Measurement of the Dentin Wall Thickness of the Maxillary Central Incisor in Relation to the Stage of Root Development: A Pilot Study

Abstract

Objective

The aim of this study was to determine the average dentin wall thickness (DWT) of the maxillary central incisor (MCI) required for performing finite element analysis (FEA) models of root development.

Material and methods

A total of 137 intraoral periapical radiographs of MCI in children aged 7 to 11 years were examined and then classified into 5 groups according to root development stages, which included 1/2 of root development (S1), 3/4 of root development (S2), more than 3/4 of root development (S3), complete development with wide-open apex (S4) and complete development with closed apex (S5). DWT was measured at three reference (horizontal) lines: at a distance of 1 mm from the apex (M), 4 mm from the apex (L) and at the cervical line (K). The distal dentin wall thickness (M1, L1, and K1), the pulp thickness (M2, L2, and K2), the mesial dentin wall thickness (M3, L3, and K3), and the apex thickness (N) were measured using the diagnostic software Soredex Scanora 5.1.2.4. Statistical analysis compared the values of the parameters K, L, and M between developmental stages (multivariate ANOVA) and the linear correlations between the parameters (Pearson's correlation analysis). All analyses were performed at significance level α = 0.05.

Results

There were statistically significant differences between the developmental stages for parameters L and M, while no significant differences were found for parameter K. Most of the correlations between the parameters were statistically significant, with the values of the Pearson correlation coefficient R > 0.6 considered practically significant. All parameters on the same reference line for distal and mesial dentin wall thickness and for pulp thickness correlated well with each other (R = 0.46 – 0.68), but there was no statistically significant correlation with total root thickness on the same reference line (parameters K, L, or M), except for parameter K3 (R = 0.42).

Conclusion

Despite the limitations of this study, the mean values of the selected parameters for the 5 groups of developmental stages of the maxillary central incisor could be used to model dentin wall thickness using finite element analysis.

Introduction

The treatment of dental trauma is not a common situation in everyday dental practice (1-4). Many clinical studies have shown that over 50% of immature teeth treated endodontically are lost in the first ten years (5-7). For these reasons, the analysis of masticatory function, especially the biomechanical response after dental trauma, is of great importance for understanding the problem of treatment failure and for finding more suitable reconstructive materials and methods (8).

The stress distribution within the tooth and the surrounding tissue is very complex due to the inhomogeneous importance of the structures that compose them, the irregularities of the contours and their external shape, and the complex internal morphology (9). The finite element method (FEM) is a new and important research tool for biomechanical analysis (10). Using mathematical equations, computer analysis converts a physical problem into a virtual model represented by finite element software (11). The method represents the simulated mechanical behavior of teeth under occlusal loading (12). The necessary step for implementation is the construction of a finite element model, followed by the specification of appropriate material properties, loads, and boundary conditions (8). Finite element analysis (FEA) effectively simulates a real clinical scenario and solves complex problems by predicting long-term failures (11). The results include information about the stress distribution in each component as opposed to single values obtained in in vitro research (12). In addition, FEM reduces research time and allows ethical and methodological constraints to be overcome, which is why it is often used for complex studies in dentistry (10, 12).

Traumatic injuries to permanent teeth are very common in school-age children, especially between the ages of eight and ten years (13), when root development is not yet complete. The maxillary central incisor (MCI) is the tooth most frequently affected by trauma, which usually results in a crown fracture (14-16). A fracture may be uncomplicated or complicated, i.e., with or without exposure of the pulp. The primary goal of treatment is to preserve the pulp vitality and restore aesthetics and function (17). Endodontic treatment is required when all efforts to preserve vitality are unsuccessful or when the patient has already presented with such a condition. Due to the immaturity of the teeth, it is considered one of the most complex challenges for clinicians (15, 18).

Many studies have evaluated the stress distribution in endodontically weakened root canals using FEM (19-21), but there have not yet been any data in the literature on the biomechanical response of MCI depending on the stage of root development. The average length values in the general population for intact MCI with completed root development were taken from the literature (22), but there have been no data on the average dentin thickness. The aim of this study was to determine the average dentin wall thickness (DWT) of MCI required for the construction of finite element analysis models of root development.

Material and methods

This study is part of a dissertation study approved by the Ethics Committee, School of Dentistry, University of Zagreb, Croatia (Approval number: 05- PA -27-5/2018.). For the use of radiographs, it was sufficient for the child's parents or guardians to sign an informed consent form before each treatment at the Department of Pediatric and Preventive Dentistry, University Hospital Centre Zagreb, which also included consent to use the radiographs for research purposes. A total of 137 intraoral periapical radiographs of MCI in children aged 7 to 11 years indicated for diagnostic purposes were examined and then classified into 5 groups according to the stages of root development, which included 1/2 of root development (S1), 3/4 of root development (S2), more than 3/4 of root development (S3), complete development with wide open apex (S4), and complete development with closed apex (S5) (Figure 1). The dentin wall thickness was measured at three reference (horizontal) lines: at a distance of 1 mm from the apex (M), 4 mm from the apex (L) and at the cervical line (K). The distal dentin wall thickness (M1, L1 and K1), the pulp thickness (M2, L2 and K2), the mesial dentin wall thickness (M3, L3 and K3) and the apex thickness (N) were measured using the diagnostic software Soredex Scanora 5.1.2.4 (Figure 2). All measurements were performed by a single person.

