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Effects of resection thickness on mechanics of resurfaced patellae
Journal of Biomechanics 46 (2013) 1568–1575
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Effects of resection thickness on mechanics of resurfaced patellae Clare K. Fitzpatrick a,n, Raymond H. Kim b, Azhar A. Ali a, Lowell M. Smoger a, Paul J. Rullkoetter a a b
Center for Orthopedic Biomechanics, University of Denver, Denver, CO, USA Colorado Joint Replacement, Denver, CO, USA
art ic l e i nf o
a b s t r a c t
Article history: Accepted 16 March 2013
Patellar resection thickness during total knee replacement (TKR) has been cited as a contributor to patellar fracture, anterior knee pain and quadriceps efficiency; however, optimal thickness required to minimize clinical complications remains unclear. The objectives of the current study were to determine how patellar resection thickness and bone quality impacts patellar bone strain, kinematics, and quadriceps efficiency. A series of specimen-specific finite element models of the knee joint with distributed patellar bone material properties were developed. Each specimen was virtually implanted with a TKR system. Each specimen was analyzed with patellar bone resected to thicknesses which varied from 9 to 14 mm. Simulations with reduced modulus bone were also performed. Each model perturbation was evaluated during a dynamic squat cycle, and bone strain, quadriceps force and sixdegree-of-freedom kinematics were predicted. Highest peak bone strain was predicted in the thinnest patellae, indicating greatest risk of patellar fracture; highest median bone strain was predicted in the thickest patellae. Consistent differences in quadriceps efficiency were predicted; in early flexion the thickest patellae required the least quadriceps force. Greater sagittal plane tilt was observed for the thinnest patellae. Reduced modulus models (50% lower modulus) demonstrated an increase in peak bone strain of up to seven times the original modulus models. Understanding the complex interactions between patellar resection thickness, muscle requirements, kinematics, bone quality, and bone property distribution may aid in developing an understanding of which patients are most at risk from patellar fracture and anterior knee pain and how best to treat individuals to reduce potential complications. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Patella Resection thickness Finite element Quadriceps efficiency Bone quality Total knee replacement
1. Introduction Early total knee replacement (TKR) procedures with resurfaced patellae reported high incidence of patellofemoral (PF) complications, contributing to up to 50% of all revisions (Brick and Scott, 1988). However, improvements in component design and materials have reduced the incidence of revisions due to PF issues. Recent studies have reported incidence of anterior patellar pain of 12% and patellar fracture rates from 0.68% to 5.2% in the TKR population (Helmy et al., 2003; Dalury and Dennis, 2003; Seijas et al., 2009). While occurrence of patellar fracture is relative low, revision surgeries have reported poor outcomes with high complication rates and reoperation (Ortiguera and Berry, 2002), leaving patellar fracture as a significant concern for the comfort and functionality of the TKR population. Patellar resection thickness has been cited as a contributor to patellar fracture, anterior knee pain and extensor mechanism efficiency (Seo et al., 2012),
n Correspondence to: Center for Orthopaedic Biomechanics, University of Denver, 2390 S. York St., Denver, CO 80208, USA. Tel.: +1 303 871 6435; fax: +1 303 871 4450. E-mail address: clare.fi[email protected] (C.K. Fitzpatrick).
0021-9290/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jbiomech.2013.03.016
however, the influence of resection thickness on patellar mechanics remains unclear. During TKR, surgeons typically aim to restore pre-operative patellar thickness, with reports suggesting that this may aid in preserving the natural mechanics of the joint (Hsu et al., 1996). There are a number of concerns associated with resection of the patellar bone that may potentially lead to complications of the PF joint. Overstuffing of the PF joint may induce ligament and muscle tightness as well as limit knee flexion (Marmor, 1988; Mihalko et al., 2006), while excessive resection of the native patellar bone stock may increase strain and the risk of patellar fracture in the remaining patellar bone (Goldstein et al., 1986; Reuben et al., 1991), increase the risk of crepitation (Hoops et al., 2012), and reduce the quadriceps muscle moment arm, leading to a decrease in extension efficiency (Mountney et al., 2008). Studies have recommended against resected bone of less than 15 mm due to increased patellar bone strain at increased resection depths (Reuben et al., 1991), while others have reported no difference in clinical outcome between groups with bone remnants of less 12 mm and those with bone remnants of greater than 12 mm (Koh et al., 2002). While clinical studies serve to identify factors which differentiate between surgical outcomes based on retrospective analysis,
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this necessitates high-volume datasets with numerous confounding factors which make it difficult or infeasible to identify the impact of a specific surgical decision, such as patellar bone resection thickness, on patellar mechanics. In vitro and in silico studies have the advantage of evaluating such factors in a controlled environment, isolated from additional sources of variability. A number of cadaveric studies have sought to investigate the effect of patellar resection thickness on patellar mechanics (using patellar strain as a surrogate measure for risk of patellar facture and anterior knee pain), with studies measuring strain on the anterior surface using uniaxial strain gauges reporting an increase in superficial strain proportional to the amount of bone removed (Wulff and Incavo, 2000; Lie et al., 2005; Reuben et al., 1991). Recent computational modeling work has developed subjectspecific finite element (FE) PF models with heterogeneous patellar bone material properties mapped from computed tomography (CT) images (Fitzpatrick et al., 2011). These models have been used to compare patellar mechanics in natural, implanted and unresurfaced conditions (Fitzpatrick and Rullkoetter, 2012). To date, however, they have not been used assess the influence of surgical decisions, such as patellar resection thickness, on mechanics of the patella. The objective of the current study was to determine how patellar resection thickness impacts patellofemoral mechanics, including kinematics and strain in the bone, and hence provide insight into the risk of fracture and anterior knee pain.
2. Methods Specimen-specific FE models of the knee joint were developed in Abaqus/ Explicit (SIMULIA, Providence, RI) from CT scans of three cadaveric male knees (65.7 79.9 years; 1.79 70.04 m; 76.9 7 13.6 kg) (Fig. 1). The specimen-specific models were implanted with a semi-constrained, posterior-stabilized TKR with dome patella (positioned under the guidance of an orthopedic surgeon) which included a fully deformable polyethylene button with nonlinear elastic-plastic representation (initial E¼ 572 MPa, v¼ 0.45 (Halloran et al., 2005)) with an intermediate cement layer (E ¼3400 MPa, v¼0.3 (Race et al., 2007)) between the patellar bone and implant. For computational efficiency, femoral and tibial bone and implant components were modeled as rigid bodies, with contact between the components defined using a pressure–overclosure relationship (Halloran et al.,
Fig. 1. Left: finite element (FE) model of the knee joint. Right: loading conditions applied to the FE model to reproduce a squat simulation.
