Computer Simulations of Patellofemoral Joint Surgery

Transcription

1 /103/ $02.00/0 THE AMERICAN JOURNAL OF SPORTS MEDICINE, Vol. 31, No American Orthopaedic Society for Sports Medicine Computer Simulations of Patellofemoral Joint Surgery Patient-Specific Models for Tuberosity Transfer Zohara A. Cohen,* PhD, Jack H. Henry, MD, Denise M. McCarthy, MD, Van C. Mow,* PhD, and Gerard A. Ateshian,* PhD From the *Departments of Mechanical Engineering and Biomedical Engineering, Columbia University, the Department of Orthopaedic Surgery, and the Department of Radiology, Columbia-Presbyterian Medical Center, New York, New York Background: Variable clinical outcomes of tibial tuberosity transfer surgery have been reported. Hypotheses: The biomechanical outcome of surgery is patient-specific; no single procedure produces superior results for all patients. Use of patient-specific computer models can optimize choice of procedure. Study Design: Computer simulation study using clinical data. Methods: We used patient-specific multibody models of the patellofemoral joints of 20 patients with a diagnosis of patellar subluxation and osteoarthritis. Four tibial tuberosity transfer procedures (two anterior and two anteromedial) were simulated for each patient and compared with their preoperative model. Results: When results for all patients were averaged, all simulated operations produced a statistically significant decrease in surface-wide mean contact stress, although no significant difference was found among them. Conclusions: The simulated surgical outcomes were patient-specific: no single procedure was consistently superior at decreasing peak or mean stress and each procedure produced a potentially detrimental outcome, an increase in either mean stress or peak stress, in at least one patient. Clinical Relevance: Computer simulation may serve as a valuable tool for tailoring procedures to specific patients American Orthopaedic Society for Sports Medicine Patellofemoral joint reconstructions have met with inconsistent clinical success. In particular, operations that aim to restore a lower stress level in the painful patellofemoral joint by shifting the tibial tuberosity have been reported to yield variable outcomes. In 1976, Maquet 30 introduced his surgical correction in which the tibial tuberosity is transferred 20 to 25 mm anteriorly to increase the moment arm of the patellar tendon and thereby decrease the amount of quadriceps muscle force needed to extend the tibia. As a modification to the Maquet procedure, Fulkerson et al. 21 recommended slicing the tibial tuberosity along an anteromedial plane and then translating it along that plane. Such a procedure yields a medial and anterior displacement of the patellar tendon insertion without requiring a Address correspondence and reprint requests to Gerard A. Ateshian, PhD, 500 West 120th Street, 220 Mudd, New York, NY No author or related institution has received any financial benefit from research in this study. bone graft. Fulkerson and his coworkers 21 performed a cadaver study in which they combined 8 mm of medialization with both 8 and 15 mm of anteriorization. They found that the procedure decreased the overall contact stress, while at the same time achieving a better balance of forces between the medial and lateral aspects of the trochlear groove. Although some clinical studies of tuberosity transfer procedures show good-to-excellent results in as many as 80% (28 of 35 knees with a 10- to 20-year follow-up) 34 or 85% (14 of 17 knees with a 1- to 4-year follow-up) 31 of patients, others report a success rate of only 54% (15 of 29 knees with 6-year follow-up). 22 In vitro cadaver studies have also shown inconsistent results with respect to decrease in contact stress. 19,20,29 Such studies have revealed that the optimal relief of stress occurs with less anteriorization than Maquet had originally suggested: 10 mm according to Ferrandez et al. 20 and 12.5 mm according to Ferguson et al. 19 Others report that 25 mm of anteriorization leads to an inconsistent decrease in stress. 29 Other 87

2 88 Cohen et al. American Journal of Sports Medicine investigators have also used general three-dimensional computer models to explore the effects of tibial tuberosity transfer. 5,10,23,33 A limitation of these in vitro studies is their use of anatomic data from cadavers, in which patellar subluxation is not likely to be present, nor verifiable if it were. Nevertheless, the variable mechanical outcomes observed in cadaver studies indicate that the reported failures of the clinical procedure may be due to mechanical causes, such as high stresses. However, given that for any tuberosity transfer procedure some operations are successful and others are not, the mechanical benefit may vary depending on the anatomic form of the particular knee. Computer-Aided Planning of Orthopaedic Surgery Computer models generated from digitized cadaver data have been used to assess the effectiveness of surgical procedures. For example, Delp et al. 14 developed a model of the lower extremity that has been used to evaluate reconstructive operations of the knee, 15,32 ankle, 16 and hip. 13,35 With the advent of medical imaging, such threedimensional joint models have been created from in vivo patient data. Indeed, several groups have explored optimizing orthopaedic procedures for a particular patient by using computer simulations. Chao et al. 6,7 used