Figure 1.

Root development stages (S1) 1/2 of the root development, (S2) 3/4 of the root development, (S3) more than 3/4 of the root development, (S4) complete development with wide-open apex, (S5) and complete development with closed apex.

Figure 2.

The dentin wall thickness at three reference (horizontal) lines: at a distance of 1mm from the apex (M), 4mm from the apex (L), and at the cervical line (K). The distal dentin wall thickness (M1, L1, and K1), the pulp thickness (M2, L2, and K2), the mesial dentin wall thickness (M3, L3, and K3), and the apex thickness (N)

The average length values in the general population for intact MCI with completed root development were taken from the literature: 23.5 mm for tooth length, 10.5 mm for crown length and 13.0 mm for root length (18). The mean root lengths for the other stages calculated from the mean lengths for MCI with complete root development were as follows: 6.5 mm for S1, 9.7 mm for S2, between 9.7 mm and 13.00 mm for S3, and 13.0 mm for S4 and S5. All stages except S3 were classified according to the proposed root-to-crown length ratio (Table 1), whereas for stage S3, the range between stages S2 and S4 was considered, i.e., root lengths from 10.0 mm to 12.5 mm and their root-to-crown length ratio to avoid errors in the final range values, which were then closer to stage 2 or 4. Stages S4 and S5 were differentiated according to apical closure status, with N above 0.45 mm considered S4 unless when the expected age of the child was a more decisive factor (> 10 years). All measurements were performed by a single person.

Table 1. The root-to-crown length ratio of mean values for MCI (18) depending on the root development stage.

Stage	Mean crown length (mm)	Mean root length (mm)	Root-to-crown ratio
S1	10.5	6.5	1:1.62
S2		9.7	1:1.08
S3		10.0 – 12.5	1:1.05 – 1:0.84
S4		13.0	1:0.81
S5		13.0	1:0.81

The normality of data distribution was evaluated using the Kolmogorov-Smirnov test and normal Q-Q diagrams. Statistical analysis compared the values of parameters K, L, and M between developmental stages (multivariate ANOVA) and linear correlations between parameters (Pearson's correlation analysis). All analyses were performed at a significance level of α = 0.05.

Results

The values of the individual numerical parameters, divided into 5 groups (stages of development), generally did not deviate significantly from the normal distribution (Figure 3). For parameters L and M, there were statistically significant differences between the developmental stages, while no significant differences were found for parameter K (Table 2). Most of the correlations between the parameters were statistically significant, with values of the Pearson correlation coefficient R > 0.6 considered practically significant. All parameters for pulp thickness correlated well with each other (R = 0.61 – 0.99) and with root thickness at a distance of 4 mm and 1 mm from the apex (R = 0.60 – 0.95), but did not correlate with root thickness at the cervical line, except for parameter K2 (R = 0.64). All parameters on the same reference line for distal and mesial dentin wall thickness and for pulp thickness correlated well with each other (R = 0.46 – 0.68), but there was no statistically significant correlation with total root thickness on the same reference line (parameters K, L, or M), except for parameter K3 (R = 0.42). Root thickness at a distance of 4 mm from the apex correlated well with pulp thickness (R = 0.90), but there was no statistically significant correlation with distal and mesial dentin wall thickness. The parameters K and K1 showed significantly lower correlations than all other parameters, while the parameter K2 correlated with all measured parameters (R = (-0.26) – 0.70).

Figure 3.

The distribution of root dimensions divided into 5 stages of root development. The boxplots show medians (bold black lines) and the boxes represent the 25% and 75% quartiles. The 1.5 × interquartile range is represented by whiskers. Outliers are presented by circles.

Table 2. Results of multivariate ANOVA for comparisons of root dimensions among developmental stages.

Dentinal wall thickness (DTW)		Type III Sum of Squares	df	Mean Square	F	Sig.
	K1	1.031a	4	,258	10,464	,000
	K2	5.369b	4	1,342	18,886	,000
	K3	.654c	4	,163	7,877	,000
	K	.345d	4	,086	,680	,608
	L1	2.135e	4	,534	25,086	,000
	L2	71.685f	4	17,921	201,326	,000
	L3	1.787g	4	,447	16,625	,000
	L	36.305h	4	9,076	79,893	,000
	M1	.865i	4	,216	8,848	,000
	M2	122.365j	4	30,591	317,497	,000
	M3	.855k	4	,214	10,910	,000
	M	93.510l	4	23,378	299,004	,000
	N	140.106m	4	35,027	327,628	,000

The mean values of dentin wall thickness for the 5 groups of developmental stages of the maxillary central incisor are shown in Table 3.

