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Identification of locations susceptible to osteoarthritis in patients with anterior cruciate ligament reconstruction: Combining knee joint computational modelling with follow-up T and T2 imaging

Open AccessPublished:August 09, 2019DOI:https://doi.org/10.1016/j.clinbiomech.2019.08.004

      Highlights

      • Patient-specific finite element models can predict location susceptible to osteoarthritis.
      • Assessment done for patient with anterior cruciate ligament reconstruction
      • Assessment done using collagen-specific and proteoglycan-specific parameters
      • Finite element model predictions matched magnetic resonance imaging follow-up information

      Abstract

      Background

      Finite element modelling can be used to evaluate altered loading conditions and failure locations in knee joint tissues. One limitation of this modelling approach has been experimental comparison. The aims of this proof-of-concept study were: 1) identify areas susceptible to osteoarthritis progression in anterior cruciate ligament reconstructed patients using finite element modelling; 2) compare the identified areas against changes in T2 and T values between 1-year and 3-year follow-up timepoints.

      Methods

      Two patient-specific finite element models of knee joints with anterior cruciate ligament reconstruction were created. The knee geometry was based on clinical magnetic resonance imaging and joint loading was obtained via motion capture. We evaluated biomechanical parameters linked with cartilage degeneration and compared the identified risk areas against T2 and T maps.

      Findings

      The risk areas identified by the finite element models matched the follow-up magnetic resonance imaging findings. For Patient 1, excessive values of maximum principal stresses and shear strains were observed in the posterior side of the lateral tibial and femoral cartilage. For Patient 2, high values of maximum principal stresses and shear strains of cartilage were observed in the posterior side of the medial joint compartment. For both patients, increased T2 and T values between the follow-up times were observed in the same areas.

      Interpretation

      Finite element models with patient-specific geometries and motions and relatively simple material models of tissues were able to identify areas susceptible to post-traumatic knee osteoarthritis. We suggest that the methodology presented here may be applied in large cohort studies.

