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Newly designed anterolateral and posterolateral locking anatomic plates for lateral tibial plateau fractures: a finite element study

Newly designed anterolateral and posterolateral locking anatomic plates for lateral tibial... Background: Lateral column tibial plateau fracture fixation with a locking screw plate has higher mechanical stability than other fixation methods. The objectives of the present study were to introduce two newly designed locking anatomic plates for lateral tibial plateau fracture and to demonstrate their characteristics of the fixation complexes under the axial loads. Methods: Three different 3D finite element models of the lateral tibial plateau fracture with the bone plates were created. Various axial forces (100, 500, 1000, and 1500 N) were applied to simulate the axial compressive load on an adult knee during daily life. The equivalent maps of displacement and stress were output, and relative displacement was calculated along the fracture lines. Results: The displacement and stresses in the fixation complexes increased with the axial force. The equivalent displacement or stress map of each fixation under different axial forces showed similar distributing characteristics. The motion characteristics of the three models differed, and the max-shear stress of trabecula increased with the axial load. Conclusions: These two novel plates could fix lateral tibial plateau fractures involving anterolateral and posterolateral fragments. Motions after open reduction and stable internal fixation should be advised to decrease the risk of trabecular microfracture. The relative displacement of the posterolateral fragments is different when using anterolateral plate and posterolateral plate, which should be considered in choosing the implants for different posterolateral plateau fractures. Keywords: Locking anatomic plate, Finite element, Equivalent map, Relative displacement Background of the knee and the biomechanics of tibiofemoral joint, Tibial plateau fractures are common injuries affecting more than 60% of the tibial plateau fractures affect its the lower extremities and compose 1% of all fractures lateral column [7, 8]. Lateral column fracture fixation [1–3]. Inadequate treatment of these fractures may with a locking screw plate has shown a higher mechan- result in joint instability and decrease in range of motion ical stability than other fixation methods [7]. Meanwhile, (RoM). Several studies have shown that open reduction researchers put forward that posterolateral column and stable internal fixation (ORIF) of displaced tibial should be considered individually [9, 10]. plateau fractures may ensure a more anatomic restor- Complications are inevitable for some patients with ation of the joint surface to allow early motion without lateral column tibial plateau fracture undergoing surgery loss of reduction [1, 4–6]. Due to the specific geometry [1, 11]. It is of clinical significance to investigate how to reduce complication and improve mechanical stability. It is reported that a raft of four 3.5-mm cortical screws is * Correspondence: 13917481191@163.com biomechanically stronger than two 6.5-mm cancellous Equal contributors screws in resisting axial compression [12]. It is also sug- Department of Orthopedics, Xinhua Hospital affiliated to Shanghai Jiaotong University School of Medicine, No. 1665 Kongjiang Road Yangpu District, gested that the use of crossed screws may improve the Shanghai 200092, China © The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Chen et al. Journal of Orthopaedic Surgery and Research (2017) 12:35 Page 2 of 9 fixation stability, compared with parallel screws [13]. In but also the load distributions in both the simulated sur- the present study, we designed two novel locking gical implants and the surrounding bones [14]. FEA has anatomic plates for lateral tibial plateau (Fig. 1). The an- been shown to potentially stand for good predictors of terolateral plate was used for the anterolateral and the bone fracture [7, 15, 16]. In the present study, FEA was posterolateral fracture fragments, while the posterolat- employed to investigate if the novel plates can provide eral plate was only used for posterolateral fracture sufficient fixation strength for lateral tibial plateau frac- fragments. ture and the respective characteristics of the fixation Finite element analysis (FEA) is one of the computa- complexes of posterolateral tibial plateau fractures when tional methods that have received wide acceptance in these novel plates were used. the field of orthopedic research, which would allow not only detailed quantitative estimations of displacement Methods A three-dimensional (3D) tibia finite element model was constructed based on computed tomography (CT) scan data of a healthy adult man, who was 33 years old, 170 cm in height, and 60 kg in body weight. Initial CT data of the tibia was obtained with 1-mm cuts from his right leg. The 3D model of the tibia was constructed from the CT data in the Digital Imaging and Communications in Medicine (DICOM) format using Mimics software (v16.0, Materialize Company, Leuven, Belgium) and then imported into Geomagic Studio Software (v2014, 3D system Inc., Rock Hill, SC, USA) for smoothing and polishing the surface. The STEP format of the 3D tibia model was saved. All the 3D models of the screws and plates were created using computer-aided design software with the characteristics shown in Fig. 1. The 3D models of tibia and plate-screw system were then imported into Hypermesh software (v13.0, Altair Engineering Inc., Michigan, USA). The fracture models were created according to our preliminary study with certain fracture line angle (Fig. 2). The plate-screw systems were then placed in the right place simulating fracture fixation models. There were threemodelsfor thefracturefixations:singleantero- lateral plateau fracture with anterolateral plate (SALF + ALP, Fig. 2a), single posterolateral plateau fracture with anterolateral plate (SPLF + ALP, Fig. 