This study was approved by the Research Ethics Committee of the Faculty of Dentistry, Cairo University. Approval number: 15636 ( Extended data).

Extracted teeth were obtained from the outpatient clinic, Oral Surgery Department, Faculty of Dentistry, Cairo University. Any researcher in the institute can obtain extracted teeth that meet the criteria of the research without requiring the researcher to contact the patients, since the patients give their consent for their extracted teeth to be used in future research when they are extracted.

Student’s t-test was performed to compare two groups (Group I: TOD; Group II: FOD), as per a previous study by Shahrbaf et al. ⁵ . The primary outcome of this study is the fracture resistance with an estimated mean value of 407.7±82.7 N for the control group (Group I) and 661.1±190 N for the test group (Group II) (effect size =1.7 with alpha 0.05 and power =0.8). Priori power showed that the required sample size should be above 14 (7 in each group) (calculated using G*power release 3.1.9.2). Accordingly, a total sample size of 20 (10 per group) was performed.

Teeth collection, endodontic treatment and coronal build up. In total, 20 human mandibular molars free of caries, defects and cracks were chosen. The mean measurement between the maximum convexity on the buccal and lingual surfaces of the selected teeth differed by ≤ 2.5% (as measured using a digital caliber (Harbor Freight Tools, CA, USA)) ⁶ . The teeth were kept in distilled water after ultrasonic scaling which was done to remove any remnants. Conventional access cavities were prepared in all teeth. Manual preparation and enlargement of root canals was performed until size # 25 (MANI, Japan) ^{7, 8} . Rotary root canal preparations were then performed with a series of ProTaper Ni-Ti rotary instruments (Dentsply Maillefer, Switzerland). The matched gutta percha points (Dentsply Maillefer, Switzerland) and resin based sealer (Adseal; META BIOMED Co, Korea) were used for obturation and the excess gutta percha was removed by a heated plugger ⁹ . Coronal cavities were then treated with 37% phosphoric acid Etch (Spident, USA) for 15 seconds, rinsed for 10 seconds and dried gently using a cotton pellet. A layer of light cure bonding agent (Adper Single Bond Plus Adhesive; 3M ESPE AG, Germany) was applied with gentle agitation and light cured for 10 seconds, then packable composite resin (3M Filtek Z250 XT Nano hybrid composite resin; 3M Deutschland GmbH, Germany) was incrementally added and light cured ¹⁰ .

Teeth mounting, grouping and preparation. A plastic ring (2.5 cm in diameter and 2 cm in length) was utilized to mount the teeth in epoxy resin (CMB, Egypt) and a custom made paralleling device ( Extended data) was used to allow accurate vertical centralization of the tooth in the ring. The mounted teeth were randomly distributed into two equal groups as follows:

Group I (TOD): Prepared teeth with two planes occlusal surface.

Group II (FOD): Prepared teeth with flat occlusal surface.

A special milling machine (AF30 Nouvag, Switzerland) was used to prepare all the teeth by the same operator ( Figure 1). The preparation parameters are detailed in Table 1.

Crown fabrication and cementation. A CAD/CAM system (CEREC AC; Sirona, Germany) was used for the fabrication of all crowns. Each prepared tooth was scanned using the CEREC Omnicam and design was carried out using CEREC Premium 4.4 software. The distance between central groove of restoration and the occlusal surface of tooth was standardized at 1.5 mm in all restorations. Milling of the crowns was done from Lithium disilicate blocks (IPS e.max CAD; Ivoclar Vivadent AG, Principality of Liechtenstein) in 4-axis milling machine CEREC MC XL. Finally, crowns were fully crystallized and glazed in Programat P510 furnace (Ivoclar Vivadent AG, Principality of Liechtenstein).

Surface treatment of the fitting surface of each crown was done as follows: Porcelain Etch (BISCO, USA) application for 20 seconds, followed by water rinsing and drying, then Silane (BISCO, USA) application for 60 seconds followed by air drying for 5 seconds. Self-adhesive resin cement (RelyX Unicem; 3M ESPE AG, Germany) was used for cementation.

Each crown was seated on its corresponding tooth and held with light pressure. The excess cement was cleared by an explorer after 2 seconds of tack-curing, then glycerine based gel (K-Y Jelly; Johnson & Johnson, USA) was applied at the margins of crown to prevent the oxygen inhibiting layer. A 5 kg load was applied parallel to the long axis of each tooth during cementation using a custom made loading device ( Extended data) ^{11, 12} . The load was applied for 5 minutes to allow the cement to self-cure as recommended by the manufacturer. This was followed by final curing of axial and occlusal surfaces with light cure for 20 seconds.