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2005). A coefficient of friction of 0.04 between components was applied (Godest et al., 2002). The models included two-dimensional (2-D) fiber-reinforced membrane representations of the quadriceps (divided into rectus femoris (RF), vastus intermedius (VI), vastus lateralis longus (VLL), vastus lateralis obliquus (VLO), vastus medialis longus (VML) and vastus medialis obliquus (VMO) bundles), patellar tendon and PF ligaments (Fitzpatrick et al., 2011). Tibiofemoral (TF) soft-tissue was represented by medial and lateral collateral ligaments (MCL, LCL—separated into anterior, medial and posterior bundles), anterior lateral capsule (ALC), popliteofibular ligament (PFL), postero-medial capsule (PMC), medial and lateral posterior capsule (MPCAP, LPCAP), and medial and lateral posterior oblique structures (MPOL, LPOL). Each ligament was represented by non-linear tension-only spring elements, with reference strains and linear stiffness parameters adopted from prior work where ligament properties and attachment sites were calibrated to subject-specific internal–external (I–E) and varus–valgus (V–V) tibiofemoral laxity data (Baldwin et al., 2012). Femoral and tibial bones and components were meshed with triangular surface elements, while the deformable patellar button and cement layer were meshed with hexahedral elements. A series of model perturbations were developed whereby the patellar bone was resected to post-operative thicknesses of 9 mm, 11 mm, 13 mm and the maximum patellar thickness possible without allowing any overhang (approximately 14 mm for each specimen) (Fig. 2). Each resected patellar bone representation was meshed using 4-noded tetrahedral elements. A convergence study was performed to determine an appropriate element size for the patellar bone mesh. Tetrahedral meshes with element edge length of 2, 1.25, 1 and 0.8 mm were compared. There were minimal differences in predicted strain values with mesh refinement beyond 1 mm, similar to that reported by Perillo-Marcone et al. (2003). Hence, an average element edge length of 1 mm, which was appropriate for capturing the material property heterogeneity described by the CT data and strain gradients within the bone, was applied (Fitzpatrick et al., 2011; Perillo-Marcone et al., 2003). Specimen-specific mapped material properties of the patellar bone were developed from the CT data using BoneMat (Taddei et al., 2007). A linear relationship taken from the literature (Peng et al., 2006) was used to correlate Hounsfield units (HU) to apparent density (ρ). The empirical relationship, Young's Modulus (E) ¼ 1990ρ3.46, was applied to convert bone density to mechanical properties (Keller, 1994). Loads and muscle forces were applied to the knee in order to reproduce a dynamic squat activity where the knee was flexed from 101 to 1001. I—E and V—V torques were applied to the tibia, with the remaining tibial DOFs constrained. Quadriceps load was applied to the RF, VI, VLL, VLO, VML and VMO actuators (with load distributed amongst the various bundles according to their physiological cross-sectional area (Farahmand et al., 1998)), vertical load was applied at the hip, anterior–posterior (A–P) force was applied to the femur, with femoral I–E rotation constrained and medial–lateral (M–L) translation free. The patella was kinematically unconstrained in all 6-DOF, with constraint provided by the patellar tendon, PF ligaments and quadriceps (Fig. 1). The loading profiles applied to the model (apart from quadriceps force) were derived from data from a telemetric TKR patient (Kutzner et al., 2010) in order to create a physiological loading condition at the TF joint. Description on how these loading profiles were derived has been described in detail in prior publications (Fitzpatrick et al., 2012a, in press)), and hence is mentioned only briefly here. Compressive, A–P, I–E and V–V loads at the TF joint were extracted for a telemetric patient performing a squat activity (Kutzner et al., 2010). As some of the load applied externally to the knee is accounted for by softtissue structures at the joint, the telemetric data (which measures just the load at the implant) could not be applied directly as external loads in the FE model. Hence, a proportional–integral (PI) control system was implemented in the model to apply external loads required to match the joint loading condition measured by the telemetric patients. Quadriceps load was applied via a PI control system which was integrated with the FE model such that knee flexion angle matched a target flexion profile (Fitzpatrick et al., in press). The target flexion profile was adopted from video recordings of the telemetric patient during a squat activity (Bergmann, 2008). Implementation in this manner allowed the quadriceps force to adapt to changes in the moment arm of the extensor mechanism, facilitating comparison of quadriceps efficiency across the various patellar composite thickness models. In order to provide insight into the interactions between quadriceps efficiency, bone quality and bone strain, additional perturbations were performed for each model. Poor patellar bone quality was simulated by locally reducing the modulus of the bone by 50% (Janssen et al., 2010). The effect of bone density distribution was evaluated by simulating uniform bone quality throughout the patellar bone; constant Young's Modulus and density values (averaged from the distributed properties model) were applied to patellar bone properties. Bone strain was compared and presented in two ways. First, a strain threshold was defined as the strain that a certain percentage of bone volume was strained above; for example, a 10% strain threshold means that at maximum load 10% of the bone volume is above the strain threshold. Strain thresholds were evaluated at 1%, 10% and 50% bone volume at each resection thickness; for instance, in Specimen 3 at a 14 mm resection thickness, 1% of bone volume was strained above a 0.029 strain threshold, 10% of bone volume was strained above a 0.0167 strain threshold, and half the bone (by volume) was strained above a 0.0055 strain threshold (Figs. 4 and 5). Strain thresholds were compared between resection thickness
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Fig. 2. A series of patellar models were developed for each specimen with resected thicknesses of 9 mm, 11 mm, 13 mm and the maximum feasible thickness (approximately 14 mm).
models. Strain threshold at 1% bone volume primarily represented peak strain (1% of the bone volume was above this threshold); while strain threshold at 50% bone volume represented median strain (half of the bone volume was above this threshold). Secondly, a highly strained bone volume was calculated and compared across models of varying patellar thickness. For this comparison, a specific strain level was selected, and the volume of bone strained above this strain level was measured. The specific strain level was nominally chosen as a strain threshold (1%, 10% or 50%, as described above) of the thinnest (9 mm resection) patellae. For instance, for Specimen 3 the strain levels of interest at a 1%, 10% and 50% strain threshold were 0.05, 0.017 and 0.0045, respectively (Figs. 4 and 5). For each specimen, the same strain level was applied to each resection thickness model and the bone volume above this strain level was measured. For instance, at a 1% strain level in Specimen 3, the volume of bone strained above 0.05 was calculated at each resection thickness. Prior work investigating patellar strain during a squat activity evaluated compressive strain to be in the order of 3X larger than tensile strain, thus the current study focused on compressive strain (Fitzpatrick and Rullkoetter, 2012; Fitzpatrick et al., 2011). Quadriceps force and TF and PF kinematics were also compared between model representations.
