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Metaphyseal sleeves in revision total knee arthroplasties: Computational analysis of bone remodeling

  • Author Footnotes
    1 Address: Av. Rovisco Pais, 1 1049-001, Portugal.
    Pedro Nogueira
    Footnotes
    1 Address: Av. Rovisco Pais, 1 1049-001, Portugal.
    Affiliations
    IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal
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  • João Folgado
    Correspondence
    Corresponding authors at: IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1 1049-001, Portugal.
    Affiliations
    IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal
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  • Carlos Quental
    Correspondence
    Corresponding authors at: IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1 1049-001, Portugal.
    Affiliations
    IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal
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  • Author Footnotes
    2 Address: Campo dos Mártires da Pátria 130, 1169-056 Lisboa, Portugal.
    João Gamelas
    Footnotes
    2 Address: Campo dos Mártires da Pátria 130, 1169-056 Lisboa, Portugal.
    Affiliations
    NOVA Medical School, Universidade NOVA de Lisboa, Lisbon, Portugal
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  • Author Footnotes
    1 Address: Av. Rovisco Pais, 1 1049-001, Portugal.
    2 Address: Campo dos Mártires da Pátria 130, 1169-056 Lisboa, Portugal.
Open AccessPublished:June 02, 2022DOI:https://doi.org/10.1016/j.knee.2022.05.006

      Highlights

      • The influence of metaphyseal sleeves on the bone remodeling of the tibia was evaluated.
      • Global bone loss ranged from −31.16% (115 mm stem) to −20.93% (75 mm stem).
      • Bone loss was more pronounced in medial regions than in lateral regions.
      • Metaphyseal sleeves reduced bone loss proximally in the lateral region, but increased it in the posterior region.
      • Overall, metaphyseal sleeves had little impact on bone remodeling.

      Abstract

      Background

      Metaphyseal sleeves help maintain long term stability and reduce revision rate for aseptic loosening in total knee arthroplasty (TKA) revision. However, their performance regarding bone remodeling is still poorly known for the long term. This study aimed to investigate the impact of metaphyseal sleeves on the bone remodeling of the tibia.

      Methods

      Five finite element models of a female tibia with different implant configurations (regarding stem length and metaphyseal sleeve application) were developed. Loading conditions included joint reaction force, muscle, and tibia-fibula loads from 6 instances of the gait cycle. The bone remodeling model applied was adapted to the subject under analysis by selecting the bone remodeling parameters that best replicated the bone density distribution of the tibia estimated from the CT data. Changes in bone density after TKA were evaluated in 8 regions of interest.

      Results

      Global bone loss ranged from −31.16%, in 115 mm stemmed configurations, to −20.93%, in 75 mm stemmed configurations. Apart from the lateral and posterior regions in the proximal tibia, whose bone loss reduced and increased, respectively, due to the incorporation of a metaphyseal sleeve, changes in bone density were similar with and without a metaphyseal sleeve for each stem length.

      Conclusion

      The results suggest that bone remodeling of the tibia is not critically affected by the incorporation of metaphyseal sleeves. Considering that sleeves are believed to present a favorable clinical outcome in stability and osseointegration, reducing the revision rate for aseptic loosening, their advantages seem to outweigh their disadvantages regarding bone remodeling.

      Keywords

      1. Introduction

      The number of total knee arthroplasties (TKA) has been increasing in the younger population, which reinforces the increasing trend of revision surgeries [
      • Bugler K.E.
      • Maheshwari R.
      • Ahmed I.
      • Brenkel I.J.
      • Walmsley P.J.
      Metaphyseal Sleeves for Revision Total Knee Arthroplasty: Good Short-Term Outcomes.
      ]. From 2010 to 2019, the number of TKA revision surgeries increased 23.8% in the United Kingdom [

      Ben-Shlomo Y, Blom A, Boulton C, Brittain R, Clark E, Craig R, et al. National Joint Registry - 17th Annual Report 2020. Natl Jt Regist 2020:138.

      ]. Aseptic loosening, often associated with bone resorption due to stress shielding and an inflammatory cellular response, is the main complication leading to revision in TKA [

      Ben-Shlomo Y, Blom A, Boulton C, Brittain R, Clark E, Craig R, et al. National Joint Registry - 17th Annual Report 2020. Natl Jt Regist 2020:138.