      Keywords

      1. Introduction

      The exact mechanisms behind the onset and development of osteoarthritis (OA) are not fully understood. The incidence of OA is generally higher in patients after anterior cruciate ligament (ACL) rupture, especially with concomitant meniscal or chondral lesions (
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      Early knee osteoarthritis is evident one year following anterior cruciate ligament reconstruction: a magnetic resonance imaging evaluation.
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      Changes in knee osteoarthritis, symptoms, and function after anterior cruciate ligament reconstruction.
      ). Additionally, a long-term follow-up study showed little difference in OA susceptibility between conservative (exercise) or surgical treatment (ACL reconstruction, ACLR) of ruptures (
      • Lohmander L.S.
      • Englund P.M.
      • Dahl L.L.
      • Roos E.M.
      The long-term consequence of anterior cruciate ligament and meniscus injuries.
      ). Postoperatively, knee OA can be present even in short-term follow-ups of ACLR (
      • Culvenor A.G.
      • Collins N.J.
      • Guermazi A.
      • Cook J.L.
      • Vicenzino B.
      • Khan K.M.
      • Beck N.
      • van Leeuwen J.
      • Crossley K.M.
      Early knee osteoarthritis is evident one year following anterior cruciate ligament reconstruction: a magnetic resonance imaging evaluation.
      ;
      • Eckstein F.
      • Wirth W.
      • Lohmander L.S.
      • Hudelmaier M.I.
      • Frobell R.B.
      Five-year followup of knee joint cartilage thickness changes after acute rupture of the anterior cruciate ligament.
      ;
      • Williams A.
      • Winalski C.S.
      • Chu C.R.
      Early articular cartilage MRI T2 changes after anterior cruciate ligament reconstruction correlate with later changes in T2 and cartilage thickness.
      ). One of the mechanisms leading to OA for ACLR patients could be altered joint biomechanics and excessive stresses and strains experienced by articular cartilage (
      • Gardinier E.S.
      • Manal K.
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      Altered loading in the injured knee after ACL rupture.
      ;
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      • Pizzolato C.
      • Vertullo C.J.
      • Barrett R.S.
      • Lloyd D.G.
      Muscle contributions to medial tibiofemoral compartment contact loading following ACL reconstruction using semitendinosus and gracilis tendon grafts.
      ;
      • Wellsandt E.
      • Gardinier E.S.
      • Manal K.
      • Axe M.J.
      • Buchanan T.S.
      • Snyder-Mackler L.
      Decreased knee joint loading associated with early knee osteoarthritis after anterior cruciate ligament injury.
      ).
      Traditional methods for OA diagnosis, such as Kellgren-Lawrence or Modified Fairbank systems, are unable to offer sufficient information on cartilage integrity or composition. Semi-quantitative evaluation methods, such as Whole-Organ Resonance Magnetic Score (WORMS) or Magnetic resonance imaging Osteoarthritis Knee Score (MOAKS), reveal global longitudinal structural changes in the knee joint (
      • Culvenor A.G.
      • Collins N.J.
      • Guermazi A.
      • Cook J.L.
      • Vicenzino B.
      • Khan K.M.
      • Beck N.
      • van Leeuwen J.
      • Crossley K.M.
      Early knee osteoarthritis is evident one year following anterior cruciate ligament reconstruction: a magnetic resonance imaging evaluation.
      ;
      • Wang A.
      • Pedoia V.
      • Su F.
      • Abramson E.
      • Kretzschmar M.
      • Nardo L.
      • Link T.M.
      • McCulloch C.E.
      • Jin C.
      • Ma C.B.
      • Li X.
      MR T1ρ and T2 of meniscus after acute anterior cruciate ligament injuries.
      ). However, both traditional methods and semi-quantitative methods are susceptible to misclassification and intra- and inter-observer variability (
      • Ding C.
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      • Cicuttini F.
      • Burgess J.
      • Zhai G.
      • Quinn S.
      • Jones G.
      Association between leptin, body composition, sex and knee cartilage morphology in older adults: the Tasmanian older adult cohort (TASOAC) study.
      ;
      • Karvonen R.L.
      • Negendank W.G.
      • Fraser S.M.
      • Mayes M.D.
      • An T.
      • Fernandez-Madrid F.
      Articular cartilage defects of the knee: correlation between magnetic resonance imaging and gross pathology.
      ;
      • Wang Y.
      • Wluka A.E.
      • Jones G.
      • Ding C.
      • Cicuttini F.M.
      Use magnetic resonance imaging to assess articular cartilage.
      ). Measurement of T2 and T (T1 in rotating frame) relaxation times offer a more quantitative method to assess local changes in the knee joint (
      • Li X.
      • Wyatt C.
      • Rivoire J.
      • Han E.
      • Chen W.
      • Schooler J.
      • Liang F.
      • Shet K.
      • Souza R.
      • Majumdar S.
      Simultaneous acquisition of T 1ρ and T 2 quantification in knee cartilage: repeatability and diurnal variation.
      ;
      • Li X.
      • Majumdar S.
      Quantitative MRI of articular cartilage and its clinical applications.
      ;
      • Mamisch T.C.
      • Trattnig S.
      • Quirbach S.
      • Marlovits S.
      • White L.M.
      • Welsch G.H.
      Quantitative T2 mapping of knee cartilage: differentiation of healthy control cartilage and cartilage repair tissue in the knee with unloading—initial results.
      ;
      • Nissi M.J.
      • Salo E.-N.
      • Tiitu V.
      • Liimatainen T.
      • Michaeli S.
      • Mangia S.
      • Ellermann J.
      • Nieminen M.T.
      Multi-parametric MRI characterization of enzymatically degraded articular cartilage.
      ;
      • Rautiainen J.
      • Nissi M.J.
      • Salo E.-N.
      • Tiitu V.
      • Finnilä M.A.J.
      • Aho O.-M.
      • Saarakkala S.
      • Lehenkari P.
      • Ellermann J.
      • Nieminen M.T.
      Multiparametric MRI assessment of human articular cartilage degeneration: correlation with quantitative histology and mechanical properties.
      ). In articular cartilage, T2 relaxation time is mainly indicative of the collagen network integrity and arrangement (
      • Hänninen N.
      • Rautiainen J.
      • Rieppo L.
      • Saarakkala S.
      • Nissi M.J.
      Orientation anisotropy of quantitative MRI relaxation parameters in ordered tissue.
      ;
      • Nissi M.J.
      • Töyräs J.
      • Laasanen M.S.
      • Rieppo J.
      • Saarakkala S.
      • Lappalainen R.
      • Jurvelin J.S.
      • Nieminen M.T.
      Proteoglycan and collagen sensitive MRI evaluation of normal and degenerated articular cartilage.
      ;
      • Xia Y.
      • Moody J.B.
      • Burton-Wurster N.
      • Lust G.
      Quantitative in situ correlation between microscopic MRI and polarized light microscopy studies of articular cartilage.
      ), while T relaxation time is primarily sensitive to proteoglycans (
      • Duvvuri U.
      • Kudchodkar S.
      • Reddy R.
      • Leigh J.S.
      T1ρ relaxation can assess longitudinal proteoglycan loss from articular cartilage in vitro.
      ;
      • Wheaton A.J.
      • Casey F.L.
      • Gougoutas A.J.
      • Dodge G.R.
      • Borthakur A.
      • Lonner J.H.
      • Schumacher H.R.
      • Reddy R.
      Correlation of T1rho with fixed charge density in cartilage.
      ), but also carries sensitivity to collagen content depending on the magnetic field strength (
      • Blumenkrantz G.
      • Majumdar S.
      Quantitative magnetic resonance imaging of articular cartilage in osteoarthritis.
      ;
      • Hänninen N.
      • Rautiainen J.
      • Rieppo L.
      • Saarakkala S.
      • Nissi M.J.
      Orientation anisotropy of quantitative MRI relaxation parameters in ordered tissue.
      ;
      • Nieminen M.T.
      • Nissi M.J.
      • Hanni M.
      • Xia Y.
      Physical properties of cartilage by relaxation anisotropy.
      ).
      Imaging cannot assess altered biomechanics and excessive joint and tissue loading. Experimental and computational studies have linked collagen matrix degeneration primarily with high tensile stresses of collagen fibrils (
      • Danso E.K.
      • Honkanen J.T.J.
      • Saarakkala S.
      • Korhonen R.K.
      Comparison of nonlinear mechanical properties of bovine articular cartilage and meniscus.
      ;
      • Henao-Murillo L.
      • Ito K.
      • van Donkelaar C.C.
      Collagen damage location in articular cartilage differs if damage is caused by excessive loading magnitude or rate.
      ;
      • Hosseini S.M.
      • Veldink M.B.
      • Ito K.
      • van Donkelaar C.C.
      Is collagen fiber damage the cause of early softening in articular cartilage?.
      ;
      • Kempson G.E.
      Relationship between the tensile properties of articular cartilage from the human knee and age.
      ) and proteoglycan (PG) loss primarily with high deviatoric or shear strains of cartilage nonfibrillar matrix (
      • Bonnevie E.D.
      • Delco M.L.
      • Jasty N.
      • Bartell L.
      • Fortier L.A.
      • Cohen I.
      • Bonassar L.J.
      Chondrocyte death and mitochondrial dysfunction are mediated by cartilage friction and shear strain.
      ;
      • Ewers B.J.
      • Dvoracek-Driksna D.
      • Orth M.W.
      • Haut R.C.
      The extent of matrix damage and chondrocyte death in mechanically traumatized articular cartilage explants depends on rate of loading.
      ;
      • Kelly P.A.
      • O'Connor J.J.
      Transmission of rapidly applied loads through articular cartilage. Part 2: cracked cartilage.
      ;
      • Wilson W.
      • van Burken C.
      • van Donkelaar C.
      • Buma P.
      • van Rietbergen B.
      • Huiskes R.
      Causes of mechanically induced collagen damage in articular cartilage.
      ). This has enabled the use of finite element (FE) modelling in assessing the potential biomechanical risks for the onset and progression of OA due to collagen degeneration and/or PG loss (
      • Gardiner B.S.
      • Woodhouse F.G.
      • Besier T.F.
      • Grodzinsky A.J.
      • Lloyd D.G.
      • Zhang L.
      • Smith D.W.
      Predicting knee osteoarthritis.
      ;
      • LaValley M.P.
      • Lo G.H.
      • Price L.L.
      • Driban J.B.
      • Eaton C.B.
      • McAlindon T.E.
      Development of a clinical prediction algorithm for knee osteoarthritis structural progression in a cohort study: value of adding measurement of subchondral bone density.
      ;
      • Mononen M.E.
      • Tanska P.
      • Isaksson H.
      • Korhonen R.K.
      New algorithm for simulation of proteoglycan loss and collagen degeneration in the knee joint: data from the osteoarthritis initiative.
      ;
      • Mootanah R.
      • Imhauser C.W.
      • Reisse F.
      • Carpanen D.
      • Walker R.W.
      • Koff M.F.
      • Lenhoff M.W.
      • Rozbruch S.R.
      • Fragomen A.T.
      • Dewan Z.
      • Kirane Y.M.
      • Cheah K.
      • Dowell J.K.
      • Hillstrom H.J.
      Development and validation of a computational model of the knee joint for the evaluation of surgical treatments for osteoarthritis.
      ). However, for better trustworthiness of the models, they should be compared against follow-up information, such as T2 and T relaxation time maps.
      In a clinical setting, the computational model has to be easy to generate and time for the converged solution has to be short. Some of the above-mentioned models applied complex materials, such as fibril-reinforced poro(visco)elastic, to describe articular cartilage, meniscus and ligaments (
      • Dabiri Y.
      • Li L.
      Focal cartilage defect compromises fluid-pressure dependent load support in the knee joint.
      ;
      • Gu K.B.
      • Li L.P.
      A human knee joint model considering fluid pressure and fiber orientation in cartilages and menisci.
      ;
      • Mononen M.E.
      • Tanska P.
      • Isaksson H.
      • Korhonen R.K.
      New algorithm for simulation of proteoglycan loss and collagen degeneration in the knee joint: data from the osteoarthritis initiative.
      ;
      • Mootanah R.
      • Imhauser C.W.
      • Reisse F.
      • Carpanen D.
      • Walker R.W.
      • Koff M.F.
      • Lenhoff M.W.
      • Rozbruch S.R.
      • Fragomen A.T.
      • Dewan Z.
      • Kirane Y.M.
      • Cheah K.
      • Dowell J.K.
      • Hillstrom H.J.
      Development and validation of a computational model of the knee joint for the evaluation of surgical treatments for osteoarthritis.
      ). This is simultaneously time consuming (in terms of implementation) and computationally demanding. Furthermore, for models that include all major knee joint structures with muscle forces, generation and simulation times become even longer (
      • Bolcos P.O.
      • Mononen M.E.
      • Mohammadi A.
      • Ebrahimi M.
      • Tanaka M.S.
      • Samaan M.A.
      • Souza R.B.
      • Li X.
      • Suomalainen J.-S.
      • Jurvelin J.S.
      • Töyräs J.
      • Korhonen R.K.
      Comparison between kinetic and kinetic-kinematic driven knee joint finite element models.
      ;
      • Orozco G.A.
      • Tanska P.
      • Mononen M.E.
      • Halonen K.S.
      • Korhonen R.K.
      The effect of constitutive representations and structural constituents of ligaments on knee joint mechanics.
      ). Recent studies have shown that simpler FE models, in terms of geometry and motion (
      • Bolcos P.O.
      • Mononen M.E.
      • Mohammadi A.
      • Ebrahimi M.
      • Tanaka M.S.
      • Samaan M.A.
      • Souza R.B.
      • Li X.
      • Suomalainen J.-S.
      • Jurvelin J.S.
      • Töyräs J.
      • Korhonen R.K.
      Comparison between kinetic and kinetic-kinematic driven knee joint finite element models.
      ), cartilage material properties (
      • Klets O.
      • Mononen M.E.
      • Tanska P.
      • Nieminen M.T.
      • Korhonen R.K.
      • Saarakkala S.
      Comparison of different material models of articular cartilage in 3D computational modeling of the knee: data from the osteoarthritis initiative (OAI).
      ) and ligament formulation (
      • Orozco G.A.
      • Tanska P.
      • Mononen M.E.
      • Halonen K.S.
      • Korhonen R.K.
      The effect of constitutive representations and structural constituents of ligaments on knee joint mechanics.
      ), produce similar results with more complex models. This enables a reduction in FE model generation and computation times. This kind of FE models for joint mechanics have not been generated before for ACLR patients with patient-specific motion. Further, to our knowledge, patient-specific OA predictions from the FE models have not been compared earlier against experimentally evaluated local changes in the knee joint cartilage, as determined by changes in T2 and T relaxation times between follow-up timepoints.
      The objectives of this proof of concept study were two-fold: (1) Using a relatively fast FE modelling approach, with a proven ability to capture mechanical responses of cartilage, to evaluate knee cartilage mechanics in patients with ACLR at 1-year follow-up, and identify areas susceptible to OA progression, due to collagen damage and/or PG loss; (2) Compare the identified areas for collagen degeneration and PG depletion against local changes in T2 and T relaxation times between the 1-year and 3-year follow-up timepoints. Our hypothesis was that the onset and development of OA in ACLR patients is patient-specific and the areas susceptible to OA at 1-year timepoint can be identified by using FE modelling and matched with local changes in T2 and T relaxation times of cartilage.

