Biomechanical evaluation of a custom-made mandibular plate

In the field of maxillofacial surgery, mandibular reconstruction with plates is one of the operations that is performed when resection of part of the jaw is unavoidable in patients suffering from pathologies such as, for example, neoplasms and osteonecrosis. Through the use of standard prostheses, which are commercially available in various models, mandibular reconstruction is possible. However, in the presence of particularly serious and complex clinical pictures, in which it is necessary to resect large parts of the mandibular bone, such as in some oncological cases, the use of serial prostheses is not always resolving. In these cases, a customized implant, designed specifically for the patient, is preferable. Aim of this work is the mechanical evaluation of a custom-made mandibular plate with an innovative bone-implant interface geometry through a finite element analysis. Three physiological loading conditions were analysed: RUC (right unilateral canine) bite, RGF (right group functional) bite and maximum opening. Finally, the maximum pull-out force acting on the fixation screws was evaluated through an experimental fatigue test.


Introduction
Thanks to improvements in technology and the advent of additive technologies to support maxillofacial surgery, it is possible to achieve better aesthetic and functional results for patients requiring major demolition surgery [1,2].The current gold standard for restoring extensive mandibular defects after surgical ablation is the insertion of a reconstructive titanium plate, however, a failure rate of such an implant related to its mechanical mobilization is still reported [3][4][5].One of the main risk factors after reconstruction of mandibular bone defects using reconstructive plates is mechanical failure.The latter may be due to loosening of the fixation screws, fracture of the plate and aseptic loosening of the implant.
The muscular forces associated with the simple opening or closing of the mandible or in some cases the occlusion forces of incisors and molars in the healthy mandible result in shear and pull-out forces on the screw that can lead over time to loosening of the screw or in the most extreme cases to mechanical failure of the plate.An improved bone-prosthesis interface could reduce shear and pull-out forces acting on the screw during normal physiological postoperative movements and thus reduce the likelihood of loosening and implant failure.
The primary stability of a mandibular plate with innovative bone-implant interface geometry was evaluated in comparison to standard plate geometry by means of a four-point bending test simulating a real-life loading condition.Furthermore, by means of a finite element analysis, a biomechanical evaluation of a custom-made mandibular prosthesis with a new bone-implant interface was carried out in collaboration with surgeons of the maxillofacial surgery department.

Description of the investigation
The traditional mandibular plates designed and manufactured in titanium alloy with 3D EBM technology, present the geometric characteristics shown as Plate A in Figure 1.Plate A has a constant thickness along the entire length, representing the state of the art currently used in maxillofacial surgery.The modified plate (Plate B) has similar geometric characteristics but different interface with the bone tissue.Plate B shows an innovative retention structure at the interface with the osteotomy plane and a fixation screw passing through it.The case study considered concerned the mandibular reconstruction of a 60-year-old male patient suffering from bisphosphonate osteonecrosis.The patient's anatomical data obtained by CT examination were used to reconstruct the 3D model of the mandible using Mimics software (Figure 2).

Plate A
The cutting planes were indicated by the prescribing physician and then used to virtually resect the jaw by dividing it into three parts: a central area to be removed and the two healthy lateral stumps.
The device shown in Figure 3 takes the form of a thin plate that follows a profile as close as possible to the lower profile of the original corrected jaw and present an innovative interface as seen previously in the plate B of experimental test.The implant is fixed with screws.The plate has a height of 10 mm, a thickness of 3 mm throughout the main body and 2 mm at the attachment points.There are also two retention structures in the interface areas with the bone resection surfaces.The plate also has a grid structure, a lateral window to facilitate the reattachment of muscles and other soft tissues that, during surgery, are disconnected from the portion of the jaw to be removed.The fixation elements are bicortical (self-tapping) screws, specific for applications in which the thread must be gripped in both corticals of the bone.The mandibular prosthesis was manufactured from titanium alloy (Ti6Al4V ELI) using the EBM (Electron Beam Melting) process.

