Influence of "MOTRCS" factors on the performance of various direct and indirect restorations: A finite element analysis.

AIM OF THE STUDY: The purpose of the study is to evaluate the occlusal relationship of the mesiobuccal cusp of a mandibular first molar with the marginal ridge of maxillary first molar and second premolar and to analyze the effect of the above occlusal relation on different direct and indirect restorations using finite element analysis (FEA).
METHODOLOGY: Four hundred volunteers studying in a dental college were screened, of which 100 volunteers were selected for studying occlusal relationships based on the inclusion and exclusion criteria. The two most common occlusal relationships were considered for analyzing two direct (amalgam and direct composite restorations) and two indirect restorations (composite and ceramic restorations). Three-dimensional (3D) scanning of the models was performed, and Class II tooth preparations specific for each restorative material were prepared digitally on 3D models. FEA was employed to study von Mises (VM) stress, principal stresses, and cuspal deflection for each restorative material, and failure of the tooth-restoration unit was calculated using the modified Mohr failure criterion.
RESULTS: Among all the analyzed materials, cuspal deformation, principal stresses, and VM stresses were high for direct composite restoration and least for ceramic inlay. According to modified Mohr criteria, except for direct composite, all other materials performed better.
CONCLUSION: Silver amalgam and ceramic restorations presented with minimal stress concentration and cuspal deflection, and Type I occlusal relationship presented with higher stress concentration compared to Type II. Copyright:

INTRODUCTION

Restoration of caries-induced loss of tooth structure, especially in posterior teeth, requires consideration of remaining tooth structure, functional occlusal load, interocclusal relationship, and type of restorative material.[1] Fracture of the tooth and or restoration is of concern since it increases the tooth's tendency for further extensive treatment or intervention termed as “Restorative death spiral” by Wilson and Lynch.[2] Braly and Maxwell regarded the occlusal relationship (worn cusps, steep cusp-fossa relationships, extensive intracoronal restorations, traumatic occlusal relationships, and bruxism) as the first factor in determining the fracture potential index of the tooth.[3]

An intact tooth and a restored tooth behave differently to occlusal loads. Enamel is a brittle material with a high modulus of elasticity, low proportional limit in tension, and low resilience modulus. However, dentin can absorb occlusal load because of the higher modulus of resilience. When an external load is applied as on biting, the load is transferred into dentin through enamel as compression. This transfer of load occurs over a large internal volume of tooth structure, and the resulting local stress concentration will be minimal. However, when a tooth is restored, the transfer of stresses will be more complex, and most of the stress concentration will be at the tooth-restoration interface. The consequence of such stress concentration can lead to microleakage and fracture of the tooth and or restoration.[4]

Finite element analysis (FEA) is a useful three-dimensional (3D) numerical method to analyze the stress patterns of a tooth restored with different dental materials using computer-generated models.[56] The advantage of FEA is its ability to incorporate all the variables that account for the failure of restorations and interpret those results to enhance the longevity of restorations in the complex oral environment.[47]

It has been well documented in the literature the effect of tooth morphology, occlusal relationship, tooth structure loss, restorative material factor, cusp deflection, and stress patterns on the performance of restorations collectively termed “MOTRCS” factors.

The aim of this FEA study is to: (a) classify the occlusal relationship of the mesiobuccal cusp of a mandibular first molar with the marginal ridges of maxillary first molar and second premolar, (b) FEA of the effect of above occlusal relations on different direct and indirect Class II (mesio-occlusal) restorations in maxillary first molar in terms of von Mises (VM) stress, principal stresses, and modified Mohr failure criterion.

METHODOLOGY

The first part of the study evaluated the occlusal relationship of the mesiobuccal cusp of a mandibular first molar with the marginal ridge of maxillary first molar and second premolar. After screening for the occlusal relationship, in the second part of the study, finite element model was generated and analyzed.

Evaluation of the occlusion relationship

Sample selection

Four hundred students studying in St. Joseph Dental College, Eluru, Andhra Pradesh, India, were screened. After taking into consideration the inclusion and exclusion criteria, 100 students were selected for studying the occlusal relationship. Students with fully developed dentition were included in this study. Students with Class II restorations, missing teeth, malocclusions (rotated, crowded, and ectopic eruptions), endodontically treated teeth, and those undergoing/underwent orthodontic treatment were excluded.

Impression, bite registration, and articulation

Upper and lower arch alginate impressions (3M ESPE Alginate impression material) were taken using sterilized perforated stock trays. After disinfecting the impressions with 2% glutaraldehyde (Glutarex 2%, 3M ESPE), casts were poured immediately with type III dental stone (Gyprock, Rajkot, India).

