Fracture Toughness of Ovine TMJ Disc: Effects of Crack Length and Orientation

Fracture Toughness of Ovine TMJ Disc: Effects of Crack Length and Orientation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Fracture Toughness of Ovine TMJ Disc: Effects of Crack Length and Orientation saeed Salehipour, Ata Hashemi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4450894/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The human mandible experiences mechanical stress from several directions as a result of activities such as speaking, chewing, and other everyday actions. The TMJ disc facilitates mandibular motion and absorbs all of the stresses associated with daily activities. Thus, the TMJ disc is likely to be susceptible to rupture. Hence, it is crucial to investigate its susceptibility to failure and rupture. The aim of this study was to determine the impact of fracture orientation, sample thickness, and crack-to-width ratio on the amount of energy needed to cause the growth of flaws on the disc. Fracture toughness was investigated by conducting cyclic tensile testing on 40 ovine TMJ discs in two different notch orientations: anteroposterior and mediolateral. The J-integral was chosen as a measure of the critical fracture energy of the TMJ disc. The Shapiro-Wilk test showed that fracture toughness data did not follow a normal distribution (P-value < 0.05). Due to unequal variances, the Kruskal-Wallis test was used to examine the data. The study revealed that the fracture toughness in the anteroposterior direction was much higher than that of the mediolateral, indicating a superior ability to resist tearing and fracture in the anteroposterior direction. Furthermore, the study's findings revealed that both the direction of the crack and its initial crack-to-width ratio influenced the TMJ disc's fracture toughness. The study also evaluated TMJ disc failure patterns to better understand its pathophysiology. The results showed that the crack growth profile in two orientations has a completely different structure. The 2D finite element analysis results also indicated a significant relationship between the fracture toughness and the percentage of cracks, demonstrating that increasing the crack-to-width ratio leads to a rise in fracture toughness. These findings help understand TMJ injuries to the disk and develop better treatments. TMJ disc Fracture toughness Mandible J-integral Notch orientation Finite element analysis Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Introduction The temporomandibular joint (TMJ) disc connects bones in the joint, facilitating movement between the glenoid fossa and the articular eminence. This joint includes a fibrocartilage disc between the temporal bone and the mandibular condyle, with fibrocartilage layers covering bone surfaces [ 1 ]. Enclosed by a capsule, connective tissue, and a synovial membrane, the TMJ disc exhibits different motions: translation in the superior part and rotation in the inferior part [ 2 ]. It endures various mechanical loads such as compression, tension, and shear, influenced by both static and dynamic forces like clenching or chewing [ 3 ]. The disc's stress is affected not only by its motion but also by its structure, shape, size, and anatomy [ 4 ]. TMJ discs lubricate, absorb stress, and stabilize joints. Compromised mainly of type I collagen (2), these discs respond to loads based on their orientation, intensity, and duration [ 5 ]. Without the TMJ, regular tasks such as speaking, eating, and drinking would be difficult. The TMJ allows complex jaw motions and absorbs mechanical force [ 6 – 8 ]. Since the TMJ allows both translational and rotational motions, it helps the jaw move smoothly with the skull. During movement, the TMJ disc aligns the articular surfaces by slipping between them as the condyle shifts Besides synovial fluid, the TMJ disc also provides lubrication. The fossa shape, articular eminence, and ligaments limit TMJ disc movement. However, failure of any joint components can cause harm to the patient[ 9 , 10 ]. The study of mechanical properties of discs has been challenging due to differences in loading rates, sample preparation, sampling regions, testing methods, temperatures, ages, and tissue quality. Despite efforts, complete understanding of biological variations, particularly between humans and animals, is difficult to determine. Herbivores like cows, goats, and rabbits demonstrate the highest compressive modulus, indicating a correlation between structure and function [ 11 ]. Different food types, masticatory patterns, and animal sizes and morphologies have been tested and analyzed. It's important to account for each species' mechanical properties under specific testing conditions that yielded these results. Porcine, bovine, and ovine exhibit closer similarity to humans in terms of both size and complex anatomy compared to other animals. [ 12 ] Several tissues, including cartilage, muscle, skin, and discs, experience dynamic loadings that may result in damage or the growth of cracks within the tissue. Such issues can lead to pain and dysfunction in the affected tissue [ 13 ]. It’s crucial for these tissues to have enough strength to endure mechanical stresses and prevent internal injuries, such as rupture and fractures. Furthermore, these tissues also contain microscopic flaws that can progressively expand and result in tissue deterioration. The fracture toughness of a material is a mechanical property that indicates how well it resists crack propagation. Typically, a fracture toughness test involves propagating a crack through a material sample [ 14 ], measuring the energy required to create a given amount of new crack area. This property indicates the material's "defect tolerance,”, demonstrating its capacity to resist cracks and other defects while retaining its strength. Studies have been performed on the fracture toughness of a wide variety of engineering materials, as well as bone and teeth, the body's hard tissues. There have been relatively few investigations to measure fracture toughness in the soft biological tissues, regardless of the fact that cartilage, muscle, skin, etc., are often damaged by cracks and mechanical injury, which may cause pain and disability [ 1 ]. During the regeneration process, these tissues must be tough enough to resist the propagation of in-vivo defects such as injuries and internal lesions. Moreover, all materials contain microscopic flaws created during the regeneration process. These inherent defects may limit a material's strength [ 15 ]. Acquiring insight into the deformation and fracture characteristics of soft tissues is crucial in order to prevent damage and to suggest effective healing approaches. So far, the mechanical factors responsible for the propagation of defects in the TMJ disc have not been previously documented in research. Therefore, the objective of the present investigation was to determine the energy required to cause a propagation of defects on the disc responsible. The J-integral was selected to quantify the critical fracture energy, due to its ability to account for the non-linear mechanical characteristics of the TMJ disc. The fracture toughness of ovine TMJ disc was investigated based on their similarity to human disc. Fracture toughness was studied in two directions for ovine TMJ discs. The primary objective of the current research was to examine the impact of crack length, orientation, and disc shape parameters on fracture toughness. Two hypotheses of the study were that first, crack propagation would exhibit greater resistance perpendicular to the fibers compared to the parallel direction, and secondly, extending the initial crack would increase fracture probability while decreasing failure energy. Material and methods Specimen Preparation: Specimens were tensile-conditioned, and notch length was ensured to be at least 25% of the sample width. For a visual representation of the testing setup, refer to Fig. 1 . Although biological differences between humans and animals cannot be fully explained, previous studies suggests that porcine and ovine are structurally most like humans [ 16 ]. The J-integral testing method, a measure of fracture toughness [ 17 ], was employed on 20 fresh 8- to 9-month-old male ovine heads, compromising a total of 40 discs. The heads were acquired from a local abattoir, transported to the lab in an ice container within an hour, and refrigerated at -5°C. Each disc of a pair was identified as right or left, placed in a labeled plastic storage container with 0.1 M phosphate buffer solution (PBS) in the lab [ 18 ], and frozen at -10°C until testing. Before testing, each disc was thawed in PBS at 22–25°C for 30 minutes and its dimensions were measured with a caliper with a resolution of 0.05 mm (Table 1 ). The crack length was measured with a 50x digital microscope. The samples were randomly split into two groups: 1) with a perpendicular notch (20 discs), and 2) with a notch parallel to the fibers (20 discs). The intermediate zone (IZ) of each disc was sectioned with a scalpel. An intact ovine TMJ disc has been shown in Fig. 2 a. Test groups: The specimens were classified into two distinct groups. 