Finite element analysis
In this study, the biomechanical behaviour of the implant was analyzed with the aim of verifying the resistance of the prosthesis to physiological loads and the distribution of deformations that these induce in the bone tissue near the fixation elements, in order to predict whether screw loosening and bone resorption phenomena may occur, both of which must absolutely be avoided for a successful implantation.
The software used for the structural analyses was MSC Marc Mentat 2019 (MSC Software Corporation, Santa Ana, CA), a non-linear finite element analysis software developed to simulate the behavior of complex materials and interaction in the presence of large deformations.
Finite element analyses of the prosthesis-bone system were conducted by subjecting a model of the same to physiological loads.The following loading conditions were analyzed: 1. bite RUC (right unilateral canine); 2.
maximum opening.The first two are unilateral static bite configurations.Only unilateral bites were analysed as the mandible, after resection and implantation, has teeth only on the right hemiarch.In particular, the incisors, canine and right premolars were present.The condition of maximum opening is that of the mandible in fully open position, considering a rotation angle of 30 deg in the sagittal plane.
The constraints and loads applied to the system vary as the condition changes: -in the RUC bite, the condyles and the occlusion surface, in this case the right canine only, were considered fixed, -in the RGF bite, the occlusion surface is constituted by the whole canine and right premolars, therefore the surfaces of these three teeth and the condyles have been fixed, -in the case of maximum opening, only the condyles are considered fixed.
The values and directions of the forces exerted by the muscles under the three conditions have been the subject of numerous studies, and can be found in the literature [6][7][8][9][10].
It was decided to carry out, for each loading condition, an analysis of the overall prosthesis-bone system considering, as a first approximation, the screws as infinitely rigid cylinders transmitting the load from the bone tissue to the prosthesis, and vice versa, as joints.Subsequently, in order to analyse in detail the stress-strain state present in the screw-bone interface zone with the real threaded profile, analyses were carried out on two sub-models: one comprising the fixation zone in the left abutment of the mandible, and another for the right one, considering real threaded profile of the screws [11].
The materials involved in the simulation are the cortical and trabecular bone tissues of the mandible, the titanium alloy Ti6Al4V ELI of the plate [12], and the titanium alloy of the Stryker self-tapping screws.In the analysis, the behaviour of all four materials was assumed to be linear elastic and isotropic, with the values of the respective elasticity constants, Young's Modulus (E) and Poisson's coefficient (ν), shown in Table 1  The 3D models of all components (prosthesis, right cortical bone, right spongy bone, left cortical bone and left spongy bone) were imported in STEP format into Marc Mentat 2019 software (MSC software).Meshes of the five solids were created with tetrahedral elements.The mesh of each component was defined as a meshed deformable contact body, so that the contacts between the bodies could subsequently be imposed.
To simulate the welded screws, Nodal Tie Type 100 (all degrees of freedom) links were set up, connecting nodes on the inner surface of each hole to a master node, positioned in the centre of the hole.This was performed for both the attachment holes on the prosthesis and the holes drilled in the bone.Subsequently, the master nodes of each pair corresponding to a screw were connected via a link of the same type (Nodal Tie Type 100).Through these, the force is transmitted between the prosthesis and the bone and represents the force acting on the screws.Two types of contact were defined, a glued type (G) to impose a perfect seal between the cortical and spongy tissues, and a touching type (T) with a friction coefficient of 0.3 to simulate contact at the plate-bone interface.Stepway forces were applied, to simulate a quasi-static loading The mechanical behavior of the prosthesis was analyzed by observing how it responds to physiological loads in terms of stress distribution.It was observed that the Equivalent Von Mises Stress in the prosthesis is far below the yield stress (930 MPa) of the Ti6Al4V-ELI alloy, and also below the fatigue limit (600 MPa).This result guarantees the excellent mechanical resistance of the plate to stress.The prosthesis, therefore, should neither fracture nor plastic deformation under physiological loading conditions.
In order to analyze the stress and deformation state in the screw-bone interface zones, two sub-models were produced: one for the left fixation zone and another for the right (Figure 4).Forces were applied to the nodes belonging to the head of the screw, obtained from the analysis of the global model, connecting them to a master node to which the overall force is applied.
Simulations conducted on the sub-models of the right and left fixation zones were carried out to analyse in detail the deformations revealed in the bone surrounding the screws.In order to check whether the values of these deformations fall within the bone remodelling and modelling zone hypothesised by Frost [9], i.e. whether they are between 200 με and 4000 με, the values of the Equivalent Elastic Strain of the bone, obtained under the three loading conditions, were verified.
The strain values obtained in the bone in the area surrounding the fixation screws fall within the zone of bone remodelling and modelling assumed by Frost, confirming that there is no bone resorption in the vicinity of the fixation screws (Figure 5).

