Biomechanical analysis of costochondral graft fracture in temporomandibular joint replacement

This study is the first attempt to explore the reason of costochondral graft fracture after lengthy mandible advancement and bilateral coronoidectomy by combining finite element analysis and mechanical test. Eleven groups of models were established to simulate costochondral graft reconstruction in different degrees of mandible advancement, ranging from 0 to 20 mm, in 2 mm increment. Force and stress distribution in the rib-cartilage area were analyzed by finite element analysis. Mechanical test was used to evaluate the resistance of the rib-cartilage complex. Results showed a sharp increase in horizontal force between 8 and 10 mm mandible advancement, from 26.7 to 196.7 N in the left side, and continue increased after 10 mm, which was beyond bone-cartilage junction resistance according to mechanical test. Therefore, we concluded that bilateral reconstruction with coronoidectomy for lengthy mandible advancement (≥ 10 mm) may lead to prominent increase in shear force and result in a costal-cartilage junction fracture, in this situation, alloplastic prosthesis could be a better choice. We also suggested that coronoidectomy should be carefully considered unless necessary.


Results
Stress distribution. Obvious distortion of the rib cartilage was observed after muscle force loading. when mandible advancement ranged from 0 to 8 mm, costal cartilage deformed forward, stress was slightly concentrated on the anterior edge of the neck. However, when the mandible advanced more than 10 mm, rib cartilage deformed backward, stress was heavily concentrated on the posterior edge of the neck (Fig. 2). Cartilage was likely to break on the posterior margin of the neck from 10 to 20 mm.

Force alteration.
To better analysis force alteration during mandibular advancement, we decomposed the resultant force into axial force parallel on the long axis, and shear force perpendicular on the long axis (Fig. 3).
Corresponding data were shown in Table 1. Prominent force changes took place between 8 and 10 mm advancements.
Resultant force behavior. When the mandible advanced from 0 to 8 mm, the resultant force on the connector increased in a linear fashion, from 421.3 N to 456.3 N in the left, from 414.7 N to 465.6 N in the right, respectively. There was a significant reduction (138.7 N in the left, 174.1 N in the right) between 8 and 10 mm, where the coronoid process had just been excised, from 456.3 N to 317.6 N in the left, from 465.6 N to 291.5 N in the right, respectively. With the mandible continue advancing from10mm to 20 mm, the force increased again in a linear fashion, from 317.6 N to 359.0 N in the left, from 291.5 N to 350.8 N in the right, respectively (Fig. 3, Table 1).     Shear Force alteration with or without coronoidectomy. The data of shear force alteration from 0 to 8 mm with or without coronoidectomy was showed in Table 3. Without coronoidectomy, the shear force decreased in a linear fashion, from -113.2 N to 26.7 N in the left, from -133.7 N to -1.9 N in the right, respectively. With coronoidectomy, it increased in a linear fashion, from 94.6 N to 188.5 N in the left, from 70.1 N to 157.7 N in the right, respectively.