1-) Perpendicular notch to the fibers (AP), 2-) Parallel notch to the fibers (ML). Both groups were tested in the same conditions, with the only difference being the length of the notch on the disc. All tests were performed at the displacement rate of 10 mm/min. A servo electrical testing machine (Santam-STM/1) was used for applying 12 displacement control cycles with a sinusoidal force waveform before each test as preconditioning. AP and ML orientations are shown in Fig. 2 b. The displacement range was incrementally increased by 0.1 mm after each test, and another set of cyclic tests consisting of 12 cycles was conducted. The initial notch length varied from 25–75%. Throughout the tests, the specimen was sprayed with PBS. An exclusive fixture was designed and manufactured to grip the samples. Tests were conducted with the loading axis parallel to the anteroposterior (AP group) and mediolateral (ML group) collagen fibers, respectively (Figs. 2 c and 2 d). A scalpel was used to cut a transverse notch in the gauge length. Different notch lengths were employed to observe crack propagation and study the effects of crack extension and notch length on fracture toughness. The average ovine disc dimensions are given In Table 1 . In addition, Table 2 presents the sample dimensions (after cutting) for the two groups. Table 1 Average dimension of the discs Specimen Overall dimensions (mm) Length (L) Width 1 (W 1 ) Width 2 (W 2 ) Ovine (present study) 22.12 ± 1.73 12.24 ± 1.23 11.41 ± 1 .62 Porcine [ 12 ] 27 ± 2.36 13.9 ± 1.29 Human [ 12 ] 23.6 ± 0.60 14 ± 1.49 Table 2 Specimen dimension in 2 groups Group Notch Orientation Load direction Dimensions (mm) Length Width Thickness perpendicular to fibers AP 10.12 ± 0.81 3.89 ± 0.89 0.84 ± 0.23 parallel to fibers ML 21.95 ± 0.53 4.27 ± 1.06 0.74 ± 0.32 Estimation of fracture toughness: Each load-displacement response of fracture tests was divided into a number of cycles(n), each consisting of a loading and subsequent unloading cycle (Fig. 3 ). U T(n) was defined as the area between the loading curve and the displacement axis for the total energy of each cycle. The dissipated energy in each cycle, U D(n) , was estimated by calculating the area enclosed by the loading and unloading curves. Area (energy) calculations were performed using trapezoidal integration [ 19 ]. The ratio of dissipated to total energy, D n , was calculated for each cycle. $${D}_{n}=\frac{{U}_{D\left(n\right)}}{{U}_{T\left(n\right)}}$$ 1 It is possible to determine the amount of energy dissipation caused by crack growth (U F(n) ) by deducting the estimated amount of energy dissipated from viscoelasticity behavior (U VD(n) ) from the total amount of dissipated energy (U D(n) ) [ 20 ] : $${U}_{F\left(n\right)}={U}_{D\left(n\right)}-{U}_{VD\left(n\right)}\cong {U}_{D\left(n\right)}-{U}_{D(n+11)}$$ 2 The failure stress for a cracked (partially torn) material for isotropic, linear, and elastic materials can be calculated using the following formula: $${\sigma }_{f}=\frac{1}{F}\sqrt{\frac{{J}_{c}\times E}{\pi a}}$$ 3 where F is a geometry factor that depends on boundary conditions and E is the Young's modulus. This relationship is only valid once it exceeds a certain duration. The significance of this finding has been substantiated for soft tissues [ 21 ]. A common method for determining the critical stress intensity value Kc, which is equivalent to the square root of (J c ×E), for linear isotropic materials involves relating the variables a and σ f . Nevertheless, because of the linear nature of its constitutive response, the fracture toughness of soft tissue is typically denoted as J c . The procedure for determining J c typically entails subjecting a test specimen with an initial crack to loading and unloading cycles. Subsequently, the crack propagation energy, U c , is measured by assessing the area of the newly formed crack. Hence, the equation for fracture toughness is: $${J}_{c\left(n\right)}=\frac{{U}_{F\left(n\right)}}{t\times \varDelta c\left(n\right)}$$ 4 t represents the thickness of the sample and ∆c(n) represents the crack growth along the sample width during the n th cycle. The presence of viscoelastic properties in soft tissue introduces challenges when attempting to measure its ultimate strength (U f ). Prior studies have suggested different techniques for accurately estimating the fracture toughness of soft tissue ([ 1 , 14 ],[ 21 – 26 ]). However, determining the fracture length at each cycle is challenging and error-prone, particularly in soft collagenous tissue (SCTs), because of the samples' relatively large thickness and deformation during the tearing process. As a result, Chin-Purcell et al. [ 24 ] have shown that the measurement of fracture propagation can become cumbersome for extremely compliant materials, leading to ambiguity in the definition of a crack. Thus, using the following relation, the tissue's single parameter fracture toughness, J c , was determined: $${J}_{c}=\frac{\sum _{n=1}^{N}{U}_{F}\left(n\right)}{t\times \sum _{n=1}^{N}\varDelta c\left(n\right)}$$ 5 At last, the area limited to each load-unload cycle was determined using trapezoidal integration in Python. Statistical Analysis: Minitab software was utilized to perform statistical analysis on the data. Shapiro-Wilk test results indicated that the fracture toughness data did not follow a normal distribution (P-value < 0.05). Consequently, due to unequal variances, the Kruskal-Wallis test was employed to analyze the data. Simulation: A two-dimensional (2D) finite element model was developed to verify the reliability of experimental test results and investigate the patterns of force and fracture toughness changes in various percentage of cracks. By considering the area around the fracture tip, triangular elements were employed to depict the singularity in stresses and strains around the fracture tip. The meshes for the finite element model were iteratively refined until the discrepancy in the J contour integral was below 1% between two consecutive meshes. The TMJ disc's mechanical behavior characterized as linear viscoelastic isotropic [ 7 , 27 ]. The Prony coefficients are shown in Table 3 . Instantaneous Young’s modulus and Poisson’s ratio was defined 0.18 MPa, 0.4 respectively [ 28 ]. The loading and boundary conditions were set to mimic the actual testing conditions, and displacement in x direction was restricted and 10 N tensile load was applied. The 2D finite element model was carried out in Abaqus CAE (Simulia, Dassault Systems) (Figure. 4). A tetrahedral element with an approximate size of 0.05 mm were selected based on result convergence and computational efficiency. Table 3 Prony terms of the mechanical properties of TMJ disc [ 28 ]. Prony terms τ i (s) e i 1 0.0384 0.5733 2 0.4925 0.1223 3 6.3499 0.0818 4 106.4815 0.0926 Results A sharp decrease in force near the end of the cycle may indicate crack growth in the force-displacement diagram, or, slipping from grips. Therefore, test images were analyzed to determine crack growth or grip slippage using a digital microscope. All tests in AP group with initial crack lengths from 20–75% showed no crack propagation. Image analysis indicated that the sample sliding from the grips decreased forces in the final two cycles of Figure. 5, which presents a sample force-displacement diagram. Other type of failures such as sliding from the grip was also observed. Testing focused on the disc's intermediate zone (IZ). The cut specimens in AP group had lower overall size than ML group due to less available length in this direction. The higher failure rate in AP group was caused by its smaller size which increased the force acting on the disc and, as a result, increased the likelihood of rupture or slipping from the support. The samples in the AP group generally failed the test in three different ways, as depicted in Figure. 6. In order to identify the crack growth, the force must decrease by raising the test displacement. The force reduction, for any other reason such as the specimen slippage or crack extension in a different direction was not considered in the Jc calculation. Stress concentration during notch creation or different orientations might lead to crack propagation (Fig. 6 a). Furthermore, the crack growth could be a result of crushing and stress concentration at the support point. (Fig. 6 b.) Figure 7 illustrates the maximum tensile force sustained by various cracks in different cycles in both the AP and ML groups, respectively. The highest force observed in AP group at the lowest crack percentage of 25% was approximately 88.2 N. While, in the ML group, the highest force recorded was 12.5 N at a crack percentage of 50%, with the highest percentage of cracks (77%) enduring a maximum force of 9.86 N. Figure 8 presents the force-displacement results of a sample from ML group, exhibiting five instances of force reduction attributed to crack propagation. Upon examining the digital microscope images, these crack growths corresponded to length of 0.08, 0.17, 0.14, 0.11, and 0.21 mm. The initial crack length in this sample was 46% of the width. Figure 9 -a demonstrates fracture toughness of specimens in various crack percentages of all samples in ML group. Figure 9 -b illustrates variations in fracture toughness over various widths. Furthermore, ML group data were fitted with a power function [ 21 ] using the following equation: $${J}_{c}=a.({\frac{\varDelta C}{W})}^{b}$$ 6 Table 4 Critical force and fracture toughness of specimen from AP, ML group AP orientation Crack % 25% − 40% 40% − 50% 50% − 60% 60% − 70% 70% - Max force (N) 63.81 ± 19.02 29.01 ± 7.87 18.32 ± 1.64 15.78 ± 0.89 10.61 ± 0.75 J 1c (KJ/m 2 ) - - - - - ML orientation Crack % 25% − 40% 40% − 50% 50% − 60% 60% − 70% 70% - Max force (N) - 9.01 ± 2.91 6.71 ± 2.96 5.40 ± 2.29 5.08 ± 2.75 J 1c (KJ/m 2 ) - 5.56 ± 2.81 13.69 ± 7.98 15.97 ± 9.7 16.61 ± 8.15 The width of the sample is represented by the variable w, while the equation involves two constants, a = 75.83 and b=-1.29. The initial propagation of cracks was observed at 43 percent, corresponding to a fracture toughness value of 4.12 kJ/m 2 . The fracture toughness and critical force for various initial cracks are shown in Table 4 . The results from the experiment and the 2D simulation are shown in Fig. 9 -a. The simulation was conducted under the assumption of linear viscoelastic mechanical properties. The fracture toughness exhibited a direct linear relationship with the incremental growth in the crack percentage during the experimental tests. During the simulation, as the crack percentage increased, the toughness also exhibited linear growth. Discussion The main purpose of this study is to investigate the fracture toughness of the ovine TMJ disc under cyclic loading and after preconditioning. The human mandible is subjected to mechanical stress from various directions due to activities such as speaking, chewing, and other routine activities. The TMJ disc facilitates the mandible's movement and absorbs the forces and stresses from these daily activities. Therefore, the TMJ disc is probably prone to rupture. Therefore, it is essential to study its resistance to failure and rupture. Also, knowing the mechanical properties of the TMJ disc can aid in designing and