Yves Pauchard Robarts Research Institute, Western University, London, ON N6A 5K8, Canada; Institute of Applied Information Technology, School of Engineering, Zurich University of Applied Sciences, Steinberggasse 13, Postfach, Winterthur CH-8401, Switzerland e-mail: [email protected]
Todor G. Ivanov Robarts Research Institute, Western University, London, ON N6A 5K8, Canada
David D. McErlain Department of Radiology, Faculty of Medicine, University of Calgary, Calgary, AB T2N 2T9, Canada
Jaques S. M ilner Robarts Research Institute, Western University, London, ON N6A 5K8, Canada
J. Robert Giffin Schulich School of Medicine and Dentistry, Western University, London, ON N6A 5C1, Canada; Wolf Orthopaedic Biomechanics Laboratory, Fowler Kennedy Sport Medicine Clinic, Faculty of Health Sciences, Western University, London, ON N6A 3K7, Canada
Trevor B. Birmingham Wolf Orthopaedic Biomechanics Laboratory, Fowler Kennedy Sport Medicine Clinic, Faculty of Health Sciences, Western University, London, ON N6A 3K7, Canada
David W. Holdsworth 1 Schulich School of Medicine and Dentistry, Western University, London, ON N6A 3K7, Canada; Wolf Orthopaedic Biomechanics Laboratory, Fowler Kennedy Sport Medicine Clinic, Faculty of Health Sciences, Western University, London, ON N6A 3K7, Canada; Imaging Research Laboratories Robarts Research Institute, Western University, P.O.Box 5015,100 Perth Drive, London, ON N6A 5K8, Canada e-mail: [email protected]
Assessing the Local Mechanical Environment in Medial Opening Wedge High Tibial Osteotomy Using Finite Element Analysis High-tibiaI osteotomy (HTO) is a surgical technique aimed at shifting load away front one tibiofemoral compartment, in order the reduce pain and progression of osteoarthritis (OA). Various implants have been designed to stabilize the osteotomy and previous stud ies have been focused on determining primary stability (a global measure) that these designs provide. It has been shown that the local mechanical environment, characterized by bone strains and segment micromotion, is important in understanding healing and these data are not currently available. Finite element (FE) modeling was utilized to assess the local mechanical environment provided by three different fixation plate designs: short plate with spacer, long plate with spacer and long plate without spacer. Image-based FE models of the knee were constructed from healthy individuals (N = 5) with normal knee alignment. An HTO gap was virtually added without changing the knee alignment and 1/10 implants were inserted. Subsequently, the local mechanical environ ment . defined by bone compressive strain and wedge micromotion, was assessed. Further more, implant stresses were calculated. Values were computed under vertical compression in zero-degree knee extension with loads set at I and 2 times the subjectspecific body weight (/ BW, 2 BW). All studied HTO implant designs provide an environ ment for successful healing at I BW and 2 BW loading. Implant von Mises stresses (99th percentile) were below 60 MPa in all experiments, below the material yield strength and significantly lower in long spacer plates. Volume fraction of high compressive strain (> 3000 microstrain) was below 5% in all experiments and no significant difference between implants was detected. Maximum vertical micromotion between bone segments was below 200 pm in all experiments and significantly larger in the implant without a tooth. Differences between plate designs generally became apparent only at 2 BW had ing. Results suggest that with compressive loading of 2 BW, long spacer plates experience the lowest implant stresses, and spacer plates (long or short) result in smaller wedge micromotion, potentially beneficial for healing. Values are sensitive to subject bone geometry, highlighting the need for subject-specific modeling. This study demonstrates the benefits of using image-based FE modeling and bone theory to fine-tune HTO implant design. [DOI: 10.1115/1.4028966]
Introduction 'Corresponding author. Manuscript received January 21, 2014; final manuscript received October 21, 2014; published online January 29, 2015. Assoc. Editor: Guy M. Genin.