The test was carried out using a computer-controlled material testing machine (Instron, Model 3345; Instron industrial, USA). Each sample was tightened to the lower fixed compartment by screws. A compressive load was applied on the occlusal surface utilizing a metallic rod with round tip (5.8 mm diameter) attached to the upper movable compartment traveling at cross-head speed of 1mm/min with tin foil sheet in-between to achieve homogenous stress distribution and to minimize the transmission of local force peaks. The load to fracture was recorded in Newtons (N) using Instron Bluehill Lite Computer Software version 2 (Instron, USA). The fracture was manifested by an audible crack and confirmed by a sharp drop at load-deflection curve.

Data from the two groups were gathered, arranged and analyzed using SPSS (version 21; IBM, USA).

High-performance Leica MZ6 Stereomicroscope (Meyer Instruments, USA) with 6.3:1 zoom was used to evaluate the fracture mode of the samples, indicating areas of interest for further examination under a scanning electron microscope (SEM; Model Quanta 250 Field Emission Gun; FEI Company, The Netherlands) attached with Energy Dispersive X-ray Analyses unit, with 30 KV accelerating voltage, 70X, 250X magnification and resolution of 1nm.

3D designing of models

3D scanning. Two of the prepared samples (one for each group) and their corresponding crowns were scanned before cementation to produce models with real geometrical measures. 3D reconstruction from cone beam computed tomography (CBCT) data of the teeth scans was found had high linear, volumetric, and geometric accuracy ¹³ . A CBCT scanner (Next Generation iCAT scanner; ISI, USA) was used to obtain CBCT images in this research. After scanning, data were exported in DICOM format. Mimics software version 17 (Materialise, Belgium) was used ^a for segmenting the scanned objects into separate elements. A definitive threshold level was set to most clearly show each element of the scanned samples with minimal interference from the surrounding structures, and once segmentation was completed the software automatically calculated the element’s volume. The resulting STL files were opened separately on Meshmixer software version 3.3.15 (Autodesk Inc., USA) for the improvement of mesh quality and its refinement.

Reverse engineering and assembly. Reverse engineering was performed by NX software version 10 (Siemens PLM, Texas, USA) ^b . The refined STL files were imported into the software and converted into solid parts. Then, cortical bone and cancellous bone were drawn as solid parts in cylindrical shapes followed by their superimposition together for Boolean subtraction. Finally, all the produced solid parts were superimposed together for Boolean subtraction and periodontal ligaments were modeled with 0.2 mm thickness to allow a fully defined simulation methodology. The generated 3D CAD geometry of all parts were then assembled using Solidworks software 2017 (Dassault Systèmes SolidWorks Corporation, France) ^c to produce the 3D CAD models, one for each group ( Figure 2).

Finite element analysis. Finite element analysis (FEA) was carried out by ANSYS R16.2 software (ANSYS, Canonsburg, USA) ^d using the 3D CAD models. It included 3 phases:

Pre-processing phase. The type of element was defined as Solid 10 node 187. All the materials’ properties were set as isotropic, homogenous and linear elastic. The modulus of elasticity and Poisson’s ratio of each material were gathered and were uploaded to the software ( Table 2). A perfect rigid bonding with no-slip condition between all the elements was simulated. Each model was divided into small parts called elements connected together at points called nodes forming a mesh structure. Parabolic tetrahedral solid elements were used to form a fine solid mesh. The overall number of elements and nodes was recorded ( Table 3).

Processing phase. Following the creation of the 3D meshes, a zero displacement boundary condition was set at all nodes of the cortical bone that were confined in X, Y, and Z directions. Posterior fixed restorations ought to have the capability to tolerate a 500 N occlusal load ^{18, 19} . Accordingly a load of 500 N was applied by a ball model of diameter 5.8 mm equal to that of metallic rod ball of the universal testing machine used for fracture resistance test in this study. The occlusal surface of the crown was loaded at the inner inclines of the mesiobuccal, distobuccal and mesiolingual cusps ²⁰ . The load was applied in vertical direction as the masticatory forces directed onto molar teeth is mostly vertical, while through the anterior guidance and lateral guidance, they are guarded by the anterior teeth ²¹ .

Post-processing phase. The output of the processing phase was displayed as graphical output and numeric output.

Fracture resistance results as a function of preparation design are summarized in Table 4.

