*4.2. Materials*

Researchers [50–52] note that one of the main criteria for the performance of NCCL restorations is adhesion between the restoration material and tooth elements. Battancs et al. concluded that the performance of the tooth-restoration system does not depend on the material. Thus, any material that already exists and is used in the treatment of an NCCL is suitable for prosthetics. Ichim et al. [3] come to the opposite conclusion and recommend the use of materials with a Young's modulus of less than 1 GPa in restorations. The results of this work confirm that a material with a lower elastic compression modulus delivers a favorable strain behavior to the tooth-restoration system. At the same time, it should be noted that in the restoration of a harder material, a lower level of deformation is observed. Machado et al. come to the conclusion that non-straight ceramic inlays in the NCCL have less roughness, which favors subsequent periodontal treatment [53]. The authors of [53] also obtain information that composite restoration materials can reduce the stress level in the tooth-inlay system, but at the same time they have significant thermal shrinkage. Ceramic inlays and crowns have become widespread in the last decade [54,55]. Ceramic inlays make it possible to obtain good adhesion with the tooth elements, which is considered an important factor, especially in the prosthetics of an NCCL [55]. The maximum values of stress and strain intensity are observed near the contact between the lower part of the inlay and the tooth, which does not contradict the study data [3]. Additionally, there is a significant excision of the size of the tooth tissues, a significant number of defects, which probably does not only affect the increase in load, but also creates additional retention losses.

Today, there is a lot of research on the applicability of innovative biomaterials in dentistry. An interesting idea is to use oral-derived stem cells together with biomaterials or scaffold-free techniques to obtain strategic tools for regenerative and translational dentistry [56]. The authors [57] have developed a synthetic P26 peptide that demonstrates a remarkable dual mineralization potential to repair incipient enamel decay and mineralization defects localized in peripheral dentin below the dentin-enamel junction. The research in [58] indicated the prospect of using black phosphorene (BP) for pharmacological applicamodel.

tional retention losses.

tions as scaffolds and prosthetic coverings. In our opinion, the combined use of innovative materials and new restorative inlay has great potential in the treatment of NCCLs and the prevention of their development. In the implementation of new clinical practices, it will be important to confirm them with the help of reliable computer models, which we are creating. practices, it will be important to confirm them with the help of reliable computer models, which we are creating. *4.3. Influence of Taking into Account the Root System on the Tooth Deformation*

## *4.3. Influence of Taking into Account the Root System on the Tooth Deformation* Creating complete parameterized tooth geometry is a complex process. The modeling of teeth with a truncated root system [4,30,59] and without taking into account the

innovative materials and new restorative inlay has great potential in the treatment of NCCLs and the prevention of their development. In the implementation of new clinical

maximum values of stress and strain intensity are observed near the contact between the lower part of the inlay and the tooth, which does not contradict the study data [3]. Additionally, there is a significant excision of the size of the tooth tissues, a significant number of defects, which probably does not only affect the increase in load, but also creates addi-

Today, there is a lot of research on the applicability of innovative biomaterials in dentistry. An interesting idea is to use oral-derived stem cells together with biomaterials or scaffold-free techniques to obtain strategic tools for regenerative and translational dentistry [56]. The authors [57] have developed a synthetic P26 peptide that demonstrates a remarkable dual mineralization potential to repair incipient enamel decay and mineralization defects localized in peripheral dentin below the dentin-enamel junction. The research in [58] indicated the prospect of using black phosphorene (BP) for pharmacological

*Materials* **2022**, *14*, x FOR PEER REVIEW 15 of 21

Creating complete parameterized tooth geometry is a complex process. The modeling of teeth with a truncated root system [4,30,59] and without taking into account the root system [47,60,61] is often encountered in practice. Such limitations can have a significant impact on the numerical simulation results. Edge effects appear in the rootless model. root system [47,60,61] is often encountered in practice. Such limitations can have a significant impact on the numerical simulation results. Edge effects appear in the rootless

The root system of a tooth is often modeled with simplified geometry to pilot studies of new treatment methodologies [62,63]. The canonical geometry in the form of a single root is modeled [62,63]. The simulation of the simple geometry of two root canals is also encountered [35,64]. The root system of a tooth is often modeled with simplified geometry to pilot studies of new treatment methodologies [62,63]. The canonical geometry in the form of a single root is modeled [62,63]. The simulation of the simple geometry of two root canals is also encountered [35,64].