Journal of Biomechanical Engineering
HTO is a surgical technique aimed at re-aligning the weight bearing axis in the knee joint in order to counter the effects of knee OA. In particular, medial opening wedge HTO, for correct ing varus alignment, has been shown to reduce the external knee
Copyright ©2015 by ASME
MARCH 2015, Vol. 137 / 031005-1
adduction moments during walking (which are highly correlated to the progression of OA), as well as pain and other outcomes [1], Besides re-aligning the knee joint, fast and successful healing to enable timely return to daily activities are primary concerns of HTO surgery. While healing is a complex process, stability of the osteotomy opening using plate and screws to provide an adequate environment for bone healing, is important [2— 4]. Many HTO implants have been designed and traditionally, cadaver knee [5,6] and synthetic bone studies [7-9] have been used to investigate the primary stability of different plate designs. These studies have shown that longer plates with locking screws provide higher stability in both compression [5,7,9] and torsion [9] than shorter plates. Additionally, a spacer (i.e., a tooth sitting within the HTO gap) might add extra stability in static compres sion [5] and dynamic loading [10]. These studies also highlighted that a breach in the lateral cortex (possibly occurring during sur gery) significantly reduces primary stability [8,9]. While these findings are important, the results are limited to overall plate stability in relation to potential fracturing of the tibia bone. In addition to general stability, it has been shown that the local mechanical environment, characterized by micromotion and bone strain, is important to understanding bone healing [11,12], More specifically, Blecha et al. [13] report that for successful ingrowth of bone into a porous implant, micromotion no larger than 100 /im is needed. Additionally, Claes et al. [11] state that micromotion of 200 fim between bony segments is able to stimulate callus forma tion in early stages of healing. However, in later stages, increased amounts of micromotion might interfere with mineralization. In contrast to micromotion, the theory of bone remodeling by Frost [12] uses bone strain to characterize the ability of bone to adapt to mechanical loads. In this theory, strains above 3000 microstrain (0.3%) will result in damage accumulation with the potential to develop microcracks and failure. Hence, successful healing is expected to take place if local bone strains do not exceed this limit [12]. Therefore, there is a need to investigate these local variables to assess healing capacity, which are not available with current experimental methods. FE modeling is a computational technique allowing calculation of local stresses and strains, and recent studies have demonstrated the potential of applying FE to HTO [13,14], Specifically, micro motion between wedge augmentation material and bone with different plate positioning was investigated [13] and stress differ ences in two different plate designs was calculated [14]. With recent advances in computational power it is now possible to obtain FE results from accurate models, which can be created rou tinely from medical images [15], making it possible to assess the healing environment of different HTO implant designs in a range of subject- and patient-specific bone geometries and possibly complex loading conditions. The aim of this study was to compare local mechanical environ ment in the tibia after a simulated HTO surgery and interpret the mechanical variables in the context of bone healing, comparing three plate designs with FE models constructed from medical images. Images were from subjects with early knee OA and nor mal knee alignment with a simulated HTO gap to represent an ideal surgical outcome. The model was focused on the tibia and the resulting implant stresses. Tibia bone strains and micromotion between wedge segments are reported. The knee model is loaded in compression at zero-degree extension to simulate early, pro tected weight-bearing provided by a locked brace during recovery after surgery. Natural force transfer between the femur and tibia was achieved through inclusion of cartilage and menisci. The knee alignment was not changed in the simulation. The model purely investigates the differences in local mechanical environ ment between plate designs in multiple subjects. Methods
Subjects and Imaging. During a previous study, 50 subjects with early radiographic knee OA (Kellgren-Lawrence score < 2) 031005-2 / Vol. 137, MARCH 2015