It was found that the fracture resistance mean ± SD value recorded for Group I was 2962.6 ± 524.2 N, with minimum value of 2206.01 N and maximum value of 4014.7 N. For Group II, the mean ± SD value recorded was 3107.2 ± 604.94 N, with minimum value of 2253.5 N and maximum value of 4153.4 N.

The difference between the mean fracture resistance between the two groups was non-statistically significant as indicated by Student’s t-test (p=0.57) ( Figure 3).

The behavior of the samples upon fracture differed ( Table 5). Five different modes were observed and categorized as restorable or non-restorable according to their relation to the cemento-enamel junction (CEJ). A fracture that ends before CEJ, implying that even after the occurrence of fracture, the tooth can be saved is a restorable one, while fractures that are non-restorable extend beyond CEJ and extraction of the tooth is expected ²² . The extensions of the cracks were verified by SEM ( Figure 4). The results are tabulated in Table 6 and classified as restorable and non-restorable.

In each model, FEA revealed stresses at every node. These results were presented as stress contours overlaid on the model. The numeric data of stress, deformation and safety factor in the models were calculated and transformed into color graphics.

Equivalent (von-Mises) stress. The "von-Mises Stress" at different areas were calculated and compared ( Table 7). The stress distribution values were generally found to be low.

Total deformation. The maximum value of total deformation denoted by the red color in Group I was 0.0158 mm. It was concentrated on the mesial half of the coronal portion of model (Crown, dentin and core) and the root (neck of the tooth) at the mesial surface and the mesial half of the lingual surface ( Figure 5). While in Group II the maximum value of total deformation was 0.01409 mm. It was located on middle and the lingual half of coronal portion of model and the lingual neck of the tooth with mesiolingual and distolingual line angles ( Figure 6). When comparing both groups, Group II yielded less total deformation values than Group I.

Safety factor. Both groups had high safety factor where the maximum equivalent stress was less than the stress limit. In Group I: the lowest safety factor recorded was 1.5575 was at the mesial neck of the tooth denoted by the orange color ( Figure 7). In Group II: the lowest safety factor recorded was 1.1571 was at the lingual neck of the tooth denoted by the orange color ( Figure 8).

The stress distribution among different layers of the model differed as well as areas of total deformation. This was correlated with the fracture behavior of samples of both groups as follows:

Group I ( Figure 9). The stress values were high at mid-mesial and mid-lingual axial walls, mid-mesial and mid-lingual finish line, and root’s mesial surface. Maximum total deformation was concentrated in the mesial half of the coronal portion of model (crown, dentin and core) and the neck of the tooth at the mesial surface and mesial half of the lingual surface.

Upon observation of fracture behavior of Group I samples of fracture resistance, the failure in most of the samples occurred at the mesial half of the crown-tooth structure including the finish line and the root (neck of the tooth).

Group II ( Figure 10). The centers of the crown and the underlying core material generated high stress values upon load application. Also, at mesiobuccal cusp, mesiolingual cusp, mesial marginal ridge, and root’s lingual surface stresses were high. Maximum total deformation was located at the middle and the lingual half of coronal portion of model (crown, dentin, and core) and the lingual neck of the tooth with mesiolingual and distolingual line angles.

Upon observation of fracture behavior of Group II samples of fracture resistance, the failure in more than half of the samples occurred at the lingual half of the crown-tooth structure, not including the finish line and the root (neck of the tooth).

The occlusal reduction of endodontically treated molars can influence the functioning of the crown-molar structure. The occlusal surface preparation design has to strengthen the prepared tooth to sustain the forces being subjected to and, upon failure, it favors a restorable mode.

This study revealed that restorable fractures were higher in flat occlusal preparation design than two planes occlusal preparation design. Therefore, clinicians may choose the flat occlusal preparation design to improve the clinical performance and longevity of the restored endodontically treated molars.

1. Clinical studies comparing the behavior of the two tested designs.

2. Designing the same research using other contemporary metal free crown materials (hybrid materials, polycrystalline materials), which may yield different outcomes.

Open Science Framework: Fracture Resistance and 3D Finite Element Analysis of Machined Ceramic Crowns Bonded to Endodontically Treated Molars with Two Planes versus Flat Occlusal Preparation Designs. “ In-Vitro Study”, https://doi.org/10.17605/OSF.IO/WMRU4 ³³ .

This project contains the following underlying data:

Open Science Framework: Fracture Resistance and 3D Finite Element Analysis of Machined Ceramic Crowns Bonded to Endodontically Treated Molars with Two Planes versus Flat Occlusal Preparation Designs. “ In-Vitro Study”, https://doi.org/10.17605/OSF.IO/WMRU4 ³³ .

This project contains the following extended data: