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Introduction

Tooth fracture is a frequent dental problem influenced by several factors, such as tooth anatomy and cavity preparation procedures. Fractures are more likely to occur in premolars due to their anatomical shape, crown volume, and unfavorable crown/root proportions* 3. From a functional point of view, premolars run a greater risk of damage because they are subjected to larger lateral forces during mastication and present a smaller amount of tooth structure compared to molars. It was demonstrated that the occlusal pressure raises progressively from the central incisors, reaches its peak at the premolars, and decreases steeply towards the second molars4. Moreover, caries-free intact premolars are the most easily available elements as their extraction is a widely accepted procedure to correct malocclusions^.

Fracture strength is defined as the ability of a tooth to resist fracture under mechanical stress, and it is routinely assessed  by simulated functional loadings. Teeth are loaded to fracture on a universal mechanical loading machine, and the maximum breaking load is recorded and expressed in Newton (kg x m/s2). Despite this approach cannot faithfully reproduce an in vivo situation, several adjustments can be made to simulate physiological occlusal forces within the oral cavity, both during sample preparation and testing7.

Test results can be influenced by variations in the loading pattern, such as the shape and diameter of the loading tip as well as its angulation with respect to the long axis of the tooth . Moreover, it is possible to vary the site of application of the force on the occlusal surface of the tooth and simulate the periodontal ligament’. Periodontal ligament is a fundamental structure that plays a crucial role in supporting and cushioning teeth during chewing function, dissipating occlusal forces   and  protecting the teeth and the study emphasized the significance of including the simulation of the periodontal ligament in fracture strength tests using finite element analysis, to better understand the impact of occlusal forces on tooth strength and fractures the periodontal ligament, load inclination, tip position, tip diameter, and thermocycling imparts on results of fracture strengths tests conducted on upper premolars was evaluated emerged that none of the above-mentioned methodological variables significantly influenced intact premolars.

To date, many studies follow different treatment protocols, highlighting a considerable lack of uniformity in the procedures and controversial results . Moreover, data on periodontal ligament simulation, tip position, and diameter are limited. Precisely, no studies were conducted to test the influence of the aforementioned variables on the results of fracture strength tests conducted on non-treated extracted premolars (NTEPs). Standardization of these procedures is required to reduce the variability of fracture strength test results and to conduct more rigorous in vitro studies. Therefore, the aim of the present study was to evaluate the influence of methodological variables, namely periodontal ligament reproduction, lead inclination (45°, 90”), and tip morphology (flat or spherical), on the fracture strength test of NTEPs. The null hypothesis  was  that periodontal ligament simulation, inclination, and morphology of the tip would not affect the fracture strength test in NTEPs.

MATERIALS AND METHODS

TIP PRODUCTION AND SELECTION
In order to select the tip diameter, spheres of various diameters were compared and tested on premolars with heterogeneous morphology and   size   (figure 1). The spheres with a diameter of 3mm and 3.5mm were found to make correct contact with almost all the tested elements. Following the selection of the samples, it was decided to use the 3mm diameter tip for the execution of the test, as it was able to exert the forces uniformly on both internal cusp sides of the selected samples. In addition to this innovative round-tipped tip, a classic 2mm-diameter flat-tipped was also used.

Figure 1. TiD selection procedure. SDheres of various diameters were comDared and tested. B and C were found to make a correct contact with almost all the tested elements.

SAMPLE SELECTION

A total of forty teeth were collected from a group of freshly extracted, intact upper premolars extracted for either periodontal or orthodontic reasons after ethical approval (project no. 7/2021). All the teeth having signs of caries, cracks, fractures, and restorations were excluded from the study after being examined with a magnifier (10x). Moreover, all the teeth were extracted no more than two months prior to the study10. Before the test, all the residual periodontal tissue, plaque, and calculus were carefully removed from each tooth using both a manual scaler and periodontal curettes (Hu-Friedy, Chicago, IL). 
Afterward, the teeth were wiped using a rubber cup (Microdont, Sk Paulo, SP, Brazil) and fine pumice (Vigodent, RJ, Brazil) water slurry and placed in a numbered container containing saline solution (0.9%) and stored at a temperature of 37° C. The vestibulo-palatal (BL) and mesio-distal (MD) dimensions of each crown were recorded, as well as the distance between the CEJ and the incisal margin (CEJ) and the total length of the element (TL). These measurements were conducted using a digital caliper (Digimatic 500, Mitutoyo, Kanagawa, Japan). Furthermore, teeth were randomly divided into four distinct groups, as shown in figure 2 (n=10):