were scanned with a prototype cone-beam computed tomography (CT) system (Multistar, Siemens Medical Solutions, Erlangen, Germany) and a 4T magnetic resonance imaging (MRI) system (Unity Inova; Varian, Palo Alto, California; Siemens, Erlangen, Germany), prior to arthroscopic surgery [16]. Informed consent was obtained in accordance with the approval from the ethics review board at Western University prior to any imaging experi ments, and all data were anonymized before FE model design and implementation. CT scan parameters were 90 kVp and 40 mAs, reconstructed three-dimensional (3D) data set with 0.55 mm iso tropic voxel spacing. Two MRI sequences, using fat suppression, were acquired in the sagittal plane: 3D Tl-weighted spoiled gradient (SPGR) sequence (512x 256 x 64 matrix, 0.23x0.47 x 1.5 mm voxels), and a 2D proton density-weighted fast spin echo (FSE) sequence (512 x 384 matrix, 0.23 x 0.32 x 3.0 mm voxels). The SPGR and FSE sequences had acquisition times of 13.6 and 12.8 min, respectively. Five subjects’ knee images (N = 5) were selected for use in our study based on image quality and a sufficient field of view to extract all relevant tissues. CT and MRI images were coregistered using 3D visualization and analy sis software ( microview, v .2.1.2, General Electric, London, Canada). Subsequently, surfaces of bones, menisci, cartilage and cruciate ligaments were extracted from images ( microview) and converted to geometrical surfaces (gf.omagic studio v .10, 3D Systems, Cary, NC). In addition to the subjects, HTO hardware was scanned. One short plate with spacer (Arthrex first Generation “Puddu,” stain less steel, 10 mm tooth width), one long plate with spacer (Arthrex third Generation “Contour-lock,” titanium, 10 mm tooth width) and corresponding cortical and trabecular bone screws were scanned using micro-CT (eXplore Locus Ultra, GE Healthcare Biosciences, London, ON). Scan parameters were 120 kVp, 20 mAs, and 0.153 mm isotropic voxel spacing. The plate and screw surfaces were extracted from the images and converted to geometric surfaces. The tooth of the long plate with spacer was removed from the geometric surface in order to model a long plate without spacer. FE Model Creation. Geometric surfaces of knee joint compo nents were imported into FE analysis software (simulia abaqus v.6.8.3, Dassault Systemes, France), assembled into a FE model (see Fig. 1) and meshed with linear tetrahedral elements with a target size of 1mm. This allowed for accurate representation of the specific bone geometries and was found to be sufficient for representing von Mises stress (maximum value changes are smaller than 1%) [15]. Note that elements on the contact surfaces, and in the tibia with embedded HTO implant and screws were allowed to be smaller to guarantee convergence of the contact problem and accurate representation of the implant/screw geome try, respectively. Bone properties were assigned on an element-by-element basis using a nonlinear, BMD-to-elastic modulus (£) conversion, derived directly from the CT scan [15,17] and a Poisson’s ratio of v = 0.3 was assumed. The use of heterogeneous bone properties is important to capture local strain patterns. Soft tissues in the tibio femoral joint were included to obtain realistic, patient-specific load transfer. These tissues were modeled as linear, elastic with isotropic material properties assigned based on reported values: menisci (£ = 59MPa, v = 0.49) [18], cartilage (£=15MPa, v = 0.475) [19] and ligaments ACL, PCL (£ = 50 MPa, v = 0.3, zero initial strain) [20]. Collateral ligaments were not present in the medical images and were not replaced by substitute structures, to avoid additional assumptions and due to restricted boundary conditions (see below). Menisci horns were attached to the bone with linear springs (10 per horn; 200N/mm each) [19] and the an terior horns were connected via a 900N/mm spring, representing the transverse ligament [21]. Joint interfaces were modeled as contact models; cartilage-cartilage contact pairs were defined as frictionless, while the cartilage-menisci pairs were assigned a coefficient of friction of 0.1 [22]. Transactions of the ASME
Fig. 1 Finite-element model geometry of original knee model (a) including boundary condi tions; knee model with simulated HTO with short plate with spacer (b), long plate with spacer (c), and long plate without spacer (d)
The loading configuration selected aimed at simulating early, protected weight-bearing post-HTO surgery. Patients use crutches and wear a hinged brace that is locked in full extension during standing. Brace and crutch-use with only “feather-touch” weight bearing is typically suggested for the first 2 weeks, with progres sively increasing partial-weight-bearing in the brace from 2-to-6 weeks. Following this protocol small loads at full extension are expected. Kutzner et al. [23] measured knee loads with instru mented implants and found loads of l time subject-specific body weight (BW) in double-leg stance, and 2.5 times subject-specific BW in single-leg stance, which would constitute a worst-case loading magnitude during recovery after HTO. In these condi tions, loads are expected at small extension angles. Therefore, a subject-specific compressive load of l and 2 BW (mass = 95.5 kg, 8 1.8 kg, 71.4 kg, 70.5 kg, 70.5 kg; mean = 77.9 kg, standard devia tion = 10.9 kg) in the vertical direction was applied wherein the femur acted upon the tibia, which was fixed at the inferior end. The relative position of femur and tibia was obtained from imag ing of the knee in MRI at full extension using a knee coil guaran teeing sufficiently repeatable positioning between patients. The