developing mandibles and TMJ implants. In this study, the fracture toughness of discs was examined in two loading directions—parallel to the fibers and perpendicular to the fibers. The study's initial hypothesis was that, first, the resistance to crack growth in the direction perpendicular to the fibers would be higher than in the parallel direction, and second, the increasing the length of the initial crack would increase the likelihood of cracking and decrease the energy needed for failure. The study's findings supported the first hypothesis, as primary cracks of 40% and higher experienced crack propagation. The sample's crack tip has developed a curve perpendicular to the fibers, and this curvature continues until the crack either tears or fails (Fig. 6 ). In the AP samples, the crack tip profile grew perpendicular to the crack and parallel to the fibers whereas in the ML group, the crack tip profile exhibited a fully curved shape. The force-displacement diagram of samples showed a decrease in force as a result of this incident. The crack continued to grow in the fiber’s direction until the rupture occurred. The high density of fibers in the IZ and in the direction perpendicular to the initial crack may be the cause of the observed pattern. Disc's fibers have a high strength that prevents crack growth, along the initial crack direction. The present observation on the TMJ disc aligns with the findings of Von Forell et al. [ 24 ], who investigated the toughness and failure modes of ligaments and tendons, emphasizing the influence of fiber orientation on crack tip profile. Upon analysis, it was observed that in the AP group, the presence of a dense bundle of fibers in the central region, along with the orientation of the crack perpendicular to the fibers, prevented any propagation of primary cracks. Consequently, owing to the strength of the fibers, the fracture toughness in this direction was found to be infinite. Several instances of a rapid decrease in force were occurred throughout cycles, prompting the notion that the cracks had expanded (Fig. 7). However, while analyzing the captured images from the test, it was observed that the decrease in force attributed to either slipping or tearing off specimen from the support. Moreover, the maximum forces in AP group samples, expressed as a percentage of cracks identical to those of ML group, were approximately six times higher. This finding demonstrates the higher ultimate force needed for crack propagation. Fracture toughness results show that crack propagates in different modes in the AP and ML group specimens. AP samples required about six times more energy in Mode I for crack extension than those of ML group. The tight alignment of fibers in AP group perpendicular to the fracture prevents crack progression. In addition, the evaluation of the results revealed that in both groups, an increasing in the thickness of the isolated disc corresponded to a proportional increase in the rupture force. This evidence confirms the concept that thicker discs need a greater amount of force to cause a fracture. Gregory A. [ 25 ], Taylor [ 21 ], and Beaty [ 18 ] observed similar responses in the ligament, tendon, and TMJ disc, respectively. Furthermore, our study revealed that alterations in the width of the specimens had no influence on the maximum force and fracture toughness within both groups. Moreover, an increase in thickness leads to a reduction in fracture toughness. By increasing the thickness from 0.45 to 1.4 mm, the fracture toughness decreases from 37.45 to 1.36 KJ/m 2 . Koomba et al. developed a three-dimensional finite element model based on experimental fracture load data to predict the fracture toughness of the temporomandibular joint (TMJ) disc. The study revealed that the fracture toughness of the disc was considerably influenced by factors such as the direction, thickness, dimensions, and anisotropy ratio of the cracks. The fracture toughness for fractures aligned with the fibers was reported to range from 0.185 to 7.155 kJ/m 2 [ 1 ]. Prior researches have examined the fracture toughness of different soft tissues. Nevertheless, factors such as the size of the test sample, the length and width of cracks, and the mechanism of fracture, all of which have been shown to significantly impact the measurements of fracture toughness [ 17 , 21 ], sometimes make direct comparisons challenging. For instance, Bircher et al. [ 29 ] introduced the term "apparent tearing energy" to quantify the fracture toughness of collagenous tissue samples. They found that this measure is strongly influenced by the initial length of the sample. Specifically, they determined the tearing energy for bovine Glisson capsule (GC) to be 0.45 J/m, and for a collagen type 1 material it was 0.021 J/m, without taking into account the thickness of the sample. Taylor et al. [ 21 ] found that the apparent toughness of porcine muscle tissue was 2.49 kJ/m 2 . Furthermore, an increase in fracture toughness was reported with a decrease in the specimen thickness from 18 to 4 mm. In 2008, Beaty et al. [ 18 ] evaluated the minimum amount of energy needed for a defect to propagate in the porcine TMJ disc when subjected to both tensile and shear forces. The findings indicated that impulsive loading resulted in tissue stiffening and an increase in fracture energy in Mode I ( opening mode), but not in Mode 3 ( tearing mode), where shear tress is parallel to the crack plane and crack front. This suggests that the TMJ disc necessitates additional energy for defect expansion under strain when such flaws are introduced by impact. This is essential for the effective integration of designed replacement tissues for injured TMJs. Values of J IC reported from 1.73–13.62 KJ/m 2 [ 18 ], closely corresponding with the findings of the current investigation. The 2D FEA results also demonstrated a significant relationship between the fracture toughness and the percentage of cracks, indicating that an increase in crack to width ratio leads to a rise in fracture toughness. However, a difference of up to 40% in fracture toughness was obtained between FEA results with those of experimental tests. This discrepancy may be attributed to the assumptions and simplifications used in the 2D model. It is more advantageous to model the disc using anisotropic, poro-hyperelastic models and taking into account the orientation and material properties of the fibers. Crack propagation with a smaller fracture propagation resistance was detected in almost all of the tests conducted in the ML group, due to cracks being parallel to the fibers. The peak force among the ML group was observed at crack percentages ranging from 40 to 50%, with e values of about 11.2 N, significantly lower than those measured in the AP group. Research on the human TMJ disc shows that the fibers in the IZ [ 30 ], primarily align in the anteroposterior direction, whereas those in the surrounding region y predominantly align in the mediolateral direction. For samples away from the intermediate zone (IZ) of the disc, the alignment of fibers becomes more random, and the density of the fiber bundle decreases in the AP direction. The variation in forces seen in ML group can be attributed to the diverse orientations of the fibers in the dissected samples. As a result of the geometric constraints in certain experiments, it was not feasible to make an exact cut from the IZ. Therefore, the alteration in the arrangement of the fibers might potentially be responsible for the variation in forces. Both findings demonstrate that when the crack % increases, the fracture toughness likewise increases. However, it is important to note that the incremental changes seen in experimental tests have a smaller slope compared to simulations. Variations in fiber orientation could be the cause of the variation in fracture propagation during the experimental testing. Conclusion The present study employed a tensile cyclic test to examine the fracture toughness of the TMJ disc. For this purpose, the J-integral method was utilized for cracks oriented parallel and perpendicular to the major axis of the collagen fibers in mode I. The investigation aimed to explore the impact of fracture orientation, sample thickness, and crack to width ratio on the material behavior of the disc. It was found that due to the orientation of the fibers, the fracture toughness in AP group significantly exceeded that of ML group, showing a greater resistance to tearing and fracture in the anteroposterior direction. In addition, the study results revealed that the fracture toughness of the TMJ disc was affected by both the orientation of the crack and its initial crack to width ratio. Declarations Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. References Koombua K, Pidaparti RM, Beatty MW (2006) Fracture toughness estimation for the TMJ disc. J Biomed Mater Res A 79(3):566–573 Garcia N et al (2021) Effect of region-dependent viscoelastic properties on the TMJ articular disc relaxation under prolonged clenching. J Mech Behav Biomed Mater 119:104522 Barrientos E et al (2016) Dynamic and stress relaxation properties of the whole porcine temporomandibular joint disc under compression. J Mech Behav Biomed Mater 57:109–115 Detamore MS (2003) Structure and function of the temporomandibular joint disc: Implications for tissue engineering. 