit-to-stand represents the closest position of PA to the edge of the liner (Figure 6). MATLAB model was verified in silico with an independent model written in SolidWorks to compare the reference planes (anterior pelvic plane, horizontal, and vertical planes) and relative to each other.

image This figure shows the motion simulation map. Each colored dot on the map shows the closest distance of the PA to the edge of the liner for each of the tested motions. For example, the colored dot which represents sit-to-stand, represents the closest position of PA to the edge of the liner during this motion when the pelvis is at this maximum anterior tilt, right before the patient gets up from the sitting position. PA, polar axis [Color figure can be viewed at wileyonlinelibrary.com] 2.6 Variables

The main predictor was the SPT change for each of the six positions or motions. For the red line (true prosthetic impingement), the main categorical outcome variable was prosthetic impingement measured by the PA reaching the red line. For the more conservative model, the main outcome was the PA reaching the blue line. Other predicting variables included the anatomical acetabular cup anteversion (range: 5–30), the anatomical cup abduction (range: 40–60), the femoral neck anteversion, the prosthetic femoral head diameter, and the femoral stem neck-shaft angle. The implant orientation range was within the range of clinical use.

2.7 Statistical analysis

The data was categorized into twelve groups based on the prosthetic femoral head diameter and femoral neck-shaft angle. Our model provided 974,688 different scenrios for motions (pivoting, sit-to-stand, squating and bending forward) and 1,249,248 different scenarios for positions (standing, sitting). All the continuous variables were described using the mean, mean difference, SD, and 95% confidence interval. Normal distribution of the values was checked by Shapiro–Wilk normality test for each series of measurements. A univariate logistic regression model analyzed each of the predicting variables seperately which showed a significant effect of the predicting variables on the prosthetic impingement for them. A multiple logitic regression model was used to analyze the effect of the change in the acetabular and femoral anteversion angles as well as other variables on the motion pattern of the hip in different daily activities. The Hosmer-Lemeshow goodness-of-fit test was used to test our logistic regression model. Multicollinearity was tested using collinearity test in Stata. There was no multicollinearity (individual vif for variables = 1; average model vif = 1). Reciever operating characteristic (ROC) curve was used to determine the SPT change that could result in prosthetic impingement for each prosthetic femoral head diameter and stem neck-shaft angle seperately. The significance level was set at less than 0.05. The data was analyzed with Stata 16.0 MP (StataCorp LP). Simulation software accumulated the data from simulation in a file with .csv format which was imported to Stata for our analysis.

3 RESULTS

The results of the regression model for true impingement are presented in Tables 2-4. As shown in the table, stems with lower neck-shaft angles increase the chance of posterior impingement and anterior dislocation in pivoting motion (132° neck-shaft angle coefficient: −4.2 compared to 127° neck-shaft angle; 135° neck-shaft angle coefficient: −6.7 compared to 127° neck-shaft angle) (p < .0001). Stems with lower neck-shaft angles are more protective against posterior dislocation in sit-to-stand and squatting (132° neck-shaft angle coefficient: 29.1 compared to 127° neck-shaft angle; 135° neck-shaft angle coefficient: 46.2 compared to 127° neck-shaft angle) (p < .0001).