The bite was recorded for each patient with bite registration material. The upper and lower casts with bite registration were articulated in the semi-adjustable articulator and analyzed for occlusal relationship. The right and left sides of each volunteer were examined. Hence, the analysis of 100 volunteers provided 200 occlusal relationships.

Classification of occlusal relationship

After analyzing the upper and lower models randomly, the occlusal relationships were classified into six groups [Table 1]. The two most common occlusal relationships were taken into consideration for further FEA analysis.

Table 1

Classification of the occlusal relationship after evaluation of study models

Types	Occlusal relationship
I	Mesiobuccal cusp of lower molar contacting the mesial marginal ridge of the upper molar and the distal marginal ridge of the upper second premolar (2MR.MP)
II	Mesiobuccal cusp of the lower molar contacting the mesial marginal ridge of the upper molar and with no contact on the distal marginal ridge of the upper second premolar (MR.M)
III	Mesiobuccal cusp of the lower molar contacting the mesial triangular fossa of the upper first molar (TF.M)
IV	Mesiobuccal cusp of the lower molar not contacting both the marginal ridges (°C)
V	Mesiobuccal cusp of the lower molar contacting the distal marginal ridge of the upper second premolar and with no contact on the mesial marginal ridge of the upper first molar (MR.P)
VI	Mesiobuccal cusp of the lower molar contacting the distal triangular fossa of the upper second premolar (TF.P)

Finite element model generation

Finite element modeling of teeth

This study is a linear static FEA. A 3D computer-aided design model was generated by digitalizing the plaster model with the Identica Blue scanning machine (DT Technologies, Medit Co, LTD) using Colab17 software in STL format, and the obtained profiles were used to generate a solid tooth model (maxillary first molar and second premolar with associated alveolar bone). The models obtained were converted into STEP format using Solidworks software (Solid works corporation, Dassault systemes, Waltham, Massachusetts, United States).

Virtual cavity preparation and restoration

Enamel, dentin, periodontal ligament, and the surrounding bone were simulated in the model. A Boolean operation (addition, intersection, or subtraction of volumes) was performed. Four different cavity preparations, two direct restorations (amalgam and composite) and two indirect restorations (ceramic and composite), were designed [Figure 1] using the parametric cutting plane in the maxillary first molar involving the mesial surface according to the dimensions given in Table 2. The cavities were restored, feeding the properties of zinc phosphate and amalgam for amalgam restoration; graded hybrid layer, an adhesive layer, and composite layer for direct composite restoration; resin cement and composite resin for indirect composite; resin cement and ceramic for ceramic restoration, required material properties are given in Table 3.

Figure 1

Finite element analysis model of tooth preparation and restoration for each group

Table 2

Dimensions of tooth preparation for different restorations

Cavity design	Silver amalgam	Direct composite resin	Composite resin inlay	Ceramic inlay
Width of cavity (mm)	2	2	3	3
Depth (mm)	3	3	2	2
Gingival seat depth below the contact point (mm)	1.5	1.5	1.5	1.5
Gingival seat width (mm)	4	4	2	2
Isthmus width (mm)	3	3	4	4
Primary flare divergence	6°	-	6°	6°
Axial wall taper	5°	-	5°	5°
Axial wall depth (mm)	2	2	1.5	1.5
Occlusal cavosurface angle	90°	90°	90°	90°

Table 3

Material properties

Material	Elastic modulus (gpa)	Thickness	Poissons ratio	References
Enamel	48		0.23	[56]
Dentin	18		0.2	[6]
Trabecular bone	1.37		0.3	[7]
Cortical bone	13.7		0.3	[7]
Zinc phosphate	13.5	0.50 mm	0.3	[8]
Amalgam	21.5		0.3	[9]
Composite resin	14.2		0.3	[10]
Hybrid layer	4 near adhesive and 1 near dentin	10 µm	0.3	[11]
Adhesive layer	4.5	5 µm	0.3	[1112]
Indirect composite resin	25.0		0.3	[121314]
Glass ceramic	90		0.3	[1516]
Resin cement	8.3	70 µm	0.3	[1012]

Briefly, four finite element models depending on the selected restorations were analyzed. Each group was further subdivided into two subgroups depending on the two most common occlusal relationships.

Meshing

The models were meshed, which comprised of second-order tetrahedral units using ANSYS Workbench Version 15 (Canonsburg, Pennsylvania, USA). The number of nodes and elements in each model is given in Table 4.