an x-ray based mathematical model to find the optimal sectioning angle for high tibial osteotomy and hip osteotomy. Other groups have focused on using computer models to optimize the surgeon s performance. For example, Joskowicz and coworkers 25 developed a CT- and fluoroscopy-based system to aid surgeons in performing closed medullary nailing of long-bone fractures. Dessenne and coworkers 17 described a guidance system for improved positioning of the patellar tendon bone graft in ACL reconstruction, and Krackow and coworkers 26 proposed techniques for computer-assisted knee replacement. Objective Our long-term objective was to determine whether computer-assisted preoperative simulations performed with patient-specific anatomic data may serve to improve the actual clinical outcome of surgery. The ultimate test of such simulations would be to perform a prospective double-blinded clinical study with patients for whom simulations are conducted preoperatively. Predictions from those simulations could then be compared with the actual postoperative outcome. Before such a clinical study can be conducted, however, more information is required. The objective of the current study was therefore to demonstrate that patient-specific computer models can be generated in a routine fashion, that the specific targeted operations can indeed be simulated meaningfully on those models, and that the predictions are consistent with findings of the clinical literature. In the current study, patient-specific multibody models of the patellofemoral joint were created from articular geometry, tendon and ligament insertion points, and kinematic data obtained from two sets of MR images from 20 patients who had a diagnosis of patellofemoral joint osteoarthritis and lateral subluxation. Four simulated procedures were performed for each patient. After each surgical simulation, the stresses in the joint were compared with the preoperative values. The hypothesis of this study was that the biomechanical outcome of surgical procedures is patient-specific, with no single procedure producing superior results for all patients. The long-term corollary hypothesis was that the choice of procedure for a given patient can be biomechanically optimized preoperatively by using such patient-specific computer models, thereby improving the clinical outcome of patellofemoral joint reconstructions. MATERIALS AND METHODS Acquisition of Patient Data The 20 patients selected for the study had a diagnosis of patellofemoral joint osteoarthritis and lateral subluxation (a condition in which the patella tracks excessively on the lateral aspect of the femoral trochlea and that is usually associated with dysplasia of the vastus medialis obliquus muscle) made by their treating orthopaedic surgeon but had undergone no prior patellofemoral joint reconstructive surgery. The topographies of the subchondral bone and articular cartilage surfaces were generated by segmenting MR images from a Signa 5.7 Horizon clinical scanner with a 1.5-T super-conducting magnet (General Electric, Milwaukee, Wisconsin) and fitting B-spline surfaces to the segmented data, as described in our prior study. 11 The imaging sequence, which was chosen for its ability to optimize the appearance of articular cartilage, was a fat-suppressed spoiled gradient-recalled acquisition (repetition time [TR], 52 ms; echo time [TE], 5 ms; flip angle, 40 ; sagittal plane; field of view, 14 cm; resolution, mm 3 ;9 minutes) acquired with an extremity coil and the knee in full extension (Fig. 1A). This data acquisition technique has been shown to yield an accuracy of 0.23 mm for topographic measurements of the articular layers and 0.37 mm for thickness measurements. 11 A second image series was acquired to determine the kinematic position of the knee bones with the knee in a flexed position. This image required the use of the scanner s full-body coil. The images were T1-weighted (TR, 550 ms; TE, 15 ms; field of view, 25 cm) with a resolution of mm 3 and required 4.5 minutes (Fig. 1B). The surface contours of the femoral, patellar, and tibial bone cortices were segmented from these images and then registered with the corresponding contours from the first image sequence (the cartilage-highlighting sequence with the knee extended). This procedure was followed to determine the correct kinematic position in which to place the higher-resolution subchondral bone and cartilage surfaces acquired from the first sequence. 12

3 Vol. 31, No. 1, 2003 Computer Simulations of Patellofemoral Joint Surgery 89 Multibody Modeling of the Patellofemoral Joint Figure 1. Magnetic resonance images of a patient s knee. A, high-resolution image with the knee in full extension; B, image with a large field of view and the knee in a flexed position. We used a three-dimensional mathematical model that employs quasistatic force and moment equilibrium analysis to predict the pose of interacting bones in diarthrodial joints. The model framework and corresponding equations are described in detail in earlier studies from our laboratory that include validation of patellofemoral joint models against experimental data from cadaver studies. 9,28 In this formulation, bones were treated as rigid bodies, and soft tissues were treated as springs (either linear or nonlinear, either tension-only or tension and compression), which is consistent with other models in the literature. 