Disadvantages of Interfragmentary Shear on Fracture Healing—Mechanical Insights through Numerical Simulation Malte Steiner,1 Lutz Claes,1 Anita Ignatius,1 Ulrich Simon,2 Tim Wehner1 1 Institute of Orthopaedic Research and Biomechanics, Center of Musculoskeletal Research Ulm, University of Ulm, Ulm, Germany, 2Scientific Computing Centre Ulm, University of Ulm, Ulm, Germany
Received 21 June 2013; accepted 24 February 2014 Published online 20 March 2014 in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/jor.22617
ABSTRACT: The outcome of secondary fracture healing processes is strongly influenced by interfragmentary motion. Shear movement is assumed to be more disadvantageous than axial movement, however, experimental results are contradictory. Numerical fracture healing models allow simulation of the fracture healing process with variation of single input parameters and under comparable, normalized mechanical conditions. Thus, a comparison of the influence of different loading directions on the healing process is possible. In this study we simulated fracture healing under several axial compressive, and translational and torsional shear movement scenarios, and compared their respective healing times. Therefore, we used a calibrated numerical model for fracture healing in sheep. Numerous variations of movement amplitudes and musculoskeletal loads were simulated for the three loading directions. Our results show that isolated axial compression was more beneficial for the fracture healing success than both isolated shearing conditions for load and displacement magnitudes which were identical as well as physiological different, and even for strain-based normalized comparable conditions. Additionally, torsional shear movements had less impeding effects than translational shear movements. Therefore, our findings suggest that osteosynthesis implants can be optimized, in particular, to limit translational interfragmentary shear under musculoskeletal loading. ß 2014 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 32:865–872, 2014. Keywords: callus healing; mechanobiology; finite element analysis; shear strain; osteosynthesis
Interfragmentary movement (IFM) is the most important mechanical parameter influencing the fracture healing process and depends on fixation stability and musculoskeletal loading.1 Moderate IFM leads to successful bone healing with the development of a fracture callus,2–3 whereas high IFM delays fracture healing or can even result in non-unions.4–5 In addition to the IFM magnitude, there is evidence from experimental studies that the direction of IFM also plays an important role.6–16 Thus, Augat et al.7 compared the effect of translational shear loading to axial compressive loading in sheep and confirmed other findings,9 stating that translational shear loading delays healing processes. In contrast, Bishop et al.8 suggested that torsional shear movements could stimulate healing. However, comparing healing outcomes under different loading directions requires comparable interfragmentary boundary conditions. Whereas Augat et al. performed a direct comparison by applying identical magnitudes of displacement in the two different loading directions, Bishop et al. normalized the boundary conditions to identical acting interfragmentary strain magnitudes. With the use of numerical models, distinct effects of different loading modes on fracture healing can be simulated.17–19 Recently, we developed a numerical fracture healing algorithm,20–22 which allows us to investigate the influence of single input parameters on the change in IFM and tissue distribution over the healing time. This enables a direct comparison beConflict of interest: None. Grant sponsor: Center of Musculoskeletal Research Ulm, University of Ulm, Germany. Correspondence to: Malte Steiner (T: þ49-731-500-55351; F: þ49731-500-55302; E-mail: [email protected]) # 2014 Orthopaedic Research Society. Published by Wiley Periodicals, Inc.
tween different mechanical conditions. Thus, according to experimental data, we identified more cartilage formation under axial compression than under shear loading conditions.22 The present study compares healing outcomes of different loading directions (i.e., axial compression, and translational and torsional shear) under normalized mechanical conditions using our calibrated sheep fracture healing algorithm. The aims were to identify adverse conditions and to explain them based on the predicted tissue development over time. From a mechanical point of view, translational shear and axial compressive loading lead to regions of compressive hydrostatic pressure (negative dilatational strain) which stimulate cartilage development, and therefore promote endochondral ossification.2,23–25 In contrast, torsional shear loading leads only to distortional strains without compressive hydrostatic pressure generation, which suppresses cartilage development. Thus, we hypothesize that differences in healing outcomes are because of differences in cartilage formation resulting from mechanical tissue strain conditions.