      2. Methods

      The workflow of the study is shown in Fig. 1. This study includes two patient-specific FE models of two subjects with ACLR. Information on both the knee joint geometry and motion was incorporated from manually segmented high-resolution 3D MR images (Fig. 1a) and motion capture gait data (Fig. 1b), respectively. The included soft-tissues were femoral and tibial cartilages and menisci, with collateral (MCL & LCL) and cruciate (ACL & PCL) ligaments (Fig. 1c). The FE model results (Fig. 1d) were then compared against follow-up information: T2 and T maps (Fig. 1e).
      Fig. 1
      Fig. 1Workflow of the study. a) Knee joint MR image segmentation; b) Knee joint rotations and ground reaction forces from motion capture; c) FE model overview, with geometry from a) and motion from b); d) Maximum principal stress distribution on the tibial cartilage. Areas susceptible to OA are indicated in black; e) T2 and T maps used for verifying the progression of OA.

      2.1 Data acquisition

      The magnetic resonance (MR) image acquisition and motion capture were performed at the University of California, San Francisco (UCSF). Both subjects gave informed consent and data acquisition was approved by and carried out in accordance with the rules and regulations of the Institutional Review Board under the Human Research Protection Program at UCSF. For each patient, two MR sequences were acquired at 1-year and 3-year follow-up timepoints after the ACLR surgery. Additionally, at each follow-up timepoint the subject gait data was measured using a previously established protocol (
      • Samaan M.A.
      • Facchetti L.
      • Pedoia V.
      • Tanaka M.S.
      • Link T.M.
      • Souza R.B.
      • Ma C.B.
      • Li X.
      Cyclops lesions are associated with altered gait patterns and medial knee joint cartilage degeneration at 1 year after ACL-reconstruction.
      ). The 1-year timepoint was used to predict the location susceptible to OA using FE modelling. The 3-year timepoint was used to verify the progression of OA predicted from the 1-year timepoint. Details on the MRI acquisition and motion capture are given in Supplementary Materials.

