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Finite element analysis of a pseudoelastic compression-generating intramedullary ankle arthrodesis nail
journal of the mechanical behavior of biomedical materials 62 (2016) 83 –92
Available online at www.sciencedirect.com
www.elsevier.com/locate/jmbbm
Research Paper
Finite element analysis of a pseudoelastic compression-generating intramedullary ankle arthrodesis nail Ryan T. Andersona, Douglas J. Pacacciob, Christopher M. Yakackia, R. Dana Carpentera,n a
Department of Mechanical Engineering, University of Colorado Denver, Denver, CO 80217, United States Advanced Foot and Ankle Surgeons, Inc., Yorkville, IL 60560, United States
b
art i cle i nfo
ab st rac t
Article history:
Tibio-talo-calcaneal (TTC) arthrodesis is an end-stage treatment for patients with severe
Received 12 November 2015
degeneration of the ankle joint. This treatment consists of using an intramedullary nail
Received in revised form
(IM) to fuse the calcaneus, talus, and tibia bones together into one construct. Poor bone
4 April 2016
quality within the joint prior to surgery is common and thus the procedure has shown
Accepted 28 April 2016
complications due to non-union. However, a new FDA-approved IM nail has been released
Available online 4 May 2016
that houses a nickel titanium (NiTi) rod that uses its inherent pseudoelastic material
Keywords:
properties to apply active compression across the fusion site. Finite element analysis was
Ankle
performed to model the mechanical response of the NiTi within the device. A bone model
Arthrodesis
was then developed based on a quantitative computed tomography (QCT) image for
NiTi
anatomical geometry and bone material properties. A total bone and device system was
Compression
modeled to investigate the effect of bone quality change and gather load-sharing proper-
Finite element
ties during gait loading. It was found that during the highest magnitude loading of gait, the
Joint
load taken by the bone was more than 50% higher than the load taken by the nail. When comparing the load distribution during gait, results from this study would suggest that the device helps to prevent stress shielding by allowing a more even distribution of load between bone and nail. In conditions where bone quality may vary patient-to-patient, the model indicates that a 10% decrease in overall bone modulus (i.e. material stiffness) due to reduced bone mineral density would result in higher stresses in the nail (3.4%) and a marginal decrease in stress for the bone (0.5%). The finite element model presented in this study can be used as a quantitative tool to further understand the stress environment of both bone and device for a TTC fusion. Furthermore, the methodology presented gives insight on how to computationally program and use the unique material properties of NiTi in an active compression state useful for bone fracture healing or fusion treatments. & 2016 Elsevier Ltd. All rights reserved.
n Correspondence to: Department of Mechanical Engineering, University of Colorado Denver, Campus Box 112, PO Box 173364, Denver, CO 80217-3364, United States. Tel.: þ1 720 309 3045. E-mail address: [email protected] (R.D. Carpenter).
http://dx.doi.org/10.1016/j.jmbbm.2016.04.037 1751-6161/& 2016 Elsevier Ltd. All rights reserved.
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1.
journal of the mechanical behavior of biomedical materials 62 (2016) 83 –92
Introduction and background
Walking is a primary function of life. Walking should be pain free, but unfortunately for some, walking can be a difficult endeavor. Movement of the ankle joint is a key component of normal gait, yet there are numerous conditions that can cause severe degeneration of the ankle, including idiopathic osteoarthritis, inflammatory arthritis, trauma, or systemic diseases like diabetes mellitus (Joseph, 2009; Nihal et al., 2008; Rogers et al., 2011). These conditions can lead to unbearable pain, loss of function, immobility, and ultimately a decreased quality of life. In cases of highly severe joint degeneration, amputation can become necessary, which entails a mortality rate of up to 86.9% within four years, specifically in diabetic and vascular limb patients (Panagakos et al., 2012; Henry et al., 2013). Alternatives to amputation involve the fusion of affected bones, such as tibio-talar, talocalcaneal, or tibio-talo-calcaneal (TTC) arthrodesis. With an estimated 26,000 ankle fusion and ankle/subtalar combination procedures performed annually, these salvage procedures aim to stabilize the joint and provide patients with pain free walking (iData-Research-Inc., 2009). For the purpose of this study, TTC arthrodesis (Fig. 1A) will be the primary focus. In TTC arthrodesis the tibia, talus, and calcaneus can be fused together using a variety of approaches, including the use of an intramedullary (IM) nail. Using this approach, an IM nail is inserted through the calcaneus and talus and into the medullary cavity of the tibia and secured using locking screws. With a relatively stiff nail, typically one composed of titanium, the goal is to rigidly fix the bones in place to ensure stability of the joint. Recent designs of IM nails aim to provide compression to the ankle via an external frame (Yakacki et al., 2010) or an internal compression generating screw. A more detailed review of the progression of IM nails has previously been published (Yakacki et al., 2011). The success rates for TTC fusion have ranged from 76% to 96%; however, complication rates can be as high as 25% (Boer et al., 2007; Gavaskar and Chowdary, 2009; Haaker et al., 2010; Huang et al., 2007; Kim et al., 2009; Klos et al., 2009; Vesely et al., 2008). Complications can arise from a variety of factors: variation in bone quality from patient to patient, especially with patients who have prior degeneration; post-surgery loading conditions; initial level of
compression; and the specific device installed. In most cases, failure arises from hardware loosening with compression and stability of the joint being lost during the healing process (Mückley et al., 2007). One of the most pertinent factors to influence instrumentation loosening is bone resorption. This can decrease the level of compression and stability of the bone–nail system, resulting in movement of the joint and ultimately a failed fusion procedure. It is known that in long-bone fracture fixation, minimizing motion and using plating to ensure bone-on-bone contact promotes primary bone healing directly across the fracture site (Mueller et al., 1979). Thus, to improve upon previous designs, current generation IM nails look to provide a means of sustained compression across the fusion site and prevent excessive movement (Gilbert et al., 1989). Compressive loading on the bones is known to help achieve successful fusion. On the other hand, high levels of sustained compression can lead to bone resorption and osteonecrosis (Carpenter and Carter, 2008). Compression, therefore, has the potential to either help or hinder bone formation and remodeling following TTC arthrodesis, depending on the magnitude of the applied load. The first step towards understanding the optimal compression necessary for ankle fusion is to gather stresses and loadsharing properties of an ankle fusion construct. Load-sharing properties can indicate if a device is stress shielding the bone, leading to a decrease in bone loading stimulus and higher likelihood of resorption. Stresses, however, can indicate localized areas under high load and potential for material failure
equating
to
bone
deformation
and
hardware
loosening. An IM nail (DynaNail, MedShape, Inc., Atlanta, GA) that has recently been FDA approved uses a nickel titanium (NiTi) rod to apply compression across the fusion site, even in the presence of bone resorption (Yakacki et al., 2011) (Fig. 1). Nickel titanium demonstrates a rare material property that is pseudoelastic in nature and exhibits a relatively flat stress plateau over a moderate range of strains. The inherent mechanical properties of NiTi allow for a steady compression load and micro-motion of the bone, as well as any bone resorption up to 6 mm. The compression properties are activated by stretching the material into its martensitic phase
Fig. 1 – Relative position of distal calcaneal locking screw in a DynaNail device (A) immediately post surgery, (B) at 8 weeks, and (C) at 1 year. (D) Bone resorption is illustrated by the superior motion of the locking screws. Radiographic images provided by D. J. Pacaccio.
journal of the mechanical behavior of biomedical materials 62 (2016) 83 –92
and then releasing the material to its pseudoelastic-recovery stress plateau. Stress as a function of strain for a pseudoelastic material such as NiTi is illustrated in Fig. 2. Starting at point A, the material is stretched through an austenite linear elastic region until a stress-induced phase transformation occurs from austenite to martensite along the plateau. Upon release at point B, the martensite phase becomes unstable and transitions back to austenite along the second lower plateau. To maximize the pseudoelastic response and apply constant compression, the material is “programmed” and locked into place at point C. Thus, the stress remains constant in response to any loss in strain throughout a large range (D). Surgically, programming of the DynaNail is achieved by first inserting the nail into the bone and locking the tibial screws (Fig. 2A). The proximal end of the NiTi rod is fixed to the nail jacket and also threaded into the sliding element. Next, the sliding element is pulled to stretch the NiTi rod to approximately 6% strain (Fig. 2B) and then relaxed to program the material to the start of the recovery plateau (Fig. 2C). Calcaneal screws are then inserted into the sliding element to lock the system in place. The sliding element allows the NiTi rod to contract in response to any bone resorption, and the pseudoelastic property of the material will maintain a constant compressive force across the joint (Fig. 2D). While the DynaNail provides a means to actively respond to bone resorption, it is unknown how this device distributes loads across the ankle region and also how the loading environment will change with respect to bone quality and external forces that might result from daily activities during healing. Finite element (FE) analysis provides the ability to determine the 3D stress and strain distribution in mechanical systems. Previous studies have used FE modeling to investigate the mechanical behavior of devices that use NiTi for its unique material properties, most notably the arterial stent (Azaouzi et al., 2012; Kleinstreuer et al., 2008; Kumar and Mathew, 2012). These stents are typically compressed to fit inside a catheter and deployed when inserted into an artery. This can oftentimes be referred to as “superelastic” where the
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material can undergo large deformations and recover its original shape upon unloading. Modeling the behavior of NiTi in a device to apply active compression in a stress-induced programmed state presents unique technical challenges. This is due to the path-dependent material behavior. Simulation of the response of a NiTi compressive device within imagebased anatomical structures has not been previously reported. Work by Vazquez et al. (2004a, 2004b, 2003) has showed that differences in bone quality, variation in screw number, and joint contours affect stability of the tibio-talar joint. However, there does not exist a computational model that investigates the loading environment within a TTC union procedure using an IM nail. The first objective of this study is to develop an FE-based technique to effectively model the behavior of a compression generating IM nail inside a realistic bone environment. The second objective of this study is to use the new simulation framework to investigate the mechanical environment in the ankle after pseudoelastic IM nailing during normal gait loading and the effect of bone quality on stresses in the system components using patient-specific bone anatomy and material properties. In this study, steps used to reach a final image-based human bone and device model will be presented. The pseudoelastic material behavior was first studied to ensure that the stress response could be replicated to the manufacturer's material. A simplified bone and device model was then constructed to ensure proper activation of the device within a bone environment. A final image-based bone model was used for studying load-sharing properties of the joint as well as effects of bone quality on stresses in the TTC-fusion construct.
