Computer Methods in Biomechanics and Biomedical Engineering
ISSN: 1025-5842 (Print) 1476-8259 (Online) Journal homepage: http://www.tandfonline.com/loi/gcmb20
Biomechanical comparison of conventional and anatomical calcaneal plates for the treatment of intraarticular calcaneal fractures – a finite element study Bin Yu, Wen-Chuan Chen, Pei-Yuan Lee, Kang-Ping Lin, Kun-Jhih Lin, ChengLun Tsai & Hung-Wen Wei To cite this article: Bin Yu, Wen-Chuan Chen, Pei-Yuan Lee, Kang-Ping Lin, Kun-Jhih Lin, Cheng-Lun Tsai & Hung-Wen Wei (2016): Biomechanical comparison of conventional and anatomical calcaneal plates for the treatment of intraarticular calcaneal fractures – a finite element study, Computer Methods in Biomechanics and Biomedical Engineering, DOI: 10.1080/10255842.2016.1142534 To link to this article: http://dx.doi.org/10.1080/10255842.2016.1142534
Published online: 27 Jan 2016.
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Computer Methods in Biomechanics and Biomedical Engineering, 2016 http://dx.doi.org/10.1080/10255842.2016.1142534
Biomechanical comparison of conventional and anatomical calcaneal plates for the treatment of intraarticular calcaneal fractures – a finite element study Bin Yua, Wen-Chuan Chenb, Pei-Yuan Leec, Kang-Ping Linb,d, Kun-Jhih Linb , Cheng-Lun Tsaib,e and Hung-Wen Weib,f a
Department of Orthopedics and Traumatology, Nanfang Hospital, Southern Medical University, GuangZhou, China; bTechnology Translation Center for Medical Device, Chung Yuan Christian University, Taoyuan, Taiwan; cDepartment of Orthopaedic Surgery, Show Chwan Memorial Hospital, Changhua City, Taiwan; dDepartment of Electrical Engineering, Chung Yuan Christian University, Taoyuan, Taiwan; eDepartment of Biomedical Engineering, Chung Yuan Christian University, Taoyuan, Taiwan; fDepartment of Physical Therapy and Assistive Technology, National Yang-Ming University, Taipei, Taiwan
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ABSTRACT
Initial stability is essential for open reduction internal fixation of intraarticular calcaneal fractures. Geometrical feature of a calcaneal plate is influential to its endurance under physiological load. It is unclear if conventional and pre-contoured anatomical calcaneal plates may exhibit differently in biomechanical perspective. A Sanders’ Type II-B intraarticular calcaneal fracture model was reconstructed to evaluate the effectiveness of calcaneal plates using finite element methods. Incremental vertical joint loads up to 450 N were exerted on the subtalar joint to evaluate the stability and safety of the calcaneal plates and bony structure. Results revealed that the anatomical calcaneal plate model had greater average structural stiffness (585.7 N/mm) and lower von Mises stress on the plate (774.5 MPa) compared to those observed in the conventional calcaneal plate model (stiffness: 430.9 N/mm; stress on plate: 867.1 MPa). Although both maximal compressive and maximal tensile stress and strain were lower in the anatomical calcaneal plate group, greater loads on fixation screws were found (average 172.7 MPa compared to 82.18 MPa in the conventional calcaneal plate). It was noted that high magnitude stress concentrations would occur where the bone plate bridges the fracture line on the lateral side of the calcaneus bone. Sufficient fixation strength at the posterolateral calcaneus bone is important for maintaining subtalar joint load after reduction and fixation of a Sanders’ Type II-B calcaneal fracture. In addition, geometrical design of a calcaneal plate should worth considering for the mechanical safety in practical usage.
Introduction Injury to the calcaneus bone may have an unexpected but great impact to the quality of life. Calcaneal fractures generally result from high-energy impacts to the foot, such as falling from a height. A high prevalence of displaced intraarticular fractures, classified as OTA-82C by the Orthopaedic Trauma Association (Zhang 2009) or the Sanders’ Type II fracture introduced by Sanders et al. (1993), have been reported after fracture of the calcaneal bone. Typical feature of the Sanders’ Type II-B fracture involves one primary fracture line that courses through the central aspect of the posterior facet. Generally, one or more accessory fracture lines will be found in this type of calcaneal fracture without involving the posterior facet. Surgical treatment of the displaced calcaneal fracture is
CONTACT Hung-Wen Wei © 2016 Taylor & Francis
[email protected]
ARTICLE HISTORY
Received 13 April 2015 Accepted 12 January 2016 KEYWORDS
Anatomical calcaneal plate; intraarticular calcaneal fracture; structural stiffness; finite element analysis
more favourable for restoring the stability of the bony structure, with evidence of better postoperative outcome (Buckley & Meek 1992; Benirschke & Sangeorzan 1993; Eastwood et al. 1993). Although controversy over the procedure arose in more recent studies (Kundel et al. 1996; Thordarson & Krieger 1996; Buckley et al. 2002; Howard et al. 2003), a higher rate of disability and morbidity has been reported with conservative treatment (Essex-Lopresti 1952; Illert et al. 2011). The anatomical bone plates, introduced in recent decades with superior conformity between the bone plate and bony structure, may facilitate the operation by reducing the operative time and assisting anatomical reduction. Conventional lateral bone plates for calcaneal fractures are generally designed with thin plates to connect the screw
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Figure 1. Reconstructed solid models of (A) conventional, and (B) anatomical calcaneal plates.
detailed comparisons between conventional and anatomical calcaneal plates have seldom been reviewed. Although better stability and fixation strength can be achieved using anatomical calcaneal plates (Sun et al. 2012), there is little understanding about the biomechanical safety of the implant itself and its influence on bony structures by using anatomical calcaneal plate. The purpose of this study was to evaluate the biomechanical performance of an anatomical calcaneal plate in comparison to a conventional design. Besides investigating the structural stiffness, stress-based analyses were conducted to examine the safety of both the bone plate and bony structure in a virtual Sanders’ type II-B calcaneal fracture.