load was distributed along the cortical bone of the femur. The femoral bone elements were limited to vertical movements to mimic protected weight-bearing and to compensate the lack of collateral ligaments and supporting tendons present in the models, which prevented nonphysiological stress concentrations or motions (see Fig. 1). Virtual HTO surgery was performed by assigning tibial bone in a wedge region reduced elastic properties (£ = 1 0 _hMPa, v= 10- ), modeling a wedge region that provided essentially no mechanical support. The HTO wedge possessed a medial opening of 10 mm and the tip was located at the lateral tibial side. For each of the subject geometries, the three plate configurations were care ful positioned into a realistic orientation without changing the wedge region (see Fig. 1). Figure 2 shows the 3D surface geome tries of the three plate designs in greater detail. The hardware was embedded into the bone material and no contact interfaces were defined. Mesh density was increased in the tibia in order to repre sent the screw geometry accurately. Stainless steel plate and screws were assigned an elastic modulus of £=193GPa, and v = 0.25 while titanium hardware was set to £=110GPa
von Mises Stress [MPa] 25
(a)
50
(b)
75
(c)
Fig. 2 Stress distribution (von Mises) in short plate with spacer (a), long plate with spacer (b), and long plate without spacer (c) arising from a compressive load of two subjectspecific BW (mass = 81.8 kg). Anatomical orientations are indicated with A (anterior) and P (posterior).
Journal of Biomechanical Engineering
MARCH 2015, Vol. 137 / 031005-3
and v = 0.34. The subject-specific compression simulation as described above was repeated at I and 2 BW. totaling 40 simula tions (/V= 5 subjects; four simulations per subject: no HTO, short spacer plate, long spacer plate and long plate without spacer; two loading cases). Numerical convergence was obtained when the residual error was smaller than 10~h (abaqus default value). To ensure convergence of this contact simulation, an increase in mesh density on contact surfaces and the use of small computation increments were configured in the software. Analysis of FE Results. In order to assess the local mechanical environment within the tibia and interpret these values in the con text of bone remodeling and healing, three variables of interest were selected and compared between plate designs. First, success ful healing is promoted by a stabile wedge region which is pro vided be a stable implant. Stability of the HTO hardware was assessed by comparing the von Mises stress calculated to the yield strength of the material. Yield strength of surgical stainless steel (AISI 316L) is expected in the range EyiC|d = 170-750 MPa and for titanium (Ti grade 4) Eyic|d = 692 MPa [24], Often, the maxi mum stress value from FE modeling is reported. Since the maxi mum value represents a single element in the mesh and the number of elements is expected to be different between the implants due to differences in geometrical details, reporting the 99th percentile of von Mises stress to summarize the expected stress in the top 1% of the elements was chosen. Second, the per centage of volume above 3000 microstrain of compressive strain was determined as an indicator of the number of bone elements experiencing potentially slow bone healing, following mechanostat theory [12], A higher percentage of high strain bone elements indicates a less favorable plate design. This information is in itself useful for improving plate design. However, in practice, a mea sure of overall healing success might be preferable. While the theory does not state a critical volume fraction above which over all healing in the bone is unsuccessful, following Pistoia et al. [25], we selected a volume fraction of 5% as a threshold above which we would expect unsuccessful healing. Third, the maxi mum amount of micromotion in the vertical direction between the bone segments in the wedge region was determined to gauge the potential for ingrowth occurring (given that micromotion is below 100 pm [13]), and that, micromotion is below 200 pm for promot ing callus formation while ensuring mineralization [II]. Statistics. Results were analyzed with two-way repeated meas ures two-way repeated measures analysis of variance (ANOVA) to estimate effects of plate type, loading magnitude and their interac tion. Specific differences between implants at each of the loading weights were determined using Tukey posthoc tests. Analysis was performed using commercial software (prism 6.0, Graphpad Soft ware, Inc., La Jolla, CA) and a significance level of p < 0.05.