Table 3. The mean values of dentin wall thickness for the 5 groups of developmental stages of the maxillary central incisor.

	K1	K2	K3	K	L1	L2	L3	L	M1	M2	M3	M	N
S1	1.840± 0.069	3.080± 0.100	1.820± 0.066	6.740± 0.102	1.000± 0.048	3.660± 0.169	0.950± 0.091	5.610± 0.160	0.420± 0.056	4.070± 0.191	0.340± 0.069	4.820± 0.125	4.240± 0.211
S2	2.033± 0.049	2.683± 0.191	1.942± 0.064	6.658± 0.192	1.075± 0.072	2.650± 0.134	1.008± 0.091	4.733± 0.109	0.583± 0.059	2.675± 0.182	0.508± 0.057	3.767± 0.175	2.871± 0.236
S3	2.148± 0.072	2.471± 0.118	2.019± 0.057	6.638± 0.162	1.210± 0.061	1.876± 0.187	1.048± 0.094	4.133± 0.144	0.581± 0.084	1.586± 0.242	0.481± 0.084	2.648± 0.175	1.490± 0.244
S4	2.086± 0.088	2.452± 0.115	2.081± 0.084	6.619± 0.206	1.267± 0.086	1.271± 0.152	1.138± 0.067	3.676± 0.210	0.543± 0.071	0.767± 0.086	0.500± 0.056	1.810± 0.111	0.683± 0.078
S5	2.200± 0.069	2.252± 0.124	2.084± 0.064	6.536± 0.141	1.460± 0.062	0.848± 0.078	1.344± 0.065	3.652± 0.133	0.736± 0.072	0.436± 0.039	0.660± 0.063	1.832± 0.098	0.400± 0.047

Discussion

Numerous studies have evaluated stress distribution in endodontically treated ("endodontically weakened”) maxillary incisors, usually after postendodontic restoration using FEM, but only a few of them evaluated immature incisors (23-28). In these studies, different methods were used to model an immature incisor for FEA, defining immaturity in general or a specific stage, but there was no protocol for creating FEA models for all stages of root development. The main reason for this is that there are no data in the literature on average dentin thickness depending on the root development stage.

CBCT is commonly used for dental measurements because it provides high accuracy and detection of surrounding tissue (29, 30). Although the absorbed dose of X-rays has been greatly reduced compared to CT, the dose is still higher than panoramic radiography (PAN) (29, 31). There is no justification for its use unless it is not primarily indicated for other diagnostic or therapeutic reasons, especially in children (32-34). Mazzotta et al. (2013) reported that it is possible to create a 3D parametric model with a clinically valid degree of accuracy starting from 2D information (35). They measured tooth height, crown and root height, CEJ width, width of the widest and highest part of the crown, and width of the root at half root length for monoradicular teeth. In our study, similar measurements were made for the root, and additional measurements were made 4 mm and 1 mm from the apex. Accordingly, data from 2D images were sufficiently accurate to obtain mesial/distal measurements, but the disadvantage was that it was impossible to obtain buccal/lingual measurements from a panoramic radiograph. Nevertheless, after reviewing the literature, we decided to use the CBCT of the maxillary central incisor with completed root development for a personalized base model so that the initial buccal-oral dimension would be considered for modelling the other models of root development. Also, the pulp canal of the central incisor is almost equidistant to all edges of the root (36), the mesio-distal and buccal-oral dimensions are almost the same.

Back in 2007, Talati et al (23) designed two models of MCI, a mature and an open-apex model. The geometry of the mature tooth was taken from the literature (37), with simulation of endodontic canal instrumentation in taper form (master apical file #40, coronal opening diameter 1.60 mm) and gutta-percha filling. Buccolingual and mesiodistal measurements for an immature tooth were taken on an extracted incisor with an open apex, additionally simulating an MTA plug and endodontic filling with gutta-percha. Although the dimensions of the mature incisor for the basic FEA model are now much more accurate, mainly due to the method of tooth isolation from the CBCT, the study still confirmed that the pattern of stress distribution is different in mature and immature teeth, paving the way for further research in this area. Since then, there have been several studies using different methods to model a weakened or immature incisor for FEA. Usually, a basic 3D geometric model was reconstructed from the CBCT of an intact or extracted incisor, and then additional models were created in the programme or directly on the extracted incisor according to the required tooth properties.