2b), and single posterolateral plateau fracture with posterolat- eral plate (SPLF + PLP, Fig. 1c). Meshing and subse- quent establishment of the finite element model were also performed with this software. Tetrahedral ten- node elements (C3D10M) were used to mesh all parts of the FE models; the nodes and elements informa- tion are summarized in Table 1. The materials of the plate-screw system were assumed to be homogeneous, isotropic, and linear elastic [7, 17]. The material properties of the plate-screw system (titan- ium alloy) were assigned according to the manufacturer Fig. 1 Brief introduction of the plates a, b: ALP: T shape, proximal: five specifications and previous studies with an elastic modu- raft locking screws (3.5 mm) and two crossed locking screws (3.5 mm), distal: six locking screws (5.0 mm), connection part: five locking screws lus of 78000 MPa and a Poisson ratio of 0.3 [18], while (3.5 mm) with different orientation. c, d: PLP: inclined T shape with an the tibia was assigned by a novel method in Mimics after angle of 66°, proximal: four locking screws (2.7 mm), distal: four locking meshing in Hypermesh. Average CT values of each tibia screws (3.5 mm) element were calculated by Mimics automatically with a Chen et al. Journal of Orthopaedic Surgery and Research (2017) 12:35 Page 3 of 9 Fig. 2 Brief introduction of the fracture models and the FE models. a SALF + ALP. b SPLF + ALP. c SPLF + PLP. d The FE model of SALF + ALP after meshing. e The FE model of SPLF + PLP with axial stress and constrain. f The location of axial stress. g A section of FE model after assigning the materials, the distribution of CT value, and the scale of materials. FLA: the green line connects the middle point of the posterior cruciate ligament’s insertion on the tibial plateau, and the medial 1/3 point of the tibial tuberosity was acted as a neutral axis; the blue line connects the two sides of fracture line corresponding elastic modulus shown in Fig. 2g and a part of the tibia was constrained without displacement Poisson ratio of 0.3. In that way, we did not need to dis- (Fig. 2e). tinguish the boundary of cortical and cancellous bones Subsequently, the finite element models were imported artificially. to Optistruct software (v13.0, Altair Engineering Inc., The contact surfaces between the plates and screws Troy, MI, USA) and performed the analysis process. In were assumed as sharing the common nodes to simulate our study, the equivalent maps of displacement and the locking screws so were the contact surfaces between stress of the fracture fixation models were output. the screws and the bone [19]. For the contact surfaces Relative displacement (RD) was calculated along the between the fragments, it was assumed with a frictional fracture lines (the displacement of the triangular frag- coefficient of 0.4 [20]. Axial forces of 100, 500, 1000, and ment side minus the shaft side). Displacement of differ- 1500 N with a distribution of 60% to the medial com- ent axes had an orientation. The positive directions of Z, partment were applied to simulate the axial compressive Y, and X axes were from distal to proximal, anterior to load on an adult knee [17, 21, 22] (Fig. 2e, f). The distal posterior, and right to left. Table 1 Parameters of the FE models Nodes/elements of SALF + ALP SPLF + ALP SPLF + PLP Nodes/elements of Plate 88505/51456 88598/51534 12252/6388 Plate Screws 104574/56866 105052/57238 23983/12455 Screws Fragment 91983/58212 76939/49743 33405/20754 Fragment Tibia shaft 829695/558153 837173/562653 466951/314994 Tibia shaft Chen et al. Journal of Orthopaedic Surgery and Research (2017) 12:35 Page 4 of 9 Results SPLF + ALP, the maximum negative relative displacement Displacement of models value was at the point between points L and M, and the The maximal displacement values of the three fixations maximum positive displacement value was between points under different loads are shown in Table 2. The displace- M and N (Fig. 3k). On Z axis, the relative displacement ment of each complex increased parallelly with the curve displayed “V” type, and the maximum negative loads; the same was true for the equivalent maps; there- displacement value was close to point M (Fig. 3k). fore, only the equivalent displacement maps of 500 N for each fixation are displayed in Fig. 3. RD along the Stresses in the fixation complex fracture lines from L to M then to N are plotted as The stress values under different loads are summarized curves which revealed the details of the fracture frag- in Table 3. Logically, the stresses recorded in the fixation ments’ movements (Fig. 3b–d, f–h, j–l). L and M were complex increased with the axial force. By comparison, two border points of fracture lines at the articular the equivalent stress map of each fixation under differ- surface, and N was the lowest point of the triangle ent axial forces showed a similar distributing character- fragment. istic, and only the stress map of 500 N was presented In 3D space (X, Y, and Z axes), the fixed fragments’ herein. Figure 4 shows the equivalent von Mises stress displacement showed heterogeneous. The maximal dis- of the three plate-screw systems and the max-shear placement values of SALF + ALP under 500 N load were stress of the bone under 500 N load. For the plates of 0.120 mm (X axis), 0.013 mm (Y axis), −0.069 mm (Z SALF + ALP and SPLF + ALP, von Mises stress concen- axis), respectively. On X and Y axes, the relative dis- trated in the bent area just below the holes for raft placement values from L to M were both positive num- screws (Fig. 4a, d, g, j). The stress concentration was ob- bers, while from M to N, they turned to negative served on the middle section of the holes for raft screws (Fig. 3b, c). On Z axis, the relative displacement value of SPLF + ALP (Fig. 3g). For the plate of SALF + ALP, was negative in most cases, except for around the M von Mises stress seemed to concentrate in the area sur- point (Fig. 3d). rounding the holes (Fig. 4m, o, p). For the screws of all The maximal displacement values of