Materials and methods Figure 2. Solid model of virtual Sanders Type II-B calcaneal fracture with assigned fracture gap of 0.5 mm.
holes (Figure 1(A)). These thin plates are easily bent and manipulated to match the geometry of the bone. As for the anatomical calcaneal plate, a pre-contoured plate body for mimicking the geometrical feature of lateral calcaneal wall has been designed. A closed-loop circumferentially-oriented screw holes are created for fixation against the posterolateral calcaneus bone, while another branch of the bone plate extends towards the anterolateral calcaneus bone for fixation beneath the subtalar joint (Figure 1(B)). Although the pre-contoured calcaneal plate may not perfectly match the practical calcaneal geometry since it is not a custom-made design, lesser time consumption for plate adjustment or bending is required during implantation. Therefore, a further verification for biomechanical performance of the anatomical calcaneal plate design should be considered. Biomechanical stability is of great importance for calcaneal plate fixation. The effect of locking/non-locking plates on structural stiffness, determined by biomechanical tests, has been widely discussed (Redfern et al. 2006; Richter et al. 2006; Blake et al. 2011; Illert et al. 2011). However,
A model of the calcaneal bony structure was reconstructed in Amira 4.1 (Mercury System, MA, United States) from a series of computed tomography images of a healthy subject (male, 69 y/o, right foot, slice thickness: 1.25 mm; with IRB approval by Show Chwan Memorial Hospital, No. 1021004). The reconstructed bone model was imported into CAD software (SolidWorks 2007, Dassault Systèmes SolidWorks Corporation, MA, United States) to create a Sanders’ type II-B calcaneal fracture, with reference to published literature (Blake et al. 2011) and the advice of an experienced orthopaedic surgeon. Three major cuts were made: (1) from midpoint of the anterior facet to the medial calcaneal tuberosity; (2) vertical cut near the angle of Gissane extending from the lateral cortex to the first cut; (3) vertical cut that separates the posterior tuberosity from the posterior facet. A 0.5 mm gap was left between fractured fragments to simulate the status of anatomical reduction after a displaced intraarticular calcaneal fracture (Figure 2). The cortical bone was assigned a thickness of 2 mm (Pang et al. 2014). Solid models of two commercially available calcaneal plates were reconstructed for implantation. Both the conventional plate model (Locking Calcaneal Plate, SYNTHES GmbH, Switzerland; size: extra small; CCP model) and the anatomical calcaneal plate model (Calcaneus TOPUS
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Computer Methods in Biomechanics and Biomedical Engineering
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Figure 3. (A–D) Orientation of cortex screws in medial views and lateral views of CCP and ACP models. Models were meshed for finite element analyses: (E) CCP model, and (F) ACP model. Table 1. Material properties utilized in finite element models (Gefen 2002; Pang et al. 2014). Materials Cortical bone Cancellous bone Titanium alloy
Young’s modulus (MPa) 7,300 100 110,000
Locking Plate, Aplus Biotechnology, Taiwan; size: small; ACP model) were constructed as 2 mm thick and with 15 locking screw holes each. The contour of the CCP model was virtually bent in the CAD software to meet the anatomical geometry of the lateral bone in the calcaneal model. The geometry of the calcaneal plate model has been kept as its original condition without modification in the ACP model. Both of the calcaneal plates were carefully placed by the calcaneus as close as possible without penetration. Fifteen locking cortex screws of identical 3.0 mm in diameter for each model were inserted with adequate screw lengths following instructions from senior orthopaedic surgeons (Figures 3(A)–(D)). The two models were then imported into ANSYS Workbench 11.0 (ANSYS, Inc., PA, United States) for finite element analyses. The screw thread contact points at both the plate-screw and screw-bone interfaces were simplified by assigning bonding features to simulate complete interface fixation. A coefficient of friction of 0.2 (Ni et al. 2015) was assigned between the fractured segments for possible contact after loading, while the contact behavior between the bone and calcaneal plate was assigned as frictionless. The material properties of the finite element models are shown in Table 1 (Gefen 2002; Pang et al. 2014). After fully constraining the posterior end of the calcanues bone (Blake et al. 2011),
Poisson’s ratio 0.3 0.3 0.3
a stepped load from 0 to 450 N (50 N per increment) was vertically exerted at the subtalar joint to evaluate the biomechanical responses of the fixation plates. The elements contained within each model were 88,622 (152,565 nodes) and 84,522 (144,304 nodes) for the CCP and ACP models, determined according to a convergence test of total strain energy (Figures 3(E) and (F)). For determining the structural stiffness of the reconstructed models, vertical displacements along the loading direction at the subtalar joint were recorded. To further evaluate the structural safety, the maximal von Mises stresses on the calcaneal plate and the maximal tensile and compressive stresses/strains on bony structures were compared.
Results Structural stiffness The dash lines in Figure 4 shows greater vertical displacement in the CCP model than the ACP model during the full period of simulation. Average structural stiffness of the full simulated period were 430.9 N/mm for the CCP model and 585.7 N/mm for the ACP model. Inflection of the curve represents the engagement of fracture segments that altered the performance of load-displacement
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during the full simulation period. With the increase of subtalar joint load, increment of stress was declined after the engagement of fracture segments. Stress concentrations can be observed on both calcaneal plates where the plates bridge the fracture line on the lateral side of the calcaneus (Figures 5(A)–(D)). Greater von Mises stresses were found on the calcaneal plate in the CCP model (867.1 MPa) than in the ACP model (774.5 MPa) at the end stage of simulation (subtalar joint load to 450 N).
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Stresses on screws
Figure 4. Diagram representing the correlation of loaddisplacement (dash lines) and load–von Mises stress on the calcaneal plates (solid lines) for CCP and ACP models.
correlation. Calculated structural stiffness before the engagement of fracture segments were 165.8 N/mm for the CCP model and 344.5 N/mm for the ACP model, whilst the magnitudes were increased to 668.5 N/mm for the CCP model and 801.9 N/mm for the ACP model after engagement. Stresses on calcaneal plates The solid lines in Figure 4 shows the maximal von Mises stresses observed in calcaneal plates, where greater magnitude of stress was found in CCP model than in ACP model
Great stresses were found on the screws around the third fracture cut (i.e. vertical cut that separates the posterior tuberosity from the posterior facet) in both models (Figures 5(E) and (F)). Magnitudes of stresses on the screws located at aforementioned area were 121.9– 291.7 MPa in CCP model, and 366.2–524.5 MPa in ACP model. Average value of all 15 screws in CCP and ACP models were respectively 82.18 and 172.7 MPa. Stresses and strains on bones The maximal tensile and compressive stresses and strains of the simulated models are listed in Table 2. High stress and strain were generally concentrated at the bone/screw interface as shown in Figures 6(A)–(D). Engagement of fracture segments occurred in both CCP and ACP models. Greater compressive stress was observed in the CCP model (61.86 MPa) than in the ACP model (20.05 MPa) at the end stage of loading period (450 N) (Figures 6(E) and (F)).
Figure 5. Distributions of (A–D) von Mises stresses on calcaneal plates and (E–F) screws in CCP and ACP models.
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Table 2. The magnitudes of maximal tensile stresses and strains, compressive stresses and strains at cortical and cancellous bones.