      ]. During revision TKA, managing bone stock, usually weakened due to stress shielding, correcting bone defects, and ensuring implant fixation are crucial challenges. Metaphyseal sleeve fixation was introduced in recent years for patients with severe bony defects requiring revision TKA. By stimulating bone growth at the metaphysis and enhancing stability through osseointegration, it compensates for the loss of bone [
      • Zanirato A.
      • Cavagnaro L.
      • Basso M.
      • Divano S.
      • Felli L.
      • Formica M.
      Metaphyseal sleeves in total knee arthroplasty revision: complications, clinical and radiological results. A systematic review of the literature.
      ]. Chalmers et al. [
      • Chalmers B.P.
      • Desy N.M.
      • Pagnano M.W.
      • Trousdale R.T.
      • Taunton M.J.
      Survivorship of Metaphyseal Sleeves in Revision Total Knee Arthroplasty.
      ] showed a 5-year survivorship free of revision for aseptic loosening of 96% and 99.5% in femoral and tibial sleeves, respectively, and Bloch et al. [
      • Bloch B.V.
      • Shannak O.A.
      • Palan J.
      • Phillips J.R.A.
      • James P.J.
      Metaphyseal Sleeves in Revision Total Knee Arthroplasty Provide Reliable Fixation and Excellent Medium to Long-Term Implant Survivorship.
      ] reported a 97.8% implant survivorship at 10 years, suggesting that revision implants with metaphyseal sleeves have good clinical and radiographic performance in the medium to long term. Yet, in a systematic literature review of 16 studies reporting results for 1801 metaphyseal sleeves, Zanirato et al. [
      • Zanirato A.
      • Formica M.
      • Cavagnaro L.
      • Divano S.
      • Burastero G.
      • Felli L.
      Metaphyseal cones and sleeves in revision total knee arthroplasty: Two sides of the same coin? Complications, clinical and radiological results—a systematic review of the literature.
      ] found an overall aseptic loosening rate of 2.2%, which highlights the need for further investigation on the long-term outcomes and complications of this technique [
      • Zanirato A.
      • Cavagnaro L.
      • Basso M.
      • Divano S.
      • Felli L.
      • Formica M.
      Metaphyseal sleeves in total knee arthroplasty revision: complications, clinical and radiological results. A systematic review of the literature.
      ,
      • Bouras T.
      • Fennema P.
      • Morgan-Jones R.
      • Agarwal S.
      Metaphyseal Sleeve Failure in Revision Total Knee Arthroplasty.
      ]. The long-term effect of metaphyseal sleeves on bone remodeling is still poorly known [
      • Quilez M.P.
      • Seral B.
      • Pérez M.A.
      • Jan Y.-K.
      Biomechanical evaluation of tibial bone adaptation after revision total knee arthroplasty: A comparison of different implant systems.
      ].
      Computational studies of TKA have focused on stress shielding [
      • Enab T.A.
      • Bondok N.E.
      Material selection in the design of the tibia tray component of cemented artificial knee using finite element method.
      ,
      • Frehill B.
      • Crocombe A.D.
      Finite element assessment of metaphyseal sleeves in total knee arthroplasty.
      ,
      • Chan Â.
      • Gamelas J.
      • Folgado J.
      • Fernandes P.R.
      Biomechanical analysis of the tibial tray design in TKA: Comparison between modular and offset tibial trays.
      ] and bone remodeling [
      • Quilez M.P.
      • Seral B.
      • Pérez M.A.
      • Jan Y.-K.
      Biomechanical evaluation of tibial bone adaptation after revision total knee arthroplasty: A comparison of different implant systems.
      ] in the tibia, but only the studies of Frehill and Crocombe [
      • Frehill B.
      • Crocombe A.D.
      Finite element assessment of metaphyseal sleeves in total knee arthroplasty.
      ] and Quilez et al. [
      • Quilez M.P.
      • Seral B.
      • Pérez M.A.
      • Jan Y.-K.
      Biomechanical evaluation of tibial bone adaptation after revision total knee arthroplasty: A comparison of different implant systems.
      ] included metaphyseal sleeves. Frehill and Crocombe [
      • Frehill B.
      • Crocombe A.D.
      Finite element assessment of metaphyseal sleeves in total knee arthroplasty.
      ] studied the influence of sleeve and stem length on the Von Mises stress distribution after TKA. Based on Wolff’s law and the obtained stress distribution, they extrapolated that large sleeves and stems increase the risk of bone resorption in proximal regions (compared with small sleeves and stems). Considering a bone remodeling mathematical model [
      • Pérez M.A.
      • Fornells P.
      • Doblaré M.
      • García-Aznar J.M.
      Comparative analysis of bone remodelling models with respect to computerised tomography-based finite element models of bone.
      ], Quilez et al. [
      • Quilez M.P.
      • Seral B.
      • Pérez M.A.
      • Jan Y.-K.
      Biomechanical evaluation of tibial bone adaptation after revision total knee arthroplasty: A comparison of different implant systems.
      ] evaluated bone remodeling after TKA revision for 5 prostheses, including the application of metaphyseal sleeves. The proximal epiphysis presented the largest loss in bone mass, of up to 50%, in all prostheses and the application of metaphyseal sleeves caused the highest bone formation in the metaphysis. Despite the contributions of these studies to the field, these are not without limitations. The fibula was disregarded in both studies and the loading conditions considered were limited, both in the number of load cases and the number of forces per load case—only knee joint reaction forces were applied—which likely impacted the results, especially those of bone remodeling. Quilez et al. [
      • Quilez M.P.
      • Seral B.
      • Pérez M.A.
      • Jan Y.-K.
      Biomechanical evaluation of tibial bone adaptation after revision total knee arthroplasty: A comparison of different implant systems.
      ] also considered the whole implant, including non-coated surfaces, tied to the bone.
      Considering that the long-term effect of metaphyseal sleeves on bone density is still not fully understood, and that computational models capable of simulating bone remodeling can be a valuable source of data, this study aimed to evaluate the impact of metaphyseal sleeves on the bone remodeling of the tibia after a TKA using the mathematical model developed by Fernandes et al. [
      • Fernandes P.
      • Rodrigues H.
      • Jacobs C.
      A model of bone adaptation using a global optimisation criterion based on the trajectorial theory of wolff.
      ]. Bone remodeling was simulated for 5 TKA prostheses using three-dimensional finite element models. Six load cases, including muscle, joint reaction force, and tibia-fibula loads, were applied.

