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Finite element analysis for LCP plates
⁎Corresponding author: Beata Świeczko-Żurek. beata.swieczko-zurek@pg.edu.pl
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Received: ,
Accepted: ,
This article was originally published by Reed Elsevier India Pvt. Ltd. and was migrated to Scientific Scholar after the change of Publisher.
Abstract
Abstract
The main assumption of modern orthopedics and trauma surgery is to return to full fitness with a short recovery period. Unfortunately, the emergence of lifestyle diseases such as osteoporosis, which is characterized by a decrease in the biological value of bone tissue, a greater number of road accidents and related injuries to the musculoskeletal system, and the increasing expectations of people with degenerative polyarticular changes to remain mobile, have significantly increased the demand for all types of implants and prostheses.
Bone fixations pose a serious challenge for doctors, especially when the bone is also osteoporotic. Previous studies on innovative LCP plates (Locking Compression Plate), which are equipped with a special locking mechanism, show their advantage over traditional methods. They are characterized by very good bone stabilization, minimization of movement around the fracture site, faster bone growth, and consequently a shorter reconvalescence period for the patient and a greater chance of returning to full mobility.
The subject of the work is the FEM analysis for bone fixation - LCP plate. Modern medicine is constantly looking for new possibilities to increase the effectiveness and shorten the treatment time, an excellent example of which are the LCP plates discussed in the work. The main goal of the work is to select the material and parameters for the plate fixing the shin bone and to create a model of the bone-plate system.
1 Introduction
Orthopedic plates (Table 1) are a form commonly used in internal osteosynthesis to hold bone fragments in place to allow the damaged bone to heal properly. In most cases, plate implantation also requires the use of special screws.1
| Bone-plate LCPTi-6Al-4V | Bone-plate LCPTi-6Al-7Nb | Bone-plate LCPTi-13Nb-13Zr | |
| Maximum value of reduced stresses [MPa] | |||
| Screw | 1637 | 1699 | 1497 |
| Bone | 1423 | 1431 | 1402 |
| Plate LCP | 759,3 | 776,1 | 690,3 |
| Maximum displacements [mm] | |||
| Screw | 0,1371 | 0,1366 | 0,1387 |
| Bone | 0,8885 | 0,8851 | 0,897 |
| Plate LCP | 0,126 | 0,1254 | 0,1278 |
In 1886, Hausmann used metal plates as a bone splint for the first time at the German University of Heidelberg. He used aluminum, silver and brass plates, which he attached to the bone with screws. The first problems concerning the biocompatibility of metals were presented in the works of the Lambotte brothers, who made a direct screw of broken bones with the use of various metals. Then, in 1893, Lane observed the problem of metal absorption into the bone and the resulting infections during the fixation of the bones with screws. In addition, 20 years later, in cooperation with Sherman, he improved the stiffness and stability of plate bonds by inventing plates with a transverse groove.2–4
For many years, a lot of was done to improve the design of platelet anastomoses, but these works did not give satisfactory clinical results.3 The modern use of orthopedic plates has its origins in the 50th of the XX century. It was then that Mautice Muller and other surgeons founded AO/ASIF (ArbeitsgemeinschaftfürOsteosynthesefragen/Association of the Study of Internal Fixation), an association working for the development and research of internal fixation of fractures. The aim of AO was to improve internal osteosynthesis techniques by analyzing the mechanisms of bone repair, fracture formation, and surgical techniques to achieve the best possible treatment outcomes.1,5
In the late 1960s, Diehl and Zenker were working on making the plate connection more flexible by using acrylic, epoxy resin and carbon composites to modify the plates and screws. Many years of research by Ramotowski and Granowski at the end of the 1980s led to the creation of a new generation of plate stabilizers – the “Zespol” stabilizers. It consisted of nuts fastening bone screws, a support plate and bone screws with support plates.2
The next original method developed in Poland was the “Polfix” stabilizer. Both of these solutions are characterized by the absence of direct pressure of the plate on the bone, thanks to which the periosteum is protected, which prevents bone ischemia.6,7
In both of the above anastomoses, only screws were inserted into the bone, and the plate itself was mounted outside the patient's tissues as a bridging plate, similar to current external fixators. One of the main assumptions of orthopedic stabilization is that the bone heals better if its fragments are pressed firmly against each other. Compression increases the contact area across the occurrence of the fracture and increases its stability. Reduction of the orthopedic gap further reduces the load on the implant (plate). Compression can be static when it is produced only by a mounted plate system, or dynamic when body weight or muscle strength is used to achieve additional compression.8