Khadar et al (24) used prepared extracted MCI to simulate immature incisors with thin dentin walls and open apex. After root instrumentation (master apical file set at # 80), the apex was enlarged to 1 mm with Peeso drills to define immaturity in general. Eram et al. (25) also prepared an extracted MCI before subjecting it to a CBCT examination to simulate an immature incisor according to Cvek’s third stage (7). The root was shortened apically by 4 mm (tooth length was 21 mm and root length was 9 mm). After root instrumentation (master apical file # 80), the open apex was extended 1 mm beyond the apex to 1.7 mm with Peeso drills. The root-canal ratio was approximately 1:1 in the mesiodistal dimension at CEJ. These dimensions were higher to our third stage of root development: apex width 1.490±0.244 mm and root-canal ratio at the CEJ 1:1.19, except for the average root width (11.0 mm). In the study by Anthrayose et al (22) CBCT scans of permanent maxillary central incisors and available literature data were used to simulate an immature MCI model at Cvek stage 3 in the programme, with an apical opening of 1.67 mm and a root length approximately 3 mm less than that of the mature tooth, i.e. 10.5 mm, which is more in agreement with our measurements. This study had a similar protocol to ours, but described only one stage of root development and the proposed root dimensions. The study by Dezzen-Gomide et al. (27) presented three different stages of MCI root development: complete rhizogenesis, incomplete rhizogenesis in the apical third of the root, and incomplete rhizogenesis in the middle third of the root. The model of complete rhizogenesis was based on a CBCT of an extracted incisor. The two models of incomplete rhizogenesis were modified based on anatomical references from 6 CBCT studies of immature MCI (patients aged 7 to 12 years) at different stages of rhizogenesis, but without describing the values obtained. Dezzen-Gomide et al. also pointed out that evaluating dental trauma outcomes in an in vivo model has significant methodological and ethical implications. This is particularly true for the evaluation of the very sensitive therapeutic treatment of revascularization on an immature MCI studied by Bucchi et al (28). The root dentin was divided into two parts to simulate the immature state after the therapeutic procedure of revascularization: a part with thin walls and missing root apex at Cvek stage 4 and a part with newly formed intracanal tissue (mechanical parameters of dentin or cementum), with the root apex classified as 20% of the root length. Accordingly, dental immaturity was presented at stage 4 of the Cvek classification (7): a widely opened apical foramen and almost complete root length. Unfortunately, as in previous studies, values for dentin wall thickness were not reported for all stages of root development.

After reviewing the literature, we decided to use a CBCT of an intact young MCI to reconstruct a basic 3D model since it provided the most accurate data but still required measurements of the dentin wall thickness of the MCI to reconstruct models of different stages of root development in the programme. For this reason, we measured DWT on intraoral periapical radiographs of maxillary incisors of children aged 7 to 11 years to obtain data for all stages. DWT was measured at three reference lines: at a distance of 1 mm from the apex, 4 mm from the apex, and at the cervical line, as these areas are considered predictors of stress (34, 38). The reference line at 4 mm was of particular interest as further studies will examine the influence of therapeutic treatment, i.e. different post and core systems placing 4 mm gutta-percha apically. Our main objective was to determine if we could use the mean values of the selected parameters for the 5 groups of MCI developmental stages for FEA modelling. No significant deviation from a normal distribution was found. There were statistically significant differences between the developmental stages for parameters L and M, while no significant differences were found for parameter K, as the numerical value of the total root width at the cervical line is always constant in all developmental stages and only the values of dentin thickness and pulp width are the one variable. Most correlations between parameters were statistically significant and consistent with root development anatomy. It is also expected that the differences between the correlations will be reflected in the load distribution of the FEA model. Further investigation of different therapeutic treatments following dental trauma in MCI in relation to the root development stage will contribute to a better understanding of treatment failure. Any information or guidance that can help keep MCI in the oral cavity longer is extremely valuable for both clinicians and patients.

The present study has some limitations. Since there are very few studies on this subject, the average values for the length of maxillary incisors with complete root development were based on the general population. In this macroscopic approach of the finite element method, all measurements were performed by a single person to minimize errors. Considering the 137 radiographs of different patients and their individual anatomy, it was not easy to identify the same angle of the radiograph. Also, the recognition of reference points was difficult. However, according to Plascencia et al (39), the intra- and interobserver agreement provided reliable results in the radiographic assessment of different stages of root development using the Cvek classification. As previously mentioned, the two-dimensional dentin wall thickness data from the intraoral radiographs could be used for 3D modelling of MCI. However, better properties would be obtained by using 137 CBCT images, which is ethically questionable in children. Finally, there were no data in the literature to which we could refer and compare our results.

Conclusion

Despite the limitations of this study, the mean values of the selected parameters for the 5 groups of developmental stages of the maxillary central incisor could be used to model dentin wall thickness using finite element analysis (FEA). However, further research is needed.