      2.2 FE model construction

      MRI and motion capture data were transferred to the University of Eastern Finland (UEF), where computational models were generated. There is a data transfer agreement between UCSF and UEF. The methodology used to generate the FE models was identical to a previous study (
      • Bolcos P.O.
      • Mononen M.E.
      • Mohammadi A.
      • Ebrahimi M.
      • Tanaka M.S.
      • Samaan M.A.
      • Souza R.B.
      • Li X.
      • Suomalainen J.-S.
      • Jurvelin J.S.
      • Töyräs J.
      • Korhonen R.K.
      Comparison between kinetic and kinetic-kinematic driven knee joint finite element models.
      ), and is summarized in Supplementary materials. In that study, it was shown that simpler knee models can produce similar cartilage responses with more complex models. The FE model with motion implemented using kinetics and kinematics (forces and rotations), and without patella and quadriceps forces, produced reaction forces and contact pressures within physiological limits (
      • Gilbert S.
      • Chen T.
      • Hutchinson I.D.
      • Choi D.
      • Voigt C.
      • Warren R.F.
      • Maher S.A.
      Dynamic contact mechanics on the tibial plateau of the human knee during activities of daily living.
      ;
      • Konrath J.M.
      • Saxby D.J.
      • Killen B.A.
      • Pizzolato C.
      • Vertullo C.J.
      • Barrett R.S.
      • Lloyd D.G.
      Muscle contributions to medial tibiofemoral compartment contact loading following ACL reconstruction using semitendinosus and gracilis tendon grafts.
      ;
      • Kutzner I.
      • Heinlein B.
      • Graichen F.
      • Bender A.
      • Rohlmann A.
      • Halder A.
      • Beier A.
      • Bergmann G.
      Loading of the knee joint during activities of daily living measured in vivo in five subjects.
      ;
      • Pizzolato C.
      • Reggiani M.
      • Saxby D.J.
      • Ceseracciu E.
      • Modenese L.
      • Lloyd D.G.
      Biofeedback for gait retraining based on real-time estimation of tibiofemoral joint contact forces.
      ). Details of the material properties for each soft tissue are shown in Table 1. Simpler models are desired when the purpose is towards clinical implementation. In this study, this relatively simple approach with kinetic-kinematic motion implementation was used.
      Table 1Material parameters of cartilage, meniscus and ligaments used in the FE models.
      Transversely isotropic (poro)elasticEp (MPa)Et (MPa)νp (−)νtp (−)Gt (MPa)k (10−15 m4/Ns)e0(−)
      Cartilage (
      • Klets O.
      • Mononen M.E.
      • Tanska P.
      • Nieminen M.T.
      • Korhonen R.K.
      • Saarakkala S.
      Comparison of different material models of articular cartilage in 3D computational modeling of the knee: data from the osteoarthritis initiative (OAI).
      )
      240.460.420.061214
      Meniscus (
      • Danso E.K.
      • Honkanen J.T.J.
      • Saarakkala S.
      • Korhonen R.K.
      Comparison of nonlinear mechanical properties of bovine articular cartilage and meniscus.
      ;
      • Klets O.
      • Mononen M.E.
      • Tanska P.
      • Nieminen M.T.
      • Korhonen R.K.
      • Saarakkala S.
      Comparison of different material models of articular cartilage in 3D computational modeling of the knee: data from the osteoarthritis initiative (OAI).
      ;
      • Vaziri A.
      • Nayeb-Hashemi H.
      • Singh A.
      • Tafti B.A.
      Influence of meniscectomy and meniscus replacement on the stress distribution in human knee joint.
      ;
      • Wilson W.
      • van Donkelaar C.C.
      • van Rietbergen B.
      • Ito K.
      • Huiskes R.
      Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study.
      )
      20159.60.300.0150
      Bi-linear springsStiffness (N/mm)Pre-strain (%)
      ACL (
      • Gantoi F.M.
      • Brown M.A.
      • Shabana A.A.
      Finite element modeling of the contact geometry and deformation in biomechanics applications 1.
      ;
      • Haut Donahue T.L.
      • Howell S.M.
      • Hull M.L.
      • Gregersen C.
      A biomechanical evaluation of anterior and posterior tibialis tendons as suitable single-loop anterior cruciate ligament grafts.
      )
      3805
      PCL (
      • Gantoi F.M.
      • Brown M.A.
      • Shabana A.A.
      Finite element modeling of the contact geometry and deformation in biomechanics applications 1.
      ;
      • Momersteeg T.J.A.
      • Blankevoort L.
      • Huiskes R.
      • Kooloos J.G.M.
      • Kauer J.M.G.
      • Hendriks J.C.M.
      The effect of variable relative insertion orientation of human knee bone-ligament-bone complexes on the tensile stiffness.
      )
      2005
      MCL(
      • Gantoi F.M.
      • Brown M.A.
      • Shabana A.A.
      Finite element modeling of the contact geometry and deformation in biomechanics applications 1.
      ;
      • Momersteeg T.J.A.
      • Blankevoort L.
      • Huiskes R.
      • Kooloos J.G.M.
      • Kauer J.M.G.
      • Hendriks J.C.M.
      The effect of variable relative insertion orientation of human knee bone-ligament-bone complexes on the tensile stiffness.
      )
      1004
      LCL (
      • Gantoi F.M.
      • Brown M.A.
      • Shabana A.A.
      Finite element modeling of the contact geometry and deformation in biomechanics applications 1.
      ;
      • Momersteeg T.J.A.
      • Blankevoort L.
      • Huiskes R.
      • Kooloos J.G.M.
      • Kauer J.M.G.
      • Hendriks J.C.M.
      The effect of variable relative insertion orientation of human knee bone-ligament-bone complexes on the tensile stiffness.
      )
      1004
      Parameters: Ep – in-plane Young's modulus, Et – out-of-plane Young's modulus, νp – in-plane Poisson's ratio, νtp – out-of-plane Poisson's ratio, Gt – out-of-plane shear modulus, k– permeability, e0 – initial void ratio.

      2.3 Analysis

      2.3.1 T2 and T maps

      Tibial and femoral cartilage were manually segmented from the combined multi-slice sequence at both 1-year at 3-year follow-up timepoints. The relaxation times were calculated using a two-parametric mono-exponential fit with Aedes (
      • Niskanen J.-P.
      Aedes - a graphical tool for analyzing medical images [WWW document].
      ) and in-house written plugins for Matlab.