Implant stress (99th percentile) *
1 BW ■K 2 BW
Fig. 3 Mean (box) and standard deviation (whiskers) of 99th percentile von Mises stress arising in the three implant designs at subject-specific compressive loads of one body weight (1 BW) and two body weight (2 BW). ‘ Significant differences between plate designs (p
Todor G. Ivanov Robarts Research Institute, Western University, London, ON N6A 5K8, Canada
David D. McErlain Department of Radiology, Faculty of Medicine, University of Calgary, Calgary, AB T2N 2T9, Canada
Jaques S. M ilner Robarts Research Institute, Western University, London, ON N6A 5K8, Canada
J. Robert Giffin Schulich School of Medicine and Dentistry, Western University, London, ON N6A 5C1, Canada; Wolf Orthopaedic Biomechanics Laboratory, Fowler Kennedy Sport Medicine Clinic, Faculty of Health Sciences, Western University, London, ON N6A 3K7, Canada
Trevor B. Birmingham Wolf Orthopaedic Biomechanics Laboratory, Fowler Kennedy Sport Medicine Clinic, Faculty of Health Sciences, Western University, London, ON N6A 3K7, Canada
David W. Holdsworth 1 Schulich School of Medicine and Dentistry, Western University, London, ON N6A 3K7, Canada; Wolf Orthopaedic Biomechanics Laboratory, Fowler Kennedy Sport Medicine Clinic, Faculty of Health Sciences, Western University, London, ON N6A 3K7, Canada; Imaging Research Laboratories Robarts Research Institute, Western University, P.O.Box 5015,100 Perth Drive, London, ON N6A 5K8, Canada e-mail: [email protected]
Assessing the Local Mechanical Environment in Medial Opening Wedge High Tibial Osteotomy Using Finite Element Analysis High-tibiaI osteotomy (HTO) is a surgical technique aimed at shifting load away front one tibiofemoral compartment, in order the reduce pain and progression of osteoarthritis (OA). Various implants have been designed to stabilize the osteotomy and previous stud ies have been focused on determining primary stability (a global measure) that these designs provide. It has been shown that the local mechanical environment, characterized by bone strains and segment micromotion, is important in understanding healing and these data are not currently available. Finite element (FE) modeling was utilized to assess the local mechanical environment provided by three different fixation plate designs: short plate with spacer, long plate with spacer and long plate without spacer. Image-based FE models of the knee were constructed from healthy individuals (N = 5) with normal knee alignment. An HTO gap was virtually added without changing the knee alignment and 1/10 implants were inserted. Subsequently, the local mechanical environ ment . defined by bone compressive strain and wedge micromotion, was assessed. Further more, implant stresses were calculated. Values were computed under vertical compression in zero-degree knee extension with loads set at I and 2 times the subjectspecific body weight (/ BW, 2 BW). All studied HTO implant designs provide an environ ment for successful healing at I BW and 2 BW loading. Implant von Mises stresses (99th percentile) were below 60 MPa in all experiments, below the material yield strength and significantly lower in long spacer plates. Volume fraction of high compressive strain (> 3000 microstrain) was below 5% in all experiments and no significant difference between implants was detected. Maximum vertical micromotion between bone segments was below 200 pm in all experiments and significantly larger in the implant without a tooth. Differences between plate designs generally became apparent only at 2 BW had ing. Results suggest that with compressive loading of 2 BW, long spacer plates experience the lowest implant stresses, and spacer plates (long or short) result in smaller wedge micromotion, potentially beneficial for healing. Values are sensitive to subject bone geometry, highlighting the need for subject-specific modeling. This study demonstrates the benefits of using image-based FE modeling and bone theory to fine-tune HTO implant design. [DOI: 10.1115/1.4028966]
Introduction 'Corresponding author. Manuscript received January 21, 2014; final manuscript received October 21, 2014; published online January 29, 2015. Assoc. Editor: Guy M. Genin.