SPLF + ALP under the three fixations, the stresses were concentrated sur- 500 N load were 0.151 mm (X axis), 0.028 mm (Y axis), rounding the fracture lines on the screws (Fig. 4b, c, h, i, and −0.136 mm (Y axis). On X axis, the relative displace- n). The maximum max-shear stresses of the fracture ment value decreased from L to a critical point which was fragments were found at the screw holes near the frac- just below the point M, and then the relative displacement ture surfaces (Fig. 4e, k, q). For the tibia shaft, stress value increased from this critical point to point N (Fig. 3f). transmitted mostly by cortical bones, especially the med- On Y axis, the relative displacement curve reversed com- ial and posterior cortical bones (Fig. 4f, l, r). pared to X axis (Fig. 3g). On Z axis, the relative displace- The maximum max-shear stresses of the trabecular ment value decreased from point L to M, and then bones are summarized in Fig. 5, illustrating the possible increased gradually to the maximum at point N. risk of trabecular fractures for each model under differ- The maximal displacement values of SPLF + PLP under ent loads or motions. 500 N load were 0.024 mm (X axis), 0.019 mm (Y axis), and −0.047 mm (Z axis). On X axis, the curve of relative Discussion displacement was similar to that of SPLF + ALP (Fig. 3j); More attention should be paid on tibial plateau frac- whilethe curvein Y axis was quite different from that of tures, especially on lateral plateau fractures, as lateral Table 2 Displacement values of different FE models SALF + ALP SPLF + ALP SPLF + PLP Max displacement 100 N 500 N 1000 N 1500 N 100 N 500 N 1000 N 1500 N 100 N 500 N 1000 N 1500 N (mm) MAG 0.02531 0.12658 0.25315 0.37973 0.03936 0.19680 0.39360 0.59040 0.01078 0.05390 0.10780 0.16170 X 0.02392 0.11961 0.23922 0.35883 0.03011 0.15056 0.30112 0.45168 0.00478 0.02391 0.04782 0.07173 −0.00008 −0.00039 −0.00078 −0.00116 −0.00009 −0.00045 −0.00089 −0.00134 −0.00004 −0.00018 −0.00036 −0.00054 Y 0.00264 0.01322 0.02644 0.03966 0.00559 0.02793 0.05586 0.08379 0.00384 0.01922 0.03843 0.05764 −0.00204 −0.01019 −0.02038 −0.03057 −0.00502 −0.02512 −0.05024 −0.07536 −0.00011 −0.00056 −0.00112 −0.00168 Z 0.00482 0.02408 0.04816 0.07224 0.00590 0.02949 0.05897 0.08846 0.00046 0.00228 0.00456 0.00684 −0.01381 −0.06907 −0.13813 −0.20720 −0.02716 −0.13578 −0.27156 −0.40734 −0.00947 −0.04734 −0.09467 −0.14200 Chen et al. Journal of Orthopaedic Surgery and Research (2017) 12:35 Page 5 of 9 Fig. 3 The results of displacement under 500 N axial stress. Total (a), X axis (b), Y axis (c), and Z axis (d) displacement and their RD curves of SALF + ALP; total (e), X axis (f), Y axis (g), and Z axis (h) displacement and their RD curves of SPLF + ALP; total (i), X axis (j), Y axis (k), and Z axis (l) displacement and their RDcurves of SPLF + PLP. Point L and M are two boundary points of tibia plateau along the fracture lines and point N is most distal point of the fracture fragments column wouldbeaffectedbymorethan60% of these space between the apex of fibular head and lateral fractures [7, 8]. Our design of two plates in the wall of plateau is sufficient for horizontal arm of the present study utilized the raft theory, resulting in a plate passing through [23]. The plates were designed more stable tibial plateau after ORIF, compared to the as T shape. PLP was inclined with T shape, resulting normal plates. It has been demonstrated that the in a more adequate visualization of the plate’sshaft Chen et al. Journal of Orthopaedic Surgery and Research (2017) 12:35 Page 6 of 9 Table 3 Values of stress of different FE models SALF + ALP SPLF + ALP SPLF + PLP Max von Mises stress (MPa) Plate 1.666 8.329 16.658 24.986 3.311 16.555 33.110 49.665 2.888 14.438 28.876 43.314 Screws 1.000 5.002 10.004 15.006 3.549 17.746 35.493 53.240 2.596 12.982 25.965 38.947 Max-shear stress (MPa) Fragment 0.196 0.978 1.957 2.935 0.394 1.968 3.935 5.903 0.249 1.247 2.494 3.741 Tibia shaft 1.298 6.492 12.985 19.477 0.790 3.950 7.900 11.850 0.691 3.457 6.914 10.371 part when screw was inserted. ALP has two backward bone healing [20]. However, when the articular surface screw holes. The two screws were crossed with the suffers a severe collapse or syntripsis, the extrusion mo- raft screws, which can be used to fix posterior plateau tion may bring the dislocation of the small fragments fragment. This structure could provide a stronger fix- along the fracture line and therefore relative stability ation [13]. without extrusion motion should be considered [20]. In In the present study, FEA was employed to demon- observations of SPLF + ALP and SPLF + PLP, although strate the strength of the three fixations and their char- they were both posterolateral fracture, the fracture frag- acteristics under axial stresses that could not be ments moved in different ways. The triangular fragment observed by other mechanical test methods. In order to of SPLF + ALP was more likely to separate slightly from achieve an accurate outcome, a quite small size of 2D the tibial shaft at the articular surface height, while it element (1 mm) was employed in these models. The was adverse of SPLF + PLP. Therefore, the ALP fitted nodes and element numbers of 3D elements are shown better the posterolateral fracture with a severe collapse in Table 1, proving the veracity of our FE models as they or syntripsis at the articular surface (Fig. 6a), while PLP were sizable. The previous methods to assign materials fitted well the posterolateral fracture with slight collapse and properties for the cortical and trabecular bones were or a whole fragment (Fig. 6b). Motions of Z axial were troublesome and imprecise as artificial or semi-artificial overall under 0.1 mm, which showed a perfect stiffness segmentation of different kinds of bone were required of the fixations. [7, 24]. However, the method utilized in the present On the other hand, the stresses were compared to the study was a convenient way with the outcome shown in maximum resistance of the simulated materials. In all Fig. 2g. As seen