      2.3.2 FE analysis

      Based on the experimental findings (
      • Danso E.K.
      • Honkanen J.T.J.
      • Saarakkala S.
      • Korhonen R.K.
      Comparison of nonlinear mechanical properties of bovine articular cartilage and meniscus.
      ;
      • Kempson G.E.
      Relationship between the tensile properties of articular cartilage from the human knee and age.
      ;
      • Mononen M.E.
      • Tanska P.
      • Isaksson H.
      • Korhonen R.K.
      A novel method to simulate the progression of collagen degeneration of cartilage in the knee: data from the osteoarthritis initiative.
      ) and previous computer simulations (
      • Mononen M.E.
      • Tanska P.
      • Isaksson H.
      • Korhonen R.K.
      A novel method to simulate the progression of collagen degeneration of cartilage in the knee: data from the osteoarthritis initiative.
      ), maximum principal stresses above 7 MPa were assumed to trigger collagen network degeneration. Generally, experimental findings (
      • D'lima D.D.
      • Hashimoto S.
      • Chen P.C.
      • Colwell C.W.
      • Lotz M.K.
      Human chondrocyte apoptosis in response to mechanical injury.
      ;
      • Ewers B.J.
      • Dvoracek-Driksna D.
      • Orth M.W.
      • Haut R.C.
      The extent of matrix damage and chondrocyte death in mechanically traumatized articular cartilage explants depends on rate of loading.
      ;
      • Kelly P.A.
      • O'Connor J.J.
      Transmission of rapidly applied loads through articular cartilage. Part 2: cracked cartilage.
      ;
      • Loening A.M.
      • James I.E.
      • Levenston M.E.
      • Badger A.M.
      • Frank E.H.
      • Kurz B.
      • Nuttall M.E.
      • Hung H.-H.
      • Blake S.M.
      • Grodzinsky A.J.
      • Lark M.W.
      Injurious mechanical compression of bovine articular cartilage induces chondrocyte apoptosis.
      ;
      • Wilson W.
      • van Burken C.
      • van Donkelaar C.
      • Buma P.
      • van Rietbergen B.
      • Huiskes R.
      Causes of mechanically induced collagen damage in articular cartilage.
      ;
      • Zamli Z.
      • Sharif M.
      Chondrocyte apoptosis: a cause or consequence of osteoarthritis?.
      ) and previous computer simulations (
      • Hosseini S.M.
      • Wilson W.
      • Ito K.
      • van Donkelaar C.C.
      A numerical model to study mechanically induced initiation and progression of damage in articular cartilage.
      ;
      • Mononen M.E.
      • Tanska P.
      • Isaksson H.
      • Korhonen R.K.
      New algorithm for simulation of proteoglycan loss and collagen degeneration in the knee joint: data from the osteoarthritis initiative.
      ) link tissue strains above 30% with condrocyte apoptosis and subsequent PG loss. Here, shear strains above 32% were assumed to lead to PG loss (
      • Bonnevie E.D.
      • Delco M.L.
      • Jasty N.
      • Bartell L.
      • Fortier L.A.
      • Cohen I.
      • Bonassar L.J.
      Chondrocyte death and mitochondrial dysfunction are mediated by cartilage friction and shear strain.
      ;
      • Hashimoto S.
      • Nishiyama T.
      • Hayashi S.
      • Fujishiro T.
      • Takebe K.
      • Kanzaki N.
      • Kuroda R.
      • Kurosaka M.
      Role of p53 in human chondrocyte apoptosis in response to shear strain.
      ;
      • Li Y.
      • Frank E.H.
      • Wang Y.
      • Chubinskaya S.
      • Huang H.-H.
      • Grodzinsky A.J.
      Moderate dynamic compression inhibits pro-catabolic response of cartilage to mechanical injury, tumor necrosis factor-α and interleukin-6, but accentuates degradation above a strain threshold.
      ). Here we evaluated:
      • 1.
        σtensile and γabs as a function of stance. The peak values of maximum principal stress (σtensile) and absolute shear strain (γabs) were calculated on the tibiofemoral contact area (cartilage-cartilage contact area) as a function of stance.
      • 2.
        σtensile and γabs distribution maps. To identify the locations prone to collagen network damage and/or PG loss, the σtensile and γabs distributions were calculated for each compartment (i.e. medial or lateral tibial/femoral cartilage). We evaluated the peak values of maximum principal stresses and absolute shear strains for each element.

      2.4 Comparison of the FE model and MRI

      The FE model results were verified against changes in T2 and T relaxation times. These are among the most established quantitative MRI parameters for articular cartilage and were shown to be highly sensitive to collagen and PG content (
      • Duvvuri U.
      • Kudchodkar S.
      • Reddy R.
      • Leigh J.S.
      T1ρ relaxation can assess longitudinal proteoglycan loss from articular cartilage in vitro.
      ;
      • Hänninen N.
      • Rautiainen J.
      • Rieppo L.
      • Saarakkala S.
      • Nissi M.J.
      Orientation anisotropy of quantitative MRI relaxation parameters in ordered tissue.
      ;
      • Li X.
      • Benjamin Ma C.
      • Link T.M.
      • Castillo D.-D.
      • Blumenkrantz G.
      • Lozano J.
      • Carballido-Gamio J.
      • Ries M.
      • Majumdar S.
      In vivo T1ρ and T2 mapping of articular cartilage in osteoarthritis of the knee using 3T MRI.
      ;
      • Nissi M.J.
      • Töyräs J.
      • Laasanen M.S.
      • Rieppo J.
      • Saarakkala S.
      • Lappalainen R.
      • Jurvelin J.S.
      • Nieminen M.T.
      Proteoglycan and collagen sensitive MRI evaluation of normal and degenerated articular cartilage.
      ;
      • Wang A.
      • Pedoia V.
      • Su F.
      • Abramson E.
      • Kretzschmar M.
      • Nardo L.
      • Link T.M.
      • McCulloch C.E.
      • Jin C.
      • Ma C.B.
      • Li X.
      MR T1ρ and T2 of meniscus after acute anterior cruciate ligament injuries.
      ;
      • Wheaton A.J.
      • Casey F.L.
      • Gougoutas A.J.
      • Dodge G.R.
      • Borthakur A.
      • Lonner J.H.
      • Schumacher H.R.
      • Reddy R.
      Correlation of T1rho with fixed charge density in cartilage.
      ;
      • Xia Y.
      • Moody J.B.
      • Burton-Wurster N.
      • Lust G.
      Quantitative in situ correlation between microscopic MRI and polarized light microscopy studies of articular cartilage.
      ).

      2.4.1 Total volumes

      To compare the identified risk areas with follow-up information the following steps were needed:
      • 1.
        For the σtensile and γabs distribution maps, we defined volumes-of-interest (VOI) for each compartment. The VOI was defined as the total volume in which the respective thresholds were exceeded. If neither σtensile nor γabs exceeded the thresholds, the VOI was defined as “0”.
      • 2.
        For each VOI from step 1, we calculated the total volume of the VOI as a percentage of the total volume of each compartment, reflecting the percentage from the total volume susceptible to damage.
      • 3.
        For the T2 and T maps, from both 1-year and 3-year follow-up timepoints we defined VOIs for each compartment. The VOI was defined as the volume of cartilage with either T2 or T relaxation times above 60 ms. This value is above the literature reported value of 50 ms for healthy cartilage (
        • Bolbos R.I.
        • Ma C.B.
        • Link T.M.
        • Majumdar S.
        • Li X.
        In vivo T1ρ quantitative assessment of knee cartilage after anterior cruciate ligament injury using 3 tesla magnetic resonance imaging.
        ;
        • Li X.
        • Kuo D.
        • Theologis A.
        • Carballido-Gamio J.
        • Stehling C.
        • Link T.M.
        • Ma C.B.
        • Majumdar S.
        Cartilage in anterior cruciate ligament-reconstructed knees: MR imaging T1{rho} and T2--initial experience with 1-year follow-up.
        ;
        • Stahl R.
        • Luke A.
        • Li X.
        • Carballido-Gamio J.
        • Ma C.B.
        • Majumdar S.
        • Link T.M.
        T1rho, T2 and focal knee cartilage abnormalities in physically active and sedentary healthy subjects versus early OA patients—a 3.0-tesla MRI study.
        ;
        • Surowiec R.K.
        • Lucas E.P.
        • Fitzcharles E.K.
        • Petre B.M.
        • Dornan G.J.
        • Giphart J.E.
        • LaPrade R.F.
        • Ho C.P.
        T2 values of articular cartilage in clinically relevant subregions of the asymptomatic knee.
        ;
        • Van Rossom S.
        • Smith C.R.
        • Zevenbergen L.
        • Thelen D.G.
        • Vanwanseele B.
        • Van Assche D.
        • Jonkers I.
        Knee cartilage thickness, T1ρ and T2 relaxation time are related to articular cartilage loading in healthy adults.
        ). Similarly, if no relaxation time exceeded this limit, the VOI was defined as “0”.
      • 4.
        For each VOI from step 3, we calculated the volume of the VOI as a percentage from the total volume of the compartment at both 1-year and 3-year follow-up timepoints.
      • 5.
        From step 4, we subtracted the VOI at 3-year timepoint from the VOI at 1-year timepoint, reflecting the percentage of potentially damaged tissue from the total volume of each compartment.
      Thus, we could evaluate changes in the relaxation times between 1-year and 3-year follow-up times and compare them with the areas susceptible to degeneration as predicted by the FE model. An example of steps 1–4 is shown in Supplementary materials.