Discussion
In 1920, Gillies firstly described the use of costochondral graft(CCG) to perform a Temporomandibular joint(TMJ) reconstruction, but it didn't become popular until 1974 17 . Since then, CCG has been a mainstream method in a long time, especially before artificial joints were developed [1][2][3][4][5] . CCG has a cartilaginous cap, the native size and morphological similarity make this type of graft a perfect match in TMJ. In addition, growth potential and minimal immunological counter-response also contribute to the advantages of CCG 6,7 . Scholars including Awal et al. 1 9 . It is worth noting that several reports 10,11 mentioned postoperative costochandral graft fracture, mostly occurred at CCG-ramus junction. Idiopathic condylar resorption (ICR) can occur with a variety of underlying factors 14 . It is mostly bilateral and seems to have a high occurrence in women aged 15 to 35, especially those with a preexisting temporomandibular joint (TMJ) dysfunction and a high mandibular plane angle. As the result, these patients tend to exhibit a decrease in posterior facial height, retrognathism, and progressive anterior open bite with a clockwise rotation of the mandible [12][13][14] . Several therapies had been proposed to treat ICR at different stages [18][19][20][21][22][23] . For patients with active ICR, condylectomy and CCG reconstruction is a considerable choice. Troulis et al. 15,16 reported long-term stability of CCG in ICR, twenty-six patients were involved and achieved a stable result.
Alloplastic prosthesis has the advantage of avoiding secondary surgery, but the price is very expensive. Besides, only one type of prosthesis has license in China by now. Based on the above facts, we performed a CCG reconstruction for this present patient who diagnosed as ICR through Detailed clinical and imaging examination. The mandible was advanced approximately 13 mm to achieved a normal occlusion, bilateral coronoidectomy was performed Simultaneously to avoid mouth opening limitation. Unfortunately, relapse happened within 6 months, the patient presented with facial asymmetry and occlusal disorders. During the second surgery, we found the patient's graft had ruptured from the bone-cartilage junction. Merkx and Freihofer 11 inferred that a significant muscular component might contribute to this disappointing result, but they did not verify it. We hypothesized that lengthy mandible advancement with coronoidectomy may alter force distribution on the CCG, hence lead to rib fracture. To explore the truth, two questions must be answered: one is the force distrubution of CCG, the Table 2. Maximum resistance of CCG samples, Horizontally (n = 5) and vertically (n = 5).  www.nature.com/scientificreports/ other is the resistance of CCG, therefore, we conducted an FEA and mechanical test as the above. As far as we know, this is the first trial to explain the reason of CCG fracture, and also the first study to combine FEA with mechanical testing of the temporomandibular joint.
As lateral pterygoid has been cut during surgery, the shear force on the CCG neck consisted of three parts: horizontal force of temporalis, medial pterygoid and masseter. Only the temporalis muscle had a backward component in the horizontal direction, the other two muscles directed forward. The balance of these three muscles determined the direction and value of shear force.
According to our experiment, when mandible advancing in the range from 0 to 8 mm, shear force directed backward, so the new condyle was acted upon by a forward and downward force from the posterior wall of the glenoid fossa, and deform forward (Fig. 2). During mandible advancing, the shear force was gradually decreased and always within safe range (Table 1). However, with the continual advancement of mandible, the coronoid progress could contact with the inner face of zygomatic bone and limit mouth opening. Therefore, coronoidectomy was performed from 10 mm advancement. Without temporalis, the former muscle force balance has been interrupted and only medial pterygoid and masseter was left. Then all the related muscles directed forward in the horizontal direction, CCG deformed backward by contacting with the anterior wall of the articular fossa, and the value of shear force increased steeply. It could be over 196.7 N (Table 1) once advancing more than 10 mm and beyond CCG's resistance, which was about 192 N according to the mechanical test ( Table 2). Hence we concluded that bilateral CCG reconstruction with coronoidectomy for large extent mandible advancement lead to a sharp increase in horizontal component, resulting in CCG fracture at the bone-cartilage junction.
During mandible advancement process, horizontal component was affected by both magnitude and angle of muscle force. To find out whether the dramatic change in horizontal component between 8 and 10 mm was due to the loss of temporal muscle or the change in angle, we compared the distribution of shear force values after and without coronoidectomy from 0 to 8 mm ( Table 3). The results showed that after coronoidectomy, there would be an increased forward shear force on the CCG neck from 94.6 N to 188.5 N in the left, 70.1 N to 157.7 N in the right, respectively. By contrast, without coronoidectomy the shear force directed backward and decreased from 113.2 N to 26.7 N in the left, 133.7 N to 1.9 N in the right, respectively. It confirmed that loss of temporalis is the main cause of prominent shear force increase between 8 to 10 mm. Besides, bilateral CCG reconstruction with coronoidectomy for mandible advancement in a small range (< 8 mm) still remained safe, which supports the fact that CCG is a mature method in the last few decades.
Autogenous bone grafts and alloplastic prosthesis were widely used for TMJ reconstruction, each with its own advantages. Controversies about these two methods exited for a long time [24][25][26] . So far, there has been no clear conclusion as to which conditions are more suitable for artificial joints. This present study suggested that the strength of CCG is not strong enough to counteract muscle strength during extensive mandibular advancement and coronal process resection, resulting in a period of postoperative instability. Some researchers have reported that the mechanical properties of artificial joints 27,28 . According to the prosthesis manual issued by TMJ Concepts Company, the average yield strength was 3514 N, which is far more resistant than CCG, enough to withstand horizontal shear forces. From this point of view, for patients with severe mandibular retraction, the artificial joint is more suitable for TMJ reconstruction.
Our study has some limitations that must be addressed: the CT data was from one specific patient while the maximal muscle forces were from literature, so the loading value can hardly accurately reflect the reality of the situation. Furthermore, the rib in mechanical test was not from human being, even though the size and cartilage height were almost the same as the pork rib, the actual rib resistance might be slightly different. Despite those shortcomings, mechanical change trends can be well simulated.
In conclusion, bilateral CCG reconstruction with coronoidectomy for mandible advancement in a large degree (≥ 10 mm) will induce a prominent force alteration and likely lead to CCG fracture, for this situation, alloplastic prosthesis should be a better choice. In addition, the coronal process plays an important role in maintaining joint balance and should not be easily detached.