24 The three material bodies of the models in this study were the femur, the patella, and the tibia. The femur body was fully constrained (that is, it was the ground ), and the kinematics of the other bodies were described relative to the femoral coordinate system (Fig. 2). 28 The tibia was constrained in a single position that it assumed when the knee was flexed to be imaged for the second MRI series. Although the position of the patella in those images provided the model program with an initial guess as to its equilibrium kinematic position under the simulated loading conditions, six degree of freedom patellar motion was unconstrained in the subsequent analysis. The patellar tendon was modeled as two linear tensiononly ligament links (to allow for a broad insertion on the patella and the tibial tuberosity), with tensile stiffnesses of 500 N/mm each. The resting length of the tendon was assumed to be 98% of the length measured from the MRI scans, based on an approximate flexion angle of 50 and the reported patellar tendon strain at that flexion angle. 3 The quadriceps muscles were modeled as tendonpulley links, which represent forces that can be redirected when the muscles wrap around the femoral bone and articular surface. Each quadriceps muscle group originated on the femur and inserted on the patella, the moving body. The magnitudes of the muscle forces to be applied in the multibody computer models were based on previous cadaver studies from our laboratory, 1,27 as there are no known methods to measure muscle forces in patients noninvasively. The quadriceps muscles were loaded in three groups: vastus lateralis, rectus femoris vastus intermedius vastus medialis longus, and vastus medialis obliquus. In previous cadaver and modeling studies 1,27,28 forces of 33%, 50%, and 17% of the total quadriceps muscle force (a ratio of 2:3:1) were applied on the vastus lateralis, rectus femoris vastus intermedius vastus medialis longus, and vastus medialis obliquus, respectively. Those magnitudes were based on values reported by Ahmed et al. 2 and were derived from the relative physiologic cross-sectional areas of the quadriceps muscles of a single cadaveric specimen. More recently, Farahmand et al. 18 published a more extensive examination of the physiologic cross-sectional areas of the quadriceps muscles in 12 cadaveric specimens and reported values for the following muscles: rectus femoris, vastus intermedius, vastus lateralis, vastus lateralis longus, vastus lateralis obliquus, vastus medialis, vastus medialis longus, and vastus medialis obliquus. We

4 90 Cohen et al. American Journal of Sports Medicine Figure 2. Schematic depiction of the three coordinate directions used to describe patellar translation and rotation. grouped the muscle physiologic cross-sectional areas reported by Farahmand et al. into the same three groups as in our previous study and found that the muscle groups contributed 40% (vastus lateralis), 50% (rectus femoris vastus intermedius vastus medialis longus), and 10% (vastus medialis obliquus) of the total quadriceps muscle force. This finding indicated that the previously employed muscle components were comparable with those of Farahmand et al., 18 with a slightly greater force on the medial muscles. The quadriceps muscle directions used in previous experimental studies were based on the fiber orientation of the muscles of six cadaveric knees. 27 When we projected the force vectors onto the coronal plane, the angles for the three muscle groups were 17, 5, and 41, respectively. Farahmand et al. 18 reported a slightly higher vastus medialis obliquus muscle angle (49 ). The slightly lower angle and higher force of the vastus medialis obliquus muscle that we used produced a medial force component on the patella that differed little from that reported by Farahmand et al. Therefore, for the sake of consistency, we continued to use the muscle force magnitudes and directions used in earlier studies from our laboratory. Two opposing articular surfaces are considered in contact when their mathematical representations overlap each other. The ratio of the amount of overlap to the surface thickness can be thought of as an approximation of the normal compressive strain. In an earlier study from our laboratory, 28 the cartilage thickness was assumed to be uniform across the surface, such that the strain was proportional to the overlap. In the current version of the model, the variation in cartilage thickness across the surface, as assessed from the MRI scans, 9 was taken into account. Strain at each point was calculated as the magnitude of overlap divided by the local thickness. Then, the local contact stress was obtained by multiplying the compressive strain with a cartilage modulus of 4 MPa, which represents an approximate measure of the dynamic stiffness of cartilage in unconfined compression. If the overlap between the mathematical representations of the surfaces exceeded the combined local thicknesses of the patellar and femoral surfaces (in the extreme case of eroded areas, this would be bone-to-bone overlap), the contact stress was increased by the product of the bony overlap and a stiffness coefficient of 10,000 N/mm, to simulate nonlinear stiffening. This refinement, accounting for the variable