Experimental tests of dynamic pull-outs
The FEM analysis made it possible to assess that the greatest force occurs on the screws positioned at the extreme points of the plate; the modulus value of this force was projected onto the direction of the axis of the screw, thus obtaining the pull-out force, which specifically for the case in question has a value of approximately 120N.The aim of the test campaign was to assess whether this force acting dynamically on the screw leads to its loosening over time and thus to the failure of the implant.For this purpose, an experimental set-up was carried out that comprised: -Grade 40 polyurethane foam block -Screw gripping system (Figure 6) specially designed and manufactured for the purpose.This system consisted of two components.The first component consisted of a plate with a through hole in the centre, suitably shaped to accommodate the screw head and two small teeth that allowed it to engage with the second component, which instead ensured the connection with the test machine.
-Foam locking system -Fixing screw with diameter 2mm and length 12mm.
The resulting system was then placed inside the test machine, as shown in Figure 6.The test machine used was the Instron 8501, a servo-hydraulic machine on which a 100 kN load cell was mounted.The characteristics of the machine did not allow the execution of the dynamic test for such small loads in relation to the full scale of the load cell.To overcome this limitation, it was decided to interpose a spring with known elastic characteristics to the test system.Specifically, a spring with an elastic constant of 31.8N/mm was used.The test was then carried out in displacement control, applying a displacement of ±3.77mm, a value for which, multiplied by the spring's elastic constant, yields a load value of approximately 120N.
The dynamic test was performed by applying 50,000 cycles at a frequency of 5Hz to the system.This number was derived from two different evaluations -the average number of chewing cycles performed by an individual over 5 years is 1 million [14].
-the time required for the implant to osseointegrate is approximately 3-5 weeks in a healthy individual [10] ,but can be up to 12 weeks in patients with diseases such as diabetes [15].
Therefore, an individual before the implant osseointegrates performs on average about 50,000 chewing cycles in the worst case, which is therefore the reference value for assessing the pull-out strength of the screw.1306 (2024) 012017 IOP Publishing doi:10.1088/1757-899X/1306/1/0120176 Tests were performed on three different samples and in all three cases tested the system showed no signs of failure, again confirming the performance of the implant from a functional point of view.

Conclusions
This study proposes a new mandibular plate with an improved bone-implant interface due to the presence of a retentive structure and a fixing screw.
The finite element analysis evaluated a case study of custom-made reconstruction of a mandibular plate with bone-tissue interface as plate B developed in collaboration with surgeons of the maxillofacial surgery department.
It showed that the resistance of the plate and the fixing screws, in the post-surgery loading conditions are lower than the yield stresses, as well as the deformation values obtained in the bone in the area surrounding the fixation screws fall within the area of bone remodeling and modeling.
Finally, the pull-out forces to which the screws are subjected are able to resist dynamic load conditions until the complete osseointegration of the implant.

Figure 1 .
Figure 1.Frontal (left), lateral (centre) view and interface (right) for traditional and modified plates.

Figure 4 .
Figure 4. Submodels of the right and left fastening zones.

Figure 6 .
Figure 6.Upper and lower supports (left) and experimental pull-out test setup (right).

Table 1 .
Mechanical properties of the materials