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Max. tensile stress (MPa) Max. tensile strain Max. compressive stress (MPa) Max. compressive strain
CCP model Cortical bone 93.34 1.38 × 10−2 97.43 1.65 × 10−2
ACP model
Cancellous bone 18.78 1.97 × 10−1 17.36 1.59 × 10−1
Cortical bone 70.57 9.53 × 10−3 71.05 8.02 × 10−3
Cancellous bone 5.96 5.44 × 10−2 5.29 5.16 × 10−2
Figure 6. Distributions of (A–B) maximal tensile stress of bony structure, (C–D) maximal compressive stress of bony structure, and (E–F) maximal compressive stress at the fracture surface in CCP and ACP models.
Discussion In order to highlight the differences in biomechanical performances with the use of conventional and anatomical calcaneal plates, finite element analyses were conducted with a virtual Sanders’ type II-B calcaneal fracture. The quantified results of this study may provide some useful information to surgeons when choosing a calcaneal plate for fracture fixation. A high prevalence of intraarticular fracture has been reported for calcaneal fractures, ranging from 60 to 79.1% (Sanders et al. 1993; Zhang 2009). Clinical studies which push arguments both for and against the use of open reduction internal fixation for calcaneal fracture have been reported (Buckley & Meek 1992; Benirschke & Sangeorzan 1993; Eastwood et al. 1993; Kundel et al. 1996; Thordarson & Krieger 1996; Buckley et al. 2002; Howard et al. 2003). Orthopaedic trauma treatments generally follow the concept that sufficient initial stability is essential
for fracture reduction. Restoration of heel shape and joint congruity are required for post-operative weight bearing and joint articulation. A cadaveric biomechanical study conducted by Yang et al. (2012) compared the strength of a conventional and custom anatomical calcaneal plate for the fixation of Sanders’ Type III fracture. With a high magnitude of cyclic loading, the anatomical design produced a 17% lower permanent displacement and showed a greater capacity for elastic displacement and a greater maximal structural strength. The results in this current finite element study showed the ACP to have structural stiffness 108% (before engagement of fracture segments) and 20% (after engagement of fracture segments) greater than the CCP model, which indicated that structural stability after fracture reduction can be better maintained by the anatomical calcaneal plate. The enhanced stiffness may be due to the circumferential fixation at the posterolateral calcaneus bone, which can provide better fixation
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strength to support the load exerted at the subtalar joint. Also the branch of the bone plate extending towards the anterolateral calcaneus bone in the ACP model is wider than that of the CCP model, thus offering greater resistance to bending moments. There is no definitive consensus on the use of locking or non-locking plate for the fixation of calcaneal fractures. A comparative study by Blake et al. (2011) did not turn up any obvious advantages of using locking screws for treating a Sanders’ Type II-B calcaneal fracture, which has been echoed by Redfern et al. (2006) in their study that did not find any statistical difference between the two groups. Although the differences were insignificant, most studies support that locking screws may still offer greater initial stability than non-locking screws (Redfern et al. 2006; Blake et al. 2011; Illert et al. 2011), for both uniaxial or polyaxial locking screws (Richter et al. 2006). To avoid potential conflicts when comparing the results, all screws utilized in this current study have been assigned as locking screws and were simulated with an identical diameter (3.0 mm). The calculated average structural stiffness for the CCP model was 430.9 N/mm, which is similar to the results (445.7 ± 148.8 N/mm for locking calcaneal plate) reported by Blake et al. (2011), while a greater structural stiffness was represented in ACP model. Referring to the further investigation in current study, the calcaneal plate in ACP model has shown superior capability in subtalar joint load bearing before the engagement of fracture segments. Difference in structural stiffness between CCP and ACP models was reduced after the engagement of fracture segments (Figure 3) since the bony structure plays a role of stabilizer and has shared the load from the calcaneal plate. Stress-based analyses in orthopaedic biomechanics may provide useful data to surgeons for choosing an appropriate implant. The stress magnitude is related to the safety of the structure under the given loading condition. A maximal load of 450 N was exerted vertically on the subtalar joint in this study. The results revealed that the von Mises stress on the calcaneal plate in the CCP model was 11% greater than in the ACP model. Obvious stress concentrations could be found at the anterior branch extending across the fracture line in both models (Figures 5(A)– (D)). As mentioned previously, the width of the extending branch in the CCP model is smaller than that of the ACP model. An insufficient capability to resist loading can possibly jeopardize the safety. Specifically, the mechanical strength of the plate branch is particularly important once the plate is placed across the fracture line, as shown in this study. On the other hand, the magnitude of stress on screw could be primarily influenced by their inserting locations but less by the screw length in current simulation. Stresses observed on screws that close to the fracture line were greater than those away from the fracture line in both
CCP and ACP models (Figures 5(E) and (F)). In current study, screw stresses found in both CCP and ACP models, which may be resulted from the smaller diameter of screw utilized and the worse stability of the fracture model, were higher than the discovery by Ni et al. (2015). Besides, the average screw stress and stresses on screws surrounding the fracture line were greater in the ACP model than in the CCP model. Although that greater structural stability can be maintained by the ACP model in current simulation, greater screw stress observed in the ACP model implies that screws may suffer from the risk of mechanical failure or reduced fatigue life during dynamic physical forces. Due to the simulated results in current study has not been well validated by practical biomechanical tests, the value of stress itself cannot be utilized to concisely predict the implant failure and fatigue performance under the given physical loads. Nevertheless, the comparative result may represent that screw failure shall not occur before the failure of calcaneal plates in both CCP and ACP models since the magnitude of stress on screws were lower than that of calcaneal plates. In addition, the contour of the commercial calcaneal plate was bent to match the anatomical geometry of the bone during surgery, rather than having a pre-contoured anatomical design. Possible residual stress after bending would also reduce the fatigue strength. Stress and strain on bony structures, which is difficult to validate by general mechanical testing, is often used to predict potential screw loosening and bone failure. Higher magnitudes of stress or strain on the bones may increase the risk of failure. Due to that the fracture pattern, implant utility, loading and boundary condition in current study were different from the previous finite element study, adequate comparison of the reported stress and strain on bony structure were not available. According to the results of this study, both of the maximal tensile/compressive stress and strain on the bony structures in CCP model were higher than those in ACP model (Table 2, Figure 6). For reducing the possible factor that would be influential to comparison of biomechanical effect of calcaneal plate design, all screws were assign by identical diameter (3.0 mm). Thus the greater stress/strain on the bony structure in CCP model may reflect that the ideal orientation of the screws was not achieved. Insufficient plate strength may also lead to an inadequate biomechanical environment for weight bearing. Furthermore, the strength of calcaneal plate in CCP model may be weaker so that a greater compressive stress on the contact surface in CCP model was found than the ACP model after the engagement of fracture segments (Figures 6(E) and (F)). However, the loading and boundary conditions in this current study were referenced from biomechanical tests reported by Blake et al. (2011), whereby the posterior end of the calcaneus bone is rigidly fixed and a vertical
Computer Methods in Biomechanics and Biomedical Engineering
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load is exerted on the subtalar joint. Certain experimental settings without additional stabilizing factors (e.g. muscle, ligament, skin, plantar fascia, etc.) may be taken as a comparatively worse status for determining the biomechanical performance after reduction of calcaneal fracture. Therefore, determination of instability in CCP model may be moderately magnified in this study. Some other limitations of this study should be noted: (1) Only finite element analyses have been performed, with assumed homogenous, isotropic, and linear elastic material properties. These results may offer guidance for predicting the outcome of biomechanical tests. However, a practical biomechanical test is essential for a complete validation of the models applied in this study. (2) A complete finite element model of the foot has not been reconstructed for this study. Full foot models are generally utilized in studies for insole design and soft tissue injury/response (Cheng et al. 2008; Hsu et al. 2008; Sun et al. 2012). This study ignored the stabilizing factors offered by surrounding soft tissues, similar to previous biomechanical tests (Blake et al. 2011). Disparities in the results obtained may be reduced if a full foot model was used for computational simulation. (3) Identical titanium alloy material properties were assigned to both calcaneal plate models to ease comparison. (4) The possible influence of bone quality was not considered in this study. Information obtained from the results may not be directly applied to clinical osteoporotic cases without further verification. (5) Individual differences in bony structure cannot be analyzed/compared since the bony model was reconstructed from only one subject. Although the Sanders’ Type II-B fracture of the calcaneus bone was confirmed by an orthopaedic surgeon, an expanded study with a larger representative population may be required.