3. Results Bone strain increased with increasing load across all resection thicknesses. Highly strained bone volume at a 1% strain level (strained above the 1% strain threshold of the thinnest (9 mm) patella) was markedly higher in the 9 mm and 11 mm resection thickness models than the 13 mm and 14 mm resection thickness models in deep flexion (Fig. 3). Calculating the peak (1%) strain threshold at each resection thickness (1% of bone volume is above this strain threshold), the thinnest patellae experienced the highest strain thresholds (Fig. 4). At a 10% strain threshold, strain thresholds were similar across resection thicknesses, while at a median (50%) strain threshold, thresholds were higher in the thickest patellae (Fig. 5). Comparing quadriceps efficiency between patellar thicknesses, subtle changes in quadriceps force were predicted, as a result of changes to composite thickness. In early flexion ( o401), thicker patellae demonstrated better quadriceps efficiency, with 14 mm patellae requiring up to 50 N (approximately 5%) less muscle force than a 9 mm patellae to achieve the same flexion profile.
Fig. 3. Highly strained bone volume at a 1% strain level, calculated as follows: for each specimen, the 1% strain threshold of the 9 mm patella was found (1% of bone volume was above this threshold at maximum load). This strain level was applied across all resection thicknesses, and the volume of bone above this level was calculated. Insets show bone strain at maximum load (and flexion) for 9 mm and 14 mm models—black indicates bone volume above the 1% strain level. 9 mm and 11 mm resection models predicted substantially larger highly strained bone volume (evaluated at the 1% strain level) than 13 mm and 14 mm resection models (showing the mean and standard deviation at 101 intervals for the three specimens).
In deepest flexion, thicker patellae experienced the poorest quadriceps efficiency, with 14 mm patellae requiring up to 200 N (approximately 8%) more muscle force than 9 mm patellae. Force was similar across all composite thickness models mid-cycle (Fig. 6). There were some notable differences in PF kinematics between patellar resection analyses. Thinner patellae demonstrated more sagittal plane patellar tilt than thicker patellae in early flexion (o401), with differences of 2–31 observed between 14 mm and
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Fig. 4. Peak strain threshold (1% bone volume was above this strain threshold) for each specimen at each resection thickness. Insets show bone strain at maximum flexion for 9 mm and 14 mm models—black indicates the 1% bone volume with the highest strain.
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models (Fig. 7). TF kinematics demonstrated greater consistency between resection thickness analyses; differences between 9 mm and 14 mm models were less than 1.51 and 2 mm throughout the cycle for I–E rotation and A–P translation, respectively. Poor bone quality (simulated by reducing bone modulus by 50%) increased the strain in the bone; the 1% strain threshold (1% bone volume was strained above this strain threshold) increased by 70% across all resection thicknesses for the reduced modulus simulations compared to the original conditions. When highly strained bone volume of the original and reduced modulus models were compared at the same strain level (strained above the 1% strain threshold of the thinnest patella in the original model), the reduced modulus model demonstrated increases in highly strained bone volume of 3 to 7 times the original model. Additionally, in the original model, 9 mm and 11 mm resected models showed substantially higher highly strained bone volumes in deep flexion than 13 mm and 14 mm models; while in the reduced modulus model, 9 mm, 11 mm and 13 mm models all predicted substantially greater highly strained bone volume than the 14 mm model (Fig. 8). Comparing between patellae with distributed bone properties, and patellae modeled with uniform bone properties, there were some notable differences between highly strained bone volume predictions. In analyses with distributed bone properties the volume of highly strained bone varied between resection thicknesses, and relative ranking between resection thickness models depended on the strain threshold selected (at high threshold (1%) larger strained volume was reported in thinner patellae, while at low threshold (50%) larger strained volume was reported in thicker patellae). In analyses with uniform bone properties, reasonably consistent highly strained bone volume was reported across patellar resection models, regardless of the strain threshold (Fig. 9).
4. Discussion
Fig. 5. 10% (10% bone volume was above this strain threshold, top) and median (50% bone volume was above this strain threshold, bottom) strain threshold for each specimen at each resection thickness. Insets show bone strain at maximum flexion for 9 mm and 14 mm models—black indicates the 50% bone volume with the highest strain.
9 mm models. Thicker patellae were consistently more externally rotated than thinner patellae throughout the squat cycle, with differences in I–E rotation of 5–61 between 14 mm and 9 mm
Understanding the mechanical consequences of patellar resection thickness is important for the clinician in determining how much bone can be safely resected without substantially increasing the risk of patellar bone fracture and anterior knee pain. This is particularly critical for patients with small patellar geometry which would leave thin bone stock remaining post-operatively in order to maintain pre-operative thickness. While there are a variety of potential sources of anterior knee pain (including softtissue strain and impingement), patellar bone, which contains numerous pain-sensing mechanoreceptors, is a likely contributor to anterior knee pain (McDougall, 2006; Barton et al., 2007; Fulkerson, 2002). Higher bone strain results in increased stimulation of the joint nerves in the subcondral bone, potentially leading to anterior knee pain. While pain is a subjective metric in clinical studies, and not feasible to quantify directly from in vitro or computational studies, strain in the patellar bone can be used as a surrogate measure. Thinner patellae demonstrated higher peak strain thresholds (1% of bone volume is above the peak strain threshold) in addition to a larger highly strained bone volume at a 1% strain level (strained above the 1% strain threshold of the thinnest patella), suggesting potential vulnerability to patellar fracture. At a median strain threshold (strained above the 50% strain threshold of the thinnest patella), bone strain volumes were higher for thicker patellae, as the volume of bone in the thicker models was almost twice the volume of bone in the 9 mm models (average of 8.1 cm3 and 15.3 cm3 for 9 mm and 14 mm models, respectively); i.e. there was a greater volume of bone for load to be distributed throughout, albeit at relatively low strain levels.