Group A (n10): load application at 90°, spherical tip diameter 3mm, reproduction of the periodontal ligament(figure 2A) - Group 8 (n1 0): load application at 90°, flat tip diameter 2mm, reproduction of the periodontal ligament (figure 28) - Group C (n10): load application at 45°, flat tip diameter 2mm, reproduction of the periodontal ligament (figure 2C) Group D (n-10): load application at 90°, spherical tip diameter 3mm, without reproduction of the periodontal ligament (figure 2D) 1=1 

Figure 2 Schematic rep esentation of the different methodological variables used to test fracture strength in the four different groups (A, B, C, D).

SAMPLE PREPARATION:
PERIODONTAL UGAMENT SIMULATION

In Groups A, B, and C, the periodontal ligament was simulated following a previously validated procedure (figure 3). Each root was immersed in molten wax (TENATEX RED, kemdent) up to 2 mm below the CEJ to simulate the biological space and to create a 0.2-0.3mm thick wax layer (figure 3A and 3In Each sample was then fixed with the crown pointing upwards by means of soft wax to the plexiglass plate of an embedding device (ED), making sure that it was positioned with the long axis perpendicular to the base of the support (figure 3C) The EDwas composed of a metal base on which a threaded stainless-steel bar was inserted perpendicularly, anchored to the base through bolts. A perforated plexiglass plate inserted inside the threaded 
base is able to slide in order to position it at the desired height, depending on the tooth to examine. Its height can be adjusted by screwing or unscrewing a butterfly-shaped bolt placed at the top of the bar, whose position is maintained by a spring (figure 3D).

After fixing the tooth in the correct position, a metal cylinder (Tigre, Rio Claro, SP Brazil) was positioned over the ED, and self-curing aaylic resin was poured into it until it reached 1 mm from the CEJ to simulate the alveolar bone crest(figure 3E). Following resin polymerization, unscrewing the butterfly bolt, the wax-coated teeth incorporated into the resin were removed from the cylinders, and the wax was removed with hot water, leaving an impression in the aaylic resin (figure 3F). To simulate the periodontal ligament, the artificial alveolus created on the acrylic resin was filled with an elastomeric impression material (elite HD +, regular body, Zherniack) (figure 3G) The sample was then reinserted BSA into the cavity, and excesses were removed with a scalpel blade (figure 31-1) At this point, the samples were ready to be tested. 

Figure 3. Schematic representation of root embedment and periodontal ligament simulation procedure. 

PHASES OF TRADITIONAL EMBEDDING EXECUTION, WITHOUT SIMULATION OF THE PERIODONTAL LIGAMENT

Group D did not undergo periodontal ligament simulation. The samples were individually fixed, by means of soft wax, to the plexiglass plate of the ED, with the crown facing upwards, making sure that they were positioned with the long axis perpendicular to the supporting base. A metal cylinder was then placed underneath (figure 4A). By screwing the wing bolt of the ED, the element was immersed so that the resin reached tmm from the enamekement junction (CEJ) in order to simulate the alveolar bone crest (figure 4B). The selkuring resin (ProBase Cold, Ivodar Vivident AG) was then poured using a special syringe in order to control its flow(figure 40 Once the resin was polymerized, the wing bolt was unscrewed in order to determine the detachment of the plexiglass plate from the tooth, which was instead incorporated into the resin (figure 4D). 

Figure 4. Schematic representation of root embedment without periodontal ligament simulation. 