Conclusion In summary, this study details the biomechanical effect of an anatomical calcaneal plate and a conventional calcaneal plate on both implants and bony structures. Circumferential fixation at the posterolateral calcaneus can provide sufficient stability to sustain subtalar joint loading after reduction and fixation of a Sanders’ Type II-B calcaneal fracture. The mechanical strength of the calcaneal
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plate is very important if the plate bridges the fracture line, and this point should be considered in the plate’s design.
Disclosure statement No potential conflict of interest was reported by the authors.
ORCID Kun-Jhih Lin
http://orcid.org/0000-0002-2704-1828
References Benirschke SK, Sangeorzan BJ. 1993. Extensive intraarticular fractures of the foot. Surgical management of calcaneal fractures. Clin Orthop Relat Res. 292:128–134. Blake MH, Owen JR, Sanford TS, Wayne JS, Adelaar RS. 2011. Biomechanical evaluation of a locking and nonlocking reconstruction plate in an osteoporotic calcaneal fracture model. Foot Ankle Int. 32:432–436. Buckley RE, Meek RN. 1992. Comparison of open versus closed reduction of intraarticular calcaneal fractures. J Orthop Trauma. 6:216–222. Buckley R, Tough S, McCormack R, Pate G, Leighton R, Petrie D, Galpin R. 2002. Operative compared with nonoperative treatment of displaced intra-articular calcaneal fractures: a prospective, randomized, controlled multicenter trial. J Bone Joint Surg Am. 84-A:1733–1744. Cheng HY, Lin CL, Wang HW, Chou SW. 2008. Finite element analysis of plantar fascia under stretch – the relative contribution of windlass mechanism and Achilles tendon force. J Biomech. 41:1937–1944. Eastwood DM, Langkamer VG, Atkins RM. 1993. Intraarticular fractures of the calcaneum. Part II: open reduction and internal fixation by the extended lateral transcalcaneal approach. J Bone Joint Surg Br. 75:189–195. Essex-Lopresti P. 1952. The mechanism, reduction technique, and results in fractures of the os calcis. Br J Surg. 39:395– 419. Gefen A. 2002. Stress analysis of the standing foot following surgical plantar fascia release. J Biomech. 35:629–637. Howard JL, Buckley R, McCormack R, Pate G, Leighton R, Petrie D, Galpin R. 2003. Complications following management of displaced intra-articular calcaneal fractures: a prospective randomized trial comparing open reduction internal fixation with nonoperative management. J Orthop Trauma. 17:241–249. Hsu YC, Gung YW, Shih SL, Feng CK, Wei SH, Yu CH, Chen CS. 2008. Using an optimization approach to design an insole for lowering plantar fascia stress – a finite element study. Ann Biomed Eng. 36(8):1345–1352. Illert T, Rammelt S, Drewes T, Grass R, Zwipp H. 2011. Stability of locking and non-locking plates in an osteoporotic calcaneal fracture model. Foot Ankle Int. 32:307–313. Kundel K, Funk E, Brutcher M, Bickel R. 1996. Calcaneal fractures: operative versus nonoperative treatment. J Trauma. 41:839–845. Ni M, Weng XH, Mei J, Niu WX. 2015. Primary stability of absorbable screw fixation for intra-articular calcaneal fractures: a finite element analysis. J Med Biol Eng. 35: 236– 241.
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B. Yu et al.
Downloaded by [134.117.10.200] at 03:19 01 February 2016
Pang QJ, Yu X, Guo ZH. 2014. The sustentaculum tali screw fixation for the treatment of Sanders type II calcaneal fracture: a finite element analysis. Pak J Med Sci. 30:1099– 1103. Redfern DJ, Oliveira ML, Campbell JT, Belkoff SM. 2006. A biomechanical comparison of locking and nonlocking plates for the fixation of calcaneal fractures. Foot Ankle Int. 27:196–201. Richter M, Droste P, Goesling T, Zech S, Krettek C. 2006. Polyaxially-locked plate screws increase stability of fracture fixation in an experimental model of calcaneal fracture. J Bone Joint Surg Br. 88-B:1257–1263. Sanders R, Fortin P, DiPasquale T, Walling A. 1993. Operative treatment in 120 displaced intraarticular calcaneal fractures. Results using a prognostic computed tomography scan classification. Clin Orthop Relat Res. 290:87–95.
Sun PC, Shih SL, Chen YL, Hsu YC, Yang RC, Chen CS. 2012. Biomechanical analysis of foot with different foot arch heights: a finite element analysis. Comput Methods Biomech Biomed Eng. 15:563–569. Thordarson DB, Krieger LE. 1996. Operative vs. nonoperative treatment of intra-articular fractures of the calcaneus: a prospective randomized trial. Foot Ankle Int. 17:2–9. Yang C, Wang H, Wu Z, Chen W, Zhang Q, Xu G, Chen Z, Chang Y. 2012. A biomechanical comparison of calcaneal anatomical plate and compression bolts versus conventional AO plate in fixation of Sanders type III calcaneus fractures. Chin J Orthop Trauma. 14:669–674. Zhang Y. 2009. Clinical epidemiology of traumatic orthopaedics. Beijing, China: People’s Medical Publishing House; p. 455–468.