Table 2. Results of logistic regression for pivoting (red line-true impingement) Logistic regressionpivoting Number of observations = 974,688 LR χ 2(9) = 1120053.26 Prob >χ 2 = 0.0000 Pseudo R 2 = 0.9285 Odds ratio Coefficient Standard error p Value 95% Confidence Interval Change in SPT angle 2.769 −1.018 0.0049 <0.0001 −1.028 −1.009 Head diameter effect as compared to head with 28 mm diameter 32 mm 0.08 −2.522 0.0273 <0.0001 −2.575 −2.469 36 mm 0.01 −4.539 0.0329 <0.0001 −4.604 −4.475 40 mm 0.002 −6.157 0.0385 <0.0001 −6.233 −6.0819 Femoral stem neck angle effect as compared to stem with 127° neck angle Stem with 132° neck angle 0.014 −4.224 0.0294 <0.0001 −4.282 −4.167 Stem with 135° neck angle 0.001 −6.792 0.039 <0.0001 −6.869 −6.716 Cup abduction angle 1.73 0.548 0.002 <0.0001 0.543 0.554 Cup anteversion angle 3.59 1.278 0.006 <0.0001 1.266 1.291 Femoral anteversion angle 2.94 1.079 0.006 <0.0001 1.069 1.091 Abbreviations: LR, likelihood ratio; SPT, sagittal pelvic tilt. Table 3. Results of logistic regression for sit-to-stand (red line-true impingement) Logistic regressionsit-to-stand Number of observations = 974,688 LR χ 2(9) = 43900.32 Prob > χ 2 = 0.0000 Pseudo R 2 = 0.966 Odds ratio Coefficient Standard error p Value 95% Confidence interval Change in SPT angle 21.6 3.073 0.112 <0.0001 2.853 3.293 Head diameter effect as compared to head with 28 mm diameter 32 mm 4.84 −12.239 0.471 <0.0001 −13.161 −11.316 36 mm 3.42 −21.797 0.812 <0.0001 −23.389 −20.205 40 mm 9.84 −29.949 1.111 <0.0001 −32.126 −27.774 Femoral stem neck angle effect as compared to stem with 127° neck angle Stem with 132° neck angle 4.36 29.105 1.165 <0.0001 26.82 31.389 Stem with 135° neck angle 1.22 46.255 1.743 <0.0001 42.839 49.67 Cup abduction angle 0.009 −4.632 0.169 <0.0001 −4.964 −4.301 Cup anteversion angle 0.046 −3.075 0.112 <0.0001 −3.295 −2.855 Femoral anteversion angle 0.131 −2.031 0.075 <0.0001 −2.179 −1.884 Abbreviations: LR, likelihood ratio; SPT, sagittal pelvic tilt. Table 4. Results of logistic regression for squatting (red line-true impingement) Logistic regression—squatting Number of observations = 974,688 LR χ 2(9) = 278557.36 Prob >χ 2 = 0.0000 Pseudo R 2 = 0.949 Odds ratio Coefficient Standard error p Value 95% Confidence interval Change in SPT angle 4.543 1.513 0.019 <0.0001 1.479 1.549 Head diameter effect as compared to head with 28 mm diameter 32 mm 0.001 −8.165 0.108 <0.0001 −8.378 −7.952 36 mm 3.16 −14.966 0.183 <0.0001 −15.326 −14.605 40 mm 1.3 −20.463 0.246 <0.0001 −20.948 −19.979 Femoral stem neck angle effect as compared to stem with 127° neck angle Stem with 132° neck angle 1.16 18.566 0.228 <0.0001 18.119 19.014 Stem with 135° neck angle 4.94 29.229 0.347 <0.0001 28.548 29.91 Cup abduction angle 0.038 −3.261 0.039 <0.0001 −3.337 −3.186 Cup anteversion angle 0.268 −1.314 0.016 <0.0001 −1.345 −1.283 Femoral anteversion angle 0.392 −0.935 0.012 <0.0001 −0.959 −0.912 Abbreviations: LR, likelihood ratio; SPT, sagittal pelvic tilt.

The cutoff points from the ROC curve (Figure 7) is presented in Table 5. Despite evaluating range of motion extremes of anterior and posterior pelvic retroversion, no prosthetic impingement (neither true prosthetic impingement represented by red line or conservative measurements represented by blue line) occurred in standing and bending forward to pick up an object. The PA stays close to the center while the patient is bending forward to pick up an object (Figure 6). Prosthetic impingement in the sitting position could only occur if the pelvis was significantly anteverted in stems with 135° neck-shaft angle with smaller diameter heads. Anterior pelvic tilt in the sitting position is extremely rare as patients usually have posterior pelvic tilt in sitting.

image This figure shows the sample ROC curve for sit-to-stand motion using a 28-mm prosthetic head and a stem with 127° neck-shaft angle. AUC, area under the ROC curve; ROC, rreceiver operating characteristic [Color figure can be viewed at wileyonlinelibrary.com] Table 5. Results of the ROC (receiver operating characteristic) curve Head sized 28 mm 32 mm 36 mm 40 mm Neck-shaft angle 127° 132° 135° 127° 132° 135° 127° 132° 135° 127° 132° 135° Standing True impingement Cutoff point Dislocation due to prosthetic impingement does not occur even with conservative approach AUC Conservative Cutoff point AUC Pivoting True impingement Cutoff point −3 −6 −8 −4 −7 −9 −5 −9 −10 −6 −9 −11 AUC 0.948 0.948 0.946 0.945

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