METHODS Numerical Fracture Healing Model We used a numerical fracture healing simulation algorithm that was described in detail elsewhere.20–21 Briefly, the algorithm combines finite element with fuzzy logic methods to simulate healing processes over time in an iterative loop. A three-dimensional idealized geometry of an ovine diaphyseal osteotomy and its healing region was created and meshed in ANSYS (ANSYS, Inc., Canonsburg, PA) using tetrahedral elements. To represent the use of intramedullary nailing for fracture fixation, the intramedullary (endosteal) healing region was not modeled. The respective fixation behavior was separately implemented using a nonlinear force-displacement function. The mechanical behavior of the bone-fixator JOURNAL OF ORTHOPAEDIC RESEARCH JULY 2014
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system and loading and boundary conditions were defined (Fig. 1a) to represent the initial state for seven input variables: two mechanical stimuli (distortional and dilatational strain derived from the strain tensor), three state variables of the element itself (local blood perfusion, and cartilage and bone concentrations), and two state variables of the adjacent elements (perfusion and bone concentration). Tissue composition (a mixture of three tissue types: woven bone, fibrocartilage, and connective tissue), material properties (assumed as linear-elastic isotropic), and blood supply were assigned to each of the finite elements. For the resulting Young’s modulus Ej of each element j, a rule of mixtures was used according to Steiner et al.22: 4:5 Ej ¼ Econn þ c3:1 cart ðEcart Econn Þ þ cbone ðEbone Econn Þ;
ð1Þ
where Econn, Ecart, and Ebone are the Young’s moduli for connective tissue, cartilage, and bone, respectively (cf. Table 1); ccart and cbone are the respective tissue fractions for cartilage and bone within one element. Iteratively, the local mechanical stimuli (dilatational and distortional strain components) are calculated, which together with the current tissue composition and blood supply are used as input to a fuzzy logic controller (Fuzzy Logic Toolbox in MATLAB (v7.11, R2010b), The MathWorks, Inc., Natick, MA). A set of 20 linguistic fuzzy logic rules controls how tissue composition and vascularization for each finite element within the healing region changes depending on
local mechanical and biological stimuli. The rules are partly based on the mechanoregulatory model proposed by Claes and Heigele23 and represent intramembraneous ossification, chondrogenesis, endochondral ossification, revascularization, and tissue destruction. Outcomes of the model are the courses of IFM and tissue distribution over the healing time. In a previous study,22 the model input parameters were calibrated to properly predict fracture healing processes under various loading conditions (particularly axial compression, and torsional and translational shear loading) in sheep. Characteristic Maps of Healing Time For the different loading conditions of axial compressive, and translational and torsional shear loading, characteristic maps of healing times were created: For varying maximal initial (post-operative) IFM (0.2 mm < IFMmax < 2.5 mm for axial compressive and translational shear load cases, and 2˚ < IFMmax < 20˚ for torsional load cases) and maximal interfragmentary loads (0.1 kN < Lmax < 3 kN for axial compression and translational shear, and between 0.5 Nm < Lmax < 10 Nm for torsional load cases), the respective healing time th (i.e. the time during which axial callus stiffness was >80% of the maximum axial callus stiffness) was calculated for a fracture gap size of 3 mm. A 3D-surface was fitted through these data points using a surface-fitting tool implemented in MATLAB (v7.11, R2010b, The MathWorks, Inc.). Healing times >24 weeks were defined as non-unions.