Over the course of many years of research, efforts were made to improve the capabilities of the plates, and so in 1969 the Dynamic Compression Plates (DCP) were patented, followed by the creation of Limited-Contact Dynamic Compression Plates (LC-DCP) in 1990. A discovery from 2001 is Locking Compression Plates (LCP).9
The main principle of DCP is based on friction between the plate and the bone and additional compression both static caused by assembly and dynamic. The screws are placed in a neutral or eccentric position. A huge disadvantage of DCP is a large area of pressure under the plate, which disturbs the blood supply to the periosteum.8,10–15
Another of the compression plates - LC-DCP - is similar to DCP in appearance and principle of operation, but its contact area with the bone has been reduced by about 50 % compared to the original. This was influenced by studies carried out, during which it was shown16–18 that a much smaller surface area of pressure on the plate to the bone reduces the risk of weakened porous zones at the points of contact. Their appearance may lead to recurrent bone fractures and even osteonecrosis.17
In the case of the last of the discussed plates – LCP – even larger indentations in the plate on the bone side were used. In addition, it has special “foot-shaped” holes, half which are a conventional hole and the other half have a threaded hole, which allows both standard screws and locking screws to be attached to them. Thanks to this, the LCP plates can perform the functions of standard assembly plates and locking plates.8,10–14
Biomechanically, the main advantage of the LCP is its design, which ensures no movement between the plate-screw planes. This design has been shown to be four times more durable than one with load sharing due to movement between individual components. Conventional inserts only meet this condition under ideal conditions, when the bone allows for high screwdriving torque of the fasteners and there is no movement between the plate and the bone. Failure to meet any of these conditions may result in the failure of the conventional board design. In contrast, in the case of LCP, it will perform its function even if one or more of these critical elements are compromised.14
The research contained in the article refers to a master's thesis19 carried out at the Gdańsk University of Technology. Their purpose is to select the material and parameters for the plate that fuses the lower leg bone and to create a model of the bone-plate system. The simulations constitute an introduction to research on artificial bone with an implant, which will be carried out at the University of Bordeaux, and the results will be shown in the next publication.
2 Research methodology
The strength analysis of the bone-plate LCP model was performed in the Inventor Provessional 2023 environment, by Autodex. During the study, the Finite Element Method (FEM) was used, which is commonly and classified as an advanced method of solving systems of differential equations.
The material constituting the basis for the bone model was medical documentation provided by the Hospital in Inowrocław, including X-ray images (Fig. 1).
The model of the plate was created on the basis of LCP plates, shared by Hospital, and on the basis of publicly available catalogues of companies involved in the production of this type of plates (Fig. 2).
3 Assumptions
1.A linearly elastic model with isotropic properties was assumed;2.The viscoelastic properties of bone tissue have been omitted;3.A case was assumed in which the entire weight of a human body weighing 100 kg is carried by one limb;4.A perfectly flat fracture surface is adopted;5.An ideal connection between the internal osteosynthetic element models and the fibula model was assumed;6.The fibula was modeled in a simplified way with the preservation of characteristic surfaces and tuberosity – a model with an approximately preserved anatomical shape;7.The following boundary conditions were assumed in the model:-the system is supported in the anatomical place of contact between the fibula and the calcaneus and in two places where it meets the tibia.-force is applied to the surface of the fibula head in the direction of the shaft axis.
4 Results
Based on the available X-ray images in the medical records and the previously cited sources, a simplified sketch of the fibula was created in Inventor Professional 2023 (Fig. 3). The bone model does not take into account the exact geometry of the bases, the presence of which is not the subject of the study and does not affect the correctness of the final result, but it could interfere with further analysis processes, including the creation of a mesh of the final model.