      2.4.2 Sagittal slices

      Due to the slice thickness of 4 mm of both T2 and T MR images, we could not ensure the accuracy of the total volume calculated in steps 4 and 5. Therefore, a slice-by-slice comparison between the relaxation times and FE models was required. Since in the sagittal plane the resolution of the MR image was the best, sagittal slices from the σtensile, γabs, T2 and T maps were taken as follows:
      • 1.
        For T2 and T maps, the sagittal slice was located in the center of the previously defined VOI. The location of this slice was approximated by calculating the number of slices to the edge of lateral side and multiplying with the slice thickness (4 mm).
      • 2.
        For the σtensile and γabs distribution maps, the sagittal slice was acquired from the same location as in step 1 (Fig. 2a and b ).
        Fig. 2
        Fig. 2a) and b) Sagittal slice locations for the FE models. Note that slice thicknesses for both the FE models and T2/T maps are indicated on the right.

      3. Results

      3.1 Stance

      The FE model revealed that on the lateral tibial cartilage in Patient 1, σtensile exceeded the 7 MPa threshold for collagen degeneration through the entire stance phase (Fig. 3a ), while γabs values were above the threshold of 32% for PG loss between 20% and 80% of the stance phase (Fig. 3b). On the lateral femoral cartilage, the thresholds were exceeded for both σtensile and γabs after the second peak force (80% of the stance) (Fig. 3c,d). On both medial tibial and femoral cartilages, neither σtensile nor γabs exceeded the degeneration thresholds (Fig. 3a–d).
      Fig. 3
      Fig. 3Maximum values of maximum principal stresses and absolute shear strains as a function of stance for Patient 1 in the tibial (a and b) and femoral cartilage (c and d). Maximum values of maximum principal stresses and absolute shear strains as a function of stance for Patient 2 for the tibial (e and f) and femoral cartilage (g and h). The values are calculated from the cartilage-cartilage contact area in both the tibial and femoral cartilage. Approximated thresholds for collagen degeneration and PG loss are indicated with dashed lines.
      For Patient 2, σtensile exceeded the threshold through the entire stance phase on the medial tibial cartilage (Fig. 3e), while γabs values were above the threshold for degeneration at 0–20% and 50–80% (after midstance) of the stance phase (Fig. 3f). On the lateral tibial cartilage, neither σtensile nor γabs exceeded the degeneration thresholds (Fig. 3e,f). For the femoral cartilage, the thresholds were exceeded for both σtensile and γabs at 30–50% of the stance phase in the lateral and at ~20% in the medial joint compartments (Fig. 3g,h).

      3.2 Distribution

      For Patient 1, σtensile exceeded the threshold of 7 MPa on the posterior side of both the lateral tibial and femoral cartilage (Fig. 4a and b ). The γabs values also exceeded the threshold of 32% with a similar distribution as σtensile (not shown). On the medial tibial and femoral cartilage, neither σtensile nor γabs exceeded the thresholds.
      Fig. 4
      Fig. 4Axial views of maximum principal (tensile) stress distributions on the tibial and femoral cartilage for Patient 1 (a and b, respectively) and Patient 2 (c and d, respectively). Peak values for tensile stresses are also indicated.
      For Patient 2, σtensile exceeded the threshold for collagen damage on the posterior side of the medial tibial and femoral cartilage (Fig. 4c and d). Further, in the lateral joint compartment, the σtensile values exceeded the threshold in the center of the cartilage, but the area with high values was smaller than that in the medial joint compartment. The γabs values were only slightly over the threshold of proteoglycan loss (PG) if at all.

      3.3 Volume change

      The total volume susceptible to OA identified by the FE model matched adequately with the total volume of increased T2 and T relaxation times (Fig. 5). For Patient 1, the FE model revealed that in ~14% of the lateral tibial cartilage and ~7% of the lateral femoral cartilage volume, the σtensile values were above the threshold. The γabs values were above the chosen threshold in ~6% of the lateral tibial cartilage and ~7% of the lateral femoral cartilage volume (Fig. 5a). Similarly, ~16% of the lateral tibial cartilage and ~6% of the lateral femoral cartilage volume experienced increased values for both T2 and T during the follow-up times. In the medial joint compartment, neither σtensile nor γabs exceeded the thresholds. Similarly, in the medial tibial cartilage, neither T2 nor T were changed between the follow-up times, while in the femoral side they were increased in ~3% of the total cartilage volume (Fig. 5a).
      Fig. 5
      Fig. 5Degenerated volumes predicted by the FE model (σtensile and γabs) and measured from the MRI follow-up (T2 and T) as a percentage of the entire cartilage volume. The volumes were calculated for the lateral and femoral tibial and femoral cartilage of Patient 1 (a) and Patient 2 (b).
      For Patient 2, the FE model revealed high σtensile values in ~2% of the lateral compartment and ~3% of the medial compartment cartilage volume. High γabs values were only seen at maximum of ~1% of the lateral femoral cartilage volume (Fig. 5b). Similarly, ~2.5% of the lateral tibial cartilage and ~1.5% of the lateral femoral cartilage volume experienced increased values for both T2 and T during the follow-up times. In the medial tibial cartilage, both T2 and T values increased between the follow-up timepoints in ~7.5% of the total volume, while in the femoral side they increased in ~1.5% of the cartilage volume (Fig. 5b).

      3.4 Sagittal slices

      For Patient 1, the FE model results and T2 and T maps of both the lateral (Fig. 6a ) and medial (Fig. 6b) compartments showed an adequate correspondence. In the areas of the lateral compartment with high σtensile or γabs values (dark gray areas in Fig. 6a), the T2 and T values were also elevated. The relaxation times more than doubled in the same areas where excessive σtensile and/or γabs values were seen. In the medial femoral compartment, only local increases in T2 and T relaxation times between the follow-up timepoints were observed, while the medial tibial cartilage was unaffected. The FE model showed neither high σtensile nor γabs values, above the chosen threshold, for either medial femoral or tibial cartilage.
      Fig. 6
      Fig. 6Sagittal slices for the FE model and corresponding sagittal T2 and T map slices at both 1-year and 3-year follow-up timepoints for the lateral and medial compartments of Patient 1 (a and b). Slice locations are indicated in a and arrows indicate the peak values. Note: All values above the selected degeneration thresholds in the FE models (7 MPa for tensile stress and 32% for shear strain) are shown in dark gray. T2 and T1ρ relaxation times above 100 ms are shown in dark red. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
      For Patient 2, the FE model showed only slightly elevated σtensile and γabs values near the cartilage surface in the lateral joint compartment (Fig. 7a ), while the T2 and T values were close to the literature reported values for healthy cartilage. In the medial joint compartment (Fig. 7b), high σtensile and γabs values were seen on the posterior side of the medial tibial and femoral cartilage. For the T2 and T relaxation times of the medial joint compartment, slightly elevated values during the follow-up were seen throughout the contacting surfaces.
      Fig. 7
      Fig. 7Sagittal slices for the FE model and corresponding sagittal T2 and T map slices at both 1-year and 3-year follow-up timepoints for the lateral and medial compartments of Patient 2 (a and b). Slice locations are indicated in b and arrows indicate the peak values. Note: All values above the selected degeneration threshold (7 MPa for tensile stress and 32% for shear strain for the FE model) are shown in dark gray. T2 and T1ρ relaxation times above 100 ms are shown in dark red. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

      4. Discussion

      In the present proof-of-concept study, two FE models of patients with ACL reconstruction were created. The knee joint geometries were based on manually segmented MRI images and the knee joint motions were based on motion capture. Each model included tibial cartilage, femoral cartilage and menisci with collateral and cruciate ligaments. To reduce model complexity and calculation times, a transversely isotropic poroelastic material was used for cartilage and a transversely isotropic elastic material for menisci. The analysis was divided in two parts. First, we identified potential failure areas for both tibial and femoral cartilage using FE modelling. Then, we compared these areas against quantitative follow-up T2 and T relaxation times. The potential failure areas predicted by the FE model matched adequately with the follow-up MRI information for both patients. Our results suggest that a relatively simple FE model, in terms of geometry, motion and materials, has potential to identify areas susceptible to cartilage degeneration and may be applied in a fast evaluation of subjects with traumatic ligament injuries and reconstructions.

      4.1 Patient 1

      Based on the FE model results, possible collagen damage and degeneration through σtensile was predicted to occur in both the lateral tibial (14% of the cartilage volume) and lateral femoral cartilage (7% of the cartilage volume). In agreement with the simulation results, primarily collagen-sensitive T2 (
      • Nissi M.J.
      • Töyräs J.
      • Laasanen M.S.
      • Rieppo J.
      • Saarakkala S.
      • Lappalainen R.
      • Jurvelin J.S.
      • Nieminen M.T.
      Proteoglycan and collagen sensitive MRI evaluation of normal and degenerated articular cartilage.
      ;
      • Xia Y.
      • Moody J.B.
      • Burton-Wurster N.
      • Lust G.
      Quantitative in situ correlation between microscopic MRI and polarized light microscopy studies of articular cartilage.
      ) more than doubled in both the lateral tibial (16% of cartilage volume) and lateral femoral cartilage (5% of cartilage volume). Moreover, the FE model revealed that the posterior side of the lateral joint compartment was the area most susceptible to collagen damage. This result was supported by the elevated T2 during the follow-up. In the lateral femoral cartilage, high γabs values indicated PG loss in ~7% of the volume. This result was confirmed by the elevated T during the follow-up, also in ~5% of the volume. This parameter has been considered to be mostly sensitive to PGs (
      • Duvvuri U.
      • Kudchodkar S.
      • Reddy R.
      • Leigh J.S.
      T1ρ relaxation can assess longitudinal proteoglycan loss from articular cartilage in vitro.
      ). Despite high values of γabs in the lateral tibial cartilage only in ~6% of the total cartilage volume, indicating PG loss, the PG-sensitive T relaxation time was elevated in ~16% of the lateral tibial cartilage volume.
      In the medial tibial cartilage, neither the FE model nor the experimental follow-up information indicated any degenerative signs by the collagen-specific (σtensile and T2) and PG-specific (γabs and T) parameters. However, in the medial femoral cartilage, despite elevated T2 and T values in local areas (~4% of the total volume) during the follow-up, the FE model did not predict tensile stresses or shear strains above the chosen thresholds. Taking into consideration that no changes were seen in the tibial compartment in any of the parameters, this increase in the femoral side may be caused by factors that could not be considered in the model. See more from limitations below.

      4.2 Patient 2

      Based on the FE model results, possible collagen damage and degeneration through σtensile was predicted to occur in the medial tibial (3% of cartilage volume) and femoral cartilage (3% of cartilage volume). In agreement with the simulation results, the collagen-sensitive T2 was elevated in the same sites during the follow-up, greatest changes seen in the medial tibial cartilage. Moreover, the FE model predicted that the posterior side of the medial joint compartment is susceptible to collagen damage, which was supported by the T2 analysis. In the medial femoral cartilage, both γabs and T indicated PG loss only in ~1% of the cartilage volume. On the other hand, in the medial tibial cartilage, the PG-sensitive T relaxation time suggested alterations in a much larger area than what was predicted by the γabs. In both the lateral tibial and femoral cartilage, both the FE model and the experimental MRI follow-up information indicated only minor degenerative signs at the posterior side of the joint and primarily at the contact area.

      4.3 Limitations

      This study has a few limitations, expanded upon in Supplementary Materials. One limitation is that the mechanical properties of cartilage were not patient-specific. However, the sensitivity study in Supplementary Materials indicated that, despite different material parameters of cartilage, all models identified the same locations susceptible to cartilage degeneration. Identification of locations likely to degenerate may reveal which kind of rehabilitation exercises would be the most beneficial for the patient to minimize stress and strain concentrations in locations at the highest risk for the progression of OA (
      • Pizzolato C.
      • Reggiani M.
      • Saxby D.J.
      • Ceseracciu E.
      • Modenese L.
      • Lloyd D.G.
      Biofeedback for gait retraining based on real-time estimation of tibiofemoral joint contact forces.
      ).
      The thresholds for defining degenerated volumes from MRI (relaxation time > 60 ms) are not unbiased, as the values depend on the specific implementation of the respective measurements (
      • Matzat S.J.
      • McWalter E.J.
      • Kogan F.
      • Chen W.
      • Gold G.E.
      T2 relaxation time quantitation differs between pulse sequences in articular cartilage.
      ). Furthermore, both T2 and T have demonstrated sensitivity to the orientation of the tissue in the magnetic field, complicating spatial analysis (
      • Hänninen N.
      • Rautiainen J.
      • Rieppo L.
      • Saarakkala S.
      • Nissi M.J.
      Orientation anisotropy of quantitative MRI relaxation parameters in ordered tissue.
      ). However, in this longitudinal study, the same measurement protocol, system and analysis was used at both follow-up times, alleviating issues related to potential differences in the results.
      We also acknowledge that the sensitivity of the mechanical and MRI parameters to either collagen degeneration or PG loss is not unambiguous. With only two subjects, it is difficult to correlate the FE model predictions and MRI follow-up information. Studies with higher number of patients are needed. This should allow for a comprehensive statistical analysis and help tune the threshold levels. In conjunction with the limitations presented here and in Supplementary Materials, these factors may account for some of the discrepancies between the FE model results and the follow-up information. However, this is a proof-of-concept study showing that it is possible to predict potential cartilage degeneration areas using patient-specific FE models.