numerically, we obtained a model with the tests, the maximum von Mises stress of the implants cortical and trabecular bones’ E-modulus similar to the was 53.240 MPa, which was far smaller than the max- research reported previously [7, 17, 25]. The cortical imum resistance of 795 MPa (titanium alloy)[7]. No thickness differed from the tibial plateau to the shaft, bending or mechanical damage of the screws and plates and the trabecular bone of the plateau and tibial medul- occurred. lary cavity were assigned as different materials. These Von Mises stress was concentrated around the con- results showed that our FE models were more precise nection of proximal raft screws and the distal shaft and closer to the reality than previous models, with a screws of ALPs so as to prevent the separation of homogeneous cortical thickness and trabecular bone as fragment. In SPLF + ALP, the stress was concentrated a whole. on the middle section of the proximal raft screws as Overall, the maximum RDs achieved in the present the plate was placed across the fracture line. The study were far below 2 mm, which is usually considered stress concentration occurred at the bottom, and cusp clinically to evaluate if the reduction of a split tibial plat- of the shaft screws on ALPs was caused by the stress eau fracture succeed [7, 26]. Therefore, all the three fixa- transmitted by the two sides of cortical bone. Von tions developed in the present study were judged Mises stress on the implants of SPLF + PLP was con- successful. centrated on the junctions of the plate and the screws For the RD value and its curves of SALF + ALP, the with a relative homogeneous distribution on the plate. fracture fragment was found getting closed to the main This may be caused by the stress transmitted by the tibia part at the articular surface height under axial lateral-side cortical bone. The stress concentrations stresses, while getting separated at the lower triangle of along the fracture lines were easy to be understood. fragment. The extrusion motion is considered as a good For the bones, the max-shear stress was calculated to result for fractures at the articular surface as it provides show the risk of trabecular microfracture. The maximum a greater possibility of absolute stability and primary max-shear stresses of the fracture fragments were found Chen et al. Journal of Orthopaedic Surgery and Research (2017) 12:35 Page 7 of 9 Fig. 4 The results of stresses. a–d Plate and screws von Mises stress of SALF + ALP. e, f Bone max-shear stress of SALF + ALP. g–j Plate and screws von Mises stress of SPLF + ALP. e, f Bone Max-shear stress of SPLF + ALP. g–j Plate and screws von Mises stress of SPLF + PLP. k, l Bone Max-shear stress of SPLF + PLP. m–p plate and screws von Mises stress of SPLF + PLP. q, r bone Maxshear stress of SPLF + PLP at the screw holes near the fracture surfaces. Trabecular joint axial stress ranged from 100 to 360% of body microfracture may bring the screw loosening, leading to weight during activities of daily living [27]. According to the failure of ORIF. Carrera et al. have summarized that these observations, our test load should be up to 2160 N the shear strength of trabecular bone might vary from as the body weight of this patient was 60 kg. The max- 2.4 to 5.8 MPa [7]. It has been reported that the knee imal axial load we performed in the tests was 1500 N, Chen et al. Journal of Orthopaedic Surgery and Research (2017) 12:35 Page 8 of 9 Conclusions The two novel plates developed in the present study can fix well lateral tibial plateau fractures involving antero- lateral fragment and posterolateral fragments. Motions after ORIF should be advised to decrease the risk of tra- becular microfracture. The RD of the posterolateral frag- ments was different when using ALP and PLP, which should be considered in choosing the implants when dealing with different posterolateral plateau fractures. Abbreviations ALP: Anterolateral plate; DICOM: Digital Imaging and Communications in Fig. 5 The Max-shear stress surround the screw holes and relation to the Medicine; FEA: Finite element analysis; ORIF: Open reduction and stable trabecular bone shear strength. a Trabecular bone shear strength, 2.4–5.8 internal; PLP: Posterolateral plate; RD: Relative displacement; ROM: Range of MPa. b Two legs standing, 600 N, 100% body weight. c Flexion motions motion; SALF: Single anterolateral plateau fracture; SPLF: Single posterolateral (bending knee, sitting down, standing up), 1320–1560 N, 220–250% body plateau fracture weight. d One leg standing, 1620 N, 270% body weight. e Up and down the stairs, 1860–2100 N, 310–350% body weight Funding The work was supported by the Science and Technology Commission of Shanghai Municipality, Shanghai, China (Grant No. 13441902500) and Xinhua Hospital affiliated to Shanghai JiaoTong University School of Medicine, Shanghai, China (15YG05). which might be an imperfection of our study. As shown in Fig. 4, the SPLF + ALP had the highest risk of tra- Availability of data and materials becular microfracture, suggesting the patient should Please contact the author for data requests. decrease taking the stairs and other drastic actions after Authors’ contributions ORIF. Other fixations also had the risks of trabecular PC and HL carried out the model construction. PC, WW, and BN performed microfracture, which needs further study. the statistical analysis. HL and JC optimized the model process. PC and HS conceived of the study, participated in its design and coordination, and helped to draft the manuscript. All authors read and approved the final manuscript. Competing interests The authors declare that they have no competing interests. Consent for publication Not applicable. 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Newly designed anterolateral and posterolateral locking anatomic plates for lateral tibial plateau fractures: a finite element study

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Springer Journals
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2017 The Author(s).