4.1 Fibula 3D model
In the last step, injuries analogous to those presented in the patient's medical records were introduced into the bone model. As a consequence of these actions, three solids were formed, jointly forming the cortical bone of the fibula. Similarly, 3 solids made of cancellous bone were created. A composite of all the elements of the fibula was formed by establishing the bonds between them (Fig. 4).
4.2 Modeling the LCP plate
Three titanium alloys (Ti6Al4V, Ti6Al7Nb, Ti13Nb13Zr) were chosen as the material for the plate. Due to the nature of the fracture of the fibula of the analyzed patient, the type of plate was selected - a plate for the fibula distal lateral. In addition, measurements were made on the plate made available for testing by Hospital. The size and location of the holes were modeled on the basis of the plate in question and publicly available catalogues of companies producing LCP plates (Fig. 5).
The plate was tried on to assemble the dice model in order to select the places where the screws were attached. Then holes were made in 8 places (Figs. 6 and 7).
The obtained assembly model was opened in the analysis mode and divided into finite elements of average size 0.1 mm, obtaining 307,797 nodes and 160,492 elements (Fig. 8). In addition, the mesh in the vicinity of the holes was compacted, changing the size of the elements to 0.05 mm, which allowed for more accurate results in these areas.
According to the anatomical position of the fibula in the system of the bones of the lower limb, an immovable bond was set (all degrees of freedom were removed) at the point of contact of the lateral malleolus of the fibula with the fibular block of the calcaneus. In addition, frictionless bonds (no movement in the radial axis) were placed at the points of contact between the fibula and the tibia (Fig. 9).
The force was applied at the point of contact between the head of the fibula and the lateral condyle of the tibia in the direction of the axis of the shaft. The value of the force, after taking into account all assumptions, is 981 N (N – unit of force) (Fig. 10).
5 Results of the FEM analysis of the platelet-bone system
The calculations were performed under the same boundary conditions and contacts for each of the 3 selected materials based on the Huber hypothesis and the Huber-Mises ductility conditions. Stress reduced for complete bone-plate LCP systems with fixtures (Fig. 11).
The biggest reduced stresses were found in the first mounting bolts. Below is a more detailed course of them after excluding the LCP plates from view and reducing the color to 100 MPa in each of the layout (Fig. 12).
The exact distribution of reduced stresses in the most loaded bolts of the systems is shown below. To better illustrate their course, the modified color was again reduced to 100 MPa) (Fig. 13).
The total displacements of the bolts with the highest value of reduced stresses are approximately shown below (Fig. 14).
In the bone-plate combination, excluding screws, in each of the systems the most loaded place was the lowest hole at the distal end of the fibula. To better illustrate their distribution, the visibility of the plates has been turned off and the color has been changed to 50 MPa (Fig. 15).
Fig. 16 shows the results of the analysis for the assembly of the fibula model and the changes occurring in it - its total displacement in each of the systems.
The behavior of the plates in the systems (displacement of each of them) is shown below (Fig. 17) with the visibility of all other assembly elements turned off.
The course of reduced stresses for LCP plates is shown in Fig. 18.
The results obtained during the analyses are presented in a summary table (Tabl.1).
6 Discussion
Despite all the potential advantages of locking plates over traditional plates, a clinical advantage of LCP has not always been observed. Many publications report good or excellent results with locking plates in both humans and animals, but in most cases the results in terms of healing time, infection rates, and nonunion are no different from other types of plates or external fixation.20–28 There are reports of increased complication rates with locking plates compared with traditional plates, clearly demonstrating that they should not be considered a universal solution.29–32
Moreover, there are many studies proving that bone growth was achieved in improperly healing fractures and the resolution of infections, including drug-resistant ones, after replacing conventional plates with blocking plates.18,20,33,34 Healthy bone is naturally resistant to infections, but it quickly becomes susceptible when deprived of blood supply, ischemic, unstable, or in the presence of a foreign body.35–37 Necrotic bone is an ideal substrate for the adhesion of bacteria in the body's bacterial flora, which gradually colonize the surface of the plate and the weakened bone adhesion zone.14 A biofilm, i.e. an inanimate biological membrane, is formed. The microorganisms that make up the biofilm structure are much more resistant to the patient's immune system, antibacterial agents and antibiotics than when they remain in the body as planktonic forms. The resulting infections are difficult to treat.2,38
In today's medicine, LCP plates (Locking Compression Plates) play an important role in stabilizing bone fractures and fusions. They are an effective method of treating bone fractures, as well as their reconstruction, leading to improved treatment outcomes and increased patient safety.