FRACTURE STRENGTH TEST

Each sample was fixed inside the  universal loading machine (Triaxal Tester T400 Digital) by means of a goniometer with a clamp correct positioning of the machine was checked by means of a laser level. The load was applied  at a speed of 1  mm/minute till fracture occurred and recorded in Newton (N) by a computer (Digimax Plus) connected to the machine. All tests were carried out on the same day. 

STATISTIC ANALYSIS
Statistical analysis was performed using an ad hoc statistical software (STATA BE, version 17.1, StataCorp LP, TX, USA), setting the level of significance at α = 0.05. A total of samples were indicated as the ideal size required for notinp significant differences usinp G∗Power v3.1 (Heinrich Heine, University of Dusseldorf, Dusseldorf, Germany) Continuous variables were reported as Mean and standard deviations. After verification of data distribution, Kruskal—Wallis was applied to evaluate the difference in fracture strength (STRENGHT) between the four study groups. Wilcoxon rank sum test was performed to evaluate their inter-group differences: A vs. D (PDL), B vs. C (Load Inclination), and A vs. B (Tip Angulation).

RESULTS
Samples dimensions for each group are presented in Table 1. No statistically significant difference was observed in terms of tooth size between the four groups (Table 1). The four groups differ significantly in terms of fracture strength (P=0.0007). The mean load values are higher for group D and lower for group C (1354.92  537.44 N and 477,47  200.79 N, respectively).  Additionally,  the  inter-group analysis    disclosed    statistically    significant group couples (A vs. B; A as. C; B vs. C; B vs.

Table 1. Teeth dimensions (mesio-distal, bucco-lingual and root length) values for each subgroup

Mesio-distal and Bucco-lingual dimensions were measured at the cement-enamel junction (CEJ). Tooth length was measured from the vestibular cusD to the root aDex3CEJ measured from the aDex of the vestibular cusp to the CE.

Table 2. Descriptive statistics per each group and differences between each group couple.

The study showed that fracture load values from groups A, B, and C, in which the ligament was reproduced, did not differ significantly from those of group D, in which periodontal ligament simulation did not occur. Group A (PDL +) revealed lower strength values compared to group D (PDL) (1298.59 ± 583,20 N and 1354.92 ± 537.44 N, respectively), however their difference in fracture strength was non-significant (P-0.9397) (figure 5). On the other hand, a statistically significant difference was detected comparing groups B and C, which differed for the load inclination (p 0.0288). Group B (90 ° inclination of the tip) showed higher fracture load values compared to group C (45 ° inclination of the tip), as shown in Table 2. In group, C mean was 471.4 N, while in group B 725.3 N. Group B showed higher strength values compared to group C, as shown in Table 2 (477.47 N ± 200,79 and 725.3±818,05 N).

Furthermore, fracture strength values between groups A and B characterized by different tip designs (3mm spherical tip and 2mm flat tip, respectively) are shown in Figure 2. Tip design is not significantly associated with changes in strength value. Indeed, no statistically significant difference (p 0.0630) was disclosed between groups A and B.

Figure 5. Box plot reporting fracture load values in group A and D differing in presence and absence of periodontal ligament simulation, respectively. 

DISCUSSION

The aim of this ex-vivo study was to evaluate the impact of tip inclination (45° and 901, tip design (spherical and flat), and periodontal ligament simulation on fracture strength test results conducted on uniformly selected NTEP. The current study showed a statistically significant correlation between fracture resistance of NTEP and tip inclination; therefore, the null hypothesis was rejected for the tip inclination, while it had to be accepted both for periodontal ligament simulation and tip design. In fact, the simulation of the periodontal ligament and type of tip did not significantly affect the results of fracture strength test. On the contrary, fracture resistance significantly increased when the load was applied at 90° instead of 45°. Teeth can fracture during normal function or due to traumatic occlusal oontacts12. From a functional point of view, premolars run a greater risk of damage due to their anatomy and position in the oral cavity. Despite its limitations, fracturetesting remains a common experimental method of evaluating fracture strengh13. Previous studiesvos revealed that intact premolars show higher fracture load values compared to teeth with fewer residual walls. Moreover, Gaeta et al. demonstrated that fracture strength is not affected by several methodological variables analyzed (i.e., periodontal ligament simulation, tip diameter, position and inclination, and thennocycling in), partially confirming our results.