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J Mech Behav Biomed Mater 112:104029 Othniel J, Aryeetey MF, Lorenz A, Pahr DH (2022) Fracture toughness determination of porcine muscle tissue based on AQLV model derived viscous dissipated energy. J Mech Behav Biomed Mater, 135 Wright G (2015) Biomechanical Characterization and Modeling of Human TMJ Disc , in Bioengineering . Clemson Univresity. p. 238 Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4450894","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":313341015,"identity":"b8bd5e1b-a873-44a1-8370-831f3eeeb116","order_by":0,"name":"saeed Salehipour","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEUlEQVRIiWNgGAWjYLACHiDmA5IHQBx+mCgbIS1sMC2SDQyMDURrAQODA1AtuIB8++GDD94w1MmzsfcePFxQcTjf+PgZ8wcMNXYMfNIHsGoxOJOWbDiH4bBhG8+5hMMzzhy23HYmx7CB4VgyAxtfAnYtDDlm0kBfMLZJ5Bgc5m07bGB2AKSF7QADGw8Oh/W///6bh6HOvk3+DUSLcf8boJZ/uLUw3MhhY+ZhYE5sk+CBaDGQANrC2IZbi8GNZ8aScwwOJ7fxAB0240y6gcSNZ4UzEvuSeXA7LPnhhzcVdbb97GeMPxdUWBvw9ydv+PDhm52cfA8Oh0EDAQyY4QIJDAy4fIIKmAkrGQWjYBSMgpEIAAXnVkNl+aOoAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0001-9801-9516","institution":"Amirkabir University of Technology Department of Biomedical Engineering","correspondingAuthor":true,"prefix":"","firstName":"saeed","middleName":"","lastName":"Salehipour","suffix":""},{"id":313341016,"identity":"b1250021-ba51-467c-ab80-a70d10a57c76","order_by":1,"name":"Ata Hashemi","email":"","orcid":"","institution":"Amirkabir University of Technology Department of Biomedical Engineering","correspondingAuthor":false,"prefix":"","firstName":"Ata","middleName":"","lastName":"Hashemi","suffix":""}],"badges":[],"createdAt":"2024-05-20 19:56:48","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4450894/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4450894/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":59180675,"identity":"6d997728-1800-4731-936a-413baef656e7","added_by":"auto","created_at":"2024-06-27 10:36:06","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":58850,"visible":true,"origin":"","legend":"\u003cp\u003etest setup schematic and displacement increment per cycle\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-4450894/v1/827348e464e5589498a8a535.png"},{"id":59181191,"identity":"8fafeee3-3f51-4cc0-b555-e6e796df39c2","added_by":"auto","created_at":"2024-06-27 10:44:06","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":330259,"visible":true,"origin":"","legend":"\u003cp\u003ea-) ovine TMJ disc, b-) The red dashed line indicates the cut areas (intermediate zone) and W\u003csub\u003e1\u003c/sub\u003e , W\u003csub\u003e2\u003c/sub\u003e indicates width of left and right side of the disc respectively, c-) perpendicular notch orientation (AP), d-) parallel notch orientation (ML)\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-4450894/v1/b11bea5f319a6aa69da23880.png"},{"id":59180677,"identity":"df0c0655-1357-4629-8291-f144c1529d76","added_by":"auto","created_at":"2024-06-27 10:36:06","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":37315,"visible":true,"origin":"","legend":"\u003cp\u003eLoading vs. Unloading cycle\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-4450894/v1/f75b796c0dafddc25a676cc1.png"},{"id":59180679,"identity":"f81e4da9-12db-4d73-8d41-3756b05424fa","added_by":"auto","created_at":"2024-06-27 10:36:06","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":194581,"visible":true,"origin":"","legend":"\u003cp\u003eGeometry of samples was assigned according to the dimension of each specimen.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-4450894/v1/87b7cc1670c564d6da372d77.png"},{"id":59180683,"identity":"6abad711-bad8-4589-9796-c541676d829a","added_by":"auto","created_at":"2024-06-27 10:36:07","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":544492,"visible":true,"origin":"","legend":"\u003cp\u003eForce displacement plot of one sample of AP group\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-4450894/v1/8fbb1f55b96ed6b9628e9240.png"},{"id":59180674,"identity":"9e42a8e3-3292-43dd-a4ab-d558ce9e95eb","added_by":"auto","created_at":"2024-06-27 10:36:06","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":543320,"visible":true,"origin":"","legend":"\u003cp\u003eDifferent pattens of specimen failure\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-4450894/v1/9241fed4f93f9fd67317e7ed.png"},{"id":59180682,"identity":"e5f28d00-584a-432c-acc3-9b64ed577cac","added_by":"auto","created_at":"2024-06-27 10:36:07","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":65253,"visible":true,"origin":"","legend":"\u003cp\u003eMaximum force of all test data in different initial crack for AP group (orange bars), (b) ML group (blue bars)\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-4450894/v1/17d345f6a182b0c958a79573.png"},{"id":59180678,"identity":"05a25c6c-e1ad-4568-95e4-1eed18016237","added_by":"auto","created_at":"2024-06-27 10:36:06","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":572459,"visible":true,"origin":"","legend":"\u003cp\u003eForce displacement plot of a sample from ML group (arrows shown force reduction caused by crack growth)\u003c/p\u003e","description":"","filename":"image8.png","url":"https://assets-eu.researchsquare.com/files/rs-4450894/v1/d4d01b93b3893bc28587dc63.png"},{"id":59181190,"identity":"c5d27dc2-9f44-4663-93fb-40665cc46b40","added_by":"auto","created_at":"2024-06-27 10:44:06","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":80184,"visible":true,"origin":"","legend":"\u003cp\u003ea-) fracture toughness of FEM and experiment results by comparing the crack percentage, (b)fracture toughness of all sample in ML group by comparing the crack extension to width ratio\u003c/p\u003e","description":"","filename":"image9.png","url":"https://assets-eu.researchsquare.com/files/rs-4450894/v1/90bb344e8a9fc49096cd4ba2.png"},{"id":62241292,"identity":"9f89b9a9-4bb9-49a2-a3bf-def99a61710c","added_by":"auto","created_at":"2024-08-12 03:19:58","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2966094,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4450894/v1/2179bd9c-b704-4720-a7ae-653b5a75fb18.pdf"}],"financialInterests":"","formattedTitle":"Fracture Toughness of Ovine TMJ Disc: Effects of Crack Length and Orientation","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe temporomandibular joint (TMJ) disc connects bones in the joint, facilitating movement between the glenoid fossa and the articular eminence. This joint includes a fibrocartilage disc between the temporal bone and the mandibular condyle, with fibrocartilage layers covering bone surfaces [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Enclosed by a capsule, connective tissue, and a synovial membrane, the TMJ disc exhibits different motions: translation in the superior part and rotation in the inferior part [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. It endures various mechanical loads such as compression, tension, and shear, influenced by both static and dynamic forces like clenching or chewing [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. The disc's stress is affected not only by its motion but also by its structure, shape, size, and anatomy [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTMJ discs lubricate, absorb stress, and stabilize joints. Compromised mainly of type I collagen (2), these discs respond to loads based on their orientation, intensity, and duration [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Without the TMJ, regular tasks such as speaking, eating, and drinking would be difficult. The TMJ allows complex jaw motions and absorbs mechanical force [\u003cspan additionalcitationids=\"CR7\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Since the TMJ allows both translational and rotational motions, it helps the jaw move smoothly with the skull. During movement, the TMJ disc aligns the articular surfaces by slipping between them as the condyle shifts Besides synovial fluid, the TMJ disc also provides lubrication. The fossa shape, articular eminence, and ligaments limit TMJ disc movement. However, failure of any joint components can cause harm to the patient[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe study of mechanical properties of discs has been challenging due to differences in loading rates, sample preparation, sampling regions, testing methods, temperatures, ages, and tissue quality. Despite efforts, complete understanding of biological variations, particularly between humans and animals, is difficult to determine. Herbivores like cows, goats, and rabbits demonstrate the highest compressive modulus, indicating a correlation between structure and function [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Different food types, masticatory patterns, and animal sizes and morphologies have been tested and analyzed. It's important to account for each species' mechanical properties under specific testing conditions that yielded these results. Porcine, bovine, and ovine exhibit closer similarity to humans in terms of both size and complex anatomy compared to other animals. [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/p\u003e \u003cp\u003eSeveral tissues, including cartilage, muscle, skin, and discs, experience dynamic loadings that may result in damage or the growth of cracks within the tissue. Such issues can lead to pain and dysfunction in the affected tissue [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. It\u0026rsquo;s crucial for these tissues to have enough strength to endure mechanical stresses and prevent internal injuries, such as rupture and fractures. Furthermore, these tissues also contain microscopic flaws that can progressively expand and result in tissue deterioration. The fracture toughness of a material is a mechanical property that indicates how well it resists crack propagation. Typically, a fracture toughness test involves propagating a crack through a material sample [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], measuring the energy required to create a given amount of new crack area. This property indicates the material's \"defect tolerance,\u0026rdquo;, demonstrating its capacity to resist cracks and other defects while retaining its strength.