      2. Methods

      2.1 Finite element model

      Three-dimensional geometries of a left tibia and left fibula were segmented from CT data of the Visible Human Female dataset, collected from the cadaver of a 59 year old female, using ITK-SNAP (version 3.6) [
      • Spitzer V.
      • Ackerman M.J.
      • Scherzinger A.L.
      • Whitlock D.
      The Visible Human Male: A Technical Report.
      ,
      • Yushkevich P.A.
      • Piven J.
      • Hazlett H.C.
      • Smith R.G.
      • Ho S.
      • Gee J.C.
      • et al.
      User-guided 3D active contour segmentation of anatomical structures: Significantly improved efficiency and reliability.
      ]. Tibial prostheses were modelled in Solidworks (version S 2019, Dassault Systèmes, Waltham, MA, USA) based on a P.F.C.® SIGMA® TC3TM Knee System, the most used in the United Kingdom [

      Ben-Shlomo Y, Blom A, Boulton C, Brittain R, Clark E, Craig R, et al. National Joint Registry - 17th Annual Report 2020. Natl Jt Regist 2020:138.

      ]. As shown in Figure 1, five configurations were modelled considering: (a) no stem (here after called stemless); (b) a 75-mm long stem; (c) a 75-mm long stem with a metaphyseal sleeve; (d) a 115-mm long stem; and (e) a 115-mm long stem with a metaphyseal sleeve. The stemless model, in Figure 1(a), was developed to define the initial density distribution of the tibia for the remaining models and to qualitatively validate the considered methodology. The prosthesis components were virtually introduced in the tibia according to the surgical technique of the manufacturer [

      Depuy. Sigma ® Revision and M.B.T. Revision Tray, 2009.

      ]. An orthopedic surgeon approved their final positioning.
      Figure thumbnail gr1
      Figure 1Geometry of the prostheses modelled based on the P.F.C.® SIGMA® TC3TM Knee System: (a) model without a stem; (b) model with a 75 mm stem; (c) model with a 75 mm stem and a metaphyseal sleeve; (d) model with a 115 mm stem, and (e) model with a 115 mm stem and a metaphyseal sleeve. The grey region in the metaphyseal sleeves highlights the porous-coated surfaces for bone osseointegration.
      Five finite element models were developed in Abaqus 2017 (Dassault Systèmes, Waltham, MA, USA), one for each configuration of the modelled prostheses, using linear tetrahedral (C3D4) elements. Mesh sizes were defined through a sensitivity analysis.
      All components of the prostheses were modelled as linear elastic, homogeneous and isotropic materials: the tibial (M.B.T.) tray, made of cobalt-chromium, was modelled with a Young's modulus of 210 GPa and a Poisson’s ratio of 0.3 [
      • Kluess D.
      • Mittelmeier W.
      • Bader R.
      Intraoperative impaction of total knee replacements: An explicit finite-element-analysis of principal stresses in ceramic vs. cobalt-chromium femoral components.
      ]; the stems and metaphyseal sleeves, made of a titanium alloy, were modelled with a Young’s modulus of 110 GPa and a Poisson’s ratio of 0.36 [
      • Darwish S.M.
      • Al-Samhan A.
      The effect of cement stiffness and tibia tray material on the stresses developed in artificial knee.
      ]; and the stabilizer insert, made of polyethylene, was modelled with a Young’s modulus of 0.5 GPa and a Poisson’s ratio of 0.3 [
      • Completo A.
      • Simões J.A.
      • Fonseca F.
      • Oliveira M.
      The influence of different tibial stem designs in load sharing and stability at the cement-bone interface in revision TKA.
      ].
      The porous-coated surface of the metaphyseal sleeves, highlighted in grey in Figure 1, was assumed tied to the bone, simulating the condition of total bone osseointegration [
      • Frehill B.
      • Crocombe A.D.
      Finite element assessment of metaphyseal sleeves in total knee arthroplasty.
      ,
      • Quental C.
      • Fernandes P.R.
      • Monteiro J.
      • Folgado J.
      Bone remodelling of the scapula after a total shoulder arthroplasty.
      ]. All remaining interactions between the implant and bone were modelled using a contact formulation with a friction coefficient that depended on the type of materials interacting, as detailed in Table 1. The different components of the prostheses were tied together to ensure no separation between them.
      Table 1Interaction properties considered in the finite element models.
      Parts interactingInteracting property
      Bone – M.B.T. trayFriction coefficient of 0.4
      Bone – SleeveFriction coefficient of 0.3