5 Vol. 31, No. 1, 2003 Computer Simulations of Patellofemoral Joint Surgery 91 thickness of the articular layers and the stiffening effect provided by the underlying subchondral bone, has been shown, from the data of our earlier cadaver study, 9 to improve the accuracy of the model predictions (Table 1). This refinement was particularly suited to the subjects of this study, patients with thin osteoarthritic cartilage and sometimes exposed subchondral bone. Simulation of Surgery In contrast to our current study of patients with patellofemoral joint malalignment, our previous cadaver studies were of knees that had no evidence of patellar subluxation (that is, normal knees). Because we sought to analyze models of knees with patellar subluxation and osteoarthritis, we modified the normative values reported earlier so as to reduce the vastus medialis obliquus force magnitude by half. This modification yielded muscle force magnitudes of 36% (vastus lateralis), 54% (rectus femoris vastus intermedius vastus medialis lateralis), and 9% (vastus medialis obliquus) of the total quadriceps muscle force (a ratio of 4:6:1). This change aimed to simulate the dysplastic vastus medialis obliquus muscles of patients who have lateral tracking. All patient-specific multibody models were first analyzed by using these baseline muscle force values to assess the state of patellofemoral joint mechanics under this assumed pathologic condition. Subsequently, surgical procedures were simulated, as later described, to assess changes in knee mechanics relative to this baseline pathologic condition. In light of prior reports regarding the optimal amount of tuberosity anteriorization, two Maquet-style tuberosity transfers, 15 mm and 20 mm (to be referred to as M15 and M20), and two Fulkerson-style procedures, 8 mm medial/8 mm anterior, and 15 mm anterior/8 mm medial tuberosity transfers (F8-8 and F15-8), were simulated, yielding a total of four simulated procedures for each patient. The tuberosity transfers were simulated by changing three inputs to the patient-specific three-dimensional multibody models. First, the force on the vastus lateralis muscle was decreased to 75% of its baseline value to simulate the lateral retinacular release that typically accompanies a tuberosity transfer. Second, the insertion points on the tibial tuberosity of the two line elements modeling the patellar tendon were translated in the anterior or anteromedial direction, depending on the type of surgery (Fig. 3). The precise anatomic directions on the tibia were determined for each model according to a previously described procedure. 28 Third, to maintain the same flexion moment about the knee, the quadriceps muscle forces were de- Figure 3. A model of the knee of a 45-year-old female patient at 53 of flexion. A, original model; B, model with simulated 20 mm of tuberosity transfer. TABLE 1 Comparison of Kinematic Errors for Uniform Thickness and Variable Thickness Models Translation (mm) Rotation (deg) Medial-lateral Proximal-distal Anterior-posterior Flexion-extension Internal-external Varus-valgus Uniform thickness Variable thickness P value a a Statistically significant.

6 92 Cohen et al. American Journal of Sports Medicine Outcome Evaluation Figure 4. Cartilage thickness maps for the left knee of a 45-year-old female patient; A, femur; B, patella. creased to properly account for the increased moment arm of the patellar tendon resulting from the transferred tuberosity. The flexion moment prescribed to the multibody model was derived from the peak closed chain moments for rising from a chair, as reported by Andriacchi et al. 4 (82.2 N m for men and 59.4 N m for women). For every simulation, including the initial preoperative simulation, the quadriceps muscle force components were iteratively adjusted, keeping the ratio among them constant, until the model produced the desired flexion moment. Several biomechanical variables were available for analyzing the results of the simulated operation. Most importantly here, the model produces contour maps showing the distribution of articular contact stress across the femoral and patellar articular cartilage surfaces. Implicit in the use of this variable as a predictor of successful surgical outcome is the assumption that elevated articular stresses cause not only cartilage wear but also joint pain. Clinically, the explicit motivation for the various patellofemoral joint tuberosity-transfer procedures is to reduce the magnitude of articular contact stress. For statistical comparison, the mean stress across the surface and the peak stress were used. The model also yields other useful data, including the kinematics of the patella relative to the femur, articular contact area size, contact force, moment arm of the patellar tendon about the knee s helical (flexion) axis, and the medial-lateral position of the centroid of the patellofemoral joint contact area. The flexion angle at which each patient s knee was imaged in the full-body coil varied, and, thus, the applied closed chain flexion moment differed from patient to patient. In the analysis of results, the dependence on the applied flexion moments was eliminated by examining the Figure 5. Patellofemoral contact stress maps for a female patient with the left knee at 53 of flexion displayed on the femoral surface: A, preoperative; B, M15; C, M20; D, F8; E, F15-8; F, same as in E, only uniform thickness distribution and linear strain law were used. See text for details of surgical procedures. Black circles show area of peak stress and white circles show centroid of contact.