ISSN: 1025-5842 (Print) 1476-8259 (Online) Journal homepage: http://www.tandfonline.com/loi/gcmb20
Biomechanical comparison of conventional and anatomical calcaneal plates for the treatment of intraarticular calcaneal fractures – a finite element study Bin Yu, Wen-Chuan Chen, Pei-Yuan Lee, Kang-Ping Lin, Kun-Jhih Lin, ChengLun Tsai & Hung-Wen Wei To cite this article: Bin Yu, Wen-Chuan Chen, Pei-Yuan Lee, Kang-Ping Lin, Kun-Jhih Lin, Cheng-Lun Tsai & Hung-Wen Wei (2016): Biomechanical comparison of conventional and anatomical calcaneal plates for the treatment of intraarticular calcaneal fractures – a finite element study, Computer Methods in Biomechanics and Biomedical Engineering, DOI: 10.1080/10255842.2016.1142534 To link to this article: http://dx.doi.org/10.1080/10255842.2016.1142534
Published online: 27 Jan 2016.
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Date: 01 February 2016, At: 03:19
Computer Methods in Biomechanics and Biomedical Engineering, 2016 http://dx.doi.org/10.1080/10255842.2016.1142534
Biomechanical comparison of conventional and anatomical calcaneal plates for the treatment of intraarticular calcaneal fractures – a finite element study Bin Yua, Wen-Chuan Chenb, Pei-Yuan Leec, Kang-Ping Linb,d, Kun-Jhih Linb , Cheng-Lun Tsaib,e and Hung-Wen Weib,f a
Department of Orthopedics and Traumatology, Nanfang Hospital, Southern Medical University, GuangZhou, China; bTechnology Translation Center for Medical Device, Chung Yuan Christian University, Taoyuan, Taiwan; cDepartment of Orthopaedic Surgery, Show Chwan Memorial Hospital, Changhua City, Taiwan; dDepartment of Electrical Engineering, Chung Yuan Christian University, Taoyuan, Taiwan; eDepartment of Biomedical Engineering, Chung Yuan Christian University, Taoyuan, Taiwan; fDepartment of Physical Therapy and Assistive Technology, National Yang-Ming University, Taipei, Taiwan
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ABSTRACT
Initial stability is essential for open reduction internal fixation of intraarticular calcaneal fractures. Geometrical feature of a calcaneal plate is influential to its endurance under physiological load. It is unclear if conventional and pre-contoured anatomical calcaneal plates may exhibit differently in biomechanical perspective. A Sanders’ Type II-B intraarticular calcaneal fracture model was reconstructed to evaluate the effectiveness of calcaneal plates using finite element methods. Incremental vertical joint loads up to 450 N were exerted on the subtalar joint to evaluate the stability and safety of the calcaneal plates and bony structure. Results revealed that the anatomical calcaneal plate model had greater average structural stiffness (585.7 N/mm) and lower von Mises stress on the plate (774.5 MPa) compared to those observed in the conventional calcaneal plate model (stiffness: 430.9 N/mm; stress on plate: 867.1 MPa). Although both maximal compressive and maximal tensile stress and strain were lower in the anatomical calcaneal plate group, greater loads on fixation screws were found (average 172.7 MPa compared to 82.18 MPa in the conventional calcaneal plate). It was noted that high magnitude stress concentrations would occur where the bone plate bridges the fracture line on the lateral side of the calcaneus bone. Sufficient fixation strength at the posterolateral calcaneus bone is important for maintaining subtalar joint load after reduction and fixation of a Sanders’ Type II-B calcaneal fracture. In addition, geometrical design of a calcaneal plate should worth considering for the mechanical safety in practical usage.
Introduction Injury to the calcaneus bone may have an unexpected but great impact to the quality of life. Calcaneal fractures generally result from high-energy impacts to the foot, such as falling from a height. A high prevalence of displaced intraarticular fractures, classified as OTA-82C by the Orthopaedic Trauma Association (Zhang 2009) or the Sanders’ Type II fracture introduced by Sanders et al. (1993), have been reported after fracture of the calcaneal bone. Typical feature of the Sanders’ Type II-B fracture involves one primary fracture line that courses through the central aspect of the posterior facet. Generally, one or more accessory fracture lines will be found in this type of calcaneal fracture without involving the posterior facet. Surgical treatment of the displaced calcaneal fracture is
CONTACT Hung-Wen Wei © 2016 Taylor & Francis
[email protected]
ARTICLE HISTORY
Received 13 April 2015 Accepted 12 January 2016 KEYWORDS
Anatomical calcaneal plate; intraarticular calcaneal fracture; structural stiffness; finite element analysis
more favourable for restoring the stability of the bony structure, with evidence of better postoperative outcome (Buckley & Meek 1992; Benirschke & Sangeorzan 1993; Eastwood et al. 1993). Although controversy over the procedure arose in more recent studies (Kundel et al. 1996; Thordarson & Krieger 1996; Buckley et al. 2002; Howard et al. 2003), a higher rate of disability and morbidity has been reported with conservative treatment (Essex-Lopresti 1952; Illert et al. 2011). The anatomical bone plates, introduced in recent decades with superior conformity between the bone plate and bony structure, may facilitate the operation by reducing the operative time and assisting anatomical reduction. Conventional lateral bone plates for calcaneal fractures are generally designed with thin plates to connect the screw
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Figure 1. Reconstructed solid models of (A) conventional, and (B) anatomical calcaneal plates.
detailed comparisons between conventional and anatomical calcaneal plates have seldom been reviewed. Although better stability and fixation strength can be achieved using anatomical calcaneal plates (Sun et al. 2012), there is little understanding about the biomechanical safety of the implant itself and its influence on bony structures by using anatomical calcaneal plate. The purpose of this study was to evaluate the biomechanical performance of an anatomical calcaneal plate in comparison to a conventional design. Besides investigating the structural stiffness, stress-based analyses were conducted to examine the safety of both the bone plate and bony structure in a virtual Sanders’ type II-B calcaneal fracture.