      (tied in porous-coated surfaces)
      Bone – StemFriction coefficient of 0.3
      Stabilizer insert – M.B.T. trayTied
      M.B.T. tray – sleeveTied
      M.B.T. tray – stemTied
      Given that the proximal part of the tibia is the most important region to evaluate the performance of the prostheses, the tibia is fixed at its distal section to prevent rigid body motion [
      • Quilez M.P.
      • Seral B.
      • Pérez M.A.
      • Jan Y.-K.
      Biomechanical evaluation of tibial bone adaptation after revision total knee arthroplasty: A comparison of different implant systems.
      ,
      • Frehill B.
      • Crocombe A.D.
      Finite element assessment of metaphyseal sleeves in total knee arthroplasty.
      ].

      2.2 Bone remodeling model and loading conditions

      The bone remodeling model applied assumes that bone adapts itself to the stiffest structure while considering a biological criterion regarding the cost of bone maintenance [
      • Fernandes P.
      • Rodrigues H.
      • Jacobs C.
      A model of bone adaptation using a global optimisation criterion based on the trajectorial theory of wolff.
      ,
      • Quental C.
      • Fernandes P.R.
      • Monteiro J.
      • Folgado J.
      Bone remodelling of the scapula after a total shoulder arthroplasty.
      ,
      • Folgado J.
      • Fernandes P.R.
      • Jacobs C.R.
      • Pellegrini V.D.
      Influence of femoral stem geometry, material and extent of porous coating on bone ingrowth and atrophy in cementless total hip arthroplasty: an iterative finite element model.
      ]. Briefly, bone is described as a cellular material that consists of a periodic repetition of cubic unit cells with rectangular holes, as depicted in Figure 2. The unit cells are made of cortical bone tissue, to which a Young’s modulus of 17 GPa and a Poisson’s ratio of 0.3 was assigned [
      • Frehill B.
      • Crocombe A.D.
      Finite element assessment of metaphyseal sleeves in total knee arthroplasty.
      ,
      • Quental C.
      • Fernandes P.R.
      • Monteiro J.
      • Folgado J.
      Bone remodelling of the scapula after a total shoulder arthroplasty.
      ]. Hole sizes (a) control bone density (μ) and cell angles (θ) control material orientation. The material properties for each bone position are computed using an homogenization technique [
      • Guedes J.
      • Kikuchi N.
      Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods.
      ]. Mathematically, the bone remodeling law (obtained through the optimality conditions of the optimization problem) can be expressed as:
      P=1NLαPEijklHaekluPeijup-kμma=0
      (1a)


      P=1NLαPEijklHθekluPeijup=0
      (1b)


      where NL is the number of applied loads, αP are load weight factors, EijklH are the homogenised bone material properties, ekl and eij are the strain field components, and uP is the displacement field computed by the finite element analysis for the load case P. Parameters k and m are bone remodeling parameters that define the cost of bone maintenance. Since they depend on several factors, such as age, gender, metabolism efficiency, hormonal status, and disease, they must be identified for each person.
      Bone remodeling simulations were performed considering 6 load cases with equal weights αP that represent 6 instances of the gait cycle. Each of these load cases included 3 types of loads: joint reaction force loads, muscle loads, and tibia-fibula loads that arise from their interaction. The joint reaction force and muscle loads were obtained through inverse dynamics considering a musculoskeletal model of the lower limb based on the cadaveric data published by Horsman et al. [
      • Klein Horsman M.D.
      • Koopman H.F.J.M.
      • van der Helm F.C.T.
      • Prosé L.P.
      • Veeger H.E.J.
      Morphological muscle and joint parameters for musculoskeletal modelling of the lower extremity.
      ,
      • Quental C.
      • Folgado J.
      • Ambrósio J.
      A window moving inverse dynamics optimization for biomechanics of motion.
      ]. Apart from the knee transverse joint reaction moment, all knee joint reaction force loads were applied at its center of rotation and distributed over the proximal surface of the stabilizer insert using coupling constraints [
      • Quental C.
      • Fernandes P.R.
      • Monteiro J.
      • Folgado J.
      Bone remodelling of the scapula after a total shoulder arthroplasty.
      ,
      • Comenda M.
      • Quental C.
      • Folgado J.
      • Sarmento M.
      • Monteiro J.
      Bone adaptation impact of stemless shoulder implants: a computational analysis.
      ]. The transverse joint reaction moment was distributed over a small proximal region of the tibia assuming that it was related with the action of soft tissues—since the implant possesses a rotating stabilizer insert, it does not transmit transverse moments. Muscle loads were applied at the centroid of their attachment sites, defined according to anatomical descriptions [