7 Vol. 31, No. 1, 2003 Computer Simulations of Patellofemoral Joint Surgery 93 Figure 6. A, average change in mean stress from preoperative value for all 20 patients (P ); B, change in mean contact stress as a percentage of preoperative values for each patient. See text for details of surgical procedures. change in mean articular contact stress and peak contact stress as a percentage of their preoperative baseline values, as opposed to absolute changes (in megapascals). Analysis of variance with repeated measures was performed to compare the preoperative and postoperative outcomes. A pairwise comparison was performed on the least-squares means to detect differences between the various operations. RESULTS Representative results for a typical patient are presented first, followed by aggregate results for all patients. The articular cartilage thickness maps of the distal femur and the retropatellar surface for a 45-year-old female patient are depicted in Figure 4. The articular contact stress pattern at the patellofemoral joint for that knee before sur-

8 94 Cohen et al. American Journal of Sports Medicine Figure 7. A, average change in peak stress from preoperative value for all 20 patients (P 0.001); B, change in peak contact stress as a percentage of preoperative stress for each patient. See text for details of surgical procedures. gery, where the model simulates a weak vastus medialis obliquus muscle and thus a tight lateral retinaculum, is presented in Figure 5A. The patient s knee was at 53 of flexion, requiring an applied flexion moment of 31 N m. In this presurgical configuration, the mean stress was 1.36 MPa and the peak stress was 2.53 MPa. After the M15 and M20 anteriorization procedures, the stress patterns were altered, as demonstrated in Figures 5B and 5C. The mean stress decreased by 11% (to 1.20 Mpa) and by 16% (to 1.14 Mpa) for the two procedures, respectively, while the peak stress decreased by 18% (to 2.07 MPa) and 21% (to 2.00 MPa), respectively. The centroid of contact shifted only 0.1 mm medially for M15 and 0.8 mm laterally for M20. The effect of an additional medialization of the tuberosity is demonstrated in Figures 5D and 5E. Here, the mean stress decreased by 16% (to 1.13 MPa) for F8-8 and by 18% (to 1.11 MPa) for F15-8, while the peak stress decreased by 15% (to 2.16 MPa) and 25% (to 1.89 MPa), respectively. The centroid of the contact area shifted by 3.8 mm (F8-8) and 2.7 mm (F15-8) medially relative to the presurgical position, yielding a more uniformly distributed contact pattern across the medial-lateral direction of the trochlea. It can be noted that, for this patient, the F15 8 procedure produced the greatest decrease in stress and the most centralized contact pattern, making it the best candidate procedure based on these biomechanical criteria. Finally, Figure 5F shows the stress pattern for the F15 8 configuration that would be obtained had the joint model used a

9 Vol. 31, No. 1, 2003 Computer Simulations of Patellofemoral Joint Surgery 95 Figure 8. A, average medial shift in contact centroid from the preoperative location for 20 patients (P ); B, medial shift in contact centroid from preoperative location for each patient. See text for details of surgical procedures. uniform thickness (1.7 mm as the mean thickness for the femur, and 2.8 mm for the patella) with a linear stressstrain law to calculate the contact stress, as in a prior cadaver modeling study. 27 For this latter case, the mean stress was 1.20 MPa (compared with 1.11 MPa for variable-thickness analysis), and the peak stress, at 2.14 MPa (compared with 1.89 MPa), occurs on the lateral rather than the medial trochlea (Fig. 5E). When we assessed outcomes for all the patients, the results were more variable (Figs. 6 through 8). Analysis of variance showed a significant effect of surgery (P ), with surgery producing a decrease in surfacewide mean contact stress relative to presurgical conditions for all procedures (Fig. 6A). The Duncan s multiplerange test indicated that the only significant difference among the various surgical procedures was between F8-8, which demonstrated a normalized stress decrease of 8.8%, and M20, which demonstrated a normalized stress decrease of 17.3%. All other procedures fell between those two values. However, when the results for individual patients are examined (Fig. 6B), only 11 of 20 knees achieved a decrease of more than 20% of the original mean stress with any of the procedures, and three knees never demonstrated a decrease of 10% or more. Three knees actually experienced an increase in mean stress from the simulated Fulkerson procedures. When changes in peak articular contact stress relative to presurgical conditions were examined (Fig. 7A), we found that, on average, surgery significantly reduced the peak contact stress (P 0.01). As was the case for the mean stress, on average, the M20 procedure caused the greatest decrease in peak stress (15.7%) and the F8-8 procedure the lowest decrease (5.7%). Duncan s multiple-range test indicated that only the F8-8 anteromedialization proce-