\u003c/p\u003e \u003cp\u003eStudies have been performed on the fracture toughness of a wide variety of engineering materials, as well as bone and teeth, the body's hard tissues. There have been relatively few investigations to measure fracture toughness in the soft biological tissues, regardless of the fact that cartilage, muscle, skin, etc., are often damaged by cracks and mechanical injury, which may cause pain and disability [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. During the regeneration process, these tissues must be tough enough to resist the propagation of in-vivo defects such as injuries and internal lesions. Moreover, all materials contain microscopic flaws created during the regeneration process. These inherent defects may limit a material's strength [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAcquiring insight into the deformation and fracture characteristics of soft tissues is crucial in order to prevent damage and to suggest effective healing approaches. So far, the mechanical factors responsible for the propagation of defects in the TMJ disc have not been previously documented in research. Therefore, the objective of the present investigation was to determine the energy required to cause a propagation of defects on the disc responsible. The J-integral was selected to quantify the critical fracture energy, due to its ability to account for the non-linear mechanical characteristics of the TMJ disc. The fracture toughness of ovine TMJ disc was investigated based on their similarity to human disc. Fracture toughness was studied in two directions for ovine TMJ discs. The primary objective of the current research was to examine the impact of crack length, orientation, and disc shape parameters on fracture toughness. Two hypotheses of the study were that first, crack propagation would exhibit greater resistance perpendicular to the fibers compared to the parallel direction, and secondly, extending the initial crack would increase fracture probability while decreasing failure energy.\u003c/p\u003e"},{"header":"Material and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eSpecimen Preparation:\u003c/h2\u003e \u003cp\u003eSpecimens were tensile-conditioned, and notch length was ensured to be at least 25% of the sample width. For a visual representation of the testing setup, refer to Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Although biological differences between humans and animals cannot be fully explained, previous studies suggests that porcine and ovine are structurally most like humans [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. The J-integral testing method, a measure of fracture toughness [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], was employed on 20 fresh 8- to 9-month-old male ovine heads, compromising a total of 40 discs. The heads were acquired from a local abattoir, transported to the lab in an ice container within an hour, and refrigerated at -5\u0026deg;C. Each disc of a pair was identified as right or left, placed in a labeled plastic storage container with 0.1 M phosphate buffer solution (PBS) in the lab [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], and frozen at -10\u0026deg;C until testing. Before testing, each disc was thawed in PBS at 22\u0026ndash;25\u0026deg;C for 30 minutes and its dimensions were measured with a caliper with a resolution of 0.05 mm (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The crack length was measured with a 50x digital microscope. The samples were randomly split into two groups: 1) with a perpendicular notch (20 discs), and 2) with a notch parallel to the fibers (20 discs). The intermediate zone (IZ) of each disc was sectioned with a scalpel. An intact ovine TMJ disc has been shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eTest groups:\u003c/h2\u003e \u003cp\u003eThe specimens were classified into two distinct groups. 1-) Perpendicular notch to the fibers (AP), 2-) Parallel notch to the fibers (ML). Both groups were tested in the same conditions, with the only difference being the length of the notch on the disc. All tests were performed at the displacement rate of 10 mm/min. A servo electrical testing machine (Santam-STM/1) was used for applying 12 displacement control cycles with a sinusoidal force waveform before each test as preconditioning. AP and ML orientations are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb.\u003c/p\u003e \u003cp\u003eThe displacement range was incrementally increased by 0.1 mm after each test, and another set of cyclic tests consisting of 12 cycles was conducted. The initial notch length varied from 25\u0026ndash;75%. Throughout the tests, the specimen was sprayed with PBS. An exclusive fixture was designed and manufactured to grip the samples. Tests were conducted with the loading axis parallel to the anteroposterior (AP group) and mediolateral (ML group) collagen fibers, respectively (Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed). A scalpel was used to cut a transverse notch in the gauge length. Different notch lengths were employed to observe crack propagation and study the effects of crack extension and notch length on fracture toughness. The average ovine disc dimensions are given In Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. In addition, Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e presents the sample dimensions (after cutting) for the two groups.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAverage dimension of the discs\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSpecimen\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eOverall dimensions (mm)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eLength (L)\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003eWidth 1 (W\u003c/b\u003e\u003csub\u003e\u003cb\u003e1\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e)\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003eWidth 2 (W\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e)\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOvine (present study)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e22.12\u0026thinsp;\u0026plusmn;\u0026thinsp;1.73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e12.24\u0026thinsp;\u0026plusmn;\u0026thinsp;1.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e11.41\u0026thinsp;\u0026plusmn;\u0026thinsp;1 .62\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePorcine [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e27\u0026thinsp;\u0026plusmn;\u0026thinsp;2.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003e13.9\u0026thinsp;\u0026plusmn;\u0026thinsp;1.29\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHuman [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e23.6\u0026thinsp;\u0026plusmn;\u0026thinsp;0.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003e14\u0026thinsp;\u0026plusmn;\u0026thinsp;1.49\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSpecimen dimension in 2 groups\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eGroup\u003c/p\u003e \u003cp\u003eNotch Orientation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eLoad direction\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e \u003cp\u003eDimensions (mm)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003eLength\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003eWidth\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cb\u003eThickness\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eperpendicular to fibers\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10.12\u0026thinsp;\u0026plusmn;\u0026thinsp;0.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e3.89\u0026thinsp;\u0026plusmn;\u0026thinsp;0.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.84\u0026thinsp;\u0026plusmn;\u0026thinsp;0.23\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eparallel to fibers\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eML\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e21.95\u0026thinsp;\u0026plusmn;\u0026thinsp;0.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e4.27\u0026thinsp;\u0026plusmn;\u0026thinsp;1.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.74\u0026thinsp;\u0026plusmn;\u0026thinsp;0.32\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eEstimation of fracture toughness:\u003c/h2\u003e \u003cp\u003eEach load-displacement response of fracture tests was divided into a number of cycles(n), each consisting of a loading and subsequent unloading cycle (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). U\u003csub\u003eT(n)\u003c/sub\u003e was defined as the area between the loading curve and the displacement axis for the total energy of each cycle. The dissipated energy in each cycle, U\u003csub\u003eD(n)\u003c/sub\u003e, was estimated by calculating the area enclosed by the loading and unloading curves. Area (energy) calculations were performed using trapezoidal integration [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. The ratio of dissipated to total energy, D\u003csub\u003en\u003c/sub\u003e, was calculated for each cycle.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${D}_{n}=\\frac{{U}_{D\\left(n\\right)}}{{U}_{T\\left(n\\right)}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIt is possible to determine the amount of energy dissipation caused by crack growth (U\u003csub\u003eF(n)\u003c/sub\u003e) by deducting the estimated amount of energy dissipated from viscoelasticity behavior (U\u003csub\u003eVD(n)\u003c/sub\u003e) from the total amount of dissipated energy (U\u003csub\u003eD(n)\u003c/sub\u003e) [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] :\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${U}_{F\\left(n\\right)}={U}_{D\\left(n\\right)}-{U}_{VD\\left(n\\right)}\\cong {U}_{D\\left(n\\right)}-{U}_{D(n+11)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe failure stress for a cracked (partially torn) material for isotropic, linear, and elastic materials can be calculated using the following formula:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$${\\sigma }_{f}=\\frac{1}{F}\\sqrt{\\frac{{J}_{c}\\times E}{\\pi a}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere F is a geometry factor that depends on boundary conditions and E is the Young's modulus. This relationship is only valid once it exceeds a certain duration. The significance of this finding has been substantiated for soft tissues [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. A common method for determining the critical stress intensity value Kc, which is equivalent to the square root of (J\u003csub\u003ec\u003c/sub\u003e \u0026times;E), for linear isotropic materials involves relating the variables a and σ\u003csub\u003ef\u003c/sub\u003e. Nevertheless, because of the linear nature of its constitutive response, the fracture toughness of soft tissue is typically denoted as J\u003csub\u003ec\u003c/sub\u003e. The procedure for determining J\u003csub\u003ec\u003c/sub\u003e typically entails subjecting a test specimen with an initial crack to loading and unloading cycles. Subsequently, the crack propagation energy, U\u003csub\u003ec\u003c/sub\u003e, is measured by assessing the area of the newly formed crack. Hence, the equation for fracture toughness is:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$${J}_{c\\left(n\\right)}=\\frac{{U}_{F\\left(n\\right)}}{t\\times \\varDelta c\\left(n\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003et represents the thickness of the sample and ∆c(n) represents the crack growth along the sample width during the n\u003csup\u003eth\u003c/sup\u003e cycle.