Table 4

Nodes and elements for different restoration tested

Restoration	Nodes	Elements
Amalgam	424,950	285,782
Direct composite	2,293,760	1,529,089
Composite resin inlay	2,452,649	1,758,115
Ceramic inlay	2,726,002	1,826,792

Virtual loading of the restored tooth

An occlusal load of 440N was applied over an area of 8 mm2 perpendicularly on both tooth (second premolar) and restoration (first molar) in the first relation and only on restoration (first molar) in the second relation.

Finite element analysis

The Ansys workbench provided the principal stresses, VM stresses, maximum principal elastic strain, and cuspal displacement of the tested models. A modified Mohr criterion for failure was employed to know the performance of the tooth-restoration unit. This criterion employs principal stresses (sigma 1, 2, and 3) along with tensile strength and compressive strength of the restorative materials to obtain a safety factor. The safety factor value less than unity indicates the failure of that restorative material. The safety value factor of unity and above indicates the safe condition of that material.[17] The formula was incorporated in Microsoft Excel, and calculations were performed.

RESULTS

Evaluation of the occlusal relationship

Out of 200 occlusion relationships evaluated, 53% had Type I occlusion, 17.5% had Type IV, and 9.5% had Type II. Since Type IV had no occlusal contact, the most common occlusal Types I and II were selected for further analysis. About 38% of students had Type I relation on both sides, 4% of students had Types II and V on both sides, 5% of students had Types IV and VI on both sides, and 1% of them had Type III on both sides. Altogether 57% of students had similar occlusal relationships on both sides.

Buccal cusp deformation

The directional deformation function in ANSYS was selected to measure the buccal cusp deformation in μm. The maximum deformation was noted for direct composite restoration in both occlusal relationships, followed by amalgam and indirect composite inlay. Indirect ceramic inlay resulted in minimum deformation of the buccal cusp in both occlusal relationships. When occlusal relationship was considered 2MR-MP type of occlusion resulted in higher buccal deformation than MR-M type [Figure 2].

Figure 2

Cuspal displacement for each restoration in 2MR-PM and MR-M occlusal types

Maximum principal elastic strain

The maximum strain measured in mm/mm was more for direct composite restoration, followed by indirect composite and silver amalgam restoration. Ceramic inlay presented with minimum strain in both types of occlusion [Figure 3d]. For direct and indirect composite restoration, the strain was located near the proximal box, specifically involving the axial line angles. For amalgam restoration, the strain was located on the gingival seat and to a lesser extent on the axial line angles. The ceramic inlay presented with minimal strain, and no strain concentration was found on the axial line angles.

Figure 3

Line graphs of (a) Principal stresses and von Mises stresses for 2MR-PM occlusal type (b) Principal stresses and von Mises stresses for MR-M occlusal type (c) Cuspal displacement (d) Maximum principal elastic strain. Higher Principal stresses and von Mises stresses values were noted for direct composite resin (a and b). Ceramic inlay demonstrated very minimal cuspal displacement (c). Silver amalgam and ceramic inlay presented with less maximum principal elastic strain values (d)

Maximum and minimum principal stress

Amalgam restoration: The tensile stress concentration was minimally limited to the buccal cavosurface margin, whereas compressive stresses were predominantly present on the axial wall and adjacent premolar proximal surface in 2MR-MP occlusal type. In the MR-M type, the tensile stress value was less and was concentrated in the mesiobuccal cusp, the tip of the mesiopalatal cusp, and along the cavosurface margins [Figure 4]. Compressive stress was concentrated in the proximal box, especially at the axial line angles [Figure 5]

Figure 4

Maximum principal stresses for restorations of 2MR-PM occlusal type. The tensile stress distribution was uniform for silver amalgam and ceramic inlay. Both direct composite resin and composite inlay had tensile stress concentration over the cusp tips. The compressive stress was noted on the axial wall for all restorations and on the proximal surface of premolar teeth (arrow mark)

Figure 5

Minimum principal stress for restorations of MR-M occlusal type: uniform stress distribution of lower values noted for ceramic inlays. Although no stress concentration was noted with direct resin composite, the values were high compared to other restorations. The location of compressive stress was on the axial wall

Direct composite restoration: In the 2MR-MP type, the tensile stresses were concentrated on the mesiobuccal, mesiopalatal cusp tip, and the gingival seat cavosurface [Figure 4]. Compressive stresses were noted along the axial wall and adjacent premolar proximal surface [Figure 5]. In the MR-M type, there was a uniform distribution of tensile stress with compressive stress concentrated along with the axial and gingival seat