      Drake, Vogl W, Mitchell. Gray’s anatomy - Flash Cards. 3rd ed. Philadelphia: Elsevier; 2015.

      ,
      • Netter F.H.
      Netter’s Clinical Anatomy.
      ], and were distributed over them. The loads transmitted by the fibula to the tibia through ligaments, cartilage, and the interosseous membrane (tibia-fibula loads) were computed considering an auxiliary finite element model in which the tibia was fixed and the muscle loads associated with the fibula were applied to it. Our aim was to allow a robust characterization of the mechanical environment of the tibia during gait while avoiding the computational complexity of the tibia-fibula interactions during the bone remodeling simulations. For further detail on the auxiliary finite element model used for the computation of the tibia-fibula loads and the applied loads, see the supplementary material.

      2.3 Bone remodeling model calibration

      To identify the bone remodeling parameters k and m that fit the subject under study, several combinations of these two parameters were evaluated using a finite element model of the intact tibia, i.e., with no implant [
      • Quental C.
      • Fernandes P.R.
      • Monteiro J.
      • Folgado J.
      Bone remodelling of the scapula after a total shoulder arthroplasty.
      ,
      • Comenda M.
      • Quental C.
      • Folgado J.
      • Sarmento M.
      • Monteiro J.
      Bone adaptation impact of stemless shoulder implants: a computational analysis.
      ,
      • Santos B.
      • Quental C.
      • Folgado J.
      • Sarmento M.
      • Monteiro J.
      Bone remodelling of the humerus after a resurfacing and a stemless shoulder arthroplasty.
      ]. The modeling conditions (material properties, loading conditions and boundary conditions) were similar to those of the implanted models. The purpose of these simulations was to find the set of parameters that best reproduced the bone density distribution of the tibia under analysis, which was obtained by extracting HU values from the CT data using the bonemapy plugin [

      Hogg M. GitHub - Mhogg/bonemapy: An ABAQUS plug-in to map bone properties from CT scans to 3D finite element bone/implant models 2013.

      ] and by converting them into density using a linear calibration procedure [
      • Quental C.
      • Fernandes P.R.
      • Monteiro J.
      • Folgado J.
      Bone remodelling of the scapula after a total shoulder arthroplasty.
      ,
      • Comenda M.
      • Quental C.
      • Folgado J.
      • Sarmento M.
      • Monteiro J.
      Bone adaptation impact of stemless shoulder implants: a computational analysis.
      ].
      For the evaluation of results, density differences between the computational simulations and CT data were computed considering non-normalized and normalized root mean square deviations (RMS and RMSN, respectively), expressed as:
      RMS=n=1NNμmodeln-μCTn2NN
      (2a)


      RMSN=n=1NNμmodeln-μCTnμCTn2NN
      (2b)


      where NN is the number of nodes, μmodeln is the density estimated for node n, and μCTn is the density from the CT data for node n. The solution deemed best considered both RMS and RMSN by combining them as:
      Dev=12RMSμ¯CT+RMSN
      (3)


      where μ¯CT is the average density of the CT data.