Figure 1. (a) Loading and boundary conditions for the different axial (left), translational (center), and torsional shear (right) loading situations. (b) Characteristic maps of healing time for the different loading conditions, depending on load magnitude and initial maximal interfragmentary movements (IFMmax). Cases where the given IFMmax was not reachable by the given load magnitude are marked white in the characteristic maps (N/A). Healing times >24 weeks are defined as non-unions. JOURNAL OF ORTHOPAEDIC RESEARCH JULY 2014
SHEAR STRAIN AND FRACTURE HEALING
Table 1. Material Properties of the Tissues Involved
Cortical bone Woven bone Fibrocartilage Connective tissue
Young’s Modulus, Etiss in MPa
Poisson’s Ratio, ntiss
15,750 538 28 1.4
0.325 0.33 0.3 0.33
Direct Comparison of Axial Compression to Translational Shear For direct comparison between the influences of axial compressive and translational shear loading on healing of a fracture gap size of 3 mm, equal magnitudes of loads and initial IFMmax were investigated, according to Augat et al.7 Therefore, axial and transversal forces were set to 500 N, and an initial IFMmax of 1.5 mm (corresponding to 50% axial interfragmentary strain, IFS) was simulated. Because shear forces are physiologically much lower than axial forces,26,27 a sixfold difference27 between 250 N shear load and 1,500 N axial load on the same initial IFMmax of 1.5 mm was additionally simulated. Normalized Comparison of Axial Compression to Translational and Torsional Shear To compare between different mechanical loading directions, a normalization of the IFMmax and loading magnitudes Lmax was performed (listed in Table 2). This normalization was based on the acting IFS, which should be constant for all different loading directions, and therefore defines the respective comparable load and displacement levels. The detailed derivation of the different correlations is described in Supplement S-1. Poisson’s ratio n was assumed to be 0.3, the dimensions of the diaphyseal bone were Rin ¼ 6 mm and Rout ¼ 8 mm. Thus, a direct comparison of matched loading situations between the different mechanical loading directions was performed by calculating the difference in healing time th.
RESULTS Characteristic Maps of Healing Time The dependence of the healing time on the combination of maximal load and initial IFMmax for all three different loading directions is displayed in Figure 1b. It is clear that fractures subjected to isolated axial compressive loading heal within an acceptable time frame of 1 kN) in combination with a large initial IFMmax (>1.5 mm, corresponding to approximately 50% IFS with a gap
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size of 3 mm) lead to non-unions. Under isolated translational shear loading, non-unions are expected for all loads >800 N. In contrast, small loads (200 N) will result in healing in 12˚) and high loads (>3 Nm), whereas small initial IFMmax will lead to healing in
Received 21 June 2013; accepted 24 February 2014 Published online 20 March 2014 in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/jor.22617
ABSTRACT: The outcome of secondary fracture healing processes is strongly influenced by interfragmentary motion. Shear movement is assumed to be more disadvantageous than axial movement, however, experimental results are contradictory. Numerical fracture healing models allow simulation of the fracture healing process with variation of single input parameters and under comparable, normalized mechanical conditions. Thus, a comparison of the influence of different loading directions on the healing process is possible. In this study we simulated fracture healing under several axial compressive, and translational and torsional shear movement scenarios, and compared their respective healing times. Therefore, we used a calibrated numerical model for fracture healing in sheep. Numerous variations of movement amplitudes and musculoskeletal loads were simulated for the three loading directions. Our results show that isolated axial compression was more beneficial for the fracture healing success than both isolated shearing conditions for load and displacement magnitudes which were identical as well as physiological different, and even for strain-based normalized comparable conditions. Additionally, torsional shear movements had less impeding effects than translational shear movements. Therefore, our findings suggest that osteosynthesis implants can be optimized, in particular, to limit translational interfragmentary shear under musculoskeletal loading. ß 2014 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 32:865–872, 2014. Keywords: callus healing; mechanobiology; finite element analysis; shear strain; osteosynthesis
Interfragmentary movement (IFM) is the most important mechanical parameter influencing the fracture healing process and depends on fixation stability and musculoskeletal loading.1 Moderate IFM leads to successful bone healing with the development of a fracture callus,2–3 whereas high IFM delays fracture healing or can even result in non-unions.4–5 In addition to the IFM magnitude, there is evidence from experimental studies that the direction of IFM also plays an important role.6–16 Thus, Augat et al.7 compared the effect of translational shear loading to axial compressive loading in sheep and confirmed other findings,9 stating that translational shear loading delays healing processes. In contrast, Bishop et al.8 suggested that torsional shear movements could stimulate healing. However, comparing healing outcomes under different loading directions requires comparable interfragmentary boundary conditions. Whereas Augat et al. performed a direct comparison by applying identical magnitudes of displacement in the two different loading directions, Bishop et al. normalized the boundary conditions to identical acting interfragmentary strain magnitudes. With the use of numerical models, distinct effects of different loading modes on fracture healing can be simulated.17–19 Recently, we developed a numerical fracture healing algorithm,20–22 which allows us to investigate the influence of single input parameters on the change in IFM and tissue distribution over the healing time. This enables a direct comparison beConflict of interest: None. Grant sponsor: Center of Musculoskeletal Research Ulm, University of Ulm, Germany. Correspondence to: Malte Steiner (T: þ49-731-500-55351; F: þ49731-500-55302; E-mail: [email protected]) # 2014 Orthopaedic Research Society. Published by Wiley Periodicals, Inc.