Indirect composite restoration: In the 2MR-MP type, the tensile stresses were uniformly distributed within the tooth structure [Figure 4], and compressive stresses were concentrated on the axial wall, part of the gingival seat, and adjacent premolar proximal surface [Figure 5]. In the MR-M type, the tensile stresses were concentrated at the mesial cusp tips, axiopulpal line angle, and pulpal floor. Higher tensile stress was noted at the gingival seat cavosurface. Compressive stresses were present on the axial wall and part of the gingival seat

Ceramic restoration: In the 2MR-MP type, tensile stresses were minimal and less concentrated except at a very small area over lingual occlusal cavosurface margin [Figure 4]. The compressive stress was also minimal on the axial wall and gingival seat. Adjacent premolar proximal surface demonstrated compressive stress [Figure 5]. In the MR-M type, the tensile stress value was minimal and less concentrated, whereas compressive stress was concentrated on the axial wall and gingival seat.

Von Mises stress

Ceramic inlays presented with less VM stress, followed by indirect composite, silver amalgam restoration. Direct composite restoration presented with higher VM stress. In all restoration, stress was concentrated in the proximal box of tooth preparation. Among the occlusal type, not many differences were noted among the restoration [Figure 6].

Figure 6

Von Mises stresses of (a) Silver amalgam (b) Direct composite resin (c) Composite resin inlay (d) Ceramic inlay. Higher Von Mises stresses were noted for direct composite resin, followed by silver amalgam, composite resin inlay, and ceramic inlay. Stress concentration noted in the proximal box of tooth preparations for all restorations

Failure criteria

Modified Mohr failure criteria were employed. With Modified Mohr criteria except for direct composite resin restoration, all others had a value of more than 1, suggesting their better performance [Table 5].

Table 5

Modified Mohr failure criterion values

Group	Modified Mohr
	2MR-PM	-M
Silver amalgam	1.412	1.414
Direct composite resin	0.640	0.873
Composite resin inlay	1.288	1.422
Ceramic inlay	0.979	1.629

DISCUSSION

The decision to perform FEA analysis on maxillary molars and premolars is based on the prevalence of Class II restoration. Furthermore, this area of dentition is subjected to an intense chewing load. Many studies performed FEA analysis on maxillary premolars or mandibular molars, and fewer studies on maxillary first molars.

The occlusal load applied in this study was 440N, and the location of the load application was dictated by the occlusal relationship. Many authors have used occlusal load varying from 100N to 600 N.[18] Bakke et al.[19] suggested that biting force varies between males (522N) and females (441N). The mean fracture resistance of intact teeth has been shown in the range of 736N to 3140N.[20]

The fracture in restored teeth is dependent on the type of restorative material and its properties, the type of enamel and dentin bonding, and the magnitude of a force. Magne and Belser.[21] have pointed out that the restorations with higher elastic modulus impart less deformation to tooth structure under the same occlusal load. Studies supporting the better performance of restorative material have misinterpreted the elastic modulus property with some authors claiming better stress distribution because of the use of low elastic modulus material (e.g., direct composite resin),[22] while others reported higher elastic modulus (e.g., ceramic) of material to be responsible for better biomechanical behavior.[12] To avoid this confusion, failure theory was employed utilizing the compressive strength, tensile strength, and elastic modulus of the material. Poisson's ratio was kept constant.

Cusp deflection is considered as a good parameter to study the fracture resistance of teeth after restoration. The type of adhesive used, interface quality, and material properties dictate the cuspal deflection. Loss of marginal ridge and inadequate remaining dentin thickness above the pulp chamber is associated with high cuspal deflection. The cuspal deflection in this study was less in ceramic inlays which is in agreement with Magne.[23] The cuspal displacement was in the order of ceramic inlays < composite resin inlays < silver amalgam < composite resin for both occlusal types [Figure 3c]. Magne reported 100% cuspal stiffness recovery with adhesive ceramic inlays and cuspal deformation of about 0.4 μm, which is similar to the present study. But the cuspal deformation in composite resin inlays was higher (1.3 μm) than in the present study.