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Fig. 6. Quadriceps force during the squat activity (shown for one representative specimen—all specimens' demonstrated similar trends and magnitudes). Higher quadriceps force was predicted for thinner patellae at low flexion ( o401), while higher quadriceps force was predicted for thicker patellae at high flexion ( 4 801). Inset shows position of extensor soft-tissues for 9 mm (light) and 14 mm (dark) models at deepest flexion.
Fig. 7. Differences in patellar kinematics between varying resection thicknesses (shown for the mean and standard deviation of the three specimens). Insets show sagittal plane tilt at 101 (left) and I–E rotation at 701 (right) for 9 mm (light) and 14 mm (dark) models.
Bone strain was sensitive to patellar bone quality; a 50% reduction in modulus resulted in up to a seven-fold increase in peak highly strained bone volume (strained above the 1% strain threshold of the thinnest patella in the original model), suggesting an increase in the risk of bone fracture and anterior knee pain with lower modulus bone (Fig. 8). In the reduced modulus bone models 9 mm, 11 mm and 13 mm models had substantially greater highly strained peak volume than the 14 mm model, indicating that maintaining a thicker residual bone volume is particularly important for patients with poor bone quality. Additionally, the heterogeneous nature of patellar bone material properties played a role in how load was distributed throughout the bone volume. Implants in thinner patellae were positioned more anterior relative to the patellar bone, which typically resulted in implant pegs embedded in denser bone. Implants in thicker patellae typically had implant pegs embedded in cancellous bone in the center of the patella, which facilitated distribution of load over a larger bone volume (Fig. 2). This was illustrated by comparing the heterogeneous models to patellar models with uniform material properties. The homogeneous models showed similar distribution of load, regardless of resection thickness of the patellae, while strain the heterogeneous models varied substantially depending
on patellar thickness (Fig. 9). This is of relevance for further computational analysis; generic homogeneous material models are not sufficient to appropriately capture the complexity necessary for bone strain predictions—models with distributed material properties are required. Small but consistent differences were observed in quadriceps efficiency as a result of changes to patellar thickness. At lower flexion angles, the reduction in moment arm due to a thinner composite patellar thickness resulted in a small increase in quadriceps force required by thinner patellae. In deep flexion, the opposite trend was observed—thinner patellae required smaller quadriceps force. In deep flexion these differences were likely a result of changes to how the medial and lateral longus and oblique quadriceps bundles wrapped around the femoral component (Fig. 6). Kinematic differences between resection thickness models altered the contact location between the quadriceps tendon and the femoral component, influencing the muscle line-of-action and correspondingly the efficiency of these structures. The current study only evaluated a single quadriceps load configuration (35% applied centrally, 40% applied laterally, and 25% applied medially). Changes to relative medial– lateral quadriceps load distribution would likely alter the differences between resection thicknesses observed in deep flexion.
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Fig. 8. Top: peak strain threshold (1% bone volume was above this strain threshold) for models with original bone properties and those with reduced modulus bone. Bottom: highly strained bone volume of the original (left) and reduced modulus (right) models compared at the same strain level (evaluated at the 1% strain threshold of the thinnest original modulus patella). Insets show 13 mm models at maximum flexion—black indicates bone above the 1% strain level.
Fig. 9. Comparison of highly strained bone volume between models with distributed bone properties (original models) and models with uniform bone properties applied throughout the patellar geometry. Results are presented at a 50% strain level (50% strain threshold of the thinnest patella), but similar results (similar highly strained bone volume between resection thicknesses in the uniform bone properties models) were observed regardless of the strain level applied. Insets show 9 mm and 14 mm models at maximum flexion—black indicates bone above the 50% strain level.
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Changes in resection thickness altered the rotation of the patella. Sagittal plane patellar tilt varied by several degrees in early flexion. More external rotation was observed in thicker patellae throughout the squat cycle; this was likely dependent on the alignment of the Q-angle in the model. A laterally pulling quadriceps would cause a thicker patella to rotate more externally. There are several important limitations associated with the current study. A single set of TKR components were evaluated under a single loading condition. Different implant systems influence TF and PF kinematics; for instance, large variation was observed in I–E rotation between different resection thicknesses with the dome-compatible patellar implant evaluated in the current study. An implant system with greater PF congruency may potentially have more repeatable I–E PF kinematics across resection thickness models. Unfortunately, there is limited experimental strain data available to directly validate FE strain predictions. However, recreation of in vivo loading conditions (the current study mimicked TF force measured in telemetric patients (Kutzner et al., 2010)) ensures reasonable, physiological conditions under which to perform analyses. Trends in quadriceps force predictions were in good agreement with musculoskeletal model predictions, with peak force of approximately 2900 N during squat-to-stand predicted by Shelburne and Pandy (2002), compared to 2500–2700 N predicted in the current study. Patellar kinematics demonstrated similar trends and magnitudes to experimentally-measured implanted knee kinematics (Baldwin et al., 2009) as well as prior computational studies (Fitzpatrick et al., 2012b). Additionally, as discussed in prior publications, FE PF contact pressure predictions have shown good agreement with experimental data (Fitzpatrick et al., 2011). While this does not validate the absolute magnitude of predicted FE strains, it does justify intra-specimen comparisons between different resection conditions, as was the focus of the current work. This analysis has been performed upon a small number of specimens; further high-volume analysis is required to determine if the trends identified in this study can be generally applied to a population. However, this study provides some interesting insight into the repercussions of patellar resection thickness on peak and median strain in the bone, the impact of bone quality and bone properties distribution, and subtle effects on quadriceps efficiency. Based on the results presented, resection thickness greater than 11 mm is appropriate for minimizing potential for patellar fracture and anterior pain.