Materials and methods Figure 2. Solid model of virtual Sanders Type II-B calcaneal fracture with assigned fracture gap of 0.5 mm.
holes (Figure 1(A)). These thin plates are easily bent and manipulated to match the geometry of the bone. As for the anatomical calcaneal plate, a pre-contoured plate body for mimicking the geometrical feature of lateral calcaneal wall has been designed. A closed-loop circumferentially-oriented screw holes are created for fixation against the posterolateral calcaneus bone, while another branch of the bone plate extends towards the anterolateral calcaneus bone for fixation beneath the subtalar joint (Figure 1(B)). Although the pre-contoured calcaneal plate may not perfectly match the practical calcaneal geometry since it is not a custom-made design, lesser time consumption for plate adjustment or bending is required during implantation. Therefore, a further verification for biomechanical performance of the anatomical calcaneal plate design should be considered. Biomechanical stability is of great importance for calcaneal plate fixation. The effect of locking/non-locking plates on structural stiffness, determined by biomechanical tests, has been widely discussed (Redfern et al. 2006; Richter et al. 2006; Blake et al. 2011; Illert et al. 2011). However,
A model of the calcaneal bony structure was reconstructed in Amira 4.1 (Mercury System, MA, United States) from a series of computed tomography images of a healthy subject (male, 69 y/o, right foot, slice thickness: 1.25 mm; with IRB approval by Show Chwan Memorial Hospital, No. 1021004). The reconstructed bone model was imported into CAD software (SolidWorks 2007, Dassault Systèmes SolidWorks Corporation, MA, United States) to create a Sanders’ type II-B calcaneal fracture, with reference to published literature (Blake et al. 2011) and the advice of an experienced orthopaedic surgeon. Three major cuts were made: (1) from midpoint of the anterior facet to the medial calcaneal tuberosity; (2) vertical cut near the angle of Gissane extending from the lateral cortex to the first cut; (3) vertical cut that separates the posterior tuberosity from the posterior facet. A 0.5 mm gap was left between fractured fragments to simulate the status of anatomical reduction after a displaced intraarticular calcaneal fracture (Figure 2). The cortical bone was assigned a thickness of 2 mm (Pang et al. 2014). Solid models of two commercially available calcaneal plates were reconstructed for implantation. Both the conventional plate model (Locking Calcaneal Plate, SYNTHES GmbH, Switzerland; size: extra small; CCP model) and the anatomical calcaneal plate model (Calcaneus TOPUS
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Figure 3. (A–D) Orientation of cortex screws in medial views and lateral views of CCP and ACP models. Models were meshed for finite element analyses: (E) CCP model, and (F) ACP model. Table 1. Material properties utilized in finite element models (Gefen 2002; Pang et al. 2014). Materials Cortical bone Cancellous bone Titanium alloy
Young’s modulus (MPa) 7,300 100 110,000
Locking Plate, Aplus Biotechnology, Taiwan; size: small; ACP model) were constructed as 2 mm thick and with 15 locking screw holes each. The contour of the CCP model was virtually bent in the CAD software to meet the anatomical geometry of the lateral bone in the calcaneal model. The geometry of the calcaneal plate model has been kept as its original condition without modification in the ACP model. Both of the calcaneal plates were carefully placed by the calcaneus as close as possible without penetration. Fifteen locking cortex screws of identical 3.0 mm in diameter for each model were inserted with adequate screw lengths following instructions from senior orthopaedic surgeons (Figures 3(A)–(D)). The two models were then imported into ANSYS Workbench 11.0 (ANSYS, Inc., PA, United States) for finite element analyses. The screw thread contact points at both the plate-screw and screw-bone interfaces were simplified by assigning bonding features to simulate complete interface fixation. A coefficient of friction of 0.2 (Ni et al. 2015) was assigned between the fractured segments for possible contact after loading, while the contact behavior between the bone and calcaneal plate was assigned as frictionless. The material properties of the finite element models are shown in Table 1 (Gefen 2002; Pang et al. 2014). After fully constraining the posterior end of the calcanues bone (Blake et al. 2011),
Poisson’s ratio 0.3 0.3 0.3
a stepped load from 0 to 450 N (50 N per increment) was vertically exerted at the subtalar joint to evaluate the biomechanical responses of the fixation plates. The elements contained within each model were 88,622 (152,565 nodes) and 84,522 (144,304 nodes) for the CCP and ACP models, determined according to a convergence test of total strain energy (Figures 3(E) and (F)). For determining the structural stiffness of the reconstructed models, vertical displacements along the loading direction at the subtalar joint were recorded. To further evaluate the structural safety, the maximal von Mises stresses on the calcaneal plate and the maximal tensile and compressive stresses/strains on bony structures were compared.
Results Structural stiffness The dash lines in Figure 4 shows greater vertical displacement in the CCP model than the ACP model during the full period of simulation. Average structural stiffness of the full simulated period were 430.9 N/mm for the CCP model and 585.7 N/mm for the ACP model. Inflection of the curve represents the engagement of fracture segments that altered the performance of load-displacement
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during the full simulation period. With the increase of subtalar joint load, increment of stress was declined after the engagement of fracture segments. Stress concentrations can be observed on both calcaneal plates where the plates bridge the fracture line on the lateral side of the calcaneus (Figures 5(A)–(D)). Greater von Mises stresses were found on the calcaneal plate in the CCP model (867.1 MPa) than in the ACP model (774.5 MPa) at the end stage of simulation (subtalar joint load to 450 N).
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Stresses on screws
Figure 4. Diagram representing the correlation of loaddisplacement (dash lines) and load–von Mises stress on the calcaneal plates (solid lines) for CCP and ACP models.
correlation. Calculated structural stiffness before the engagement of fracture segments were 165.8 N/mm for the CCP model and 344.5 N/mm for the ACP model, whilst the magnitudes were increased to 668.5 N/mm for the CCP model and 801.9 N/mm for the ACP model after engagement. Stresses on calcaneal plates The solid lines in Figure 4 shows the maximal von Mises stresses observed in calcaneal plates, where greater magnitude of stress was found in CCP model than in ACP model
Great stresses were found on the screws around the third fracture cut (i.e. vertical cut that separates the posterior tuberosity from the posterior facet) in both models (Figures 5(E) and (F)). Magnitudes of stresses on the screws located at aforementioned area were 121.9– 291.7 MPa in CCP model, and 366.2–524.5 MPa in ACP model. Average value of all 15 screws in CCP and ACP models were respectively 82.18 and 172.7 MPa. Stresses and strains on bones The maximal tensile and compressive stresses and strains of the simulated models are listed in Table 2. High stress and strain were generally concentrated at the bone/screw interface as shown in Figures 6(A)–(D). Engagement of fracture segments occurred in both CCP and ACP models. Greater compressive stress was observed in the CCP model (61.86 MPa) than in the ACP model (20.05 MPa) at the end stage of loading period (450 N) (Figures 6(E) and (F)).
Figure 5. Distributions of (A–D) von Mises stresses on calcaneal plates and (E–F) screws in CCP and ACP models.
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Table 2. The magnitudes of maximal tensile stresses and strains, compressive stresses and strains at cortical and cancellous bones.