Journal of Biomechanical Engineering
HTO is a surgical technique aimed at re-aligning the weight bearing axis in the knee joint in order to counter the effects of knee OA. In particular, medial opening wedge HTO, for correct ing varus alignment, has been shown to reduce the external knee
Copyright ©2015 by ASME
MARCH 2015, Vol. 137 / 031005-1
adduction moments during walking (which are highly correlated to the progression of OA), as well as pain and other outcomes [1], Besides re-aligning the knee joint, fast and successful healing to enable timely return to daily activities are primary concerns of HTO surgery. While healing is a complex process, stability of the osteotomy opening using plate and screws to provide an adequate environment for bone healing, is important [2— 4]. Many HTO implants have been designed and traditionally, cadaver knee [5,6] and synthetic bone studies [7-9] have been used to investigate the primary stability of different plate designs. These studies have shown that longer plates with locking screws provide higher stability in both compression [5,7,9] and torsion [9] than shorter plates. Additionally, a spacer (i.e., a tooth sitting within the HTO gap) might add extra stability in static compres sion [5] and dynamic loading [10]. These studies also highlighted that a breach in the lateral cortex (possibly occurring during sur gery) significantly reduces primary stability [8,9]. While these findings are important, the results are limited to overall plate stability in relation to potential fracturing of the tibia bone. In addition to general stability, it has been shown that the local mechanical environment, characterized by micromotion and bone strain, is important to understanding bone healing [11,12], More specifically, Blecha et al. [13] report that for successful ingrowth of bone into a porous implant, micromotion no larger than 100 /im is needed. Additionally, Claes et al. [11] state that micromotion of 200 fim between bony segments is able to stimulate callus forma tion in early stages of healing. However, in later stages, increased amounts of micromotion might interfere with mineralization. In contrast to micromotion, the theory of bone remodeling by Frost [12] uses bone strain to characterize the ability of bone to adapt to mechanical loads. In this theory, strains above 3000 microstrain (0.3%) will result in damage accumulation with the potential to develop microcracks and failure. Hence, successful healing is expected to take place if local bone strains do not exceed this limit [12]. Therefore, there is a need to investigate these local variables to assess healing capacity, which are not available with current experimental methods. FE modeling is a computational technique allowing calculation of local stresses and strains, and recent studies have demonstrated the potential of applying FE to HTO [13,14], Specifically, micro motion between wedge augmentation material and bone with different plate positioning was investigated [13] and stress differ ences in two different plate designs was calculated [14]. With recent advances in computational power it is now possible to obtain FE results from accurate models, which can be created rou tinely from medical images [15], making it possible to assess the healing environment of different HTO implant designs in a range of subject- and patient-specific bone geometries and possibly complex loading conditions. The aim of this study was to compare local mechanical environ ment in the tibia after a simulated HTO surgery and interpret the mechanical variables in the context of bone healing, comparing three plate designs with FE models constructed from medical images. Images were from subjects with early knee OA and nor mal knee alignment with a simulated HTO gap to represent an ideal surgical outcome. The model was focused on the tibia and the resulting implant stresses. Tibia bone strains and micromotion between wedge segments are reported. The knee model is loaded in compression at zero-degree extension to simulate early, pro tected weight-bearing provided by a locked brace during recovery after surgery. Natural force transfer between the femur and tibia was achieved through inclusion of cartilage and menisci. The knee alignment was not changed in the simulation. The model purely investigates the differences in local mechanical environ ment between plate designs in multiple subjects. Methods
Subjects and Imaging. During a previous study, 50 subjects with early radiographic knee OA (Kellgren-Lawrence score < 2) 031005-2 / Vol. 137, MARCH 2015