2.
Methods
2.1.
NiTi material modeling
Mechanical testing was used to measure the NiTi material parameters that were implemented in ABAQUS 6.12 using the superelastic material subroutine based on a proposed model
Fig. 2 – A pseudoelastic material behavior allows the NiTi material to apply compression by programming a constant stress state. After the nail is installed into the patient (A), the NiTi rod is stretched (B) and unloaded to a “programmed” state (C). Any bone resorption up to 6 mm is countered by a steady compression (D).
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journal of the mechanical behavior of biomedical materials 62 (2016) 83 –92
by Auricchio et al., (1997). Uniaxial testing was performed on a sample supplied by the manufacturer of the NiTi rod to gather key transition points for the stress–strain response. A uniaxial tester (MTS Insight 30, MTS, Eden Prairie, MN, USA) equipped with custom threaded grip attachments and a 30 kN load cell was used for testing. A constant deformation rate of 0.1 mm/s was used throughout the test with strain being measured using an MTS LX500 laser extensometer. Temperature during testing was maintained at 36 1C using a thermal chamber (ThermCraft, Winston Salem, NC, USA). The sample was first strained to 5.5% strain in tension and then relaxed back to 4.5% strain; this will be referred to as “programmed.” Following the programmed state, a reloading occurs back to 4.8% strain. This is followed by a similar unload at 3% and reload at 3.3% strain, and ends with an unloading of the sample. This testing procedure essentially programmed the NiTi and then simulated a response to tension loading/unloading. This would represent a patient constraining the foot and trying to elevate their leg, thus inducing tension in the NiTi rod. The loss in strain between 4.5% and 3% would represent a reaction to bone resorption and, in result, a loss in total stretched length of the rod. Values gathered from the experimental results include the elastic modulus values for both austenite and martensite phases as well as stress transition points. A full list of variables used for modeling purposes as well as the corresponding ABAQUS built in superelastic illustration can be found in the online supplement. Following mechanical testing, the material model was implemented in an FE model of the NiTi rod. The rod geometry was extracted from the manufacturer's computeraided draft (CAD) model and input into ScanIPþFEþCAD software suite (Simpleware, Exeter, UK). A built in adaptive meshing algorithm (FEFree) was used to apply 12,796 tetrahedral finite elements to the geometry. Within ABAQUS, the model was assigned the superelastic material properties found in experimental testing. Pin boundary conditions were applied to the nodes on the distal end of the rod to constrain movement in all three directions while a displacement boundary condition (BC) was given to nodes at the proximal end of the rod. A combination of stretch/relax steps was used to mimic the experimental procedure by modifying the displacement BC. Non-linear geometry was accounted for in each step due to the relatively large strain and an energy dissipation fraction of 0.0002 was used for solution stability control. During this analysis, it was assumed that the temperature remained constant. A selection of elements at the center of the rod was probed for stress and strain levels in the axial direction for each solution frame. Stress as a function of strain was plotted for both experimental and computational models simultaneously to allow comparison.
and allowing nail contraction. CAD-based models of the other nail components were combined with the NiTi rod and inserted into the model at the center of the bone sections. Both bone sections were assigned linear isotropic material properties with the normal bone section having an elastic modulus of 17 GPa and a Poisson's ratio of 0.3, while the compliant bone section was given an elastic modulus of 1 GPa and a Poisson's ratio of 0.001 (Carpenter and Carter, 2008). All other nail components were prescribed linear isotropic properties of titanium with an elastic modulus of 110 GPa and a Poisson's ratio of 0.3. The total tetrahedral element count for the model was 493,117. Because of the path-dependent material behavior of NiTi, a series of five steps were implemented to program the rod and simulate the behavior of the IM nail after implantation in the bone block. To achieve programming of the NiTi rod at a site with only two interacting parts, displacements were applied to the NiTi material at the proximal end of the rod. In order to lock the NiTi rod to the nail jacket after programming, it was necessary to add a “locking material” between the two components. The mesh input file from ScanIP was manually modified to add two large locking elements. These elements were assigned the same titanium material properties as other device components. In ABAQUS, superelastic material properties were applied to the NiTi rod. Analysis parameters, including step settings, were identical to the bare NiTi rod model. Between the bone sections and the nail jacket outer surface, normal contact was defined as “hard,” and tangential contact was assumed frictionless. Bone-to-bone contact nodes were defined as tied to simulate a “fused” bone joint. Initially, all bone sections and the locking material were applied a model change condition, essentially omitting the elements from the analysis. The sliding element and calcaneal screws were first prescribed a pin boundary condition. Next, a displacement was applied to the proximal end of the NiTi rod to program the material. Once the material was programmed, the bone and locking material were reactivated into the model strain free. Upon reactivation, the pin condition on the sliding element and the calcaneal screws was deactivated, as was the displacement condition on the proximal end of the NiTi rod. A new boundary condition was then activated to pin the proximal end of the bone block to prevent rigid body movement. To confirm the operation of the device, the compliant bone material allowed a contraction between the two regions of normal bone. Displacement values of nodes within the compliant material were monitored to ensure that contracting movement was occurring. Stress distributions within the system were constructed to give a visual representation of the contraction.
2.2.
2.3.
Programming NiTi in a simplified bone model
A simplified bone and device model was created to implement the programming of the NiTi material within a bone environment. A rectangular block was created with the dimensions of 36.0 40.8 224.7 mm3 with an additional rectangular section of compliant material proximal to the proximal calcaneal screw. The compliant material section was added to allow a hypothetical simulation of loss in bone
Anatomical bone and device modeling
A bone model was created that retained anatomical geometry by using quantitative computed tomography (QCT) imagery of a cadaver specimen. A below-knee cadaver specimen was imaged in a CT system (Gemini TF TOF 64, Philips, Amsterdam, The Netherlands) along with a volumetric bone mineral density (BMD) reference phantom (Mindways Software, Inc., Austin, TX, USA) with an in-plane pixel size of 0.72 mm and a
journal of the mechanical behavior of biomedical materials 62 (2016) 83 –92
slice thickness of 0.90 mm. Clinically relevant positioning of the ankle for the scan was verified on a scout scan before imaging. Using ScanIP, the bone model was segmented into 3 bone regions: tibia, talus, and calcaneus. Geometry of the bone was modified at the distal end of the tibia, proximal and distal sides of the talus, and the proximal side of the calcaneus to mimic bone preparation during surgery. Utilizing the reference phantom, the material properties of each bone voxel were assigned based on the voxel's BMD using empirically-defined relationships between ash density and elastic modulus (Keyak et al., 2005). ScanIPþFEþCAD software was used to position the device within the bone model and the FEFree meshing algorithm applied a volumetric mesh to the combined bone/device model. Manual addition of locking material was employed in this final model as well, leading to a total of 1,892,399 elements in the model. A mesh convergence study was performed by varying element density of the bone model and applying a simple compression test within ABAQUS to confirm relative stiffness results were not varying at the density level used for analysis. The final bone/device FE model was used to test two conditions: first, in a static equilibrium situation, such that only the programmed NiTi rod applied load; and second, a quasi-static loading that simulated one cycle of normal human gait. The same approach used to program the NiTi rod in the bone block model was implemented in the human bone model. Contact properties were defined between the bones and nail jacket as before. Instead of pinning the bone block, the final boundary condition in this model pinned the proximal tibia. Stress distributions were gathered for the distal tibia metaphysis as well as midway through the calcaneus. During the static analysis, the effect of bone quality was studied by varying the total elastic modulus of each element. Bone quality ranged from 30% loss to 20% gain in 10%
87
increments. A selection of bone and nail jacket elements was made at the distal tibia metaphysis level. Average von Mises stress values were gathered for each change in bone quality. Stress as a function of bone quality was plotted for both bone and nail to allow comparison. To simulate gait loading in the quasi-static analysis, a selection of nodes equally spaced about the nail jacket on the inferior side of the calcaneus were applied point loads. The magnitude of each point load was varied to match experimental patient data provided by the Neuromuscular Physiology Lab at The Georgia Institute of Technology. During the analysis, the device was first programmed and allowed to apply compression to the joint. The proximal end of the tibia was pinned and then the gait load was applied. Note that the bone quality in the quasi-static analysis was not modified. Reaction force values were taken at mid length of the nail for the NiTi rod, tibia, and during each loading magnitude. These reaction force values were compared to quantify load-sharing characteristics of the system.