      4.4 Clinical application

      Generation of a subject-specific computational model requires a lot of manual work and time in segmentation of soft tissues, meshing and making models to converge. In future studies, the methodology presented here should be coupled with semi-automatic or fully automatic segmentation techniques (
      • Chandra S.S.
      • Surowiec R.
      • Ho C.
      • Xia Y.
      • Engstrom C.
      • Crozier S.
      • Fripp J.
      Automated analysis of hip joint cartilage combining MR T2 and three-dimensional fast-spin-echo images.
      ;
      • Dodin P.
      • Pelletier J.
      • Martel-Pelletier J.
      • Abram F.
      Automatic human knee cartilage segmentation from 3-D magnetic resonance images.
      ;
      • Folkesson J.
      • Dam E.B.
      • Olsen O.F.
      • Pettersen P.C.
      • Christiansen C.
      Segmenting articular cartilage automatically using a voxel classification approach.
      ;
      • Lee J.-G.
      • Gumus S.
      • Moon C.H.
      • Kwoh C.K.
      • Bae K.T.
      Fully automated segmentation of cartilage from the MR images of knee using a multi-atlas and local structural analysis method.
      ;
      • Liukkonen M.K.
      • Mononen M.E.
      • Tanska P.
      • Saarakkala S.
      • Nieminen M.T.
      • Korhonen R.K.
      Application of a semi-automatic cartilage segmentation method for biomechanical modeling of the knee joint.
      ;
      • Paproki A.
      • Engstrom C.
      • Chandra S.S.
      • Neubert A.
      • Fripp J.
      • Crozier S.
      Automated segmentation and analysis of normal and osteoarthritic knee menisci from magnetic resonance images – data from the osteoarthritis initiative.
      ;
      • Shan L.
      • Zach C.
      • Charles C.
      • Niethammer M.
      Automatic atlas-based three-label cartilage segmentation from MR knee images.
      ;
      • Tamez-Pena J.G.
      • Farber J.
      • Gonzalez P.C.
      • Schreyer E.
      • Schneider E.
      • Totterman S.
      Unsupervised segmentation and quantification of anatomical knee features: data from the osteoarthritis initiative.
      ;
      • Yang Z.
      • Fripp J.
      • Chandra S.S.
      • Neubert A.
      • Xia Y.
      • Strudwick M.
      • Paproki A.
      • Engstrom C.
      • Crozier S.
      Automatic bone segmentation and bone-cartilage interface extraction for the shoulder joint from magnetic resonance images.
      ;
      • Yu H.J.
      • Chang A.
      • Fukuda Y.
      • Terada Y.
      • Nozaki T.
      • Yoshioka H.
      Comparison of semi-automated and manual segmentation of knee cartilage.
      ) and with automated meshing tools (
      • Rodriguez-Vila B.
      • Sánchez-González P.
      • Oropesa I.
      • Gomez E.J.
      • Pierce D.M.
      Automated hexahedral meshing of knee cartilage structures – application to data from the osteoarthritis initiative.
      ). As motion capture systems are not readily available in clinical settings, a simple and fast method should be developed to obtain and implement patient's gait. For instance, differences between patient-specific and population-specific (e.g. normal, early/advanced/medial OA populations) motions could be studied. If the population-specific approach would produce similar results with the patient-specific method, it could be used without motion capture. These aforementioned methods would ease the applications of the FE models in large cohort studies to identify areas susceptible to OA development (
      • Gardiner B.S.
      • Woodhouse F.G.
      • Besier T.F.
      • Grodzinsky A.J.
      • Lloyd D.G.
      • Zhang L.
      • Smith D.W.
      Predicting knee osteoarthritis.
      ;
      • Hosseini S.M.
      • Wilson W.
      • Ito K.
      • van Donkelaar C.C.
      A numerical model to study mechanically induced initiation and progression of damage in articular cartilage.
      ;
      • Kar S.
      • Smith D.W.
      • Gardiner B.S.
      • Li Y.
      • Wang Y.
      • Grodzinsky A.J.
      Modeling IL-1 induced degradation of articular cartilage.
      ;
      • Liukkonen M.K.
      • Mononen M.E.
      • Klets O.
      • Arokoski J.P.
      • Saarakkala S.
      • Korhonen R.K.
      Simulation of subject-specific progression of knee osteoarthritis and comparison to experimental follow-up data: data from the osteoarthritis initiative.
      ). They could also be coupled with iterative computational models to predict collagen degeneration and proteoglycan loss for a patient in time (
      • Gardiner B.S.
      • Woodhouse F.G.
      • Besier T.F.
      • Grodzinsky A.J.
      • Lloyd D.G.
      • Zhang L.
      • Smith D.W.
      Predicting knee osteoarthritis.
      ;
      • LaValley M.P.
      • Lo G.H.
      • Price L.L.
      • Driban J.B.
      • Eaton C.B.
      • McAlindon T.E.
      Development of a clinical prediction algorithm for knee osteoarthritis structural progression in a cohort study: value of adding measurement of subchondral bone density.
      ;
      • Mononen M.E.
      • Tanska P.
      • Isaksson H.
      • Korhonen R.K.
      New algorithm for simulation of proteoglycan loss and collagen degeneration in the knee joint: data from the osteoarthritis initiative.
      ).
      In conclusion, our results suggest that the FE models, as presented here, could be used to identify areas susceptible to OA onset and development. They would be particularly useful in assessing the effect of surgical interventions, such as ACL reconstruction. Moreover, it would be possible to evaluate non-surgical management options for avoiding or delaying OA onset and/or progression, such as the gait retraining method proposed by (
      • Pizzolato C.
      • Reggiani M.
      • Saxby D.J.
      • Ceseracciu E.
      • Modenese L.
      • Lloyd D.G.
      Biofeedback for gait retraining based on real-time estimation of tibiofemoral joint contact forces.
      ). In conjunction with the improvements mentioned above, the presented methodology could provide a pathway towards clinical implementation.

      Declaration of competing interest

      The authors have no potential conflicts of interest to declare.

      Acknowledgements

      This project has received funding from the Doctoral Programme in Science, Technology and Computing (SCITECO) of the University of Eastern Finland , the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 755037 ), Academy of Finland (grants 285909 , 307932 and 286526 ), Sigrid Jusélius Foundation , and National Institutes of Health ( NIH/NIAMS P50 AR060752 ). CSC-IT Center for Science, Finland, is acknowledged for providing computing resources.

      Appendix A. Supplementary data

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