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Max. tensile stress (MPa) Max. tensile strain Max. compressive stress (MPa) Max. compressive strain
CCP model Cortical bone 93.34 1.38 × 10−2 97.43 1.65 × 10−2
ACP model
Cancellous bone 18.78 1.97 × 10−1 17.36 1.59 × 10−1
Cortical bone 70.57 9.53 × 10−3 71.05 8.02 × 10−3
Cancellous bone 5.96 5.44 × 10−2 5.29 5.16 × 10−2
Figure 6. Distributions of (A–B) maximal tensile stress of bony structure, (C–D) maximal compressive stress of bony structure, and (E–F) maximal compressive stress at the fracture surface in CCP and ACP models.
Discussion In order to highlight the differences in biomechanical performances with the use of conventional and anatomical calcaneal plates, finite element analyses were conducted with a virtual Sanders’ type II-B calcaneal fracture. The quantified results of this study may provide some useful information to surgeons when choosing a calcaneal plate for fracture fixation. A high prevalence of intraarticular fracture has been reported for calcaneal fractures, ranging from 60 to 79.1% (Sanders et al. 1993; Zhang 2009). Clinical studies which push arguments both for and against the use of open reduction internal fixation for calcaneal fracture have been reported (Buckley & Meek 1992; Benirschke & Sangeorzan 1993; Eastwood et al. 1993; Kundel et al. 1996; Thordarson & Krieger 1996; Buckley et al. 2002; Howard et al. 2003). Orthopaedic trauma treatments generally follow the concept that sufficient initial stability is essential
for fracture reduction. Restoration of heel shape and joint congruity are required for post-operative weight bearing and joint articulation. A cadaveric biomechanical study conducted by Yang et al. (2012) compared the strength of a conventional and custom anatomical calcaneal plate for the fixation of Sanders’ Type III fracture. With a high magnitude of cyclic loading, the anatomical design produced a 17% lower permanent displacement and showed a greater capacity for elastic displacement and a greater maximal structural strength. The results in this current finite element study showed the ACP to have structural stiffness 108% (before engagement of fracture segments) and 20% (after engagement of fracture segments) greater than the CCP model, which indicated that structural stability after fracture reduction can be better maintained by the anatomical calcaneal plate. The enhanced stiffness may be due to the circumferential fixation at the posterolateral calcaneus bone, which can provide better fixation
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strength to support the load exerted at the subtalar joint. Also the branch of the bone plate extending towards the anterolateral calcaneus bone in the ACP model is wider than that of the CCP model, thus offering greater resistance to bending moments. There is no definitive consensus on the use of locking or non-locking plate for the fixation of calcaneal fractures. A comparative study by Blake et al. (2011) did not turn up any obvious advantages of using locking screws for treating a Sanders’ Type II-B calcaneal fracture, which has been echoed by Redfern et al. (2006) in their study that did not find any statistical difference between the two groups. Although the differences were insignificant, most studies support that locking screws may still offer greater initial stability than non-locking screws (Redfern et al. 2006; Blake et al. 2011; Illert et al. 2011), for both uniaxial or polyaxial locking screws (Richter et al. 2006). To avoid potential conflicts when comparing the results, all screws utilized in this current study have been assigned as locking screws and were simulated with an identical diameter (3.0 mm). The calculated average structural stiffness for the CCP model was 430.9 N/mm, which is similar to the results (445.7 ± 148.8 N/mm for locking calcaneal plate) reported by Blake et al. (2011), while a greater structural stiffness was represented in ACP model. Referring to the further investigation in current study, the calcaneal plate in ACP model has shown superior capability in subtalar joint load bearing before the engagement of fracture segments. Difference in structural stiffness between CCP and ACP models was reduced after the engagement of fracture segments (Figure 3) since the bony structure plays a role of stabilizer and has shared the load from the calcaneal plate. Stress-based analyses in orthopaedic biomechanics may provide useful data to surgeons for choosing an appropriate implant. The stress magnitude is related to the safety of the structure under the given loading condition. A maximal load of 450 N was exerted vertically on the subtalar joint in this study. The results revealed that the von Mises stress on the calcaneal plate in the CCP model was 11% greater than in the ACP model. Obvious stress concentrations could be found at the anterior branch extending across the fracture line in both models (Figures 5(A)– (D)). As mentioned previously, the width of the extending branch in the CCP model is smaller than that of the ACP model. An insufficient capability to resist loading can possibly jeopardize the safety. Specifically, the mechanical strength of the plate branch is particularly important once the plate is placed across the fracture line, as shown in this study. On the other hand, the magnitude of stress on screw could be primarily influenced by their inserting locations but less by the screw length in current simulation. Stresses observed on screws that close to the fracture line were greater than those away from the fracture line in both
CCP and ACP models (Figures 5(E) and (F)). In current study, screw stresses found in both CCP and ACP models, which may be resulted from the smaller diameter of screw utilized and the worse stability of the fracture model, were higher than the discovery by Ni et al. (2015). Besides, the average screw stress and stresses on screws surrounding the fracture line were greater in the ACP model than in the CCP model. Although that greater structural stability can be maintained by the ACP model in current simulation, greater screw stress observed in the ACP model implies that screws may suffer from the risk of mechanical failure or reduced fatigue life during dynamic physical forces. Due to the simulated results in current study has not been well validated by practical biomechanical tests, the value of stress itself cannot be utilized to concisely predict the implant failure and fatigue performance under the given physical loads. Nevertheless, the comparative result may represent that screw failure shall not occur before the failure of calcaneal plates in both CCP and ACP models since the magnitude of stress on screws were lower than that of calcaneal plates. In addition, the contour of the commercial calcaneal plate was bent to match the anatomical geometry of the bone during surgery, rather than having a pre-contoured anatomical design. Possible residual stress after bending would also reduce the fatigue strength. Stress and strain on bony structures, which is difficult to validate by general mechanical testing, is often used to predict potential screw loosening and bone failure. Higher magnitudes of stress or strain on the bones may increase the risk of failure. Due to that the fracture pattern, implant utility, loading and boundary condition in current study were different from the previous finite element study, adequate comparison of the reported stress and strain on bony structure were not available. According to the results of this study, both of the maximal tensile/compressive stress and strain on the bony structures in CCP model were higher than those in ACP model (Table 2, Figure 6). For reducing the possible factor that would be influential to comparison of biomechanical effect of calcaneal plate design, all screws were assign by identical diameter (3.0 mm). Thus the greater stress/strain on the bony structure in CCP model may reflect that the ideal orientation of the screws was not achieved. Insufficient plate strength may also lead to an inadequate biomechanical environment for weight bearing. Furthermore, the strength of calcaneal plate in CCP model may be weaker so that a greater compressive stress on the contact surface in CCP model was found than the ACP model after the engagement of fracture segments (Figures 6(E) and (F)). However, the loading and boundary conditions in this current study were referenced from biomechanical tests reported by Blake et al. (2011), whereby the posterior end of the calcaneus bone is rigidly fixed and a vertical
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load is exerted on the subtalar joint. Certain experimental settings without additional stabilizing factors (e.g. muscle, ligament, skin, plantar fascia, etc.) may be taken as a comparatively worse status for determining the biomechanical performance after reduction of calcaneal fracture. Therefore, determination of instability in CCP model may be moderately magnified in this study. Some other limitations of this study should be noted: (1) Only finite element analyses have been performed, with assumed homogenous, isotropic, and linear elastic material properties. These results may offer guidance for predicting the outcome of biomechanical tests. However, a practical biomechanical test is essential for a complete validation of the models applied in this study. (2) A complete finite element model of the foot has not been reconstructed for this study. Full foot models are generally utilized in studies for insole design and soft tissue injury/response (Cheng et al. 2008; Hsu et al. 2008; Sun et al. 2012). This study ignored the stabilizing factors offered by surrounding soft tissues, similar to previous biomechanical tests (Blake et al. 2011). Disparities in the results obtained may be reduced if a full foot model was used for computational simulation. (3) Identical titanium alloy material properties were assigned to both calcaneal plate models to ease comparison. (4) The possible influence of bone quality was not considered in this study. Information obtained from the results may not be directly applied to clinical osteoporotic cases without further verification. (5) Individual differences in bony structure cannot be analyzed/compared since the bony model was reconstructed from only one subject. Although the Sanders’ Type II-B fracture of the calcaneus bone was confirmed by an orthopaedic surgeon, an expanded study with a larger representative population may be required.