3.
Results
The stress–strain behavior of the NiTi rod was compared between the experimental and FE model (Fig. 3). Starting in the austenite phase, a linear stress–strain response was seen up to approximately 1% strain. A stress plateau occurred near 400 MPa and continued to 5% strain due to the austenite– martensite transition. Once the phase transition to martensite was completed, the behavior continued with a linear elastic response. Upon release, a hysteretic behavior was seen in which the stress plateau started at 4.5% strain and 200 MPa. Reloading actions resulted in two linear sections of increased stress along the lower plateau, first near 4.5% strain and again at 3% strain. Positioning of the reloading between
Fig. 3 – A uniaxial test was performed both experimentally and computationally to compare the NiTi material stress–strain relationship. The reloading test scheme was used as an extreme case of normal daily activities to ensure the material response. In a “real life” situation (gait), the magnitude of the load/unload would be substantially smaller but still similar in shape. For illustrative purposes, the magnitude was increased to allow comparison between experimental and computational response.
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the model and experiment were nearly identical. However, the experimental results produced a loop response while the model was only able to predict a linear response. Additionally, the computational model deviated during the linear austenite response by reaching the first plateau at an earlier strain of 0.9%. The ABAQUS model also transitioned to the martensite phase earlier (4.9%) and thus traveled up the martensite linear response further than the experimental data. Overall, relative stress levels matched closely between the model and experiment during the programmed state and following the second plateau back to being unstretched. The simplified bone block model revealed the stress distribution occurring directly after programming. This model utilizes a fully continuous block of bone, which would exist in a fused ankle. Bone stresses were seen to be higher between the tibial locking screws and the posterior calcaneal screw (Fig. 4), demonstrating the compression applied by the NiTi rod. The highest observed stresses in the bone occurred in the region surrounding the proximal calcaneal locking screw. Overall, stress magnitudes were less than 1 MPa for bone regions. The nail jacket experienced higher stresses when compared to bone ( 6 MPa), and the proximal head of the nail jacket experienced lower stresses than the rest of the nail. Displacement of nodes within the compliant bone material section showed an average axial displacement of 0.5 mm for this particular model with very little stress as highlighted by the outlined rectangular section. This result demonstrated the ability of the device to maintain compression while accommodating bone resorption (i.e. loss of bone height). The source of axial compression in the nail jacket was investigated by running simulations with and without contact conditions activated. Approximately 80% of axial compression can be attributed to the contact of the bone along the nail jacket and slots, while the other 20% of compression occurred due to a bending component resulting from asymmetric contraction in the NiTi rod.
A 3D rendering of the bone model following the material property assignment is provided in Fig. 5. It can be seen that the elastic modulus values had a maximum value near 20 GPa. When observing the material property distribution, the outer cortical shell had a higher elastic modulus due to its relatively high volumetric bone mineral density, whereas the inner trabecular bone and medullary cavity had a much lower elastic modulus. Stresses in the combined bone/device model were higher in the stiffer cortical bone and nail components than in the more compliant trabecular bone, a result that is to be expected from any load-sharing system. The left image in
Fig. 5 – Quantitative Computed Tomography (QCT) imaging was used to develop a 3D model of the TTC bones (A). Elastic modulus values for each element were assigned based on greyscale values gathered from the scans (B). Simpleware's ScanIP was used for segmentation of the bone geometry and þCAD was used for integrating the device into the bone model (C).
Fig. 4 – A model change is used to remove bone in the initial state, stretch, and relax steps. While the distal calcaneal screw is pinned, the proximal end of the NiTi rod is displaced. Stress free locking elements are added after the NiTi is programmed to secure the NiTi rod to the nail jacket and the bone is reactivated. Compressive stress is developed in the bone between the calcaneal and tibial screws after the boundary conditions are released. Bright red elements in “Locking Elements” inset show locking elements and their attachment to the NiTi rod and nail jacket. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).
journal of the mechanical behavior of biomedical materials 62 (2016) 83 –92
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Fig. 6 – Relative differences in stress between the bone and nail show load-bearing properties. Stress gradients (see nail jacket) indicate an occurrence of bending within the model with respect to the medial (M) and lateral (L) directions.
Fig. 6 shows stresses on the tibia cortex in the range of approximately 1–2 MPa. Bone closer to the lateral side carried higher stress than the medial side. The nail jacket demonstrated a similar trend, where a gradient of increasing stress occurred when moving from the medial to lateral sides. In the calcaneus, the opposite trend was observed, with higher stress on the medial side and a gradient to lower stress laterally. Highest stresses in the calcaneus occurred surrounding the nail jacket and locking screw. During simulated gait, the total force borne by the bone was greater than force borne by the nail jacket (Fig. 7). The nail jacket was in compression during most of gait, whereas the NiTi rod was in tension. During the highest magnitude loading of gait (just before 75% of the gait cycle), the load taken by the bone was more than 50% higher than the load taken by the nail jacket. The overall magnitudes of load borne by the nail jacket and bone were influenced by the applied load. However, the magnitude of the NiTi load stayed relatively constant throughout the gait cycle. It can be seen that, near 100% gait, the applied load was nearly zero, but the bone remained under a compressive load close to 350 N. Data gathered from the bone quality study showed a relatively modest transfer of stress from the bone to the nail jacket as the bone stiffness decreased. Overall the results indicated a relatively inverse linear relationship between stress within the tibia and stress within the nail as bone modulus changed (Fig. 8). A total bone loss of 10% resulted in a 0.5% decrease in stress of the bone and a 3.4% increase in stress on the nail jacket. Given a 10% loss in bone elastic modulus, this equates to a 4.7% loss in BMD for trabecular bone, or a 5.1% loss in BMD for cortical bone.
4.
Fig. 7 – A simulated gait load was modeled by applying an axial force to the calcaneus and load sharing characteristics were studied. The bone was observed to carry higher loads in comparison with the nail jacket throughout the gait simulation.
Discussion
This study set forth to develop a mechanical analysis model to achieve two main objectives: simulate the operation of a compression generating IM nail; and use the model to both investigate the operation of the device during simulated gait loading and quantify load-sharing changes as a function of
Fig. 8 – During static compression generated from the NiTi rod, the effect of bone quality was studied. Bone elastic modulus values were varied and stress values at the distal tibia diaphysis level were measured for the bone and nail.
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bone quality. It can be seen from the results of modeling the NiTi rod that the material behavior was successfully activated within the device and then programmed while inside a simulated bone block. Deviation between the NiTi model and experimental material response exists during phase transition regions (Fig. 3); however, for this study, the material response after the programmed state is of primary importance. During the pseudoelastic recovery on the unloading plateau, the computational model represents the NiTi material unloading and reloading response closely. Referencing Fig. 4, there is an apparent stress gradient when looking at bone in between the two locking screw attachment points (proximal tibia, mid-calcaneus) and the other bone sections. Compression in the bone was generated internally from the NiTi rod, since the only other external forces were due to the pin condition at the proximal end of the system. A similar behavior was observed when the device was modeled within a human bone. The use of a cadaver specimen allowed anatomical geometry to be obtained and patient-specific bone quality parameters to be established. In QCT-based FE modeling, the assignment of bone material properties can have a large influence on the results. In an attempt to maintain bone quality accuracy, voxel-based calibration using the reference phantom throughout the length of the scan was used to avoid beam-hardening effects, and well-established relationships between QCT-based BMD and bone properties were used (Keyak et al., 2005). With the anatomical bone and programmed device combined into one model, stresses were shown to be concentrated in between the proximal tibia screws and the proximal calcaneus screw as can be seen in Fig. 6. Relative levels of stress were computed for the tibia and talus bones and gave insight to areas of high stress and also stress-sharing characteristics of the bones. Von Mises stress levels observed in the model due to static compression were far below the stress levels needed to cause bone failure or damage. During static loading from the internal compression of the nail, it was observed that compression was on the medial side of the tibia, whereas a small amount of tension was on the lateral side. This would suggest a bending moment as can been seen in Fig. 6A. The opposite can be seen in the calcaneus, where there is compression on the lateral side and tension on the medial side. When the device is activated, the NiTi rod contracts and the three TTC bones are compressed together. Due to the geometry of the talus, the applied compression results in a bending moment, causing a medial-to-lateral change in compression between the calcaneus and the tibia. Additionally, there were axial compression and bending loads observed within the nail jacket. Axial compression was developed because of load transfer from bone segments that were in contact normal to the nail jacket surface as well as regions on bone entering the axial slots for the locking screws. The latter was assumed to occur in patients once fusion developed and bone growth occurred in these regions. Using a simulated gait load, results indicated a higher load borne by the bone rather than the device throughout a full gait cycle. Stress shielding occurs in many different orthopedic applications and is commonly known as a factor resulting