Influence estimates of the tooth root system on the modeling results are of interest. It was decided to consider the tooth deformation (Figures 1 and 3), taking into account the root system in order to clarify quantitative patterns. The tooth root system is modeled in a simplified setting (Figure 12). Influence estimates of the tooth root system on the modeling results are of interest. It was decided to consider the tooth deformation (Figures 1 and 3), taking into account the root system in order to clarify quantitative patterns. The tooth root system is modeled in a simplified setting (Figure 12).

**Figure 12.** Models of teeth taking into account the root system simple geometry: (**a**) is without defect; (**b**) is with a defect; (**c**) is with the restoration new type. **Figure 12.** Models of teeth taking into account the root system simple geometry: (**a**) is without defect; (**b**) is with a defect; (**c**) is with the restoration new type.

The tooth root is modeled as a truncated cone. The boundary conditions are: the prohibition of the normal displacement of the side surfaces; the prohibition of all coordinates displacements of the root system lower part.

It has been established that taking into account the root system has little effect on the tooth deformation qualitative picture. A significant influence on the quantitative values of the deformation state parameters and the contact characteristics of the tooth-inlay system can be noted in this case.

The analysis of quantitative differences in the deformation behavior parameters of teeth with and without taking into account the root system will be performed according to the formula, where we take the model taking into account the root as reference values: teeth with and without taking into account the root system will be performed according to the formula, where we take the model taking into account the root as reference values: ( ) 1000 without root with root with root 100 100 10 *F A A A A* = = − %, (1)

The tooth root is modeled as a truncated cone. The boundary conditions are: the prohibition of the normal displacement of the side surfaces; the prohibition of all coordinates

It has been established that taking into account the root system has little effect on the tooth deformation qualitative picture. A significant influence on the quantitative values of the deformation state parameters and the contact characteristics of the tooth-inlay sys-

The tooth root is modeled as a truncated cone. The boundary conditions are: the prohibition of the normal displacement of the side surfaces; the prohibition of all coordinates

It has been established that taking into account the root system has little effect on the tooth deformation qualitative picture. A significant influence on the quantitative values of the deformation state parameters and the contact characteristics of the tooth-inlay sys-

The analysis of quantitative differences in the deformation behavior parameters of teeth with and without taking into account the root system will be performed according to the formula, where we take the model taking into account the root as reference values:

The analysis of quantitative differences in the deformation behavior parameters of

$$\text{The formula, where we take the model taking into account the root as reference values:}$$

$$\Delta A = \sum\_{F=100}^{1000} \left[ (|A|\_{\text{without root}} - |A|\_{\text{with root}}) / |A|\_{\text{with root}} \cdot 100 \right] / 10\%,\tag{1}$$

*K*

*K*

where *A* is maximum parameters *σ*int (Figure 13), *ε*int (Figure 14), *P<sup>K</sup>* and *τ<sup>K</sup>* (Figure 15). The difference percentage in deformation parameters slightly depends on the load. ∆*A* is the arithmetic mean of the deviation. The parameters were compared in terms of materials volumes in the crown area. The root volume was not taken into account when determining the parameters maxima. ure 15). The difference percentage in deformation parameters slightly depends on the load. *A* is the arithmetic mean of the deviation. The parameters were compared in terms of materials volumes in the crown area. The root volume was not taken into account when determining the parameters maxima. terms of materials volumes in the crown area. The root volume was not taken into account when determining the parameters maxima.

*Materials* **2022**, *14*, x FOR PEER REVIEW 16 of 21

*Materials* **2022**, *14*, x FOR PEER REVIEW 16 of 21

displacements of the root system lower part.

displacements of the root system lower part.

1000

tem can be noted in this case.

tem can be noted in this case.

where

load.

where

*A*

*A*

*A*

**Figure 13.** max int **:** (**a**) is enamel; (**b**) is dentine; (**c**) is inlay; dark-grey is model without defect; light-grey is model with defect; green is model with material 1 inlay, red is model with material 2 **Figure 13.** ∆max*σ*int: (**a**) is enamel; (**b**) is dentine; (**c**) is inlay; dark-grey is model without defect; light-grey is model with defect; green is model with material 1 inlay, red is model with material 2 inlay, blue is model with material 3 inlay. light-grey is model with defect; green is model with material 1 inlay, red is model with material 2 inlay, blue is model with material 3 inlay.

inlay, blue is model with material 3 inlay.

**Figure 14.** ∆max*ε*int: (**a**) is enamel; (**b**) is dentine; (**c**) is inlay; dark-grey is model without defect; light-grey is model with defect; green is model with material 1 inlay, red is model with material 2 inlay, blue is model with material 3 inlay.

**Figure 14.**

max int

inlay, blue is model with material 3 inlay.