\u003c/p\u003e \u003cp\u003eThe presence of viscoelastic properties in soft tissue introduces challenges when attempting to measure its ultimate strength (U\u003csub\u003ef\u003c/sub\u003e). Prior studies have suggested different techniques for accurately estimating the fracture toughness of soft tissue ([\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e],[\u003cspan additionalcitationids=\"CR22 CR23 CR24 CR25\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]). However, determining the fracture length at each cycle is challenging and error-prone, particularly in soft collagenous tissue (SCTs), because of the samples' relatively large thickness and deformation during the tearing process. As a result, Chin-Purcell et al. [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] have shown that the measurement of fracture propagation can become cumbersome for extremely compliant materials, leading to ambiguity in the definition of a crack. Thus, using the following relation, the tissue's single parameter fracture toughness, J\u003csub\u003ec\u003c/sub\u003e, was determined:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$${J}_{c}=\\frac{\\sum _{n=1}^{N}{U}_{F}\\left(n\\right)}{t\\times \\sum _{n=1}^{N}\\varDelta c\\left(n\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAt last, the area limited to each load-unload cycle was determined using trapezoidal integration in Python.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eStatistical Analysis:\u003c/h2\u003e \u003cp\u003eMinitab software was utilized to perform statistical analysis on the data. Shapiro-Wilk test results indicated that the fracture toughness data did not follow a normal distribution (P-value\u0026thinsp;\u0026lt;\u0026thinsp;0.05). Consequently, due to unequal variances, the Kruskal-Wallis test was employed to analyze the data.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003eSimulation:\u003c/h2\u003e \u003cp\u003eA two-dimensional (2D) finite element model was developed to verify the reliability of experimental test results and investigate the patterns of force and fracture toughness changes in various percentage of cracks. By considering the area around the fracture tip, triangular elements were employed to depict the singularity in stresses and strains around the fracture tip. The meshes for the finite element model were iteratively refined until the discrepancy in the J contour integral was below 1% between two consecutive meshes. The TMJ disc's mechanical behavior characterized as linear viscoelastic isotropic [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. The Prony coefficients are shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Instantaneous Young\u0026rsquo;s modulus and Poisson\u0026rsquo;s ratio was defined 0.18 MPa, 0.4 respectively [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. The loading and boundary conditions were set to mimic the actual testing conditions, and displacement in x direction was restricted and 10 N tensile load was applied. The 2D finite element model was carried out in Abaqus CAE (Simulia, Dassault Systems) (Figure. 4). A tetrahedral element with an approximate size of 0.05 mm were selected based on result convergence and computational efficiency.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eProny terms of the mechanical properties of TMJ disc [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProny terms\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eτ\u003csub\u003ei\u003c/sub\u003e (s)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ee\u003csub\u003ei\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0384\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.5733\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.4925\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.1223\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6.3499\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0818\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e106.4815\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0926\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cp\u003eA sharp decrease in force near the end of the cycle may indicate crack growth in the force-displacement diagram, or, slipping from grips. Therefore, test images were analyzed to determine crack growth or grip slippage using a digital microscope. All tests in AP group with initial crack lengths from 20\u0026ndash;75% showed no crack propagation. Image analysis indicated that the sample sliding from the grips decreased forces in the final two cycles of Figure. 5, which presents a sample force-displacement diagram. Other type of failures such as sliding from the grip was also observed. Testing focused on the disc's intermediate zone (IZ).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe cut specimens in AP group had lower overall size than ML group due to less available length in this direction. The higher failure rate in AP group was caused by its smaller size which increased the force acting on the disc and, as a result, increased the likelihood of rupture or slipping from the support. The samples in the AP group generally failed the test in three different ways, as depicted in Figure. 6. In order to identify the crack growth, the force must decrease by raising the test displacement. The force reduction, for any other reason such as the specimen slippage or crack extension in a different direction was not considered in the Jc calculation. Stress concentration during notch creation or different orientations might lead to crack propagation (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea). Furthermore, the crack growth could be a result of crushing and stress concentration at the support point. (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb.)\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure 7 illustrates the maximum tensile force sustained by various cracks in different cycles in both the AP and ML groups, respectively. The highest force observed in AP group at the lowest crack percentage of 25% was approximately 88.2 N. While, in the ML group, the highest force recorded was 12.5 N at a crack percentage of 50%, with the highest percentage of cracks (77%) enduring a maximum force of 9.86 N. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e presents the force-displacement results of a sample from ML group, exhibiting five instances of force reduction attributed to crack propagation. Upon examining the digital microscope images, these crack growths corresponded to length of 0.08, 0.17, 0.14, 0.11, and 0.21 mm. The initial crack length in this sample was 46% of the width.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e-a demonstrates fracture toughness of specimens in various crack percentages of all samples in ML group. Figure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e-b illustrates variations in fracture toughness over various widths. Furthermore, ML group data were fitted with a power function [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] using the following equation:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$${J}_{c}=a.({\\frac{\\varDelta C}{W})}^{b}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCritical force and fracture toughness of specimen from AP, ML group\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e \u003cp\u003eAP orientation\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCrack %\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e25% \u0026minus;\u0026thinsp;40%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e40% \u0026minus;\u0026thinsp;50%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e50% \u0026minus;\u0026thinsp;60%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e60% \u0026minus;\u0026thinsp;70%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e70% -\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMax force (N)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e63.81\u0026thinsp;\u0026plusmn;\u0026thinsp;19.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e29.01\u0026thinsp;\u0026plusmn;\u0026thinsp;7.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e18.32\u0026thinsp;\u0026plusmn;\u0026thinsp;1.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e15.78\u0026thinsp;\u0026plusmn;\u0026thinsp;0.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e10.61\u0026thinsp;\u0026plusmn;\u0026thinsp;0.75\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJ\u003csub\u003e1c\u003c/sub\u003e (KJ/m\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e \u003cp\u003eML orientation\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCrack %\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e25% \u0026minus;\u0026thinsp;40%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e40% \u0026minus;\u0026thinsp;50%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e50% \u0026minus;\u0026thinsp;60%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e60% \u0026minus;\u0026thinsp;70%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e70% -\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMax force (N)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e9.01\u0026thinsp;\u0026plusmn;\u0026thinsp;2.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.71\u0026thinsp;\u0026plusmn;\u0026thinsp;2.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.40\u0026thinsp;\u0026plusmn;\u0026thinsp;2.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e5.08\u0026thinsp;\u0026plusmn;\u0026thinsp;2.75\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJ\u003csub\u003e1c\u003c/sub\u003e (KJ/m\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5.56\u0026thinsp;\u0026plusmn;\u0026thinsp;2.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e13.69\u0026thinsp;\u0026plusmn;\u0026thinsp;7.