in a failed device (Huiskes et al., 1992). Stress shielding has also been documented as a factor to decrease overall BMD in retained tibial IM nails (Allen et al., 2008). Additionally, a complication with TTC fusion procedures is the necessity to remove the IM nail after fusion to relieve patient pain caused by implant loosening due to stress shielding. With the results presented in this study, it appears this device allows more evenly distributed loading between the bone and device during gait loading. This suggests that the device could potentially help reduce stress shielding and maintain compression across the fusion site. Patient-specific analysis could be applied to this modeling technique by modifying the gait load. One method that could be followed is to gather gait characteristic data from a patient post surgery and scale the analysis loading based upon body weight. Variation in bone quality showed a system response of stresses shifting to the nail when bone modulus levels were decreased. For a bone modulus loss, the given percent increase in stress for the nail was larger than the given percent increase in stress for the bone, indicating that the stress does not evenly transfer between the regions during bone loss. One potential explanation for this behavior is that, as the bone density decreases, there is a larger relative decrease in cortical bone modulus, making a decrease in overall bone quality more influential to the cortical compartment. The cortex will inherently carry higher loads due to its relative stiffness and will transfer those loads to the nail. Studying the effects of varied bone quality can offer understanding of how the system will react with patients of lower or higher bone quality. Many TTC fusion procedures are either salvage or revision procedures, where the patient has been immobile for extended periods of time, potentially leading to decreased bone quality. As the patient recovers and begins reambulation, it is likely that changes in BMD will occur throughout the lower limb. In this situation, forces due to walking would be expected to shift from the nail to the bone as BMD increases. A recent clinical study on the DynaNail demonstrated encouraging early results (Hsu et al., 2015), but additional longitudinal measurements are needed to monitor temporal changes in BMD. By providing a quantitative analysis of the mechanical implications of changing BMD, a longitudinal clinical study could be augmented with the new modeling framework presented here. While this study achieved the aims of accurately simulating NiTi behavior, investigating load sharing during simulated gait, and revealing the effects of altered bone quality, the study had some limitations. First, the FE nodes on the articulating surfaces of the three bones were tied together, disallowing sliding contact between the bones. Prior to bone fusion in a real patient, micro-motion is expected to occur between the bone-to-bone surfaces. Therefore, this study simulated a presumed “fused” bone-to-bone connection. Further modeling could investigate the contact pressures as well as relative movement of the bone-to-bone surfaces to help determine what levels are appropriate for a bone fusion environment. The contact between the nail jacket and bone could also be investigated if modified to include friction. It was assumed that since the outer finish of the device is manufactured smoothed and polished, any interstitial fluid present between the nail and bone would produce friction
journal of the mechanical behavior of biomedical materials 62 (2016) 83 –92
force magnitudes negligible in comparison to stresses present in the model. Tetrahedral elements were selected for modeling because of their ability to fit complex shapes of bone anatomy. Since meshing was performed simultaneously for bone and device, varying element type for meshing the model was not considered. However, the use of tetrahedral elements leads to some considerations. For example, using tetrahedral elements to mesh a cylindrical component does not allow for a direct axial strain within the elements. This resulted in slight bending upon contraction of the NiTi rod and led to a small bending moment in the simplified block model. It should be noted that the bending moment experienced in the patient-specific model was largely caused by the asymmetric geometry of the bone. Furthermore, even though frictionless contact was assumed, the shape of the tetrahedral elements allows the transfer of force along the interface of the bone and nail jacket. These limitations were considered in meshing decisions, but the use of tetrahedral elements more accurately represented the geometry of the device and bone compared to other options such as hexahedral elements. The presented method of programming NiTi for sustained compression using locking elements differs from the clinical environment. In practice, the NiTi rod would be secured at the proximal end using a setscrew and would undergo stretching and partial release from the distal end (Fig. 2); however, in our model we programed the NiTi by constraining the NiTi at the distal end and performing the stretchrelease steps at the proximal end (Fig. 4). Once the material was programmed correctly, locking elements (shown as bright red in Fig. 4 “Locking Elements” inset) were used to link the NiTi rod to the nail jacket in lieu of the setscrew. The locking elements that were manually added could experience extreme distortion in situations where the element size is small. In this case, using hexahedral elements could potentially remedy the situation. The relatively large strains observed in this study for the locking elements could result in distortion and provide inaccurate results. However, the sole purpose of the locking material was to allow the NiTi rod to be programmed and locked, such that loads are transferred to the nail jacket. The region of high distortion surrounding the locking elements was very localized, and realistic stress and strain levels were computed throughout the remainder of the model. This study used a cadaver specimen from a donor of relatively normal weight (180 lb), whereas TTC arthrodesis patients are often overweight. Differences in bone geometry as well as bone mineral distribution could exist for overweight patients. Furthermore, this study was limited to a single bone preparation style but geometry of bones and bone positioning can vary with patient needs and surgeon preference. Modeling the bone loss as an overall percent loss throughout all bone regions might not capture the spatiallyvarying effects of bone loss seen clinically. Bone quality has been seen to vary differently between cortical and trabecular regions when measuring disuse-related bone loss (Martin, 1984). Due to the higher surface area available for bone resorption, trabecular bone loses a higher fraction of BMD when compared with the cortical shell, as shown by
91
Carpenter et al. (2010) in microgravity situations (similar to decreased levels of loading on Earth). Lastly, the relative magnitudes for normal gait loading were gathered from a healthy patient without a TTC fusion. Modification to the anatomy of the ankle and side-favored walking patterns pre-surgery could undoubtedly change the gait load. Application of the gait loading was also assumed to act directly axial to the nail device. A more realistic load would change location during gait such as during the heel strike the load would be applied at the posterior calcaneus and shift anteriorly as gait progresses. By applying the load axially, this study did not take into account increased bending stresses from the moment created from a heal strike. Moreover, this study did not investigate the effects of soft tissue and muscles surrounding the joint construct, which may have an effect on the load sharing. These key anatomical features could be included in future work to more accurately represent the joint environment. Future work can also be performed experimentally to validate the computational model presented in this study. Cadaveric testing has previously been used to show compression levels in two other IM devices and the methodology can be directly applied to this device (Yakacki et al., 2010). In summary, this study successfully modeled a device with a pseudoelastic NiTi rod that can be activated to apply compression across a long range of strains. The device was simulated within a human bone model that possessed patient-specific material assignment. Effects of bone quality and gait loading were also studied. Findings of this study suggest that the DynaNail device can maintain compression across the fusion site under conditions of bone loss. The results also showed that, by sharing gait-generated loads with the surrounding bone, the device has the potential to help decrease the incidence of bone loss due to stress shielding. The methodology used in this study can aid in further investigation of TTC arthrodesis and the accompanying devices. Furthermore, the simulation procedure can be applied to any other device (e.g. fracture fixation devices or other arthrodesis devices) that utilizes the pseudoelastic material behavior of NiTi to apply constant compression across a bone–bone interface. With this tool, investigations of the bone and device interactions in these procedures can lead to a better understanding of the fusion and healing process of bone.
5.
Conclusions
1. A finite element model can be used to simulate nickel titanium's pseudoelastic behavior within an intramedullary nail device. This method can be extended to a patientspecific bone model with voxel based material assignment to explore the stress distribution and load-sharing characteristics in a tibio-talo-calcaneal (TTC) fusion construct. 2. Gait loading was applied to an anatomic TTC bone model and showed an initial compression from the device of 350 N. Load borne by the bone was 50% higher than load borne by the nail during maximum loading in gait.
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3. An overall decrease in bone modulus values of 10% resulted in an increase of stress within the nail of 3.4% while a decrease in stress of 0.5% occurred in the bone.
Acknowledgments Research reported in this publication was supported by the National Institute of Arthritis and Musculoskeletal and Skin Diseases of the National Institutes of Health under Award number R21AR065713. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. The authors would like to thank MedShape, Inc. for providing the CAD files for the DynaNail device in this study as well as Vasily Buharin for the gait forces during walking. The authors would like to thank Samuel Welch for his advice in modeling the programmed NiTi rod. CMY and DJP have a financial interest in MedShape, Inc.
Appendix A.
Supplementary material
Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jmbbm. 2016.04.037.
