From January to December 2018, we collected 200 intact teeth extracted using minimally invasive techniques for periodontal or orthodontic reasons at the Department of Oral and Maxillofacial Surgery, Stomatological Hospital of Tianjin Medical University. This study was approved by the ethics committee of the Stomatological Hospital of Tianjin Medical University (TMUhMEC2019014). The inclusion criterion was the absence of enamel cracks that were visible to the naked eye. The exclusion criteria were the presence of dental caries, wedge-shaped defects, and VRFs, and a previous history of root canal therapy or restoration. Finally, 40 teeth that met the criteria were screened in vitro.
An in vitro artificial simulation cracked tooth model was established. All the 40 screened intact teeth were cleaned to remove soft tissue and calculus, and soaked in 0.1% thymol solution for 24 h. Subsequently, they were placed in 0.9% saline solution, soaked in liquid nitrogen (− 196 °C) for 1 min and immediately transferred into hot water (90 °C) for 5 min [23, 33]. The teeth were then observed under a surgical operating microscope (OMS2350; Zumax, Suzhou, China) under 17 × magnification. If there were visible cracks, the teeth were regarded as artificially cracked. Among the 40 teeth, 31 were selected as artificially cracked; the remaining 9 teeth were excluded due to splits or absence of cracks. The 31 cracked teeth were randomly embedded in four trays, and the root portion of each tooth was wrapped in modeling wax to simulate the periodontal tissue.
The pre-CBCT (KaVo 3D eXam, Germany) parameters were as follows: voltage, 120 kV; current, 8 mA; matrix size, 640 × 640; field of view, 8 × 8 cm; and pixel size, 0.125 mm × 0.125 mm. To ensure better pre-CBCT imaging quality, the operations were performed by a technician. The pre-CBCT results were stored in a database, and pre-CBCT images were analyzed using the Vision Q (KaVo eXam Vision) software package.
The micro-CT (SIEMENS, Munich, Germany) parameters were as follows: voltage, 80 kV; current, 500 μA; resolution, 9.08 μm; exposure time, 1000 ms. The Inveon Research Workplace software (SIEMENS, Munich, Germany) was used to reconstruct three-dimensional (3D) images. The presence of cracks and their extension depths, as measured from the micro-CT images, was recorded by a radiologist who was blinded to the evaluation of the pre-CBCT images.
The procedure to measure crack depth extending from the crown to the root on micro-CT images (Fig. 1A–C) was as follows: The cracked tooth was adjusted to an upright position in the coronal and sagittal planes and the cracks were observed from the crown to the root in the horizontal plane. When the crack appeared in the crown for the first time on the horizontal plane, the layer was recorded as “a”; the crack was observed extending to the root, always on the horizontal plane. When the crack began to disappear on the root, the layer was recorded as “b”; the distance from “a” to “b,” measured with the ruler tool, was considered to be the crack depth, not the actual crack length.
Ioversol solution (C18H24I3N3O9; Hengrui Pharmaceutical, Jiangsu, China) was diluted in a ratio of 3:1 in normal saline to increase its fluidity. The crown and root of each cracked tooth were isolated with a rubber dam, and the crown was filled with the diluted ioversol solution. The teeth and the rubber dam were kept in place using a rubber band and a paper cup (Fig. 2A). The teeth were placed in a closed glass jar, connected to the suction pump with a rubber tube (Fig. 2B). The crack was infiltrated with ioversol under vacuum conditions (Fig. 2C). This procedure was repeated once again and the teeth were then removed from the jar. After infiltration, the cracked teeth remained in the trays with wax and underwent contrast-enhanced CBCT with the same parameters as used for pre-CBCT.
Two observers, an endodontics graduate student and an experienced radiologist, were involved in the evaluation. Before the study, the two observers were trained to achieve a high degree of consistency. Thereafter, the presence and absence of cracks were determined using pre-CBCT and contrast-enhanced CBCT by the two observers. In the event of disagreement between the observers, the image was re-examined until a consensus was reached. The following 2-point rating scale was used to determine whether cracks were present on pre-CBCT: (i) probably or definitely not a lesion, (ii) probably or definitely a lesion.
On contrast-enhanced CBCT, a high-density linear crack was considered to mark a cracked tooth. The method used for measuring cracks on contrast-enhanced CBCT was the same as that used for micro-CT: the position of the tooth was adjusted in the sagittal and coronal planes to set it upright; the coronal plane of the crack shows its path (Fig. 3A); the cracks were observed from the crown to the root on the horizontal plane. When the high-density crack appeared in the crown for the first time on the horizontal plane, a horizontal line was marked as “1” in the coronal plane with the "distance" tool, indicating the level of the first occurrence of the crack (Fig. 3B). The crack extending to the root was always observed in the horizontal plane (Fig. 3C). When the high-density crack disappeared completely, the layer was marked as “2” in the coronal plane and represented the apical point of the crack (Fig. 3D). The "distance" tool was used to draw a vertical line from 1 to 2 in the coronal plane, and was marked as “3,” representing the crack depth as measured by contrast-enhanced CBCT (Fig. 3E). The extension depth of the cracked teeth on the contrast-enhanced CBCT was measured by the radiologist. Each crack depth value was measured three times at one-week intervals by the same radiologist, and the average value was considered as the final crack depth.
SPSS v.26.0 software (IBM Corp, Somers, NY), R software, version 3.6.0 (R Foundation for Statistical Computing; http://www.r-project.org/), and RStudio 1.1.463 (RStudio, PBC, Boston, MA, US) were used to perform the statistical analysis for the study.
The K-means clustering algorithm, first published in 1955, has been proposed over 50 years ago and is still widely used even though thousands of clustering algorithms have been published ever since [34]. Moreover, it is undoubtedly the most widely used partitional clustering algorithm [35]. Crack depths measured by micro-CT were transformed into categorical variables according to the K-means clusters.
For further analysis, the Bland–Altman plot was used to analyze the consistency of the crack depths between pre-CBCT and contrast-enhanced CBCT. The intraclass correlation coefficient (ICC) was used to evaluate the consistency of the crack depths as measured on pre-CBCT and contrast-enhanced CBCT, as well as between contrast-enhanced CBCT and micro-CT. The cracked teeth that could be detected by pre-CBCT and contrast-enhanced CBCT were included in the receiver operating characteristic (ROC) analysis. The crack depth of pre-CBCT and contrast-enhanced CBCT were continuous variables, and the crack depth of micro-CT was changed into a binary variable to study the predictive ability of pre-CBCT and contrast-enhanced CBCT for crack depth.
Moreover, we used restricted cubic splines (RCS) with 4 knots at the 5th, 35th, 65th, and 95th percentiles to model the non-linear relationship between the crack depths of contrast-enhanced CBCT and micro-CT.