Conclusion In summary, this study details the biomechanical effect of an anatomical calcaneal plate and a conventional calcaneal plate on both implants and bony structures. Circumferential fixation at the posterolateral calcaneus can provide sufficient stability to sustain subtalar joint loading after reduction and fixation of a Sanders’ Type II-B calcaneal fracture. The mechanical strength of the calcaneal
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plate is very important if the plate bridges the fracture line, and this point should be considered in the plate’s design.
Disclosure statement No potential conflict of interest was reported by the authors.
ORCID Kun-Jhih Lin
http://orcid.org/0000-0002-2704-1828
References Benirschke SK, Sangeorzan BJ. 1993. Extensive intraarticular fractures of the foot. Surgical management of calcaneal fractures. Clin Orthop Relat Res. 292:128–134. Blake MH, Owen JR, Sanford TS, Wayne JS, Adelaar RS. 2011. Biomechanical evaluation of a locking and nonlocking reconstruction plate in an osteoporotic calcaneal fracture model. Foot Ankle Int. 32:432–436. Buckley RE, Meek RN. 1992. Comparison of open versus closed reduction of intraarticular calcaneal fractures. J Orthop Trauma. 6:216–222. Buckley R, Tough S, McCormack R, Pate G, Leighton R, Petrie D, Galpin R. 2002. Operative compared with nonoperative treatment of displaced intra-articular calcaneal fractures: a prospective, randomized, controlled multicenter trial. J Bone Joint Surg Am. 84-A:1733–1744. Cheng HY, Lin CL, Wang HW, Chou SW. 2008. Finite element analysis of plantar fascia under stretch – the relative contribution of windlass mechanism and Achilles tendon force. J Biomech. 41:1937–1944. Eastwood DM, Langkamer VG, Atkins RM. 1993. Intraarticular fractures of the calcaneum. Part II: open reduction and internal fixation by the extended lateral transcalcaneal approach. J Bone Joint Surg Br. 75:189–195. Essex-Lopresti P. 1952. The mechanism, reduction technique, and results in fractures of the os calcis. Br J Surg. 39:395– 419. Gefen A. 2002. Stress analysis of the standing foot following surgical plantar fascia release. J Biomech. 35:629–637. Howard JL, Buckley R, McCormack R, Pate G, Leighton R, Petrie D, Galpin R. 2003. Complications following management of displaced intra-articular calcaneal fractures: a prospective randomized trial comparing open reduction internal fixation with nonoperative management. J Orthop Trauma. 17:241–249. Hsu YC, Gung YW, Shih SL, Feng CK, Wei SH, Yu CH, Chen CS. 2008. Using an optimization approach to design an insole for lowering plantar fascia stress – a finite element study. Ann Biomed Eng. 36(8):1345–1352. Illert T, Rammelt S, Drewes T, Grass R, Zwipp H. 2011. Stability of locking and non-locking plates in an osteoporotic calcaneal fracture model. Foot Ankle Int. 32:307–313. Kundel K, Funk E, Brutcher M, Bickel R. 1996. Calcaneal fractures: operative versus nonoperative treatment. J Trauma. 41:839–845. Ni M, Weng XH, Mei J, Niu WX. 2015. Primary stability of absorbable screw fixation for intra-articular calcaneal fractures: a finite element analysis. J Med Biol Eng. 35: 236– 241.
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Pang QJ, Yu X, Guo ZH. 2014. The sustentaculum tali screw fixation for the treatment of Sanders type II calcaneal fracture: a finite element analysis. Pak J Med Sci. 30:1099– 1103. Redfern DJ, Oliveira ML, Campbell JT, Belkoff SM. 2006. A biomechanical comparison of locking and nonlocking plates for the fixation of calcaneal fractures. Foot Ankle Int. 27:196–201. Richter M, Droste P, Goesling T, Zech S, Krettek C. 2006. Polyaxially-locked plate screws increase stability of fracture fixation in an experimental model of calcaneal fracture. J Bone Joint Surg Br. 88-B:1257–1263. Sanders R, Fortin P, DiPasquale T, Walling A. 1993. Operative treatment in 120 displaced intraarticular calcaneal fractures. Results using a prognostic computed tomography scan classification. Clin Orthop Relat Res. 290:87–95.
Sun PC, Shih SL, Chen YL, Hsu YC, Yang RC, Chen CS. 2012. Biomechanical analysis of foot with different foot arch heights: a finite element analysis. Comput Methods Biomech Biomed Eng. 15:563–569. Thordarson DB, Krieger LE. 1996. Operative vs. nonoperative treatment of intra-articular fractures of the calcaneus: a prospective randomized trial. Foot Ankle Int. 17:2–9. Yang C, Wang H, Wu Z, Chen W, Zhang Q, Xu G, Chen Z, Chang Y. 2012. A biomechanical comparison of calcaneal anatomical plate and compression bolts versus conventional AO plate in fixation of Sanders type III calcaneus fractures. Chin J Orthop Trauma. 14:669–674. Zhang Y. 2009. Clinical epidemiology of traumatic orthopaedics. Beijing, China: People’s Medical Publishing House; p. 455–468.