10 96 Cohen et al. American Journal of Sports Medicine dure was not significantly different from the control with regard to changes in peak stress. The patient-specific results (Fig. 7B) indicated that certain surgical procedures might actually increase peak stresses in some subjects, as demonstrated for 8 of the 20 patients. Three of these eight patients demonstrated an increase in peak stress from the simulated Fulkerson procedures while achieving a decrease of greater than 20% from the Maquet procedures. Increasing the amount of tuberosity transfer, for example, from M15 to M20 or from F8-8 to F15-8, did not consistently lead to a decrease in mean or peak stress. This finding further emphasizes that the patient-specific articular topography strongly influences the potential success of these surgical procedures. The amount by which the contact area centroid shifted medially was another outcome measure of the simulated surgical procedures (Fig. 8). Not surprisingly, the Fulkerson procedures (F8-8 or F15-8) produced a consistent and statistically significant medial shift of the contact area relative to preoperative conditions (by 4.4 mm on average for F8-8, and 3.8 mm for F15-8). The outcomes of the simulated Maquet procedures (M15 and M20) were less consistent, showing no statistical difference relative to the preoperative condition. DISCUSSION As a result of the simulated operations performed on the 20 patients in this study, the mean stress across the articular surfaces of the patellofemoral joint decreased, although the magnitude of decrease varied considerably among patients. With regard to the Maquet procedures, the advantage of increasing the tuberosity anteriorization from 15 to 20 mm was not always apparent. Therefore, the tradeoffs associated with the extra elevation of the tibial tuberosity should be taken into account in clinical practice. The additional medialization of the tuberosity performed in the simulated Fulkerson procedure demonstrated the desired effect of medializing the contact area on average, although not necessarily reducing the articular contact stresses. Neither the Maquet nor the Fulkerson procedure stands out as generally superior to the other. However, when the requirements of a specific patient are considered, it is often possible to identify one procedure as being superior to the others and even to determine whether a particular procedure may be detrimental to that patient. With respect to decrease in mean stress (Fig. 6), M15 achieved the best result in 2 patients, M20 in 10 patients, F8-8 in 2 patients, and F8-15 in 6 patients, thus demonstrating the variability among patients. In terms of the peak contact stress (Fig. 7), a potentially detrimental increase was observed in two patients with use of M15, in eight patients with M20, in two patients with F8-8, and in eight patients with F15-8. Although all four simulated surgical procedures reduced the contact stress relative to preoperative conditions when the results of all of the patients were averaged, this outcome did not necessarily hold for individual patients. For example, a particular patient may have shown a decrease in contact stress as a result of three of the procedures but an increase as a result of the fourth procedure. For that patient, the fourth procedure would appear detrimental according to the surgical simulation findings. The hypothesis that patient-specific outcomes might be predicted from these simulations provided the rationale for conducting this study. The variable outcomes of the procedures in different patients confirmed the hypothesis that the biomechanical outcome of tuberosity transfer procedures is patient-specific. In practice, many surgeons tend to choose a single procedure and use it in all cases. The findings of this study suggest that surgical outcomes could be improved by choosing tibial tuberosity procedures and their parameters, such as the preferable amount of medialization or anteriorization, according to the needs of a specific patient by using patient-specific multibody model analysis. The results of this study are consistent with clinical findings that suggest that not all patients respond equally well to a given reconstructive procedure of the patellofemoral joint. 22,31,34 The analyses of this study were performed on patellofemoral joint models constructed by using data from symptomatic patients rather than from cadavers with an unknown clinical history. The patient-specific models described the topography of each patient s articular layers and, thus, accounted for the cartilage lesions and defects that are expected in this population. If the surgical simulation resulted in shifting of the contact to a location with thicker cartilage, the contact stress typically decreased because its calculation was based on the local cartilage thickness. Similarly, contact on thinner cartilage produced an increase in contact stress. This phenomenon was evidenced by the increase in contact stress observed in some patients for some of the surgical