**Figure 15.**  max *<sup>K</sup> P* (**а**) and max *<sup>K</sup>* (**b**): green is model with material 1 inlay, red is model with material 2 inlay, blue is model with material 3 inlay. **Figure 15.** ∆max*P<sup>K</sup>* (**a**) and ∆max*τ<sup>K</sup>* (**b**): green is model with material 1 inlay, red is model with material 2 inlay, blue is model with material 3 inlay.

**:** (**a**) is enamel; (**b**) is dentine; (**c**) is inlay; dark-grey is model without defect;

light-grey is model with defect; green is model with material 1 inlay, red is model with material 2

Accounting for the root has the maximum effect on the behavior of the tooth without and with the defect. The maximum intensity of stresses and strains has a more pro-Accounting for the root has the maximum effect on the behavior of the tooth without and with the defect. The maximum intensity of stresses and strains has a more pronounced localization in the defect area in this case.

nounced localization in the defect area in this case. The intensity of stresses and strain in the enamel is approximately two times lower in the tooth-inlay system when the root is taken into account. Accounting for the root The intensity of stresses and strain in the enamel is approximately two times lower in the tooth-inlay system when the root is taken into account. Accounting for the root system has an insignificant effect on the dentin deformation parameters (less than 20%).

system has an insignificant effect on the dentin deformation parameters (less than 20%). The effect of taking into account the root on the contact parameters depends on the inlay material. For contact pressure: in material 1, there is a decrease in the parameter maximum level by approximately 40%; in materials 2 and 3, there is a slight increase in the parameter maximum level by 14 and 2%, respectively. The contact tangential stress in The effect of taking into account the root on the contact parameters depends on the inlay material. For contact pressure: in material 1, there is a decrease in the parameter maximum level by approximately 40%; in materials 2 and 3, there is a slight increase in the parameter maximum level by 14 and 2%, respectively. The contact tangential stress in the model taking into account the root is higher.

the model taking into account the root is higher. The model without taking into account the root system gives only a qualitative idea of the tooth deformation. The refinement of models taking into account the root system close to real geometry is required. An analysis of the possibility of tooth root truncation The model without taking into account the root system gives only a qualitative idea of the tooth deformation. The refinement of models taking into account the root system close to real geometry is required. An analysis of the possibility of tooth root truncation to increase the computational procedures speed is also necessary.

to increase the computational procedures speed is also necessary. This research direction is a priority for the scientific group. The rationalization of calculation schemes is necessary due to the wide scope of future research: influence analysis of the geometry cutout under inlay, inlay materials, occlusal load, the conjugation This research direction is a priority for the scientific group. The rationalization of calculation schemes is necessary due to the wide scope of future research: influence analysis of the geometry cutout under inlay, inlay materials, occlusal load, the conjugation patterns tooth-inlay, etc.

## patterns tooth-inlay, etc. *4.4. Main Results*

*4.4. Main Results* The distribution nature and the stress intensity level in a tooth with an NCCL are comparable to the results obtained by Jakupović et al. [9]. According to [3], the maximum stresses in the interface between the restoration and the tooth are observed near the edge of the lower surface of the inlay. The data obtained in this work show a similar result. An important result of the article is the investigation of a new technology for the restoration of an NCCL that allows the use of ceramic inlays that contribute to the creation of the required adhesion with the tooth elements. The use of a contact strain mechanism of the biomechanical system tooth restoration brings the nature of the strain closer to the real case. Many works on numerical analysis consider the strain of a tooth with the restoration of an NCCL within the framework of joint strain of the elements, which does not reflect all the features of the strain of a biomechanical assembly [3,9,32–35]. At the moment, a The distribution nature and the stress intensity level in a tooth with an NCCL are comparable to the results obtained by Jakupovi´c et al. [9]. According to [3], the maximum stresses in the interface between the restoration and the tooth are observed near the edge of the lower surface of the inlay. The data obtained in this work show a similar result. An important result of the article is the investigation of a new technology for the restoration of an NCCL that allows the use of ceramic inlays that contribute to the creation of the required adhesion with the tooth elements. The use of a contact strain mechanism of the biomechanical system tooth restoration brings the nature of the strain closer to the real case. Many works on numerical analysis consider the strain of a tooth with the restoration of an NCCL within the framework of joint strain of the elements, which does not reflect all the features of the strain of a biomechanical assembly [3,9,32–35]. At the moment, a significant increase in stress in the dentine has been established, with a decrease in the stress level in the enamel at the inlay from the CEREC Blocs material. This effect can be avoided by the rational selection of the prosthetic inlay geometry and analyzing the influence of the tooth-restoration interface nature.