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e15.97\u0026thinsp;\u0026plusmn;\u0026thinsp;9.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e16.61\u0026thinsp;\u0026plusmn;\u0026thinsp;8.15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe width of the sample is represented by the variable w, while the equation involves two constants, a\u0026thinsp;=\u0026thinsp;75.83 and b=-1.29. The initial propagation of cracks was observed at 43 percent, corresponding to a fracture toughness value of 4.12 kJ/m\u003csup\u003e2\u003c/sup\u003e. The fracture toughness and critical force for various initial cracks are shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. The results from the experiment and the 2D simulation are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e-a. The simulation was conducted under the assumption of linear viscoelastic mechanical properties. The fracture toughness exhibited a direct linear relationship with the incremental growth in the crack percentage during the experimental tests. During the simulation, as the crack percentage increased, the toughness also exhibited linear growth.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe main purpose of this study is to investigate the fracture toughness of the ovine TMJ disc under cyclic loading and after preconditioning. The human mandible is subjected to mechanical stress from various directions due to activities such as speaking, chewing, and other routine activities. The TMJ disc facilitates the mandible's movement and absorbs the forces and stresses from these daily activities. Therefore, the TMJ disc is probably prone to rupture. Therefore, it is essential to study its resistance to failure and rupture. Also, knowing the mechanical properties of the TMJ disc can aid in designing and developing mandibles and TMJ implants.\u003c/p\u003e \u003cp\u003eIn this study, the fracture toughness of discs was examined in two loading directions\u0026mdash;parallel to the fibers and perpendicular to the fibers. The study's initial hypothesis was that, first, the resistance to crack growth in the direction perpendicular to the fibers would be higher than in the parallel direction, and second, the increasing the length of the initial crack would increase the likelihood of cracking and decrease the energy needed for failure. The study's findings supported the first hypothesis, as primary cracks of 40% and higher experienced crack propagation.\u003c/p\u003e \u003cp\u003eThe sample's crack tip has developed a curve perpendicular to the fibers, and this curvature continues until the crack either tears or fails (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). In the AP samples, the crack tip profile grew perpendicular to the crack and parallel to the fibers whereas in the ML group, the crack tip profile exhibited a fully curved shape. The force-displacement diagram of samples showed a decrease in force as a result of this incident. The crack continued to grow in the fiber\u0026rsquo;s direction until the rupture occurred. The high density of fibers in the IZ and in the direction perpendicular to the initial crack may be the cause of the observed pattern. Disc's fibers have a high strength that prevents crack growth, along the initial crack direction. The present observation on the TMJ disc aligns with the findings of Von Forell et al. [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e], who investigated the toughness and failure modes of ligaments and tendons, emphasizing the influence of fiber orientation on crack tip profile.\u003c/p\u003e \u003cp\u003eUpon analysis, it was observed that in the AP group, the presence of a dense bundle of fibers in the central region, along with the orientation of the crack perpendicular to the fibers, prevented any propagation of primary cracks. Consequently, owing to the strength of the fibers, the fracture toughness in this direction was found to be infinite. Several instances of a rapid decrease in force were occurred throughout cycles, prompting the notion that the cracks had expanded (Fig.\u0026nbsp;7). However, while analyzing the captured images from the test, it was observed that the decrease in force attributed to either slipping or tearing off specimen from the support. Moreover, the maximum forces in AP group samples, expressed as a percentage of cracks identical to those of ML group, were approximately six times higher. This finding demonstrates the higher ultimate force needed for crack propagation.\u003c/p\u003e \u003cp\u003eFracture toughness results show that crack propagates in different modes in the AP and ML group specimens. AP samples required about six times more energy in Mode I for crack extension than those of ML group. The tight alignment of fibers in AP group perpendicular to the fracture prevents crack progression. In addition, the evaluation of the results revealed that in both groups, an increasing in the thickness of the isolated disc corresponded to a proportional increase in the rupture force. This evidence confirms the concept that thicker discs need a greater amount of force to cause a fracture. Gregory A. [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], Taylor [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], and Beaty [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] observed similar responses in the ligament, tendon, and TMJ disc, respectively.\u003c/p\u003e \u003cp\u003eFurthermore, our study revealed that alterations in the width of the specimens had no influence on the maximum force and fracture toughness within both groups. Moreover, an increase in thickness leads to a reduction in fracture toughness. By increasing the thickness from 0.45 to 1.4 mm, the fracture toughness decreases from 37.45 to 1.36 KJ/m\u003csup\u003e2\u003c/sup\u003e. Koomba et al. developed a three-dimensional finite element model based on experimental fracture load data to predict the fracture toughness of the temporomandibular joint (TMJ) disc. The study revealed that the fracture toughness of the disc was considerably influenced by factors such as the direction, thickness, dimensions, and anisotropy ratio of the cracks. The fracture toughness for fractures aligned with the fibers was reported to range from 0.185 to 7.155 kJ/m\u003csup\u003e2\u003c/sup\u003e [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e].\u003c/p\u003e \u003cp\u003ePrior researches have examined the fracture toughness of different soft tissues. Nevertheless, factors such as the size of the test sample, the length and width of cracks, and the mechanism of fracture, all of which have been shown to significantly impact the measurements of fracture toughness [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], sometimes make direct comparisons challenging. For instance, Bircher et al. [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] introduced the term \"apparent tearing energy\" to quantify the fracture toughness of collagenous tissue samples. They found that this measure is strongly influenced by the initial length of the sample. Specifically, they determined the tearing energy for bovine Glisson capsule (GC) to be 0.45 J/m, and for a collagen type 1 material it was 0.021 J/m, without taking into account the thickness of the sample. Taylor et al. [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] found that the apparent toughness of porcine muscle tissue was 2.49 kJ/m\u003csup\u003e2\u003c/sup\u003e. Furthermore, an increase in fracture toughness was reported with a decrease in the specimen thickness from 18 to 4 mm.\u003c/p\u003e \u003cp\u003eIn 2008, Beaty et al. [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] evaluated the minimum amount of energy needed for a defect to propagate in the porcine TMJ disc when subjected to both tensile and shear forces. The findings indicated that impulsive loading resulted in tissue stiffening and an increase in fracture energy in Mode I ( opening mode), but not in Mode 3 ( tearing mode), where shear tress is parallel to the crack plane and crack front. This suggests that the TMJ disc necessitates additional energy for defect expansion under strain when such flaws are introduced by impact. This is essential for the effective integration of designed replacement tissues for injured TMJs. Values of J\u003csub\u003eIC\u003c/sub\u003e reported from 1.73\u0026ndash;13.62 KJ/m\u003csup\u003e2\u003c/sup\u003e [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], closely corresponding with the findings of the current investigation.\u003c/p\u003e \u003cp\u003eThe 2D FEA results also demonstrated a significant relationship between the fracture toughness and the percentage of cracks, indicating that an increase in crack to width ratio leads to a rise in fracture toughness. However, a difference of up to 40% in fracture toughness was obtained between FEA results with those of experimental tests. This discrepancy may be attributed to the assumptions and simplifications used in the 2D model. It is more advantageous to model the disc using anisotropic, poro-hyperelastic models and taking into account the orientation and material properties of the fibers.\u003c/p\u003e \u003cp\u003eCrack propagation with a smaller fracture propagation resistance was detected in almost all of the tests conducted in the ML group, due to cracks being parallel to the fibers. The peak force among the ML group was observed at crack percentages ranging from 40 to 50%, with e values of about 11.2 N, significantly lower than those measured in the AP group. Research on the human TMJ disc shows that the fibers in the IZ [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e], primarily align in the anteroposterior direction, whereas those in the surrounding region y predominantly align in the mediolateral direction. For samples away from the intermediate zone (IZ) of the disc, the alignment of fibers becomes more random, and the density of the fiber bundle decreases in the AP direction. The variation in forces seen in ML group can be attributed to the diverse orientations of the fibers in the dissected samples. As a result of the geometric constraints in certain experiments, it was not feasible to make an exact cut from the IZ. Therefore, the alteration in the arrangement of the fibers might potentially be responsible for the variation in forces. Both findings demonstrate that when the crack % increases, the fracture toughness likewise increases. However, it is important to note that the incremental changes seen in experimental tests have a smaller slope compared to simulations. Variations in fiber orientation could be the cause of the variation in fracture propagation during the experimental testing.