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Perillo-Marcone, A., Alonso-Vazquez, A., Taylor, M., 2003. Assessment of the effect of mesh density on the material property discretisation within QCT based FE models: a practical example using the implanted proximal tibia. Computer Methods in Biomechanics and Biomedical Engineering 6, 17–26. Race, A., Mann, K.A., Edidin, A.A., 2007. Mechanics of bone/PMMA composite structures: an in vitro study of human vertebrae. Journal of Biomechanics 40, 1002–1010. Reuben, J.D., McDonald, C.L., Woodard, P.L., Hennington, L.J., 1991. Effect of patella thickness on patella strain following total knee arthroplasty. Journal of Arthroplasty 6, 251–258. Seijas, R., Orduna, J.M., Castro, M.C., Granados, N., Baliarda, J., Alcantara, E., 2009. Fracture of the unresurfaced patella after total knee arthroplasty: a report of two cases. Journal of Orthopedic Surgery (Hong Kong) 17, 251–254. Seo, J.G., Moon, Y.W., Park, S.H., Lee, J.H., Kang, H.M., Kim, S.M., 2012. A case-control study of spontaneous patellar fractures following primary total knee replacement. Journal of Bone and Joint Surgery 94-B, 908–913.
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Contents lists available at SciVerse ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
Effects of resection thickness on mechanics of resurfaced patellae Clare K. Fitzpatrick a,n, Raymond H. Kim b, Azhar A. Ali a, Lowell M. Smoger a, Paul J. Rullkoetter a a b
Center for Orthopedic Biomechanics, University of Denver, Denver, CO, USA Colorado Joint Replacement, Denver, CO, USA
art ic l e i nf o
a b s t r a c t
Article history: Accepted 16 March 2013
Patellar resection thickness during total knee replacement (TKR) has been cited as a contributor to patellar fracture, anterior knee pain and quadriceps efficiency; however, optimal thickness required to minimize clinical complications remains unclear. The objectives of the current study were to determine how patellar resection thickness and bone quality impacts patellar bone strain, kinematics, and quadriceps efficiency. A series of specimen-specific finite element models of the knee joint with distributed patellar bone material properties were developed. Each specimen was virtually implanted with a TKR system. Each specimen was analyzed with patellar bone resected to thicknesses which varied from 9 to 14 mm. Simulations with reduced modulus bone were also performed. Each model perturbation was evaluated during a dynamic squat cycle, and bone strain, quadriceps force and sixdegree-of-freedom kinematics were predicted. Highest peak bone strain was predicted in the thinnest patellae, indicating greatest risk of patellar fracture; highest median bone strain was predicted in the thickest patellae. Consistent differences in quadriceps efficiency were predicted; in early flexion the thickest patellae required the least quadriceps force. Greater sagittal plane tilt was observed for the thinnest patellae. Reduced modulus models (50% lower modulus) demonstrated an increase in peak bone strain of up to seven times the original modulus models. Understanding the complex interactions between patellar resection thickness, muscle requirements, kinematics, bone quality, and bone property distribution may aid in developing an understanding of which patients are most at risk from patellar fracture and anterior knee pain and how best to treat individuals to reduce potential complications. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Patella Resection thickness Finite element Quadriceps efficiency Bone quality Total knee replacement
1. Introduction Early total knee replacement (TKR) procedures with resurfaced patellae reported high incidence of patellofemoral (PF) complications, contributing to up to 50% of all revisions (Brick and Scott, 1988). However, improvements in component design and materials have reduced the incidence of revisions due to PF issues. Recent studies have reported incidence of anterior patellar pain of 12% and patellar fracture rates from 0.68% to 5.2% in the TKR population (Helmy et al., 2003; Dalury and Dennis, 2003; Seijas et al., 2009). While occurrence of patellar fracture is relative low, revision surgeries have reported poor outcomes with high complication rates and reoperation (Ortiguera and Berry, 2002), leaving patellar fracture as a significant concern for the comfort and functionality of the TKR population. Patellar resection thickness has been cited as a contributor to patellar fracture, anterior knee pain and extensor mechanism efficiency (Seo et al., 2012),
n Correspondence to: Center for Orthopaedic Biomechanics, University of Denver, 2390 S. York St., Denver, CO 80208, USA. Tel.: +1 303 871 6435; fax: +1 303 871 4450. E-mail address: clare.fi[email protected] (C.K. Fitzpatrick).
0021-9290/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jbiomech.2013.03.016
however, the influence of resection thickness on patellar mechanics remains unclear. During TKR, surgeons typically aim to restore pre-operative patellar thickness, with reports suggesting that this may aid in preserving the natural mechanics of the joint (Hsu et al., 1996). There are a number of concerns associated with resection of the patellar bone that may potentially lead to complications of the PF joint. Overstuffing of the PF joint may induce ligament and muscle tightness as well as limit knee flexion (Marmor, 1988; Mihalko et al., 2006), while excessive resection of the native patellar bone stock may increase strain and the risk of patellar fracture in the remaining patellar bone (Goldstein et al., 1986; Reuben et al., 1991), increase the risk of crepitation (Hoops et al., 2012), and reduce the quadriceps muscle moment arm, leading to a decrease in extension efficiency (Mountney et al., 2008). Studies have recommended against resected bone of less than 15 mm due to increased patellar bone strain at increased resection depths (Reuben et al., 1991), while others have reported no difference in clinical outcome between groups with bone remnants of less 12 mm and those with bone remnants of greater than 12 mm (Koh et al., 2002). While clinical studies serve to identify factors which differentiate between surgical outcomes based on retrospective analysis,
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this necessitates high-volume datasets with numerous confounding factors which make it difficult or infeasible to identify the impact of a specific surgical decision, such as patellar bone resection thickness, on patellar mechanics. In vitro and in silico studies have the advantage of evaluating such factors in a controlled environment, isolated from additional sources of variability. A number of cadaveric studies have sought to investigate the effect of patellar resection thickness on patellar mechanics (using patellar strain as a surrogate measure for risk of patellar facture and anterior knee pain), with studies measuring strain on the anterior surface using uniaxial strain gauges reporting an increase in superficial strain proportional to the amount of bone removed (Wulff and Incavo, 2000; Lie et al., 2005; Reuben et al., 1991). Recent computational modeling work has developed subjectspecific finite element (FE) PF models with heterogeneous patellar bone material properties mapped from computed tomography (CT) images (Fitzpatrick et al., 2011). These models have been used to compare patellar mechanics in natural, implanted and unresurfaced conditions (Fitzpatrick and Rullkoetter, 2012). To date, however, they have not been used assess the influence of surgical decisions, such as patellar resection thickness, on mechanics of the patella. The objective of the current study was to determine how patellar resection thickness impacts patellofemoral mechanics, including kinematics and strain in the bone, and hence provide insight into the risk of fracture and anterior knee pain.