tween different mechanical conditions. Thus, according to experimental data, we identified more cartilage formation under axial compression than under shear loading conditions.22 The present study compares healing outcomes of different loading directions (i.e., axial compression, and translational and torsional shear) under normalized mechanical conditions using our calibrated sheep fracture healing algorithm. The aims were to identify adverse conditions and to explain them based on the predicted tissue development over time. From a mechanical point of view, translational shear and axial compressive loading lead to regions of compressive hydrostatic pressure (negative dilatational strain) which stimulate cartilage development, and therefore promote endochondral ossification.2,23–25 In contrast, torsional shear loading leads only to distortional strains without compressive hydrostatic pressure generation, which suppresses cartilage development. Thus, we hypothesize that differences in healing outcomes are because of differences in cartilage formation resulting from mechanical tissue strain conditions.
METHODS Numerical Fracture Healing Model We used a numerical fracture healing simulation algorithm that was described in detail elsewhere.20–21 Briefly, the algorithm combines finite element with fuzzy logic methods to simulate healing processes over time in an iterative loop. A three-dimensional idealized geometry of an ovine diaphyseal osteotomy and its healing region was created and meshed in ANSYS (ANSYS, Inc., Canonsburg, PA) using tetrahedral elements. To represent the use of intramedullary nailing for fracture fixation, the intramedullary (endosteal) healing region was not modeled. The respective fixation behavior was separately implemented using a nonlinear force-displacement function. The mechanical behavior of the bone-fixator JOURNAL OF ORTHOPAEDIC RESEARCH JULY 2014
865
866
STEINER ET AL.
system and loading and boundary conditions were defined (Fig. 1a) to represent the initial state for seven input variables: two mechanical stimuli (distortional and dilatational strain derived from the strain tensor), three state variables of the element itself (local blood perfusion, and cartilage and bone concentrations), and two state variables of the adjacent elements (perfusion and bone concentration). Tissue composition (a mixture of three tissue types: woven bone, fibrocartilage, and connective tissue), material properties (assumed as linear-elastic isotropic), and blood supply were assigned to each of the finite elements. For the resulting Young’s modulus Ej of each element j, a rule of mixtures was used according to Steiner et al.22: 4:5 Ej ¼ Econn þ c3:1 cart ðEcart Econn Þ þ cbone ðEbone Econn Þ;
ð1Þ
where Econn, Ecart, and Ebone are the Young’s moduli for connective tissue, cartilage, and bone, respectively (cf. Table 1); ccart and cbone are the respective tissue fractions for cartilage and bone within one element. Iteratively, the local mechanical stimuli (dilatational and distortional strain components) are calculated, which together with the current tissue composition and blood supply are used as input to a fuzzy logic controller (Fuzzy Logic Toolbox in MATLAB (v7.11, R2010b), The MathWorks, Inc., Natick, MA). A set of 20 linguistic fuzzy logic rules controls how tissue composition and vascularization for each finite element within the healing region changes depending on