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1749-799X
DOI
10.1186/s13018-017-0531-1
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Abstract

Background: Lateral column tibial plateau fracture fixation with a locking screw plate has higher mechanical stability than other fixation methods. The objectives of the present study were to introduce two newly designed locking anatomic plates for lateral tibial plateau fracture and to demonstrate their characteristics of the fixation complexes under the axial loads. Methods: Three different 3D finite element models of the lateral tibial plateau fracture with the bone plates were created. Various axial forces (100, 500, 1000, and 1500 N) were applied to simulate the axial compressive load on an adult knee during daily life. The equivalent maps of displacement and stress were output, and relative displacement was calculated along the fracture lines. Results: The displacement and stresses in the fixation complexes increased with the axial force. The equivalent displacement or stress map of each fixation under different axial forces showed similar distributing characteristics. The motion characteristics of the three models differed, and the max-shear stress of trabecula increased with the axial load. Conclusions: These two novel plates could fix lateral tibial plateau fractures involving anterolateral and posterolateral fragments. Motions after open reduction and stable internal fixation should be advised to decrease the risk of trabecular microfracture. The relative displacement of the posterolateral fragments is different when using anterolateral plate and posterolateral plate, which should be considered in choosing the implants for different posterolateral plateau fractures. Keywords: Locking anatomic plate, Finite element, Equivalent map, Relative displacement Background of the knee and the biomechanics of tibiofemoral joint, Tibial plateau fractures are common injuries affecting more than 60% of the tibial plateau fractures affect its the lower extremities and compose 1% of all fractures lateral column [7, 8]. Lateral column fracture fixation [1–3]. Inadequate treatment of these fractures may with a locking screw plate has shown a higher mechan- result in joint instability and decrease in range of motion ical stability than other fixation methods [7]. Meanwhile, (RoM). Several studies have shown that open reduction researchers put forward that posterolateral column and stable internal fixation (ORIF) of displaced tibial should be considered individually [9, 10]. plateau fractures may ensure a more anatomic restor- Complications are inevitable for some patients with ation of the joint surface to allow early motion without lateral column tibial plateau fracture undergoing surgery loss of reduction [1, 4–6]. Due to the specific geometry [1, 11]. It is of clinical significance to investigate how to reduce complication and improve mechanical stability. It is reported that a raft of four 3.5-mm cortical screws is * Correspondence: 13917481191@163.com biomechanically stronger than two 6.5-mm cancellous Equal contributors screws in resisting axial compression [12]. It is also sug- Department of Orthopedics, Xinhua Hospital affiliated to Shanghai Jiaotong University School of Medicine, No. 1665 Kongjiang Road Yangpu District, gested that the use of crossed screws may improve the Shanghai 200092, China © The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Chen et al. Journal of Orthopaedic Surgery and Research (2017) 12:35 Page 2 of 9 fixation stability, compared with parallel screws [13]. In but also the load distributions in both the simulated sur- the present study, we designed two novel locking gical implants and the surrounding bones [14]. FEA has anatomic plates for lateral tibial plateau (Fig. 1). The an- been shown to potentially stand for good predictors of terolateral plate was used for the anterolateral and the bone fracture [7, 15, 16]. In the present study, FEA was posterolateral fracture fragments, while the posterolat- employed to investigate if the novel plates can provide eral plate was only used for posterolateral fracture sufficient fixation strength for lateral tibial plateau frac- fragments. ture and the respective characteristics of the fixation Finite element analysis (FEA) is one of the computa- complexes of posterolateral tibial plateau fractures when tional methods that have received wide acceptance in these novel plates were used. the field of orthopedic research, which would allow not only detailed quantitative estimations of displacement Methods A three-dimensional (3D) tibia finite element model was constructed based on computed tomography (CT) scan data of a healthy adult man, who was 33 years old, 170 cm in height, and 60 kg in body weight. Initial CT data of the tibia was obtained with 1-mm cuts from his right leg. The 3D model of the tibia was constructed from the CT data in the Digital Imaging and Communications in Medicine (DICOM) format using Mimics software (v16.0, Materialize Company, Leuven, Belgium) and then imported into Geomagic Studio Software (v2014, 3D system Inc., Rock Hill, SC, USA) for smoothing and polishing the surface. The STEP format of the 3D tibia model was saved. All the 3D models of the screws and plates were created using computer-aided design software with the characteristics shown in Fig. 1. The 3D models of tibia and plate-screw system were then imported into Hypermesh software (v13.0, Altair Engineering Inc., Michigan, USA). The fracture models were created according to our preliminary study with certain fracture line angle (Fig. 2). The plate-screw systems were then placed in the right place simulating fracture fixation models. There were threemodelsfor thefracturefixations:singleantero- lateral plateau fracture with anterolateral plate (SALF + ALP, Fig. 2a), single posterolateral plateau fracture with anterolateral plate (SPLF + ALP, Fig. 2b), and single posterolateral plateau fracture with posterolat- eral