were scanned with a prototype cone-beam computed tomography (CT) system (Multistar, Siemens Medical Solutions, Erlangen, Germany) and a 4T magnetic resonance imaging (MRI) system (Unity Inova; Varian, Palo Alto, California; Siemens, Erlangen, Germany), prior to arthroscopic surgery [16]. Informed consent was obtained in accordance with the approval from the ethics review board at Western University prior to any imaging experi ments, and all data were anonymized before FE model design and implementation. CT scan parameters were 90 kVp and 40 mAs, reconstructed three-dimensional (3D) data set with 0.55 mm iso tropic voxel spacing. Two MRI sequences, using fat suppression, were acquired in the sagittal plane: 3D Tl-weighted spoiled gradient (SPGR) sequence (512x 256 x 64 matrix, 0.23x0.47 x 1.5 mm voxels), and a 2D proton density-weighted fast spin echo (FSE) sequence (512 x 384 matrix, 0.23 x 0.32 x 3.0 mm voxels). The SPGR and FSE sequences had acquisition times of 13.6 and 12.8 min, respectively. Five subjects’ knee images (N = 5) were selected for use in our study based on image quality and a sufficient field of view to extract all relevant tissues. CT and MRI images were coregistered using 3D visualization and analy sis software ( microview, v .2.1.2, General Electric, London, Canada). Subsequently, surfaces of bones, menisci, cartilage and cruciate ligaments were extracted from images ( microview) and converted to geometrical surfaces (gf.omagic studio v .10, 3D Systems, Cary, NC). In addition to the subjects, HTO hardware was scanned. One short plate with spacer (Arthrex first Generation “Puddu,” stain less steel, 10 mm tooth width), one long plate with spacer (Arthrex third Generation “Contour-lock,” titanium, 10 mm tooth width) and corresponding cortical and trabecular bone screws were scanned using micro-CT (eXplore Locus Ultra, GE Healthcare Biosciences, London, ON). Scan parameters were 120 kVp, 20 mAs, and 0.153 mm isotropic voxel spacing. The plate and screw surfaces were extracted from the images and converted to geometric surfaces. The tooth of the long plate with spacer was removed from the geometric surface in order to model a long plate without spacer. FE Model Creation. Geometric surfaces of knee joint compo nents were imported into FE analysis software (simulia abaqus v.6.8.3, Dassault Systemes, France), assembled into a FE model (see Fig. 1) and meshed with linear tetrahedral elements with a target size of 1mm. This allowed for accurate representation of the specific bone geometries and was found to be sufficient for representing von Mises stress (maximum value changes are smaller than 1%) [15]. Note that elements on the contact surfaces, and in the tibia with embedded HTO implant and screws were allowed to be smaller to guarantee convergence of the contact problem and accurate representation of the implant/screw geome try, respectively. Bone properties were assigned on an element-by-element basis using a nonlinear, BMD-to-elastic modulus (£) conversion, derived directly from the CT scan [15,17] and a Poisson’s ratio of v = 0.3 was assumed. The use of heterogeneous bone properties is important to capture local strain patterns. Soft tissues in the tibio femoral joint were included to obtain realistic, patient-specific load transfer. These tissues were modeled as linear, elastic with isotropic material properties assigned based on reported values: menisci (£ = 59MPa, v = 0.49) [18], cartilage (£=15MPa, v = 0.475) [19] and ligaments ACL, PCL (£ = 50 MPa, v = 0.3, zero initial strain) [20]. Collateral ligaments were not present in the medical images and were not replaced by substitute structures, to avoid additional assumptions and due to restricted boundary conditions (see below). Menisci horns were attached to the bone with linear springs (10 per horn; 200N/mm each) [19] and the an terior horns were connected via a 900N/mm spring, representing the transverse ligament [21]. Joint interfaces were modeled as contact models; cartilage-cartilage contact pairs were defined as frictionless, while the cartilage-menisci pairs were assigned a coefficient of friction of 0.1 [22]. Transactions of the ASME
Fig. 1 Finite-element model geometry of original knee model (a) including boundary condi tions; knee model with simulated HTO with short plate with spacer (b), long plate with spacer (c), and long plate without spacer (d)
The loading configuration selected aimed at simulating early, protected weight-bearing post-HTO surgery. Patients use crutches and wear a hinged brace that is locked in full extension during standing. Brace and crutch-use with only “feather-touch” weight bearing is typically suggested for the first 2 weeks, with progres sively increasing partial-weight-bearing in the brace from 2-to-6 weeks. Following this protocol small loads at full extension are expected. Kutzner et al. [23] measured knee loads with instru mented implants and found loads of l time subject-specific body weight (BW) in double-leg stance, and 2.5 times subject-specific BW in single-leg stance, which would constitute a worst-case loading magnitude during recovery after HTO. In these condi tions, loads are expected at small extension angles. Therefore, a subject-specific compressive load of l and 2 BW (mass = 95.5 kg, 8 1.8 kg, 71.4 kg, 70.5 kg, 70.5 kg; mean = 77.9 kg, standard devia tion = 10.9 kg) in the vertical direction was applied wherein the femur acted upon the tibia, which was fixed at the inferior end. The relative position of femur and tibia was obtained from imag ing of the knee in MRI at full extension using a knee coil guaran teeing sufficiently repeatable positioning between patients. The