references
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Haaker, R., Kohja, E.Y., Wojciechowski, M., Gruber, G., 2010. Tibiotalo-calcaneal arthrodesis by a retrograde intramedullary nail. Ortop. Traumatol. Rehabil. 12, 245. Henry, A.J., et al., 2013. Factors predicting resource utilization and survival after major amputation. J. Vasc. Surg. 57, 784. Hsu, A.R., Ellington, J.K., Adams, S.B., 2015. Tibiotalocalcaneal arthrodesis using a nitinol intramedullary hindfoot nail. Foot Ankle Spec. 8, 389. Huang, P.J., Fu, Y.C., Lu, C.C., Wu, W.L., Cheng, Y.M., 2007. Hindfoot arthrodesis for neuropathic deformity. Kaohsiung J. Med. Sci. 23, 120. Huiskes, R., Weinans, H., Rietbergen, B.V., 1992. The relationship between stress shielding and bone resorption around total hip stems and the effects of flexible materials. Clin. Orthop. Relat. Res. 274, 124. iData-Research-Inc., 2009. US Market for Small Bone and Joint Orthopedic Devices. Joseph, R.M., 2009. Osteoarthritis of the ankle: bridging concepts in basic science with clinical care. Clin. Podiatr. Med. Surg. 26, 169. Keyak, J.H., Kaneko, T.S., Tehranzadeh, J., Skinner, H.B., 2005. Predicting proximal femoral strength using structural engineering models. Clin. Orthop. Relat. Res. 219. Kim, C., Catanzariti, A.R., Mendicino, R.W., 2009. Tibiotalocalcaneal arthrodesis for salvage of severe ankle degeneration. Clin. Podiatr. Med. Surg. 26, 283. Kleinstreuer, C., Li, Z., Basciano, C.A., Seelecke, S., Farber, M.A., 2008. Computational mechanics of Nitinol stent grafts. J. Biomech. 41, 2370. Klos, K., et al., 2009. Tibiotalocalcaneal arthrodesis using a compressive retrograde locking nail with hindfoot valgus. Z. Orthop. Unfall. 147, 445. Kumar, G.P., Mathew, L., 2012. Self-expanding aortic valve stentmaterial optimization. Comput. Biol. Med. 42, 1060. Mu¨ckley, T., et al., 2007. Biomechanical evaluation of primary stiffness of tibiotalocalcaneal fusion with intramedullary nails. Foot Ankle Int. 28, 224. Martin, R.B., 1984. Porosity and specific surface of bone. Crit. Rev. Biomed. Eng. 10, 179. Mueller, M., Allgower, M., Schneider, R., Willenegger, H., 1979. In: Manual of Internal Fixation: Techniques Recommended by the AO Group. Springer-Verlag, Berlin. Nihal, A., Gellman, R.E., Embil, J.M., Trepman, E., 2008. Ankle arthrodesis. Foot Ankle Surg. 14, 1. Panagakos, P., Ullom, N., Boc, S.F., 2012. Salvage arthrodesis for charcot arthropathy. Clin. Podiatr. Med. Surg. 29, 115. Rogers, L.C., et al., 2011. The Charcot foot in diabetes. J. Am. Podiatr. Med. Assoc. 101, 437. Vazquez, A.A., Lauge-Pedersen, H., Lidgren, L., Taylor, M., 2003. Finite element analysis of the initial stability of ankle arthrodesis with internal fixation: flat cut versus intact joint contours. Clin. Biomech. 18, 244. Vesely, R., Prochazka, V., Visna, P., Valentova, J., Savolt, J., 2008. Tibiotalocalcaneal arthrodesis using a retrograde nail locked in the sagittal plane. Acta Chir. Orthop. Traumatol. Cechoslov. 75, 129. Yakacki, C.M., Gall, K., Dirschl, D.R., Pacaccio, D.J., 2011. Pseudoelastic intramedullary nailing for tibio-talo-calcaneal arthrodesis. Expert Rev. Med. Devices 8, 159. Yakacki, C.M., Khalil, H.F., Dixon, S.A., Gall, K., Pacaccio, D.J., 2010. Compression forces of internal and external ankle fixation devices with simulated bone resorption. Foot Ankle Int. 31, 76.
Available online at www.sciencedirect.com
www.elsevier.com/locate/jmbbm
Research Paper
Finite element analysis of a pseudoelastic compression-generating intramedullary ankle arthrodesis nail Ryan T. Andersona, Douglas J. Pacacciob, Christopher M. Yakackia, R. Dana Carpentera,n a
Department of Mechanical Engineering, University of Colorado Denver, Denver, CO 80217, United States Advanced Foot and Ankle Surgeons, Inc., Yorkville, IL 60560, United States
b
art i cle i nfo
ab st rac t
Article history:
Tibio-talo-calcaneal (TTC) arthrodesis is an end-stage treatment for patients with severe
Received 12 November 2015
degeneration of the ankle joint. This treatment consists of using an intramedullary nail
Received in revised form
(IM) to fuse the calcaneus, talus, and tibia bones together into one construct. Poor bone
4 April 2016
quality within the joint prior to surgery is common and thus the procedure has shown
Accepted 28 April 2016
complications due to non-union. However, a new FDA-approved IM nail has been released
Available online 4 May 2016
that houses a nickel titanium (NiTi) rod that uses its inherent pseudoelastic material
Keywords:
properties to apply active compression across the fusion site. Finite element analysis was
Ankle
performed to model the mechanical response of the NiTi within the device. A bone model
Arthrodesis
was then developed based on a quantitative computed tomography (QCT) image for
NiTi
anatomical geometry and bone material properties. A total bone and device system was
Compression
modeled to investigate the effect of bone quality change and gather load-sharing proper-
Finite element
ties during gait loading. It was found that during the highest magnitude loading of gait, the
Joint
load taken by the bone was more than 50% higher than the load taken by the nail. When comparing the load distribution during gait, results from this study would suggest that the device helps to prevent stress shielding by allowing a more even distribution of load between bone and nail. In conditions where bone quality may vary patient-to-patient, the model indicates that a 10% decrease in overall bone modulus (i.e. material stiffness) due to reduced bone mineral density would result in higher stresses in the nail (3.4%) and a marginal decrease in stress for the bone (0.5%). The finite element model presented in this study can be used as a quantitative tool to further understand the stress environment of both bone and device for a TTC fusion. Furthermore, the methodology presented gives insight on how to computationally program and use the unique material properties of NiTi in an active compression state useful for bone fracture healing or fusion treatments. & 2016 Elsevier Ltd. All rights reserved.
n Correspondence to: Department of Mechanical Engineering, University of Colorado Denver, Campus Box 112, PO Box 173364, Denver, CO 80217-3364, United States. Tel.: þ1 720 309 3045. E-mail address: [email protected] (R.D. Carpenter).
http://dx.doi.org/10.1016/j.jmbbm.2016.04.037 1751-6161/& 2016 Elsevier Ltd. All rights reserved.
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1.
journal of the mechanical behavior of biomedical materials 62 (2016) 83 –92
Introduction and background
Walking is a primary function of life. Walking should be pain free, but unfortunately for some, walking can be a difficult endeavor. Movement of the ankle joint is a key component of normal gait, yet there are numerous conditions that can cause severe degeneration of the ankle, including idiopathic osteoarthritis, inflammatory arthritis, trauma, or systemic diseases like diabetes mellitus (Joseph, 2009; Nihal et al., 2008; Rogers et al., 2011). These conditions can lead to unbearable pain, loss of function, immobility, and ultimately a decreased quality of life. In cases of highly severe joint degeneration, amputation can become necessary, which entails a mortality rate of up to 86.9% within four years, specifically in diabetic and vascular limb patients (Panagakos et al., 2012; Henry et al., 2013). Alternatives to amputation involve the fusion of affected bones, such as tibio-talar, talocalcaneal, or tibio-talo-calcaneal (TTC) arthrodesis. With an estimated 26,000 ankle fusion and ankle/subtalar combination procedures performed annually, these salvage procedures aim to stabilize the joint and provide patients with pain free walking (iData-Research-Inc., 2009). For the purpose of this study, TTC arthrodesis (Fig. 1A) will be the primary focus. In TTC arthrodesis the tibia, talus, and calcaneus can be fused together using a variety of approaches, including the use of an intramedullary (IM) nail. Using this approach, an IM nail is inserted through the calcaneus and talus and into the medullary cavity of the tibia and secured using locking screws. With a relatively stiff nail, typically one composed of titanium, the goal is to rigidly fix the bones in place to ensure stability of the joint. Recent designs of IM nails aim to provide compression to the ankle via an external frame (Yakacki et al., 2010) or an internal compression generating screw. A more detailed review of the progression of IM nails has previously been published (Yakacki et al., 2011). The success rates for TTC fusion have ranged from 76% to 96%; however, complication rates can be as high as 25% (Boer et al., 2007; Gavaskar and Chowdary, 2009; Haaker et al., 2010; Huang et al., 2007; Kim et al., 2009; Klos et al., 2009; Vesely et al., 2008). Complications can arise from a variety of factors: variation in bone quality from patient to patient, especially with patients who have prior degeneration; post-surgery loading conditions; initial level of
compression; and the specific device installed. In most cases, failure arises from hardware loosening with compression and stability of the joint being lost during the healing process (Mückley et al., 2007). One of the most pertinent factors to influence instrumentation loosening is bone resorption. This can decrease the level of compression and stability of the bone–nail system, resulting in movement of the joint and ultimately a failed fusion procedure. It is known that in long-bone fracture fixation, minimizing motion and using plating to ensure bone-on-bone contact promotes primary bone healing directly across the fracture site (Mueller et al., 1979). Thus, to improve upon previous designs, current generation IM nails look to provide a means of sustained compression across the fusion site and prevent excessive movement (Gilbert et al., 1989). Compressive loading on the bones is known to help achieve successful fusion. On the other hand, high levels of sustained compression can lead to bone resorption and osteonecrosis (Carpenter and Carter, 2008). Compression, therefore, has the potential to either help or hinder bone formation and remodeling following TTC arthrodesis, depending on the magnitude of the applied load. The first step towards understanding the optimal compression necessary for ankle fusion is to gather stresses and loadsharing properties of an ankle fusion construct. Load-sharing properties can indicate if a device is stress shielding the bone, leading to a decrease in bone loading stimulus and higher likelihood of resorption. Stresses, however, can indicate localized areas under high load and potential for material failure
equating
to
bone
deformation
and
hardware
loosening. An IM nail (DynaNail, MedShape, Inc., Atlanta, GA) that has recently been FDA approved uses a nickel titanium (NiTi) rod to apply compression across the fusion site, even in the presence of bone resorption (Yakacki et al., 2011) (Fig. 1). Nickel titanium demonstrates a rare material property that is pseudoelastic in nature and exhibits a relatively flat stress plateau over a moderate range of strains. The inherent mechanical properties of NiTi allow for a steady compression load and micro-motion of the bone, as well as any bone resorption up to 6 mm. The compression properties are activated by stretching the material into its martensitic phase
Fig. 1 – Relative position of distal calcaneal locking screw in a DynaNail device (A) immediately post surgery, (B) at 8 weeks, and (C) at 1 year. (D) Bone resorption is illustrated by the superior motion of the locking screws. Radiographic images provided by D. J. Pacaccio.