      2.4 Bone remodeling analysis after TKA

      After the identification of the parameters k and m, bone remodeling simulations after TKA were performed for 300 iterations. Since this study focuses on TKA revision, the initial density distribution for the stemmed configurations was the final bone density distribution obtained after the adaptation of the bone to the stemless prosthesis. The initial density distribution for the stemless prosthesis was the final density distribution obtained for the intact tibia. To evaluate the influence of the revision prostheses on bone remodeling, bone densities were compared between stemmed and stemless models. For the sake of comparison, the stemless model was also run for 300 iterations, starting from the same solution as the stemmed models. Because clinical data for the stemmed prostheses were not found, results from the stemless model were also compared with the literature for further qualitative validation of the applied bone remodeling model. Figure 3 summarizes the methodology followed for the evaluation of bone remodeling.
      Figure thumbnail gr3
      Figure 3Flowchart illustrating the methodology followed for the evaluation of bone remodeling. Blue arrows denote the initial density distribution considered for each simulation. Orange arrows indicate the comparisons performed between models for the evaluation of bone remodeling.
      Differences in bone density were quantitatively evaluated in eight regions of interest (RoI) –proximal and distal regions, and each one of these divided into medial, lateral, anterior, and posterior regions. Figure 4 illustrates the eight RoIs. Note that the volume of these regions differs depending on the configuration under analysis—the application of metaphyseal sleeves reduces the bone volume of the proximal RoIs since it is a more invasive technique. For each RoI, an average change in bone density was computed as follows between the stemless and intact models, and the stemmed and stemless models:
      %ΔμROI=n=1NNROIμstemn-μrefnVnn=1NNROIμrefnVn×100
      (4)


      where NNROI is the number of nodes of the RoI; μstemn is the density of node n from the stemmed or stemless model, depending on the evaluation being made; μrefn is the density of node n from the reference model, i.e., the stemless model for the stemmed model or the intact model for the stemless model; and Vn is the volume associated with node n.
      Figure thumbnail gr4
      Figure 4Regions of interest considered for the evaluation of bone density changes. Proximal and distal regions are color coded pink and green, respectively. M, Medial; L, Lateral.

      3. Results

      3.1 Bone remodeling model calibration

      Table 2 presents the deviation (Dev) between the computational simulations and CT data for a set of bone remodeling parameters selected around the minimum obtained value. The best solution was obtained for m=2 and k=2,5×10-2.
      Table 2Deviation (Dev) between the bone density distribution estimated computationally for the intact tibia and that from the CT data.

      3.2 Bone remodeling analysis after TKA

      Average differences in bone density between the stemless and intact models are presented in Table 3. The largest bone loss and bone formation were estimated in RoI 4 (proximal and medial) and 1 (proximal and anterior), respectively. The loss of bone mass was more pronounced in medial RoIs than lateral RoIs. The anterior and posterior regions gained bone mass compared to the intact model.
      Table 3Percent changes in bone density %ΔμROIintact of the stemless model with respect to the intact model for the 8 RoIs of the tibia. Positive values are color coded green and represent bone apposition, whereas negative values are color coded from yellow to orange based on the amount of bone resorption.
      Table 4 shows the percentage change in bone density for the four stemmed configurations with respect to the stemless configuration. All RoIs presented bone loss; the proximal RoIs lost more than the distal RoIs and the medial RoIs lost more than the lateral RoIs. The application of metaphyseal sleeves reduced bone loss in the proximal and lateral region (RoI 2), but increased bone loss in the proximal and posterior region (RoI 3). For all remaining regions, differences between models with and without a metaphyseal sleeve were smaller than 5%.
      Table 4Percent changes in bone density %ΔμROI for the stemmed models with respect to the stemless model for the 8 RoIs of the tibia. Density changes are color coded from yellow to orange as bone loss increases.
      Figure 5 presents the density distribution obtained for all considered models, including the intact model, at the end of the bone remodeling simulations for an anterior longitudinal section of the tibia. All stemmed models show low proximal bone density, reduction in cortical bone stock in the diaphysis, and end-of-stem apposition.
      Figure thumbnail gr5
      Figure 5Color coded bone density distribution of the tibia for an anterior longitudinal view: (a) model before TKA, without any implant; (b) model without a stem; (c) model with a 75 mm stem; (d) model with a 75 mm stem and a metaphyseal sleeve; (e) model with a 115 mm stem; (f) model with a 115 mm stem and a metaphyseal sleeve.