2. Methods Specimen-specific FE models of the knee joint were developed in Abaqus/ Explicit (SIMULIA, Providence, RI) from CT scans of three cadaveric male knees (65.7 79.9 years; 1.79 70.04 m; 76.9 7 13.6 kg) (Fig. 1). The specimen-specific models were implanted with a semi-constrained, posterior-stabilized TKR with dome patella (positioned under the guidance of an orthopedic surgeon) which included a fully deformable polyethylene button with nonlinear elastic-plastic representation (initial E¼ 572 MPa, v¼ 0.45 (Halloran et al., 2005)) with an intermediate cement layer (E ¼3400 MPa, v¼0.3 (Race et al., 2007)) between the patellar bone and implant. For computational efficiency, femoral and tibial bone and implant components were modeled as rigid bodies, with contact between the components defined using a pressure–overclosure relationship (Halloran et al.,
Fig. 1. Left: finite element (FE) model of the knee joint. Right: loading conditions applied to the FE model to reproduce a squat simulation.
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2005). A coefficient of friction of 0.04 between components was applied (Godest et al., 2002). The models included two-dimensional (2-D) fiber-reinforced membrane representations of the quadriceps (divided into rectus femoris (RF), vastus intermedius (VI), vastus lateralis longus (VLL), vastus lateralis obliquus (VLO), vastus medialis longus (VML) and vastus medialis obliquus (VMO) bundles), patellar tendon and PF ligaments (Fitzpatrick et al., 2011). Tibiofemoral (TF) soft-tissue was represented by medial and lateral collateral ligaments (MCL, LCL—separated into anterior, medial and posterior bundles), anterior lateral capsule (ALC), popliteofibular ligament (PFL), postero-medial capsule (PMC), medial and lateral posterior capsule (MPCAP, LPCAP), and medial and lateral posterior oblique structures (MPOL, LPOL). Each ligament was represented by non-linear tension-only spring elements, with reference strains and linear stiffness parameters adopted from prior work where ligament properties and attachment sites were calibrated to subject-specific internal–external (I–E) and varus–valgus (V–V) tibiofemoral laxity data (Baldwin et al., 2012). Femoral and tibial bones and components were meshed with triangular surface elements, while the deformable patellar button and cement layer were meshed with hexahedral elements. A series of model perturbations were developed whereby the patellar bone was resected to post-operative thicknesses of 9 mm, 11 mm, 13 mm and the maximum patellar thickness possible without allowing any overhang (approximately 14 mm for each specimen) (Fig. 2). Each resected patellar bone representation was meshed using 4-noded tetrahedral elements. A convergence study was performed to determine an appropriate element size for the patellar bone mesh. Tetrahedral meshes with element edge length of 2, 1.25, 1 and 0.8 mm were compared. There were minimal differences in predicted strain values with mesh refinement beyond 1 mm, similar to that reported by Perillo-Marcone et al. (2003). Hence, an average element edge length of 1 mm, which was appropriate for capturing the material property heterogeneity described by the CT data and strain gradients within the bone, was applied (Fitzpatrick et al., 2011; Perillo-Marcone et al., 2003). Specimen-specific mapped material properties of the patellar bone were developed from the CT data using BoneMat (Taddei et al., 2007). A linear relationship taken from the literature (Peng et al., 2006) was used to correlate Hounsfield units (HU) to apparent density (ρ). The empirical relationship, Young's Modulus (E) ¼ 1990ρ3.46, was applied to convert bone density to mechanical properties (Keller, 1994). Loads and muscle forces were applied to the knee in order to reproduce a dynamic squat activity where the knee was flexed from 101 to 1001. I—E and V—V torques were applied to the tibia, with the remaining tibial DOFs constrained. Quadriceps load was applied to the RF, VI, VLL, VLO, VML and VMO actuators (with load distributed amongst the various bundles according to their physiological cross-sectional area (Farahmand et al., 1998)), vertical load was applied at the hip, anterior–posterior (A–P) force was applied to the femur, with femoral I–E rotation constrained and medial–lateral (M–L) translation free. The patella was kinematically unconstrained in all 6-DOF, with constraint provided by the patellar tendon, PF ligaments and quadriceps (Fig. 1). The loading profiles applied to the model (apart from quadriceps force) were derived from data from a telemetric TKR patient (Kutzner et al., 2010) in order to create a physiological loading condition at the TF joint. Description on how these loading profiles were derived has been described in detail in prior publications (Fitzpatrick et al., 2012a, in press)), and hence is mentioned only briefly here. Compressive, A–P, I–E and V–V loads at the TF joint were extracted for a telemetric patient performing a squat activity (Kutzner et al., 2010). As some of the load applied externally to the knee is accounted for by softtissue structures at the joint, the telemetric data (which measures just the load at the implant) could not be applied directly as external loads in the FE model. Hence, a proportional–integral (PI) control system was implemented in the model to apply external loads required to match the joint loading condition measured by the telemetric patients. Quadriceps load was applied via a PI control system which was integrated with the FE model such that knee flexion angle matched a target flexion profile (Fitzpatrick et al., in press). The target flexion profile was adopted from video recordings of the telemetric patient during a squat activity (Bergmann, 2008). Implementation in this manner allowed the quadriceps force to adapt to changes in the moment arm of the extensor mechanism, facilitating comparison of quadriceps efficiency across the various patellar composite thickness models. In order to provide insight into the interactions between quadriceps efficiency, bone quality and bone strain, additional perturbations were performed for each model. Poor patellar bone quality was simulated by locally reducing the modulus of the bone by 50% (Janssen et al., 2010). The effect of bone density distribution was evaluated by simulating uniform bone quality throughout the patellar bone; constant Young's Modulus and density values (averaged from the distributed properties model) were applied to patellar bone properties. Bone strain was compared and presented in two ways. First, a strain threshold was defined as the strain that a certain percentage of bone volume was strained above; for example, a 10% strain threshold means that at maximum load 10% of the bone volume is above the strain threshold. Strain thresholds were evaluated at 1%, 10% and 50% bone volume at each resection thickness; for instance, in Specimen 3 at a 14 mm resection thickness, 1% of bone volume was strained above a 0.029 strain threshold, 10% of bone volume was strained above a 0.0167 strain threshold, and half the bone (by volume) was strained above a 0.0055 strain threshold (Figs. 4 and 5). Strain thresholds were compared between resection thickness
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Fig. 2. A series of patellar models were developed for each specimen with resected thicknesses of 9 mm, 11 mm, 13 mm and the maximum feasible thickness (approximately 14 mm).