journal of the mechanical behavior of biomedical materials 62 (2016) 83 –92
and then releasing the material to its pseudoelastic-recovery stress plateau. Stress as a function of strain for a pseudoelastic material such as NiTi is illustrated in Fig. 2. Starting at point A, the material is stretched through an austenite linear elastic region until a stress-induced phase transformation occurs from austenite to martensite along the plateau. Upon release at point B, the martensite phase becomes unstable and transitions back to austenite along the second lower plateau. To maximize the pseudoelastic response and apply constant compression, the material is “programmed” and locked into place at point C. Thus, the stress remains constant in response to any loss in strain throughout a large range (D). Surgically, programming of the DynaNail is achieved by first inserting the nail into the bone and locking the tibial screws (Fig. 2A). The proximal end of the NiTi rod is fixed to the nail jacket and also threaded into the sliding element. Next, the sliding element is pulled to stretch the NiTi rod to approximately 6% strain (Fig. 2B) and then relaxed to program the material to the start of the recovery plateau (Fig. 2C). Calcaneal screws are then inserted into the sliding element to lock the system in place. The sliding element allows the NiTi rod to contract in response to any bone resorption, and the pseudoelastic property of the material will maintain a constant compressive force across the joint (Fig. 2D). While the DynaNail provides a means to actively respond to bone resorption, it is unknown how this device distributes loads across the ankle region and also how the loading environment will change with respect to bone quality and external forces that might result from daily activities during healing. Finite element (FE) analysis provides the ability to determine the 3D stress and strain distribution in mechanical systems. Previous studies have used FE modeling to investigate the mechanical behavior of devices that use NiTi for its unique material properties, most notably the arterial stent (Azaouzi et al., 2012; Kleinstreuer et al., 2008; Kumar and Mathew, 2012). These stents are typically compressed to fit inside a catheter and deployed when inserted into an artery. This can oftentimes be referred to as “superelastic” where the
85
material can undergo large deformations and recover its original shape upon unloading. Modeling the behavior of NiTi in a device to apply active compression in a stress-induced programmed state presents unique technical challenges. This is due to the path-dependent material behavior. Simulation of the response of a NiTi compressive device within imagebased anatomical structures has not been previously reported. Work by Vazquez et al. (2004a, 2004b, 2003) has showed that differences in bone quality, variation in screw number, and joint contours affect stability of the tibio-talar joint. However, there does not exist a computational model that investigates the loading environment within a TTC union procedure using an IM nail. The first objective of this study is to develop an FE-based technique to effectively model the behavior of a compression generating IM nail inside a realistic bone environment. The second objective of this study is to use the new simulation framework to investigate the mechanical environment in the ankle after pseudoelastic IM nailing during normal gait loading and the effect of bone quality on stresses in the system components using patient-specific bone anatomy and material properties. In this study, steps used to reach a final image-based human bone and device model will be presented. The pseudoelastic material behavior was first studied to ensure that the stress response could be replicated to the manufacturer's material. A simplified bone and device model was then constructed to ensure proper activation of the device within a bone environment. A final image-based bone model was used for studying load-sharing properties of the joint as well as effects of bone quality on stresses in the TTC-fusion construct.
2.
Methods
2.1.
NiTi material modeling
Mechanical testing was used to measure the NiTi material parameters that were implemented in ABAQUS 6.12 using the superelastic material subroutine based on a proposed model
Fig. 2 – A pseudoelastic material behavior allows the NiTi material to apply compression by programming a constant stress state. After the nail is installed into the patient (A), the NiTi rod is stretched (B) and unloaded to a “programmed” state (C). Any bone resorption up to 6 mm is countered by a steady compression (D).
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journal of the mechanical behavior of biomedical materials 62 (2016) 83 –92
by Auricchio et al., (1997). Uniaxial testing was performed on a sample supplied by the manufacturer of the NiTi rod to gather key transition points for the stress–strain response. A uniaxial tester (MTS Insight 30, MTS, Eden Prairie, MN, USA) equipped with custom threaded grip attachments and a 30 kN load cell was used for testing. A constant deformation rate of 0.1 mm/s was used throughout the test with strain being measured using an MTS LX500 laser extensometer. Temperature during testing was maintained at 36 1C using a thermal chamber (ThermCraft, Winston Salem, NC, USA). The sample was first strained to 5.5% strain in tension and then relaxed back to 4.5% strain; this will be referred to as “programmed.” Following the programmed state, a reloading occurs back to 4.8% strain. This is followed by a similar unload at 3% and reload at 3.3% strain, and ends with an unloading of the sample. This testing procedure essentially programmed the NiTi and then simulated a response to tension loading/unloading. This would represent a patient constraining the foot and trying to elevate their leg, thus inducing tension in the NiTi rod. The loss in strain between 4.5% and 3% would represent a reaction to bone resorption and, in result, a loss in total stretched length of the rod. Values gathered from the experimental results include the elastic modulus values for both austenite and martensite phases as well as stress transition points. A full list of variables used for modeling purposes as well as the corresponding ABAQUS built in superelastic illustration can be found in the online supplement. Following mechanical testing, the material model was implemented in an FE model of the NiTi rod. The rod geometry was extracted from the manufacturer's computeraided draft (CAD) model and input into ScanIPþFEþCAD software suite (Simpleware, Exeter, UK). A built in adaptive meshing algorithm (FEFree) was used to apply 12,796 tetrahedral finite elements to the geometry. Within ABAQUS, the model was assigned the superelastic material properties found in experimental testing. Pin boundary conditions were applied to the nodes on the distal end of the rod to constrain movement in all three directions while a displacement boundary condition (BC) was given to nodes at the proximal end of the rod. A combination of stretch/relax steps was used to mimic the experimental procedure by modifying the displacement BC. Non-linear geometry was accounted for in each step due to the relatively large strain and an energy dissipation fraction of 0.0002 was used for solution stability control. During this analysis, it was assumed that the temperature remained constant. A selection of elements at the center of the rod was probed for stress and strain levels in the axial direction for each solution frame. Stress as a function of strain was plotted for both experimental and computational models simultaneously to allow comparison.
and allowing nail contraction. CAD-based models of the other nail components were combined with the NiTi rod and inserted into the model at the center of the bone sections. Both bone sections were assigned linear isotropic material properties with the normal bone section having an elastic modulus of 17 GPa and a Poisson's ratio of 0.3, while the compliant bone section was given an elastic modulus of 1 GPa and a Poisson's ratio of 0.001 (Carpenter and Carter, 2008). All other nail components were prescribed linear isotropic properties of titanium with an elastic modulus of 110 GPa and a Poisson's ratio of 0.3. The total tetrahedral element count for the model was 493,117. Because of the path-dependent material behavior of NiTi, a series of five steps were implemented to program the rod and simulate the behavior of the IM nail after implantation in the bone block. To achieve programming of the NiTi rod at a site with only two interacting parts, displacements were applied to the NiTi material at the proximal end of the rod. In order to lock the NiTi rod to the nail jacket after programming, it was necessary to add a “locking material” between the two components. The mesh input file from ScanIP was manually modified to add two large locking elements. These elements were assigned the same titanium material properties as other device components. In ABAQUS, superelastic material properties were applied to the NiTi rod. Analysis parameters, including step settings, were identical to the bare NiTi rod model. Between the bone sections and the nail jacket outer surface, normal contact was defined as “hard,” and tangential contact was assumed frictionless. Bone-to-bone contact nodes were defined as tied to simulate a “fused” bone joint. Initially, all bone sections and the locking material were applied a model change condition, essentially omitting the elements from the analysis. The sliding element and calcaneal screws were first prescribed a pin boundary condition. Next, a displacement was applied to the proximal end of the NiTi rod to program the material. Once the material was programmed, the bone and locking material were reactivated into the model strain free. Upon reactivation, the pin condition on the sliding element and the calcaneal screws was deactivated, as was the displacement condition on the proximal end of the NiTi rod. A new boundary condition was then activated to pin the proximal end of the bone block to prevent rigid body movement. To confirm the operation of the device, the compliant bone material allowed a contraction between the two regions of normal bone. Displacement values of nodes within the compliant material were monitored to ensure that contracting movement was occurring. Stress distributions within the system were constructed to give a visual representation of the contraction.
2.2.
2.3.