      4. Discussion

      This study aimed to evaluate the impact of metaphyseal sleeves on the bone remodeling of the tibia after TKA revision using three-dimensional finite element models. To validate the application of the bone remodeling model, the bone remodeling parameters that best replicated the CT-scan bone density distribution of the tibia under analysis were selected. TKA revision results were compared with the stemless model to evaluate the performance of the revision implant. The stemless model was compared with clinical results available in the literature to provide additional confidence in the methodology followed.
      Global bone loss ranged from −31.16%, in 115 mm stemmed configurations, to −20.93%, in 75 mm stemmed configurations. The application of metaphyseal sleeves had little impact on bone remodeling—global bone loss was larger by only 0.36% and 0.33% in 75 mm and 115 mm stemmed configurations, respectively. The most pronounced differences were observed in RoI 2 (proximal and lateral) and 3 (proximal and posterior), which lost less and more bone, respectively, compared with the conditions without metaphyseal sleeves. Quilez et al. [
      • Quilez M.P.
      • Seral B.
      • Pérez M.A.
      • Jan Y.-K.
      Biomechanical evaluation of tibial bone adaptation after revision total knee arthroplasty: A comparison of different implant systems.
      ] predicted the largest bone loss of 50% at the proximal RoIs of the tibia for stemmed and sleeved models, which is consistent with the findings of this study (49%), but predicted a gain in bone mass at the distal RoIs (Figure 4), which diverges from this study. The estimated gain in bone mass at the distal RoIs is puzzling, especially because a similar gain in bone mass was obtained for sleeved models with and without a long stem, which differs from the literature on the influence of long stems on bone remodeling [
      • Frehill B.
      • Crocombe A.D.
      Finite element assessment of metaphyseal sleeves in total knee arthroplasty.
      ,
      • Chong D.Y.R.
      • Hansen U.N.
      • Amis A.A.
      The influence of tibial prosthesis design features on stresses related to aseptic loosening and stress shielding.
      ]. Like Frehill and Crocombe [
      • Frehill B.
      • Crocombe A.D.
      Finite element assessment of metaphyseal sleeves in total knee arthroplasty.
      ], who suggested long stems to increase stress shielding and bone resorption, our results also suggest a more relevant contribution of stem length to bone remodeling than metaphyseal sleeve application. For the distal RoIs, it was the most determinant factor – the longer the stem, the larger the bone loss. For the proximal RoIs, the mechanical environment was independent of stem length as the differences between configurations were limited.
      Studies about metaphyseal sleeve fixation showed that sleeves play a key role in implant stability and survivability to aseptic loosening [
      • Chalmers B.P.
      • Desy N.M.
      • Pagnano M.W.
      • Trousdale R.T.
      • Taunton M.J.
      Survivorship of Metaphyseal Sleeves in Revision Total Knee Arthroplasty.
      ,
      • Bloch B.V.
      • Shannak O.A.
      • Palan J.
      • Phillips J.R.A.
      • James P.J.
      Metaphyseal Sleeves in Revision Total Knee Arthroplasty Provide Reliable Fixation and Excellent Medium to Long-Term Implant Survivorship.
      ,
      • Graichen H.
      • Scior W.
      • Strauch M.
      Direct, Cementless, Metaphyseal Fixation in Knee Revision Arthroplasty With Sleeves-Short-Term Results.
      ]. According to Graichen et al. [
      • Graichen H.
      • Scior W.
      • Strauch M.
      Direct, Cementless, Metaphyseal Fixation in Knee Revision Arthroplasty With Sleeves-Short-Term Results.
      ], fixation in the metaphysis overcomes the shortcomings of standard stem-based fixation methods, such as stem pain, radio-lucencies in cementless stems or potential mal-alignment in cemented stems. Additionally, sleeves are the only available option for direct metaphyseal fixation aside from bone cement [
      • Bloch B.V.
      • Shannak O.A.
      • Palan J.
      • Phillips J.R.A.
      • James P.J.
      Metaphyseal Sleeves in Revision Total Knee Arthroplasty Provide Reliable Fixation and Excellent Medium to Long-Term Implant Survivorship.
      ,
      • Graichen H.
      • Scior W.
      • Strauch M.
      Direct, Cementless, Metaphyseal Fixation in Knee Revision Arthroplasty With Sleeves-Short-Term Results.
      ], which is associated with long term aseptic loosening [

      Ben-Shlomo Y, Blom A, Boulton C, Brittain R, Clark E, Craig R, et al. National Joint Registry - 17th Annual Report 2020. Natl Jt Regist 2020:138.