models. Strain threshold at 1% bone volume primarily represented peak strain (1% of the bone volume was above this threshold); while strain threshold at 50% bone volume represented median strain (half of the bone volume was above this threshold). Secondly, a highly strained bone volume was calculated and compared across models of varying patellar thickness. For this comparison, a specific strain level was selected, and the volume of bone strained above this strain level was measured. The specific strain level was nominally chosen as a strain threshold (1%, 10% or 50%, as described above) of the thinnest (9 mm resection) patellae. For instance, for Specimen 3 the strain levels of interest at a 1%, 10% and 50% strain threshold were 0.05, 0.017 and 0.0045, respectively (Figs. 4 and 5). For each specimen, the same strain level was applied to each resection thickness model and the bone volume above this strain level was measured. For instance, at a 1% strain level in Specimen 3, the volume of bone strained above 0.05 was calculated at each resection thickness. Prior work investigating patellar strain during a squat activity evaluated compressive strain to be in the order of 3X larger than tensile strain, thus the current study focused on compressive strain (Fitzpatrick and Rullkoetter, 2012; Fitzpatrick et al., 2011). Quadriceps force and TF and PF kinematics were also compared between model representations.
3. Results Bone strain increased with increasing load across all resection thicknesses. Highly strained bone volume at a 1% strain level (strained above the 1% strain threshold of the thinnest (9 mm) patella) was markedly higher in the 9 mm and 11 mm resection thickness models than the 13 mm and 14 mm resection thickness models in deep flexion (Fig. 3). Calculating the peak (1%) strain threshold at each resection thickness (1% of bone volume is above this strain threshold), the thinnest patellae experienced the highest strain thresholds (Fig. 4). At a 10% strain threshold, strain thresholds were similar across resection thicknesses, while at a median (50%) strain threshold, thresholds were higher in the thickest patellae (Fig. 5). Comparing quadriceps efficiency between patellar thicknesses, subtle changes in quadriceps force were predicted, as a result of changes to composite thickness. In early flexion ( o401), thicker patellae demonstrated better quadriceps efficiency, with 14 mm patellae requiring up to 50 N (approximately 5%) less muscle force than a 9 mm patellae to achieve the same flexion profile.
Fig. 3. Highly strained bone volume at a 1% strain level, calculated as follows: for each specimen, the 1% strain threshold of the 9 mm patella was found (1% of bone volume was above this threshold at maximum load). This strain level was applied across all resection thicknesses, and the volume of bone above this level was calculated. Insets show bone strain at maximum load (and flexion) for 9 mm and 14 mm models—black indicates bone volume above the 1% strain level. 9 mm and 11 mm resection models predicted substantially larger highly strained bone volume (evaluated at the 1% strain level) than 13 mm and 14 mm resection models (showing the mean and standard deviation at 101 intervals for the three specimens).
In deepest flexion, thicker patellae experienced the poorest quadriceps efficiency, with 14 mm patellae requiring up to 200 N (approximately 8%) more muscle force than 9 mm patellae. Force was similar across all composite thickness models mid-cycle (Fig. 6). There were some notable differences in PF kinematics between patellar resection analyses. Thinner patellae demonstrated more sagittal plane patellar tilt than thicker patellae in early flexion (o401), with differences of 2–31 observed between 14 mm and
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Fig. 4. Peak strain threshold (1% bone volume was above this strain threshold) for each specimen at each resection thickness. Insets show bone strain at maximum flexion for 9 mm and 14 mm models—black indicates the 1% bone volume with the highest strain.
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models (Fig. 7). TF kinematics demonstrated greater consistency between resection thickness analyses; differences between 9 mm and 14 mm models were less than 1.51 and 2 mm throughout the cycle for I–E rotation and A–P translation, respectively. Poor bone quality (simulated by reducing bone modulus by 50%) increased the strain in the bone; the 1% strain threshold (1% bone volume was strained above this strain threshold) increased by 70% across all resection thicknesses for the reduced modulus simulations compared to the original conditions. When highly strained bone volume of the original and reduced modulus models were compared at the same strain level (strained above the 1% strain threshold of the thinnest patella in the original model), the reduced modulus model demonstrated increases in highly strained bone volume of 3 to 7 times the original model. Additionally, in the original model, 9 mm and 11 mm resected models showed substantially higher highly strained bone volumes in deep flexion than 13 mm and 14 mm models; while in the reduced modulus model, 9 mm, 11 mm and 13 mm models all predicted substantially greater highly strained bone volume than the 14 mm model (Fig. 8). Comparing between patellae with distributed bone properties, and patellae modeled with uniform bone properties, there were some notable differences between highly strained bone volume predictions. In analyses with distributed bone properties the volume of highly strained bone varied between resection thicknesses, and relative ranking between resection thickness models depended on the strain threshold selected (at high threshold (1%) larger strained volume was reported in thinner patellae, while at low threshold (50%) larger strained volume was reported in thicker patellae). In analyses with uniform bone properties, reasonably consistent highly strained bone volume was reported across patellar resection models, regardless of the strain threshold (Fig. 9).
4. Discussion
Fig. 5. 10% (10% bone volume was above this strain threshold, top) and median (50% bone volume was above this strain threshold, bottom) strain threshold for each specimen at each resection thickness. Insets show bone strain at maximum flexion for 9 mm and 14 mm models—black indicates the 50% bone volume with the highest strain.
9 mm models. Thicker patellae were consistently more externally rotated than thinner patellae throughout the squat cycle, with differences in I–E rotation of 5–61 between 14 mm and 9 mm
Understanding the mechanical consequences of patellar resection thickness is important for the clinician in determining how much bone can be safely resected without substantially increasing the risk of patellar bone fracture and anterior knee pain. This is particularly critical for patients with small patellar geometry which would leave thin bone stock remaining post-operatively in order to maintain pre-operative thickness. While there are a variety of potential sources of anterior knee pain (including softtissue strain and impingement), patellar bone, which contains numerous pain-sensing mechanoreceptors, is a likely contributor to anterior knee pain (McDougall, 2006; Barton et al., 2007; Fulkerson, 2002). Higher bone strain results in increased stimulation of the joint nerves in the subcondral bone, potentially leading to anterior knee pain. While pain is a subjective metric in clinical studies, and not feasible to quantify directly from in vitro or computational studies, strain in the patellar bone can be used as a surrogate measure. Thinner patellae demonstrated higher peak strain thresholds (1% of bone volume is above the peak strain threshold) in addition to a larger highly strained bone volume at a 1% strain level (strained above the 1% strain threshold of the thinnest patella), suggesting potential vulnerability to patellar fracture. At a median strain threshold (strained above the 50% strain threshold of the thinnest patella), bone strain volumes were higher for thicker patellae, as the volume of bone in the thicker models was almost twice the volume of bone in the 9 mm models (average of 8.1 cm3 and 15.3 cm3 for 9 mm and 14 mm models, respectively); i.e. there was a greater volume of bone for load to be distributed throughout, albeit at relatively low strain levels.