plate (SPLF + PLP, Fig. 1c). Meshing and subse- quent establishment of the finite element model were also performed with this software. Tetrahedral ten- node elements (C3D10M) were used to mesh all parts of the FE models; the nodes and elements informa- tion are summarized in Table 1. The materials of the plate-screw system were assumed to be homogeneous, isotropic, and linear elastic [7, 17]. The material properties of the plate-screw system (titan- ium alloy) were assigned according to the manufacturer Fig. 1 Brief introduction of the plates a, b: ALP: T shape, proximal: five specifications and previous studies with an elastic modu- raft locking screws (3.5 mm) and two crossed locking screws (3.5 mm), distal: six locking screws (5.0 mm), connection part: five locking screws lus of 78000 MPa and a Poisson ratio of 0.3 [18], while (3.5 mm) with different orientation. c, d: PLP: inclined T shape with an the tibia was assigned by a novel method in Mimics after angle of 66°, proximal: four locking screws (2.7 mm), distal: four locking meshing in Hypermesh. Average CT values of each tibia screws (3.5 mm) element were calculated by Mimics automatically with a Chen et al. Journal of Orthopaedic Surgery and Research (2017) 12:35 Page 3 of 9 Fig. 2 Brief introduction of the fracture models and the FE models. a SALF + ALP. b SPLF + ALP. c SPLF + PLP. d The FE model of SALF + ALP after meshing. e The FE model of SPLF + PLP with axial stress and constrain. f The location of axial stress. g A section of FE model after assigning the materials, the distribution of CT value, and the scale of materials. FLA: the green line connects the middle point of the posterior cruciate ligament’s insertion on the tibial plateau, and the medial 1/3 point of the tibial tuberosity was acted as a neutral axis; the blue line connects the two sides of fracture line corresponding elastic modulus shown in Fig. 2g and a part of the tibia was constrained without displacement Poisson ratio of 0.3. In that way, we did not need to dis- (Fig. 2e). tinguish the boundary of cortical and cancellous bones Subsequently, the finite element models were imported artificially. to Optistruct software (v13.0, Altair Engineering Inc., The contact surfaces between the plates and screws Troy, MI, USA) and performed the analysis process. In were assumed as sharing the common nodes to simulate our study, the equivalent maps of displacement and the locking screws so were the contact surfaces between stress of the fracture fixation models were output. the screws and the bone [19]. For the contact surfaces Relative displacement (RD) was calculated along the between the fragments, it was assumed with a frictional fracture lines (the displacement of the triangular frag- coefficient of 0.4 [20]. Axial forces of 100, 500, 1000, and ment side minus the shaft side). Displacement of differ- 1500 N with a distribution of 60% to the medial com- ent axes had an orientation. The positive directions of Z, partment were applied to simulate the axial compressive Y, and X axes were from distal to proximal, anterior to load on an adult knee [17, 21, 22] (Fig. 2e, f). The distal posterior, and right to left. Table 1 Parameters of the FE models Nodes/elements of SALF + ALP SPLF + ALP SPLF + PLP Nodes/elements of Plate 88505/51456 88598/51534 12252/6388 Plate Screws 104574/56866 105052/57238 23983/12455 Screws Fragment 91983/58212 76939/49743 33405/20754 Fragment Tibia shaft 829695/558153 837173/562653 466951/314994 Tibia shaft Chen et al. Journal of Orthopaedic Surgery and Research (2017) 12:35 Page 4 of 9 Results SPLF + ALP, the maximum negative relative displacement Displacement of models value was at the point between points L and M, and the The maximal displacement values of the three fixations maximum positive displacement value was between points under different loads are shown in Table 2. The displace- M and N (Fig. 3k). On Z axis, the relative displacement ment of each complex increased parallelly with the curve displayed “V” type, and the maximum negative loads; the same was true for the equivalent maps; there- displacement value was close to point M (Fig. 3k). fore, only the equivalent displacement maps of 500 N for each fixation are displayed in Fig. 3. RD along the Stresses in the fixation complex fracture lines from L to M then to N are plotted as The stress values under different loads are summarized curves which revealed the details of the fracture frag- in Table 3. Logically, the stresses recorded in the fixation ments’ movements (Fig. 3b–d, f–h, j–l). L and M were complex increased with the axial force. By comparison, two border points of fracture lines at the articular the equivalent stress map of each fixation under differ- surface, and N was the lowest point of the triangle ent axial forces showed a similar distributing character- fragment. istic, and only the stress map of 500 N was presented In 3D space (X, Y, and Z axes), the fixed fragments’ herein. Figure 4 shows the equivalent von Mises stress displacement showed heterogeneous. The maximal dis- of the three plate-screw systems and the max-shear placement values of SALF + ALP under 500 N load were stress of the bone under 500 N load. For the plates of 0.120 mm (X axis), 0.013 mm (Y axis), −0.069 mm (Z SALF + ALP and SPLF + ALP, von Mises stress concen- axis), respectively. On X and Y axes, the relative dis- trated in the bent area just below the holes for raft placement values from L to M were both positive num- screws (Fig. 4a, d, g, j). The stress concentration was ob- bers, while from M to N, they turned to negative served on the middle section of the holes for raft screws (Fig. 3b, c). On Z axis, the relative displacement value of SPLF + ALP (Fig. 3g). For the plate of SALF + ALP, was negative in most cases, except for around the M von Mises stress seemed to concentrate in the area sur- point (Fig. 3d). rounding the holes (Fig. 4m, o, p). For the screws of all The maximal displacement values of SPLF + ALP under the