Programming NiTi in a simplified bone model
A simplified bone and device model was created to implement the programming of the NiTi material within a bone environment. A rectangular block was created with the dimensions of 36.0 40.8 224.7 mm3 with an additional rectangular section of compliant material proximal to the proximal calcaneal screw. The compliant material section was added to allow a hypothetical simulation of loss in bone
Anatomical bone and device modeling
A bone model was created that retained anatomical geometry by using quantitative computed tomography (QCT) imagery of a cadaver specimen. A below-knee cadaver specimen was imaged in a CT system (Gemini TF TOF 64, Philips, Amsterdam, The Netherlands) along with a volumetric bone mineral density (BMD) reference phantom (Mindways Software, Inc., Austin, TX, USA) with an in-plane pixel size of 0.72 mm and a
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slice thickness of 0.90 mm. Clinically relevant positioning of the ankle for the scan was verified on a scout scan before imaging. Using ScanIP, the bone model was segmented into 3 bone regions: tibia, talus, and calcaneus. Geometry of the bone was modified at the distal end of the tibia, proximal and distal sides of the talus, and the proximal side of the calcaneus to mimic bone preparation during surgery. Utilizing the reference phantom, the material properties of each bone voxel were assigned based on the voxel's BMD using empirically-defined relationships between ash density and elastic modulus (Keyak et al., 2005). ScanIPþFEþCAD software was used to position the device within the bone model and the FEFree meshing algorithm applied a volumetric mesh to the combined bone/device model. Manual addition of locking material was employed in this final model as well, leading to a total of 1,892,399 elements in the model. A mesh convergence study was performed by varying element density of the bone model and applying a simple compression test within ABAQUS to confirm relative stiffness results were not varying at the density level used for analysis. The final bone/device FE model was used to test two conditions: first, in a static equilibrium situation, such that only the programmed NiTi rod applied load; and second, a quasi-static loading that simulated one cycle of normal human gait. The same approach used to program the NiTi rod in the bone block model was implemented in the human bone model. Contact properties were defined between the bones and nail jacket as before. Instead of pinning the bone block, the final boundary condition in this model pinned the proximal tibia. Stress distributions were gathered for the distal tibia metaphysis as well as midway through the calcaneus. During the static analysis, the effect of bone quality was studied by varying the total elastic modulus of each element. Bone quality ranged from 30% loss to 20% gain in 10%
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increments. A selection of bone and nail jacket elements was made at the distal tibia metaphysis level. Average von Mises stress values were gathered for each change in bone quality. Stress as a function of bone quality was plotted for both bone and nail to allow comparison. To simulate gait loading in the quasi-static analysis, a selection of nodes equally spaced about the nail jacket on the inferior side of the calcaneus were applied point loads. The magnitude of each point load was varied to match experimental patient data provided by the Neuromuscular Physiology Lab at The Georgia Institute of Technology. During the analysis, the device was first programmed and allowed to apply compression to the joint. The proximal end of the tibia was pinned and then the gait load was applied. Note that the bone quality in the quasi-static analysis was not modified. Reaction force values were taken at mid length of the nail for the NiTi rod, tibia, and during each loading magnitude. These reaction force values were compared to quantify load-sharing characteristics of the system.
3.
Results
The stress–strain behavior of the NiTi rod was compared between the experimental and FE model (Fig. 3). Starting in the austenite phase, a linear stress–strain response was seen up to approximately 1% strain. A stress plateau occurred near 400 MPa and continued to 5% strain due to the austenite– martensite transition. Once the phase transition to martensite was completed, the behavior continued with a linear elastic response. Upon release, a hysteretic behavior was seen in which the stress plateau started at 4.5% strain and 200 MPa. Reloading actions resulted in two linear sections of increased stress along the lower plateau, first near 4.5% strain and again at 3% strain. Positioning of the reloading between
Fig. 3 – A uniaxial test was performed both experimentally and computationally to compare the NiTi material stress–strain relationship. The reloading test scheme was used as an extreme case of normal daily activities to ensure the material response. In a “real life” situation (gait), the magnitude of the load/unload would be substantially smaller but still similar in shape. For illustrative purposes, the magnitude was increased to allow comparison between experimental and computational response.
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the model and experiment were nearly identical. However, the experimental results produced a loop response while the model was only able to predict a linear response. Additionally, the computational model deviated during the linear austenite response by reaching the first plateau at an earlier strain of 0.9%. The ABAQUS model also transitioned to the martensite phase earlier (4.9%) and thus traveled up the martensite linear response further than the experimental data. Overall, relative stress levels matched closely between the model and experiment during the programmed state and following the second plateau back to being unstretched. The simplified bone block model revealed the stress distribution occurring directly after programming. This model utilizes a fully continuous block of bone, which would exist in a fused ankle. Bone stresses were seen to be higher between the tibial locking screws and the posterior calcaneal screw (Fig. 4), demonstrating the compression applied by the NiTi rod. The highest observed stresses in the bone occurred in the region surrounding the proximal calcaneal locking screw. Overall, stress magnitudes were less than 1 MPa for bone regions. The nail jacket experienced higher stresses when compared to bone ( 6 MPa), and the proximal head of the nail jacket experienced lower stresses than the rest of the nail. Displacement of nodes within the compliant bone material section showed an average axial displacement of 0.5 mm for this particular model with very little stress as highlighted by the outlined rectangular section. This result demonstrated the ability of the device to maintain compression while accommodating bone resorption (i.e. loss of bone height). The source of axial compression in the nail jacket was investigated by running simulations with and without contact conditions activated. Approximately 80% of axial compression can be attributed to the contact of the bone along the nail jacket and slots, while the other 20% of compression occurred due to a bending component resulting from asymmetric contraction in the NiTi rod.
A 3D rendering of the bone model following the material property assignment is provided in Fig. 5. It can be seen that the elastic modulus values had a maximum value near 20 GPa. When observing the material property distribution, the outer cortical shell had a higher elastic modulus due to its relatively high volumetric bone mineral density, whereas the inner trabecular bone and medullary cavity had a much lower elastic modulus. Stresses in the combined bone/device model were higher in the stiffer cortical bone and nail components than in the more compliant trabecular bone, a result that is to be expected from any load-sharing system. The left image in
Fig. 5 – Quantitative Computed Tomography (QCT) imaging was used to develop a 3D model of the TTC bones (A). Elastic modulus values for each element were assigned based on greyscale values gathered from the scans (B). Simpleware's ScanIP was used for segmentation of the bone geometry and þCAD was used for integrating the device into the bone model (C).
Fig. 4 – A model change is used to remove bone in the initial state, stretch, and relax steps. While the distal calcaneal screw is pinned, the proximal end of the NiTi rod is displaced. Stress free locking elements are added after the NiTi is programmed to secure the NiTi rod to the nail jacket and the bone is reactivated. Compressive stress is developed in the bone between the calcaneal and tibial screws after the boundary conditions are released. Bright red elements in “Locking Elements” inset show locking elements and their attachment to the NiTi rod and nail jacket. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).
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Fig. 6 – Relative differences in stress between the bone and nail show load-bearing properties. Stress gradients (see nail jacket) indicate an occurrence of bending within the model with respect to the medial (M) and lateral (L) directions.
Fig. 6 shows stresses on the tibia cortex in the range of approximately 1–2 MPa. Bone closer to the lateral side carried higher stress than the medial side. The nail jacket demonstrated a similar trend, where a gradient of increasing stress occurred when moving from the medial to lateral sides. In the calcaneus, the opposite trend was observed, with higher stress on the medial side and a gradient to lower stress laterally. Highest stresses in the calcaneus occurred surrounding the nail jacket and locking screw. During simulated gait, the total force borne by the bone was greater than force borne by the nail jacket (Fig. 7). The nail jacket was in compression during most of gait, whereas the NiTi rod was in tension. During the highest magnitude loading of gait (just before 75% of the gait cycle), the load taken by the bone was more than 50% higher than the load taken by the nail jacket. The overall magnitudes of load borne by the nail jacket and bone were influenced by the applied load. However, the magnitude of the NiTi load stayed relatively constant throughout the gait cycle. It can be seen that, near 100% gait, the applied load was nearly zero, but the bone remained under a compressive load close to 350 N. Data gathered from the bone quality study showed a relatively modest transfer of stress from the bone to the nail jacket as the bone stiffness decreased. Overall the results indicated a relatively inverse linear relationship between stress within the tibia and stress within the nail as bone modulus changed (Fig. 8). A total bone loss of 10% resulted in a 0.5% decrease in stress of the bone and a 3.4% increase in stress on the nail jacket. Given a 10% loss in bone elastic modulus, this equates to a 4.7% loss in BMD for trabecular bone, or a 5.1% loss in BMD for cortical bone.
4.
Fig. 7 – A simulated gait load was modeled by applying an axial force to the calcaneus and load sharing characteristics were studied. The bone was observed to carry higher loads in comparison with the nail jacket throughout the gait simulation.
Discussion
This study set forth to develop a mechanical analysis model to achieve two main objectives: simulate the operation of a compression generating IM nail; and use the model to both investigate the operation of the device during simulated gait loading and quantify load-sharing changes as a function of
Fig. 8 – During static compression generated from the NiTi rod, the effect of bone quality was studied. Bone elastic modulus values were varied and stress values at the distal tibia diaphysis level were measured for the bone and nail.