procedures. Because the size and shape of the patellofemoral joint surfaces and the size and location of lesions were not consistent among patients, it was not surprising that the biomechanical outcomes of these surgical simulations produced results that varied from patient to patient. Which of the biomechanical variables derived from the three-dimensional multibody model provide better predictions of surgical outcome than others remains to be determined. For example, it is not known whether peak articular contact stress correlates better with joint pain than mean contact stress and whether a 10% decrease in contact stress will yield changes in clinical symptoms. Future studies must be performed by observing those patients who have undergone surgery and by comparing their clinical outcome against the predictions of the various biomechanical variables used in this analysis. Such studies can also be used to further validate the assumptions employed in our modeling approach. These assumptions include the estimation of normative muscle forces, the simulation of pathologic conditions (for example, by using half of the normal vastus medialis obliquus muscle force to simulate muscular dysplasia), and the simulation of surgery (for example, by decreasing the vastus lateralis muscle force to simulate a lateral retinacular release). Because it is not yet possible to measure muscle force magnitudes noninvasively or soft tissue properties in vivo, it may seem that

11 Vol. 31, No. 1, 2003 Computer Simulations of Patellofemoral Joint Surgery 97 TABLE 2 Correlation of Selected Outcome Variables with Flexion Angle Correlation with flexion angle (r) Variable M15 M20 F8-8 F8-15 Mean stress Peak stress Centroid position the use of estimates of these quantities could represent a significant limitation of computer-assisted surgical simulations. However, it should be emphasized that the same muscle force assumptions and soft tissue properties were used for all of the surgical procedures that were simulated in a particular patient model. Thus, with everything else being equal, the differences in simulation outcomes for a given patient could be attributed to the differences in the surgical procedures. Although the absolute values of the contact stresses estimated from the analyses may not have reflected the true stress magnitudes in the patient s joint, the relative changes in the stresses resulting from the various surgical simulations may nevertheless have correlated well with the clinical outcome. Another potential limitation of this study was that analyses were performed for each patient at a single flexion angle. This protocol was principally guided by practical considerations: limitation of patient discomfort and the financial cost of imaging the joint in more than two positions. Although it would have been interesting to see surgical simulation results reported for several flexion angles for each patient, the current study relied on the assumption that predictions from surgical simulations would not vary significantly as a result of differences in the flexion angle. As shown in Table 2, the decrease in mean and peak contact stresses as a result of simulations of surgery showed only a moderate correlation with flexion angle when assessed over all of the patients, with r values ranging from 0.30 to 0.40 (except for the F8-15 procedure, which showed no correlation for the decrease in mean contact stress). The medial shift of the contact centroid showed a large correlation with flexion angle (r 0.61) for the M15 procedure, a moderate correlation (r 0.49) for the M20 procedure, and small correlations with flexion angle for the two Fulkerson procedures. (For these inferences, an r value of 0.1 to 0.3 is considered a small correlation, 0.3 to 0.5 a moderate correlation, and a value greater than 0.5 a large correlation, according to the methods of Cohen. 8 ) These results suggest that we should rely more on the indications of the stress measures than of the centroid measure, until such time as we acquire data for a more complete set of flexion angles. With the advent of open MRI systems and high-resolution surface coils, it may be possible in future studies to image a patient through a range of motion and, by using the methods outlined in this paper, determine the surgical procedure that produces optimal results throughout the range of motion. The results of this study demonstrate that it is now possible to perform relevant surgical simulations of patellofemoral joint surgery for correction of patellar maltracking and subluxation in a routine setting by using patientspecific anatomic data from standard clinical scanners to generate computer models. The results suggest that the outcome of a particular surgical procedure is very dependent on the patient s specific articular surface anatomy and cartilage thickness. No specific procedure produced consistently superior outcomes in all patients, which is in agreement with clinical findings reported in the literature. 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