      ]. Considering these data, and the findings of this study, which showed a negligible impact of metaphyseal sleeves on the bone remodeling of the tibia, the benefits of their application seem to outweigh their downsides as far as bone remodeling is concerned.
      To the authors knowledge, no clinical studies have quantified bone loss in stemmed or sleeved configurations [
      • Gundry M.
      • Hopkins S.
      • Knapp K.
      A Review on Bone Mineral Density Loss in Total Knee Replacements Leading to Increased Fracture Risk.
      ]. To increase confidence in the results, changes in bone mass were evaluated for the stemless model, for which clinical data are available [
      • Hernandez-Vaquero D.
      • Garcia-Sandoval M.A.
      • Fernandez-Carreira J.M.
      • Gava R.
      Influence of the tibial stem design on bone density after cemented total knee arthroplasty: A prospective seven-year follow-up study.
      ,
      • Murahashi Y.
      • Teramoto A.
      • Jimbo S.
      • Okada Y.
      • Kamiya T.
      • Imamura R.
      • et al.
      Denosumab prevents periprosthetic bone mineral density loss in the tibial metaphysis in total knee arthroplasty.
      ,
      • Small S.R.
      • Ritter M.A.
      • Merchun J.G.
      • Davis K.E.
      • Rogge R.D.
      Changes in tibial bone density measured from standard radiographs in cemented and uncemented total knee replacements after ten years’ follow-up.
      ,
      • Jaroma A.
      • Soininvaara T.
      • Kröger H.
      Periprosthetic tibial bone mineral density changes after total knee arthroplasty: A 7-year follow-up of 86 patients.
      ,
      • Soininvaara T.A.
      • Miettinen H.J.A.
      • Jurvelin J.S.
      • Suomalainen O.T.
      • Alhava E.M.
      • Kröger H.P.J.
      Periprosthetic tibial bone mineral density changes after total knee arthroplasty: One-year follow-up study of 69 patients.
      ]. Changes in bone density estimated computationally, ranging between −10.12% and 9.74%, were within those reported by clinical studies: compared with the pre-operative condition, Jaroma et al. [
      • Jaroma A.
      • Soininvaara T.
      • Kröger H.
      Periprosthetic tibial bone mineral density changes after total knee arthroplasty: A 7-year follow-up of 86 patients.
      ] reported a maximum bone loss of −25% for medial regions and Murahashi et al. [
      • Murahashi Y.
      • Teramoto A.
      • Jimbo S.
      • Okada Y.
      • Kamiya T.
      • Imamura R.
      • et al.
      Denosumab prevents periprosthetic bone mineral density loss in the tibial metaphysis in total knee arthroplasty.
      ] reported a maximum bone formation of 7.82% (with a standard deviation of 24.35%) for lateral regions. Like this study, all studies reported larger bone loss in medial regions than in lateral regions. The consistency of the results obtained for the stemless model with clinical data provides confidence in the methodology followed for the evaluation of bone remodeling after TKA revision. Nonetheless, the findings of this study should be considered along with its limitations. Only the geometry of one left leg was evaluated due to the high modeling and simulation computational costs. Although the results are expected to be representative of tibia in general, anatomical variabilities in geometry and bone density may impact bone remodeling—several clinical studies show differences in bone remodeling between patients [
      • Abu-Rajab R.B.
      • Watson W.S.
      • Walker B.
      • Roberts J.
      • Gallacher S.J.
      • Meek R.M.D.
      Peri-prosthetic bone mineral density after total knee arthroplasty.
      ]. Compared to previous computational studies, this study considered more detailed loading conditions by including joint reaction force, muscle, and tibia-fibula loads. Nevertheless, these loads were computed for a single gait cycle, and no other lower limb activities were considered. One of the most contributing factors for the limitation in the lower limb activities considered was the high computational cost of the simulations. Another limitation of this study was the assumption of a perfectly osseointegrated condition between the porous-coated surface of the metaphyseal sleeves and bone. Even though several studies report successful radiographic osseointegration of metaphyseal sleeves [
      • Zanirato A.
      • Cavagnaro L.
      • Basso M.
      • Divano S.
      • Felli L.
      • Formica M.
      Metaphyseal sleeves in total knee arthroplasty revision: complications, clinical and radiological results. A systematic review of the literature.
      ], Ihekweazu et al. [
      • Ihekweazu U.N.
      • Weitzler L.
      • Wright T.M.
      • Padgett D.E.
      Distribution of Bone Ongrowth in Metaphyseal Sleeves for Revision Total Knee Arthroplasty: A Retrieval Analysis.
      ] found while analyzing 14 retrieved metaphyseal sleeves that, on average, only 14.7% of the porous surface of metaphyseal sleeves demonstrated osseointegration. Finally, as in other computational studies of bone remodeling [
      • Comenda M.
      • Quental C.
      • Folgado J.
      • Sarmento M.
      • Monteiro J.
      Bone adaptation impact of stemless shoulder implants: a computational analysis.
      ,
      • Sharma G.B.
      • Debski R.E.
      • McMahon P.J.
      • Robertson D.D.
      Adaptive glenoid bone remodeling simulation.
      ], no direct validation of the results was possible due to the lack of data. To provide confidence in the results, the applied bone remodeling model was demonstrated to be able to reproduce the actual bone density distribution of the tibia under analysis and to show qualitative predictions of bone remodeling consistent with clinical data available in the literature for stemless implants.

      5. Conclusion

      The 3D finite element analyses performed in this study provide insight into the impact of metaphyseal sleeves on the bone remodeling of the tibia after revision of a total knee arthroplasty. Overall, the impact of metaphyseal sleeves on bone remodeling was limited. The computational remodeling data presented here, along with clinical data available in the literature, suggests that the benefits of metaphyseal sleeves outweigh their disadvantages regarding bone remodeling.

      Funding

      This work was supported by the Portuguese Foundation for Science and Technology (FCT), through IDMEC, under LAETA, project UIDB/50022/2020.

      Declaration of Competing Interest

      The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

      Appendix A. Supplementary material

      The following are the Supplementary data to this article:

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