three fixations, the stresses were concentrated sur- 500 N load were 0.151 mm (X axis), 0.028 mm (Y axis), rounding the fracture lines on the screws (Fig. 4b, c, h, i, and −0.136 mm (Y axis). On X axis, the relative displace- n). The maximum max-shear stresses of the fracture ment value decreased from L to a critical point which was fragments were found at the screw holes near the frac- just below the point M, and then the relative displacement ture surfaces (Fig. 4e, k, q). For the tibia shaft, stress value increased from this critical point to point N (Fig. 3f). transmitted mostly by cortical bones, especially the med- On Y axis, the relative displacement curve reversed com- ial and posterior cortical bones (Fig. 4f, l, r). pared to X axis (Fig. 3g). On Z axis, the relative displace- The maximum max-shear stresses of the trabecular ment value decreased from point L to M, and then bones are summarized in Fig. 5, illustrating the possible increased gradually to the maximum at point N. risk of trabecular fractures for each model under differ- The maximal displacement values of SPLF + PLP under ent loads or motions. 500 N load were 0.024 mm (X axis), 0.019 mm (Y axis), and −0.047 mm (Z axis). On X axis, the curve of relative Discussion displacement was similar to that of SPLF + ALP (Fig. 3j); More attention should be paid on tibial plateau frac- whilethe curvein Y axis was quite different from that of tures, especially on lateral plateau fractures, as lateral Table 2 Displacement values of different FE models SALF + ALP SPLF + ALP SPLF + PLP Max displacement 100 N 500 N 1000 N 1500 N 100 N 500 N 1000 N 1500 N 100 N 500 N 1000 N 1500 N (mm) MAG 0.02531 0.12658 0.25315 0.37973 0.03936 0.19680 0.39360 0.59040 0.01078 0.05390 0.10780 0.16170 X 0.02392 0.11961 0.23922 0.35883 0.03011 0.15056 0.30112 0.45168 0.00478 0.02391 0.04782 0.07173 −0.00008 −0.00039 −0.00078 −0.00116 −0.00009 −0.00045 −0.00089 −0.00134 −0.00004 −0.00018 −0.00036 −0.00054 Y 0.00264 0.01322 0.02644 0.03966 0.00559 0.02793 0.05586 0.08379 0.00384 0.01922 0.03843 0.05764 −0.00204 −0.01019 −0.02038 −0.03057 −0.00502 −0.02512 −0.05024 −0.07536 −0.00011 −0.00056 −0.00112 −0.00168 Z 0.00482 0.02408 0.04816 0.07224 0.00590 0.02949 0.05897 0.08846 0.00046 0.00228 0.00456 0.00684 −0.01381 −0.06907 −0.13813 −0.20720 −0.02716 −0.13578 −0.27156 −0.40734 −0.00947 −0.04734 −0.09467 −0.14200 Chen et al. Journal of Orthopaedic Surgery and Research (2017) 12:35 Page 5 of 9 Fig. 3 The results of displacement under 500 N axial stress. Total (a), X axis (b), Y axis (c), and Z axis (d) displacement and their RD curves of SALF + ALP; total (e), X axis (f), Y axis (g), and Z axis (h) displacement and their RD curves of SPLF + ALP; total (i), X axis (j), Y axis (k), and Z axis (l) displacement and their RDcurves of SPLF + PLP. Point L and M are two boundary points of tibia plateau along the fracture lines and point N is most distal point of the fracture fragments column wouldbeaffectedbymorethan60% of these space between the apex of fibular head and lateral fractures [7, 8]. Our design of two plates in the wall of plateau is sufficient for horizontal arm of the present study utilized the raft theory, resulting in a plate passing through [23]. The plates were designed more stable tibial plateau after ORIF, compared to the as T shape. PLP was inclined with T shape, resulting normal plates. It has been demonstrated that the in a more adequate visualization of the plate’sshaft Chen et al. Journal of Orthopaedic Surgery and Research (2017) 12:35 Page 6 of 9 Table 3 Values of stress of different FE models SALF + ALP SPLF + ALP SPLF + PLP Max von Mises stress (MPa) Plate 1.666 8.329 16.658 24.986 3.311 16.555 33.110 49.665 2.888 14.438 28.876 43.314 Screws 1.000 5.002 10.004 15.006 3.549 17.746 35.493 53.240 2.596 12.982 25.965 38.947 Max-shear stress (MPa) Fragment 0.196 0.978 1.957 2.935 0.394 1.968 3.935 5.903 0.249 1.247 2.494 3.741 Tibia shaft 1.298 6.492 12.985 19.477 0.790 3.950 7.900 11.850 0.691 3.457 6.914 10.371 part when screw was inserted. ALP has two backward bone healing [20]. However, when the articular surface screw holes. The two screws were crossed with the suffers a severe collapse or syntripsis, the extrusion mo- raft screws, which can be used to fix posterior plateau tion may bring the dislocation of the small fragments fragment. This structure could provide a stronger fix- along the fracture line and therefore relative stability ation [13]. without extrusion motion should be considered [20]. In In the present study, FEA was employed to demon- observations of SPLF + ALP and SPLF + PLP, although strate the strength of the three fixations and their char- they were both posterolateral fracture, the fracture frag- acteristics under axial stresses that could not be ments moved in different ways. The triangular fragment observed by other mechanical test methods. In order to of SPLF + ALP was more likely to separate slightly from achieve an accurate outcome, a quite small size of 2D the tibial shaft at the articular surface height, while it element (1 mm) was employed in these models. The was adverse of SPLF + PLP. Therefore, the ALP fitted nodes and element numbers of 3D elements are shown better the posterolateral fracture with a severe collapse in Table 1, proving the veracity of our FE models as they or syntripsis at the articular surface (Fig. 6a), while PLP were sizable. The previous methods to assign materials fitted well the posterolateral fracture with slight collapse and properties for the cortical and trabecular bones were or a whole fragment (Fig. 6b). Motions of Z axial were troublesome and imprecise as artificial or semi-artificial overall under 0.1 mm, which showed a perfect stiffness segmentation of different kinds of bone were required of the fixations. [7, 24]. However, the method utilized in the present On the other hand, the stresses were compared to the study was a convenient way with the outcome shown in maximum resistance of the simulated materials. In