The subject of considerations in the paper was the selection of parameters and material for the LCP plate anastomosing the fibula, for this purpose this anastomosis for the fractured fibula was modeled. The influence of the selection of parameters and the structural material of the plate on the state of stresses and displacements in the bone-plate system was analyzed, assuming that the entire body weight is transferred during standing by one of the lower limbs. For each of the analyzed titanium alloys, the results of analyses with a similar course were obtained.
Ignoring the results of reduced stresses in bolted connections, the tensile strength limit values specified by Będzinski39 were not exceeded in the bone model, which was shown after modifying the color strip value to 50 MPa. The division of the model into structures with different strength properties allowed for a simulation analogous to the anatomical structure of bones. In the same way, during the analysis of the board, the values of the color bar were lowered to 30 MPa, in order to better illustrate the areas most susceptible to force. The values of reduced stresses did not exceed the limit values for the analyzed titanium alloys determined in the study by A. Ryniewicz and M. Otto 40. In undercuts characteristic of LCP plates, the values of reduced stresses reached safe values in the range of 20–30 MPa. These results indicated the correct selection of overall dimensions and undercuts of the tile. In none of the analyses carried out did the total displacement of the elements exceed 1 mm. This was particularly important in the case of fracture fissures, as the low results obtained promote the formation of callus, which was emphasized in their study by B. Kozub et al..41
The main difference between the presented studies and those described in the literature40–47 is the fact that the anastomosis for the fibula is analyzed using the LCP plate model. For example, the research conducted by B. Kozub et al.41 concerned the tibia stabilized using the ZESPOL method. On the other hand, K. Koczułap et al.48 analyzed the state of stress during tibial fusion with a fixator made of a combination of several plates connected to the bone with screws.
7 Conclusions
1.The maximum and minimum values occur in the same places, assuming similar values.2.The maximum values of reduced stresses in bone-plate systems have always occurred at the point of connection between the upper screw and the plate. The results of the conducted tests suggest the defectiveness of the designed bolted connections due to the occurrence of the highest, exceeding the permissible, stress values for each of the elements of the plate-bone assembly. Further research in this direction could include the selection of the shape of the holes and the design features of the locking bolts placed.3.In addition, in order to obtain full results of the influence of the plate on the anastomosis, it would be necessary to carry out tests in various phases of gait, taking into account the variable values and directions of the forces acting, because the static analyses carried out concerned only the load of the assembly in the standing position.4.The tests showed that the lowest reduced stresses occurred when the titanium alloy plate Ti-13Nb-13Zr was used. At the same time, it was in the case of this plate that the largest total displacements occurred. For the Ti-6Al-7Nb material, the reduced stresses reached the highest values among the three analyzed materials. Intermediate values were obtained by the LCP bone-plate system made of titanium alloy Ti-6Al-4V, however, its presence in the study was only a control, because due to the highly carcinogenic effect of vanadium, even with short-term contact with the body, it should not be used on implants. Taking into account the results obtained, including the given minimum difference in the values of total displacements, the most suitable of the tested materials would be titanium alloy Ti-13Nb-13Zr.
The authors of the manuscript declare that there is no conflict of interest.
CRediT authorship contribution statement
Monika Bajerska: Conceptualization, Methodology, Software, Formal analysis, Writing – original draft. Beata Świeczko-Żurek: Validation, Writing – review & editing, Supervision, Project administration. Marcin Nowak: Resources, Visualization.
Patient's consent
The images used for the examination do not in any way allow for the identification of the patient. X-ray images are not sensitive data and there is no need to obtain permission for their publication.
The article does not contain any information that would require the patient's consent.
Ethical statement
This publication is devoted to a retrospective study. The trauma and surgical treatment the results of which have been described have already taken place in the past and have not been carried out for the purposes of this article.
Funding
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
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