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bone quality. It can be seen from the results of modeling the NiTi rod that the material behavior was successfully activated within the device and then programmed while inside a simulated bone block. Deviation between the NiTi model and experimental material response exists during phase transition regions (Fig. 3); however, for this study, the material response after the programmed state is of primary importance. During the pseudoelastic recovery on the unloading plateau, the computational model represents the NiTi material unloading and reloading response closely. Referencing Fig. 4, there is an apparent stress gradient when looking at bone in between the two locking screw attachment points (proximal tibia, mid-calcaneus) and the other bone sections. Compression in the bone was generated internally from the NiTi rod, since the only other external forces were due to the pin condition at the proximal end of the system. A similar behavior was observed when the device was modeled within a human bone. The use of a cadaver specimen allowed anatomical geometry to be obtained and patient-specific bone quality parameters to be established. In QCT-based FE modeling, the assignment of bone material properties can have a large influence on the results. In an attempt to maintain bone quality accuracy, voxel-based calibration using the reference phantom throughout the length of the scan was used to avoid beam-hardening effects, and well-established relationships between QCT-based BMD and bone properties were used (Keyak et al., 2005). With the anatomical bone and programmed device combined into one model, stresses were shown to be concentrated in between the proximal tibia screws and the proximal calcaneus screw as can be seen in Fig. 6. Relative levels of stress were computed for the tibia and talus bones and gave insight to areas of high stress and also stress-sharing characteristics of the bones. Von Mises stress levels observed in the model due to static compression were far below the stress levels needed to cause bone failure or damage. During static loading from the internal compression of the nail, it was observed that compression was on the medial side of the tibia, whereas a small amount of tension was on the lateral side. This would suggest a bending moment as can been seen in Fig. 6A. The opposite can be seen in the calcaneus, where there is compression on the lateral side and tension on the medial side. When the device is activated, the NiTi rod contracts and the three TTC bones are compressed together. Due to the geometry of the talus, the applied compression results in a bending moment, causing a medial-to-lateral change in compression between the calcaneus and the tibia. Additionally, there were axial compression and bending loads observed within the nail jacket. Axial compression was developed because of load transfer from bone segments that were in contact normal to the nail jacket surface as well as regions on bone entering the axial slots for the locking screws. The latter was assumed to occur in patients once fusion developed and bone growth occurred in these regions. Using a simulated gait load, results indicated a higher load borne by the bone rather than the device throughout a full gait cycle. Stress shielding occurs in many different orthopedic applications and is commonly known as a factor resulting
in a failed device (Huiskes et al., 1992). Stress shielding has also been documented as a factor to decrease overall BMD in retained tibial IM nails (Allen et al., 2008). Additionally, a complication with TTC fusion procedures is the necessity to remove the IM nail after fusion to relieve patient pain caused by implant loosening due to stress shielding. With the results presented in this study, it appears this device allows more evenly distributed loading between the bone and device during gait loading. This suggests that the device could potentially help reduce stress shielding and maintain compression across the fusion site. Patient-specific analysis could be applied to this modeling technique by modifying the gait load. One method that could be followed is to gather gait characteristic data from a patient post surgery and scale the analysis loading based upon body weight. Variation in bone quality showed a system response of stresses shifting to the nail when bone modulus levels were decreased. For a bone modulus loss, the given percent increase in stress for the nail was larger than the given percent increase in stress for the bone, indicating that the stress does not evenly transfer between the regions during bone loss. One potential explanation for this behavior is that, as the bone density decreases, there is a larger relative decrease in cortical bone modulus, making a decrease in overall bone quality more influential to the cortical compartment. The cortex will inherently carry higher loads due to its relative stiffness and will transfer those loads to the nail. Studying the effects of varied bone quality can offer understanding of how the system will react with patients of lower or higher bone quality. Many TTC fusion procedures are either salvage or revision procedures, where the patient has been immobile for extended periods of time, potentially leading to decreased bone quality. As the patient recovers and begins reambulation, it is likely that changes in BMD will occur throughout the lower limb. In this situation, forces due to walking would be expected to shift from the nail to the bone as BMD increases. A recent clinical study on the DynaNail demonstrated encouraging early results (Hsu et al., 2015), but additional longitudinal measurements are needed to monitor temporal changes in BMD. By providing a quantitative analysis of the mechanical implications of changing BMD, a longitudinal clinical study could be augmented with the new modeling framework presented here. While this study achieved the aims of accurately simulating NiTi behavior, investigating load sharing during simulated gait, and revealing the effects of altered bone quality, the study had some limitations. First, the FE nodes on the articulating surfaces of the three bones were tied together, disallowing sliding contact between the bones. Prior to bone fusion in a real patient, micro-motion is expected to occur between the bone-to-bone surfaces. Therefore, this study simulated a presumed “fused” bone-to-bone connection. Further modeling could investigate the contact pressures as well as relative movement of the bone-to-bone surfaces to help determine what levels are appropriate for a bone fusion environment. The contact between the nail jacket and bone could also be investigated if modified to include friction. It was assumed that since the outer finish of the device is manufactured smoothed and polished, any interstitial fluid present between the nail and bone would produce friction
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force magnitudes negligible in comparison to stresses present in the model. Tetrahedral elements were selected for modeling because of their ability to fit complex shapes of bone anatomy. Since meshing was performed simultaneously for bone and device, varying element type for meshing the model was not considered. However, the use of tetrahedral elements leads to some considerations. For example, using tetrahedral elements to mesh a cylindrical component does not allow for a direct axial strain within the elements. This resulted in slight bending upon contraction of the NiTi rod and led to a small bending moment in the simplified block model. It should be noted that the bending moment experienced in the patient-specific model was largely caused by the asymmetric geometry of the bone. Furthermore, even though frictionless contact was assumed, the shape of the tetrahedral elements allows the transfer of force along the interface of the bone and nail jacket. These limitations were considered in meshing decisions, but the use of tetrahedral elements more accurately represented the geometry of the device and bone compared to other options such as hexahedral elements. The presented method of programming NiTi for sustained compression using locking elements differs from the clinical environment. In practice, the NiTi rod would be secured at the proximal end using a setscrew and would undergo stretching and partial release from the distal end (Fig. 2); however, in our model we programed the NiTi by constraining the NiTi at the distal end and performing the stretchrelease steps at the proximal end (Fig. 4). Once the material was programmed correctly, locking elements (shown as bright red in Fig. 4 “Locking Elements” inset) were used to link the NiTi rod to the nail jacket in lieu of the setscrew. The locking elements that were manually added could experience extreme distortion in situations where the element size is small. In this case, using hexahedral elements could potentially remedy the situation. The relatively large strains observed in this study for the locking elements could result in distortion and provide inaccurate results. However, the sole purpose of the locking material was to allow the NiTi rod to be programmed and locked, such that loads are transferred to the nail jacket. The region of high distortion surrounding the locking elements was very localized, and realistic stress and strain levels were computed throughout the remainder of the model. This study used a cadaver specimen from a donor of relatively normal weight (180 lb), whereas TTC arthrodesis patients are often overweight. Differences in bone geometry as well as bone mineral distribution could exist for overweight patients. Furthermore, this study was limited to a single bone preparation style but geometry of bones and bone positioning can vary with patient needs and surgeon preference. Modeling the bone loss as an overall percent loss throughout all bone regions might not capture the spatiallyvarying effects of bone loss seen clinically. Bone quality has been seen to vary differently between cortical and trabecular regions when measuring disuse-related bone loss (Martin, 1984). Due to the higher surface area available for bone resorption, trabecular bone loses a higher fraction of BMD when compared with the cortical shell, as shown by
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Carpenter et al. (2010) in microgravity situations (similar to decreased levels of loading on Earth). Lastly, the relative magnitudes for normal gait loading were gathered from a healthy patient without a TTC fusion. Modification to the anatomy of the ankle and side-favored walking patterns pre-surgery could undoubtedly change the gait load. Application of the gait loading was also assumed to act directly axial to the nail device. A more realistic load would change location during gait such as during the heel strike the load would be applied at the posterior calcaneus and shift anteriorly as gait progresses. By applying the load axially, this study did not take into account increased bending stresses from the moment created from a heal strike. Moreover, this study did not investigate the effects of soft tissue and muscles surrounding the joint construct, which may have an effect on the load sharing. These key anatomical features could be included in future work to more accurately represent the joint environment. Future work can also be performed experimentally to validate the computational model presented in this study. Cadaveric testing has previously been used to show compression levels in two other IM devices and the methodology can be directly applied to this device (Yakacki et al., 2010). In summary, this study successfully modeled a device with a pseudoelastic NiTi rod that can be activated to apply compression across a long range of strains. The device was simulated within a human bone model that possessed patient-specific material assignment. Effects of bone quality and gait loading were also studied. Findings of this study suggest that the DynaNail device can maintain compression across the fusion site under conditions of bone loss. The results also showed that, by sharing gait-generated loads with the surrounding bone, the device has the potential to help decrease the incidence of bone loss due to stress shielding. The methodology used in this study can aid in further investigation of TTC arthrodesis and the accompanying devices. Furthermore, the simulation procedure can be applied to any other device (e.g. fracture fixation devices or other arthrodesis devices) that utilizes the pseudoelastic material behavior of NiTi to apply constant compression across a bone–bone interface. With this tool, investigations of the bone and device interactions in these procedures can lead to a better understanding of the fusion and healing process of bone.
5.
Conclusions
1. A finite element model can be used to simulate nickel titanium's pseudoelastic behavior within an intramedullary nail device. This method can be extended to a patientspecific bone model with voxel based material assignment to explore the stress distribution and load-sharing characteristics in a tibio-talo-calcaneal (TTC) fusion construct. 2. Gait loading was applied to an anatomic TTC bone model and showed an initial compression from the device of 350 N. Load borne by the bone was 50% higher than load borne by the nail during maximum loading in gait.
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3. An overall decrease in bone modulus values of 10% resulted in an increase of stress within the nail of 3.4% while a decrease in stress of 0.5% occurred in the bone.
Acknowledgments Research reported in this publication was supported by the National Institute of Arthritis and Musculoskeletal and Skin Diseases of the National Institutes of Health under Award number R21AR065713. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. The authors would like to thank MedShape, Inc. for providing the CAD files for the DynaNail device in this study as well as Vasily Buharin for the gait forces during walking. The authors would like to thank Samuel Welch for his advice in modeling the programmed NiTi rod. CMY and DJP have a financial interest in MedShape, Inc.
Appendix A.
Supplementary material
Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jmbbm. 2016.04.037.
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