local mechanical and biological stimuli. The rules are partly based on the mechanoregulatory model proposed by Claes and Heigele23 and represent intramembraneous ossification, chondrogenesis, endochondral ossification, revascularization, and tissue destruction. Outcomes of the model are the courses of IFM and tissue distribution over the healing time. In a previous study,22 the model input parameters were calibrated to properly predict fracture healing processes under various loading conditions (particularly axial compression, and torsional and translational shear loading) in sheep. Characteristic Maps of Healing Time For the different loading conditions of axial compressive, and translational and torsional shear loading, characteristic maps of healing times were created: For varying maximal initial (post-operative) IFM (0.2 mm < IFMmax < 2.5 mm for axial compressive and translational shear load cases, and 2˚ < IFMmax < 20˚ for torsional load cases) and maximal interfragmentary loads (0.1 kN < Lmax < 3 kN for axial compression and translational shear, and between 0.5 Nm < Lmax < 10 Nm for torsional load cases), the respective healing time th (i.e. the time during which axial callus stiffness was >80% of the maximum axial callus stiffness) was calculated for a fracture gap size of 3 mm. A 3D-surface was fitted through these data points using a surface-fitting tool implemented in MATLAB (v7.11, R2010b, The MathWorks, Inc.). Healing times >24 weeks were defined as non-unions.
Figure 1. (a) Loading and boundary conditions for the different axial (left), translational (center), and torsional shear (right) loading situations. (b) Characteristic maps of healing time for the different loading conditions, depending on load magnitude and initial maximal interfragmentary movements (IFMmax). Cases where the given IFMmax was not reachable by the given load magnitude are marked white in the characteristic maps (N/A). Healing times >24 weeks are defined as non-unions. JOURNAL OF ORTHOPAEDIC RESEARCH JULY 2014
SHEAR STRAIN AND FRACTURE HEALING
Table 1. Material Properties of the Tissues Involved
Cortical bone Woven bone Fibrocartilage Connective tissue
Young’s Modulus, Etiss in MPa
Poisson’s Ratio, ntiss
15,750 538 28 1.4
0.325 0.33 0.3 0.33
Direct Comparison of Axial Compression to Translational Shear For direct comparison between the influences of axial compressive and translational shear loading on healing of a fracture gap size of 3 mm, equal magnitudes of loads and initial IFMmax were investigated, according to Augat et al.7 Therefore, axial and transversal forces were set to 500 N, and an initial IFMmax of 1.5 mm (corresponding to 50% axial interfragmentary strain, IFS) was simulated. Because shear forces are physiologically much lower than axial forces,26,27 a sixfold difference27 between 250 N shear load and 1,500 N axial load on the same initial IFMmax of 1.5 mm was additionally simulated. Normalized Comparison of Axial Compression to Translational and Torsional Shear To compare between different mechanical loading directions, a normalization of the IFMmax and loading magnitudes Lmax was performed (listed in Table 2). This normalization was based on the acting IFS, which should be constant for all different loading directions, and therefore defines the respective comparable load and displacement levels. The detailed derivation of the different correlations is described in Supplement S-1. Poisson’s ratio n was assumed to be 0.3, the dimensions of the diaphyseal bone were Rin ¼ 6 mm and Rout ¼ 8 mm. Thus, a direct comparison of matched loading situations between the different mechanical loading directions was performed by calculating the difference in healing time th.
RESULTS Characteristic Maps of Healing Time The dependence of the healing time on the combination of maximal load and initial IFMmax for all three different loading directions is displayed in Figure 1b. It is clear that fractures subjected to isolated axial compressive loading heal within an acceptable time frame of 1 kN) in combination with a large initial IFMmax (>1.5 mm, corresponding to approximately 50% IFS with a gap
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size of 3 mm) lead to non-unions. Under isolated translational shear loading, non-unions are expected for all loads >800 N. In contrast, small loads (200 N) will result in healing in 12˚) and high loads (>3 Nm), whereas small initial IFMmax will lead to healing in