all Fig. 2g. As seen numerically, we obtained a model with the tests, the maximum von Mises stress of the implants cortical and trabecular bones’ E-modulus similar to the was 53.240 MPa, which was far smaller than the max- research reported previously [7, 17, 25]. The cortical imum resistance of 795 MPa (titanium alloy)[7]. No thickness differed from the tibial plateau to the shaft, bending or mechanical damage of the screws and plates and the trabecular bone of the plateau and tibial medul- occurred. lary cavity were assigned as different materials. These Von Mises stress was concentrated around the con- results showed that our FE models were more precise nection of proximal raft screws and the distal shaft and closer to the reality than previous models, with a screws of ALPs so as to prevent the separation of homogeneous cortical thickness and trabecular bone as fragment. In SPLF + ALP, the stress was concentrated a whole. on the middle section of the proximal raft screws as Overall, the maximum RDs achieved in the present the plate was placed across the fracture line. The study were far below 2 mm, which is usually considered stress concentration occurred at the bottom, and cusp clinically to evaluate if the reduction of a split tibial plat- of the shaft screws on ALPs was caused by the stress eau fracture succeed [7, 26]. Therefore, all the three fixa- transmitted by the two sides of cortical bone. Von tions developed in the present study were judged Mises stress on the implants of SPLF + PLP was con- successful. centrated on the junctions of the plate and the screws For the RD value and its curves of SALF + ALP, the with a relative homogeneous distribution on the plate. fracture fragment was found getting closed to the main This may be caused by the stress transmitted by the tibia part at the articular surface height under axial lateral-side cortical bone. The stress concentrations stresses, while getting separated at the lower triangle of along the fracture lines were easy to be understood. fragment. The extrusion motion is considered as a good For the bones, the max-shear stress was calculated to result for fractures at the articular surface as it provides show the risk of trabecular microfracture. The maximum a greater possibility of absolute stability and primary max-shear stresses of the fracture fragments were found Chen et al. Journal of Orthopaedic Surgery and Research (2017) 12:35 Page 7 of 9 Fig. 4 The results of stresses. a–d Plate and screws von Mises stress of SALF + ALP. e, f Bone max-shear stress of SALF + ALP. g–j Plate and screws von Mises stress of SPLF + ALP. e, f Bone Max-shear stress of SPLF + ALP. g–j Plate and screws von Mises stress of SPLF + PLP. k, l Bone Max-shear stress of SPLF + PLP. m–p plate and screws von Mises stress of SPLF + PLP. q, r bone Maxshear stress of SPLF + PLP at the screw holes near the fracture surfaces. Trabecular joint axial stress ranged from 100 to 360% of body microfracture may bring the screw loosening, leading to weight during activities of daily living [27]. According to the failure of ORIF. Carrera et al. have summarized that these observations, our test load should be up to 2160 N the shear strength of trabecular bone might vary from as the body weight of this patient was 60 kg. The max- 2.4 to 5.8 MPa [7]. It has been reported that the knee imal axial load we performed in the tests was 1500 N, Chen et al. Journal of Orthopaedic Surgery and Research (2017) 12:35 Page 8 of 9 Conclusions The two novel plates developed in the present study can fix well lateral tibial plateau fractures involving antero- lateral fragment and posterolateral fragments. Motions after ORIF should be advised to decrease the risk of tra- becular microfracture. The RD of the posterolateral frag- ments was different when using ALP and PLP, which should be considered in choosing the implants when dealing with different posterolateral plateau fractures. Abbreviations ALP: Anterolateral plate; DICOM: Digital Imaging and Communications in Fig. 5 The Max-shear stress surround the screw holes and relation to the Medicine; FEA: Finite element analysis; ORIF: Open reduction and stable trabecular bone shear strength. a Trabecular bone shear strength, 2.4–5.8 internal; PLP: Posterolateral plate; RD: Relative displacement; ROM: Range of MPa. b Two legs standing, 600 N, 100% body weight. c Flexion motions motion; SALF: Single anterolateral plateau fracture; SPLF: Single posterolateral (bending knee, sitting down, standing up), 1320–1560 N, 220–250% body plateau fracture weight. d One leg standing, 1620 N, 270% body weight. e Up and down the stairs, 1860–2100 N, 310–350% body weight Funding The work was supported by the Science and Technology Commission of Shanghai Municipality, Shanghai, China (Grant No. 13441902500) and Xinhua Hospital affiliated to Shanghai JiaoTong University School of Medicine, Shanghai, China (15YG05). which might be an imperfection of our study. As shown in Fig. 4, the SPLF + ALP had the highest risk of tra- Availability of data and materials becular microfracture, suggesting the patient should Please contact the author for data requests. decrease taking the stairs and other drastic actions after Authors’ contributions ORIF. Other fixations also had the risks of trabecular PC and HL carried out the model construction. PC, WW, and BN performed microfracture, which needs further study. the statistical analysis. HL and JC optimized the model process. PC and HS conceived of the study, participated in its design and coordination, and helped to draft the manuscript. All authors read and approved the final manuscript. Competing interests The authors declare that they have no competing interests. Consent for publication Not applicable. 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Journal

Journal of Orthopaedic Surgery and Research – Springer Journals

Published: Dec 1, 2017

Keywords: orthopedics; surgical orthopedics

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