Methods
All methods were carried out in accordance with relevant guidelines and regulations. All experimental protocols were approved by Shanghai Ninth People's Hospital Ethical Committee (SH9H-2019-T288-1). Informed consent has been obtained in this study.

Establishment of computer-aided design (CAD) models.
CT data were obtained from the relapsed patient, a 25-year-old female who suffered from condylar resorption several times without clear etiology (slice thickness, 0.625 mm; GE Healthcare, Buckinghamshire, England). Data were stored and then imported into Mimics software (Version 20.0, Medical, Leuven, Belgium) for 3D reconstruction. The surgical procedure was simulated in a 3D model. Contralateral seventh rib was selected and cut into suitable size, the cartilage side was contacted with the middle of glenoid fossa, the bone side was smoothly contact with the posterior margin of mandible ramus.
In order to simulate the different distances of mandibular advancement, eleven groups of models were established advancing from 0 to 20 mm in 2 mm increments (Fig. 4). It is worth noting that once mandible advanced more than 8 mm, mouth opening would be limited as the inner face of the frontal section of the zygomatic bone blocks the coronoid process, so coronoidectomy must be performed from 10 mm and over groups (Fig. 5).
Establishment of finite element model. Finite element models (FEM) are key tools which can be applied to mandible biomechanics 29 . We used Hypermesh, a finite element grid generation module software Scientific Reports | (2020) 10:17754 | https://doi.org/10.1038/s41598-020-74548-1 www.nature.com/scientificreports/ by Hyper Works, for pre-processing. LS-DYNA, the dynamic explicit algorithm module software from LSTC software, was used as the solver and processor. Analysis only included skull regions in contact with the CCG. Distant regions were simplified by applying boundary conditions. Tetrahedral mesh was used in the analysis while locations of the prosthesis and areas with large deformation were treated with mesh densification. The average mesh size of the mandibular was 2 mm. For locations with large curvature and possibly large stress, the mesh size of 1 mm was used for intensify. The average mesh size for rib was 0.8 mm, and the costochondral cartilage in contact with the articular fossa was 0.4 mm. The whole calculation model has a total of 45,700 elements and 155,200 nodes (Fig. 6a).
Computation can be reduced by simplifying screw connections. In our analysis, the rigid deformation mode of the tetrahedral element and low calculation accuracy were resolved by using the selective reduction integral form with node rotation for the tetrahedral element.
Material parameters and boundary conditions. In the FEA, the 'engineering stress-strain curve' of the material was converted into the 'real stress-strain curve' . Converted material data 30 were listed in Table 4.  www.nature.com/scientificreports/ To ensure the stability of the bone graft, the stress of each part of the complex should be less than the yield strength of the material. Following related references, we exerted maximum muscle force on the models to simulate extreme conditions. Parameters 29,31 of six principal jaw-closing muscles were listed in Table 5. The six main muscles involved: superficial masseter(SM), deep masseter(DM), medial pterygoid(MP), anterior temporalis(AT), middle temporalis(MT), posterior temporalis(PT) were simulated to both sides of the mandible from corresponding muscle attachment (Fig. 6b).
As the mandible moves forward, the muscle length and strength changed, based on the formula: F = PAi (F = muscle force; P = the intrinsic muscle strength constant, P = 0.37*106 N; A = the physiological cross-sectional area of the muscle) with the constant muscle volume, we deduced the formula: Fx = F 0 *L 0 /L X , enabling the calculation of direction and value of muscle forces (Table 6).    www.nature.com/scientificreports/ Reprints and permissions information is available at www.nature.com/reprints.
Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/.