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Fig. 6. Quadriceps force during the squat activity (shown for one representative specimen—all specimens' demonstrated similar trends and magnitudes). Higher quadriceps force was predicted for thinner patellae at low flexion ( o401), while higher quadriceps force was predicted for thicker patellae at high flexion ( 4 801). Inset shows position of extensor soft-tissues for 9 mm (light) and 14 mm (dark) models at deepest flexion.
Fig. 7. Differences in patellar kinematics between varying resection thicknesses (shown for the mean and standard deviation of the three specimens). Insets show sagittal plane tilt at 101 (left) and I–E rotation at 701 (right) for 9 mm (light) and 14 mm (dark) models.
Bone strain was sensitive to patellar bone quality; a 50% reduction in modulus resulted in up to a seven-fold increase in peak highly strained bone volume (strained above the 1% strain threshold of the thinnest patella in the original model), suggesting an increase in the risk of bone fracture and anterior knee pain with lower modulus bone (Fig. 8). In the reduced modulus bone models 9 mm, 11 mm and 13 mm models had substantially greater highly strained peak volume than the 14 mm model, indicating that maintaining a thicker residual bone volume is particularly important for patients with poor bone quality. Additionally, the heterogeneous nature of patellar bone material properties played a role in how load was distributed throughout the bone volume. Implants in thinner patellae were positioned more anterior relative to the patellar bone, which typically resulted in implant pegs embedded in denser bone. Implants in thicker patellae typically had implant pegs embedded in cancellous bone in the center of the patella, which facilitated distribution of load over a larger bone volume (Fig. 2). This was illustrated by comparing the heterogeneous models to patellar models with uniform material properties. The homogeneous models showed similar distribution of load, regardless of resection thickness of the patellae, while strain the heterogeneous models varied substantially depending
on patellar thickness (Fig. 9). This is of relevance for further computational analysis; generic homogeneous material models are not sufficient to appropriately capture the complexity necessary for bone strain predictions—models with distributed material properties are required. Small but consistent differences were observed in quadriceps efficiency as a result of changes to patellar thickness. At lower flexion angles, the reduction in moment arm due to a thinner composite patellar thickness resulted in a small increase in quadriceps force required by thinner patellae. In deep flexion, the opposite trend was observed—thinner patellae required smaller quadriceps force. In deep flexion these differences were likely a result of changes to how the medial and lateral longus and oblique quadriceps bundles wrapped around the femoral component (Fig. 6). Kinematic differences between resection thickness models altered the contact location between the quadriceps tendon and the femoral component, influencing the muscle line-of-action and correspondingly the efficiency of these structures. The current study only evaluated a single quadriceps load configuration (35% applied centrally, 40% applied laterally, and 25% applied medially). Changes to relative medial– lateral quadriceps load distribution would likely alter the differences between resection thicknesses observed in deep flexion.
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Fig. 8. Top: peak strain threshold (1% bone volume was above this strain threshold) for models with original bone properties and those with reduced modulus bone. Bottom: highly strained bone volume of the original (left) and reduced modulus (right) models compared at the same strain level (evaluated at the 1% strain threshold of the thinnest original modulus patella). Insets show 13 mm models at maximum flexion—black indicates bone above the 1% strain level.
Fig. 9. Comparison of highly strained bone volume between models with distributed bone properties (original models) and models with uniform bone properties applied throughout the patellar geometry. Results are presented at a 50% strain level (50% strain threshold of the thinnest patella), but similar results (similar highly strained bone volume between resection thicknesses in the uniform bone properties models) were observed regardless of the strain level applied. Insets show 9 mm and 14 mm models at maximum flexion—black indicates bone above the 50% strain level.
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Changes in resection thickness altered the rotation of the patella. Sagittal plane patellar tilt varied by several degrees in early flexion. More external rotation was observed in thicker patellae throughout the squat cycle; this was likely dependent on the alignment of the Q-angle in the model. A laterally pulling quadriceps would cause a thicker patella to rotate more externally. There are several important limitations associated with the current study. A single set of TKR components were evaluated under a single loading condition. Different implant systems influence TF and PF kinematics; for instance, large variation was observed in I–E rotation between different resection thicknesses with the dome-compatible patellar implant evaluated in the current study. An implant system with greater PF congruency may potentially have more repeatable I–E PF kinematics across resection thickness models. Unfortunately, there is limited experimental strain data available to directly validate FE strain predictions. However, recreation of in vivo loading conditions (the current study mimicked TF force measured in telemetric patients (Kutzner et al., 2010)) ensures reasonable, physiological conditions under which to perform analyses. Trends in quadriceps force predictions were in good agreement with musculoskeletal model predictions, with peak force of approximately 2900 N during squat-to-stand predicted by Shelburne and Pandy (2002), compared to 2500–2700 N predicted in the current study. Patellar kinematics demonstrated similar trends and magnitudes to experimentally-measured implanted knee kinematics (Baldwin et al., 2009) as well as prior computational studies (Fitzpatrick et al., 2012b). Additionally, as discussed in prior publications, FE PF contact pressure predictions have shown good agreement with experimental data (Fitzpatrick et al., 2011). While this does not validate the absolute magnitude of predicted FE strains, it does justify intra-specimen comparisons between different resection conditions, as was the focus of the current work. This analysis has been performed upon a small number of specimens; further high-volume analysis is required to determine if the trends identified in this study can be generally applied to a population. However, this study provides some interesting insight into the repercussions of patellar resection thickness on peak and median strain in the bone, the impact of bone quality and bone properties distribution, and subtle effects on quadriceps efficiency. Based on the results presented, resection thickness greater than 11 mm is appropriate for minimizing potential for patellar fracture and anterior pain.
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