The periodontal ligament is an important structure that connects the tooth root and the alveolar bone, whose main function is the absorption of occlusal loads. When a load is applied, tension is transmitted to the periodontal fibers, which compress and slightly displace the tooth, leadng to alveolar bone deformation in the direction of the root movement. The resistance of the periodontal fibers to tooth displacement is initially low, but as soon as the root begins to compress the socket, their resistance progressively increases. However, in the current study, periodontal ligament simulation did not significantly modify fracture load values. In accordance with our findings, a recent study by Marchionatti etal. showed that simulation of the periodontal ligament is unable to influence fracture strength, and therefore it may not be mandatory to reproduce this anatomical structure in fracture test studies. However, our results are in disagreement with previous studies, which demonstrated that fracture strength test requires periodontal ligament simulation to enable a more accurate in vitro reproduction of the oral environment.

Indeed, Soares et al proved through fracture mode analysis that periodontal ligament reproduction influenced the fracture pattern rather than the fracture load values by modifying stress distribution. Precisely, the absence of periodontal ligament simulation led to a large number of fractures characterized by a failure at the interface between the resin cylinder and the corona! structure. The divergent findings in previous research might be related to the inherent limitations of fracture strength testing, such as the use of extracted teeth, moreover, different teeth chosen for the test. In fact, this is the first study testing the influence of periodontal ligament of intact human premolars, while previous studies were conducted on bovine teeth.

The absence of a consensus among studies in the literature could be related to the intrinsic challenges and limitations of fracture tests, leading to a lack of consistency. One of the hardest challenges in these tests is the use of extracted human teeth and precisely sample standardization. The main reason relies on their large anatomical variability, aging, and morphological alterations mainly caused by acid erosions, abrasions, and fatigue cracks. In the present study, to control for variables that could have affected the study outcomes, only maxillary premolars with similar dimensions (MD, BL, CFJ, TL) were selected, as shown in Table 1. Although Group A reported higher fracture load values compared to Group B (figure 6), the difference is not statically significant.

Therefore, according to our findings, the tip diameter and tip designs do not affect ex vivo fracture strength test results, as confined by a recent meta-analysis. According to Yang et al, load angulation influences stress distribution and accumubtion both at the crown and root level confirming our results. Indeed, in the present study, the tip inclination variable seemed to influence fracture resistance. Indeed, lower fracture load values were recorded when the force was applied at 45° instead of at a right angle (Figure 7).

However, our findings are in disagreement with Gaeta et al., who demonstrated that tip inclination does not affect fracture strength test in intact premolars; on the contrary, significant results emerged in premolars with a lower number of residual wane. However, the authors reported that this lack of statistically significant difference in fracture strength could probably be due to the scarcity of data available regarding tip.

Conflict of Interest Statement: 

The authors deny any conflict of interest.

Funding Statement:
The research received no external fundings.

Acknowledgement Statement:
We declare that this manuscript is original, has not been published before and is not currently being considered for publication elsewhere. As Corresponding Author, confirm that the manuscript has been read and approved for submission by all the named authors.

Data Availability Statement:
The data used in this research has been properly cited and reported in the main text. Further enquiries can be directed to the corresponding author.

Author Contributions:

Carlo Gaeta participated in the conceptual design of the work, data acquisition, and drafting of the manuscript. Giulia Malvicini participated in statistical analysis, data acquisition and revision of the manuscript. Emanuele Mignosa participated in data acquisition and conceptual design of the work. Gianmarco Cecot participated in data acquisition and drafting of the manuscript. Simone Grandini participated in conceptual design of the work and revision of the manuscript. Crystal Marruganti participated in the conceptual design and drafting of the manuscript.

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