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThe present study employed a tensile cyclic test to examine the fracture toughness of the TMJ disc. For this purpose, the J-integral method was utilized for cracks oriented parallel and perpendicular to the major axis of the collagen fibers in mode I. The investigation aimed to explore the impact of fracture orientation, sample thickness, and crack to width ratio on the material behavior of the disc. It was found that due to the orientation of the fibers, the fracture toughness in AP group significantly exceeded that of ML group, showing a greater resistance to tearing and fracture in the anteroposterior direction. In addition, the study results revealed that the fracture toughness of the TMJ disc was affected by both the orientation of the crack and its initial crack to width ratio.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eDeclaration of competing interest\u003c/h2\u003e \u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eKoombua K, Pidaparti RM, Beatty MW (2006) Fracture toughness estimation for the TMJ disc. J Biomed Mater Res A 79(3):566\u0026ndash;573\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGarcia N et al (2021) Effect of region-dependent viscoelastic properties on the TMJ articular disc relaxation under prolonged clenching. J Mech Behav Biomed Mater 119:104522\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBarrientos E et al (2016) Dynamic and stress relaxation properties of the whole porcine temporomandibular joint disc under compression. J Mech Behav Biomed Mater 57:109\u0026ndash;115\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDetamore MS (2003) Structure and function of the temporomandibular joint disc: Implications for tissue engineering. J Oral Maxillofac Surg 61(4):494\u0026ndash;506\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eEiji Tanaka TvE (2003) Biomechanical behavior of the temporomandibular joint disk. Crit Rev Oral Biol Med 14(2):138\u0026ndash;150\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRunci Anastasi M et al (2021) Articular Disc of a Human Temporomandibular Joint: Evaluation through Light Microscopy, Immunofluorescence and Scanning Electron Microscopy. J Funct Morphol Kinesiol, 6(1)\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKijak E, Margielewicz J, Pihut M (2020) \u003cem\u003eIdentification of Biomechanical Properties of Temporomandibular Discs.\u003c/em\u003e Pain Res Manag, 2020: p. 6032832\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eEva Barrientos FP, Eiji Tanaka (2020) Effects of loading direction in prolonged clenching on stressdistribution in the temporomandibular joint. J Mech Behav Biomed Mater, 112\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eErica Hattori-Hara SNM, Mori H, Arafurue K, Kawaoka T, Ueda K, Yasue A, Kuroda S, Koolstra JH, Tanaka E (2014) The influence of unilateral disc displacement on stress in the contralateral joint with a normally positioned disc in a human temporomandibular joint: An analytic approach using the finite element method. J Cranio-Maxillofacial Surg 42(8):2018\u0026ndash;2024\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eEiji Tanaka FP, Kim N, Lamela Mar\u0026iacute;aJes\u0026uacute;s, Kawai N (2014) Alfonso Fern\u0026aacute;ndez-Canteli, \u003cem\u003eStress relaxation behaviors of articular cartilages in porcine temporomandibular\u003c/em\u003e. J Biomech 47(7):1582\u0026ndash;1587\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJames Deschner BR-D, Reimann S, Bourauel C, G\u0026ouml;tz W, Jepsen S, J\u0026auml;ger A (2007) Regulatory effects of biophysical strain on rat TMJ discs. Annals Anat 189(4):326\u0026ndash;328\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKalpakci KN, Wong WV, Athanasiou ME (2011) An interspecies comparison of the temporomandibular joint disc. J Dent Res 90(2):193\u0026ndash;198\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWoodhouse JB, McNally EG (2011) Ultrasound of skeletal muscle injury: an update. Semin Ultrasound CT MR 32(2):91\u0026ndash;100\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOyen-Tiesma M, Cook RF (2001) Technique for estimating fracture resistance of cultured neocartilage. 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Ann Biomed Eng 36(5):801\u0026ndash;812\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSabouri P, Hashemi A (2021) Influence of crack length and anatomical location on the fracture toughness of annulus fibrosus. Med Eng Phys 88:1\u0026ndash;8\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBrendan E, Koop JLL (2003) A model of fracture testing of soft viscoelastic tissues. J Biomech 36(4):605\u0026ndash;608\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTaylor D et al (2012) The fracture toughness of soft tissues. J Mech Behav Biomed Mater 6:139\u0026ndash;147\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eStok K (2007) Conceptual fracture parameters for articular cartilage. Clin Biomech Elsevier Ltd 22(6):725\u0026ndash;735\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePurslow PP (1985) The physical basis of meat texture: Observations on the fracture behaviour of cooked bovine. Meat Sci 12(1):39\u0026ndash;60\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChin-Purcell MV (1996), \u003cem\u003efracture of articular cartilage\u003c/em\u003e. J Biomech Eng 118:545\u0026ndash;556\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGregory A, Von Forell PSH, Anton E, Bowden (2014) Failure modes and fracture toughness in partially torn ligaments and tendons. J Mech Behav Biomed Mater 35:77\u0026ndash;84\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTaylor D (2018) Measuring fracture toughness in biological materials. J Mech Behav Biomed Mater 77:776\u0026ndash;782\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFazaeli S et al (2019) The dynamic mechanical viscoelastic properties of the temporomandibular joint disc: The role of collagen and elastin fibers from a perspective of polymer dynamics. J Mech Behav Biomed Mater 100:103406\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBarrientos E et al (2020) Effects of loading direction in prolonged clenching on stress distribution in the temporomandibular joint. J Mech Behav Biomed Mater 112:104029\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOthniel J, Aryeetey MF, Lorenz A, Pahr DH (2022) Fracture toughness determination of porcine muscle tissue based on AQLV model derived viscous dissipated energy. J Mech Behav Biomed Mater, 135\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWright G (2015) \u003cem\u003eBiomechanical Characterization and Modeling of Human TMJ Disc\u003c/em\u003e, in \u003cem\u003eBioengineering\u003c/em\u003e. Clemson Univresity. p. 238\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"TMJ disc, Fracture toughness, Mandible, J-integral, Notch orientation, Finite element analysis","lastPublishedDoi":"10.21203/rs.3.rs-4450894/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4450894/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe human mandible experiences mechanical stress from several directions as a result of activities such as speaking, chewing, and other everyday actions. The TMJ disc facilitates mandibular motion and absorbs all of the stresses associated with daily activities. Thus, the TMJ disc is likely to be susceptible to rupture. Hence, it is crucial to investigate its susceptibility to failure and rupture. The aim of this study was to determine the impact of fracture orientation, sample thickness, and crack-to-width ratio on the amount of energy needed to cause the growth of flaws on the disc. Fracture toughness was investigated by conducting cyclic tensile testing on 40 ovine TMJ discs in two different notch orientations: anteroposterior and mediolateral. The J-integral was chosen as a measure of the critical fracture energy of the TMJ disc. The Shapiro-Wilk test showed that fracture toughness data did not follow a normal distribution (P-value\u0026thinsp;\u0026lt;\u0026thinsp;0.05). Due to unequal variances, the Kruskal-Wallis test was used to examine the data. The study revealed that the fracture toughness in the anteroposterior direction was much higher than that of the mediolateral, indicating a superior ability to resist tearing and fracture in the anteroposterior direction. Furthermore, the study's findings revealed that both the direction of the crack and its initial crack-to-width ratio influenced the TMJ disc's fracture toughness. The study also evaluated TMJ disc failure patterns to better understand its pathophysiology. The results showed that the crack growth profile in two orientations has a completely different structure. The 2D finite element analysis results also indicated a significant relationship between the fracture toughness and the percentage of cracks, demonstrating that increasing the crack-to-width ratio leads to a rise in fracture toughness. These findings help understand TMJ injuries to the disk and develop better treatments.\u003c/p\u003e","manuscriptTitle":"Fracture Toughness of Ovine TMJ Disc: Effects of Crack Length and Orientation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-06-27 10:36:01","doi":"10.21203/rs.3.rs-4450894/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"a8f92217-02b7-45fe-b058-9a42adcc3a46","owner":[],"postedDate":"June 27th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-08-12T03:11:49+00:00","versionOfRecord":[],"versionCreatedAt":"2024-06-27 10:36:01","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4450894","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4450894","identity":"rs-4450894","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}