load was distributed along the cortical bone of the femur. The femoral bone elements were limited to vertical movements to mimic protected weight-bearing and to compensate the lack of collateral ligaments and supporting tendons present in the models, which prevented nonphysiological stress concentrations or motions (see Fig. 1). Virtual HTO surgery was performed by assigning tibial bone in a wedge region reduced elastic properties (£ = 1 0 _hMPa, v= 10- ), modeling a wedge region that provided essentially no mechanical support. The HTO wedge possessed a medial opening of 10 mm and the tip was located at the lateral tibial side. For each of the subject geometries, the three plate configurations were care ful positioned into a realistic orientation without changing the wedge region (see Fig. 1). Figure 2 shows the 3D surface geome tries of the three plate designs in greater detail. The hardware was embedded into the bone material and no contact interfaces were defined. Mesh density was increased in the tibia in order to repre sent the screw geometry accurately. Stainless steel plate and screws were assigned an elastic modulus of £=193GPa, and v = 0.25 while titanium hardware was set to £=110GPa
von Mises Stress [MPa] 25
(a)
50
(b)
75
(c)
Fig. 2 Stress distribution (von Mises) in short plate with spacer (a), long plate with spacer (b), and long plate without spacer (c) arising from a compressive load of two subjectspecific BW (mass = 81.8 kg). Anatomical orientations are indicated with A (anterior) and P (posterior).
Journal of Biomechanical Engineering
MARCH 2015, Vol. 137 / 031005-3
and v = 0.34. The subject-specific compression simulation as described above was repeated at I and 2 BW. totaling 40 simula tions (/V= 5 subjects; four simulations per subject: no HTO, short spacer plate, long spacer plate and long plate without spacer; two loading cases). Numerical convergence was obtained when the residual error was smaller than 10~h (abaqus default value). To ensure convergence of this contact simulation, an increase in mesh density on contact surfaces and the use of small computation increments were configured in the software. Analysis of FE Results. In order to assess the local mechanical environment within the tibia and interpret these values in the con text of bone remodeling and healing, three variables of interest were selected and compared between plate designs. First, success ful healing is promoted by a stabile wedge region which is pro vided be a stable implant. Stability of the HTO hardware was assessed by comparing the von Mises stress calculated to the yield strength of the material. Yield strength of surgical stainless steel (AISI 316L) is expected in the range EyiC|d = 170-750 MPa and for titanium (Ti grade 4) Eyic|d = 692 MPa [24], Often, the maxi mum stress value from FE modeling is reported. Since the maxi mum value represents a single element in the mesh and the number of elements is expected to be different between the implants due to differences in geometrical details, reporting the 99th percentile of von Mises stress to summarize the expected stress in the top 1% of the elements was chosen. Second, the per centage of volume above 3000 microstrain of compressive strain was determined as an indicator of the number of bone elements experiencing potentially slow bone healing, following mechanostat theory [12], A higher percentage of high strain bone elements indicates a less favorable plate design. This information is in itself useful for improving plate design. However, in practice, a mea sure of overall healing success might be preferable. While the theory does not state a critical volume fraction above which over all healing in the bone is unsuccessful, following Pistoia et al. [25], we selected a volume fraction of 5% as a threshold above which we would expect unsuccessful healing. Third, the maxi mum amount of micromotion in the vertical direction between the bone segments in the wedge region was determined to gauge the potential for ingrowth occurring (given that micromotion is below 100 pm [13]), and that, micromotion is below 200 pm for promot ing callus formation while ensuring mineralization [II]. Statistics. Results were analyzed with two-way repeated meas ures two-way repeated measures analysis of variance (ANOVA) to estimate effects of plate type, loading magnitude and their interac tion. Specific differences between implants at each of the loading weights were determined using Tukey posthoc tests. Analysis was performed using commercial software (prism 6.0, Graphpad Soft ware, Inc., La Jolla, CA) and a significance level of p < 0.05.
Implant stress (99th percentile) *
1 BW ■K 2 BW
Fig. 3 Mean (box) and standard deviation (whiskers) of 99th percentile von Mises stress arising in the three implant designs at subject-specific compressive loads of one body weight (1 BW) and two body weight (2 BW). ‘ Significant differences between plate designs (p