The tensile stresses, compressive stresses, and VM stress were compared among the restorations for both occlusal types [Figure 3a and b]. The tensile stress was in the order of silver amalgam < ceramic inlay ≤ composite resin inlay < direct composite resins for 2MR-M occlusal type. For MR-M occlusal type, it was in the order of ceramic inlay < silver amalgam < composite resin inlay < direct composite resins. The compressive stress for the 2MR-PM occlusal type was in the order of ceramic inlay < composite resin inlay < silver amalgam < direct composite resin. For MR-M type, it was in the order of ceramic inlay < silver amalgam < composite resin inlay < direct composite resin. VM stress for each occlusal type was in the order of ceramic inlays < composite resin inlay < silver amalgam < direct composite resin.

In this study for all restorations, most of the tensile stresses were concentrated in the gingival seat cavosurface margin, and axial line angles of the proximal box, with compressive stresses, present predominantly on the axial wall. This may be expected to happen because of the location of occlusal load, which was decided based on the occlusal contact evaluated on 100 cast models.

Dejak and Mlotkowski.[12] employed modified VM failure criterion to analyze tooth and restorative materials. According to this criterion, the failure occurs when the VM stress exceeds the tensile strength of the material. They considered the tensile strength of enamel and dentin as 11.5 and 105.5 Mpa, respectively. In our study, when utilizing this criterion, all restorations resulted in VM stress in enamel and dentin within the tensile strength of the enamel and dentin except direct composite resin, which had von Misses stress in dentin marginally higher.

Comparing the occlusal type, 2MR-PM resulted in higher cuspal displacement along with higher stress values compared to MR-M in all restorations. The amalgam restoration, 2MR-PM type of occlusion resulted in uniform distribution of stresses, whereas all other restorative types displayed varied stresses within the tooth structure. The 2MR-PM type of occlusion has contact on the marginal ridge of restored molar and unrestored premolar, which may create wedging forces (plunger cusp), creating high tensile stresses near gingival seat cavosurface margin and interdentally causing separation of teeth during occlusal contact and food lodgment. All the FEA models tested had high tensile stress concentration in the interdental region, predominantly for the 2MR-PM type.

The superior performance of silver amalgam may be related to less number of interfaces in the tooth-restoration unit. The same can be assumed with composite resin inlay and ceramic inlay. In contrast, direct composite resin has dentin/hybrid layer, graded hybrid layer, hybrid layer/adhesive, and adhesive/composite interface. The elastic modulus in these interfaces is a mismatch, resulting in stress concentration in high elastic modulus material, i.e., enamel and dentin.[23]

The performance of ceramic inlays in comparison to composite resin or composite inlay was reviewed with other studies comparing indirect restorations.[24] In the present study, ceramic inlays resulted in minimal principal stress magnitude and values compared to composite resin inlay, attributed to its high elastic modulus. Furthermore, modified Mohr failure criteria values of 1.0 and 1.6 were noted for 2MR-PM and MR-M occlusal types, respectively.

Ausiello et al.[25] compared low elastic modulus and high elastic modulus composite resin with ceramic Class II MOD restoration taking into consideration the polymerization shrinkage associated with resin cement and composite resin. They noted that shrinkage stress results in greater stress concentration than the occlusal loading stress. The presence of multiple interfaces with differing elastic modulus may result in adverse stress distribution within the tooth structure and tooth-restoration interfaces. They suggested indirect lithium disilicate ceramic as the material of choice for replacing enamel and dentin in posterior teeth. The same author comparing the bulk-fill composite, block composite inlay, and lithium disilicate inlay reported elastic biomechanical behavior close to the sound tooth model with ceramic inlay and block composite inlay. When compared to lithium disilicate and block composite inlay, bulk fill composite resulted in higher stresses concentrated at margins and wall angles. Dejak and Mlotkowski[12] reported Mohr–Coulomb failure values at the resin cement-dentin interface two to four times lower around the ceramic inlay than composite resin inlay. Contact tensile and shear stresses at the cement-tissue interface were also lower around the ceramic inlay, thereby providing better marginal adaptation compared to composite resin inlay.

The lower principal stress values of ceramic inlay depicts its efficiency to absorb the tensile stress rather than transfering to underlying tooth structure which is observed in direct composite restoration. These higher tensile stresses within the ceramic inlay result in a ceramic fracture before the tooth fracture occurs. The modulus of elasticity of composite resin is three times lower than the enamel. When low elastic modulus materials such as composite resin are used as a replacement of enamel, crown stiffness recovery of 76%–88% was obtained. The use of ceramic inlay with high elastic modulus resulted in 100% recovery of crown stiffness, as evident by the values of cuspal displacement in the present study. Furthermore, composite resins, in addition to low elastic modulus, have a high coefficient of thermal expansion (~20 to 50-6/°C) compared to tooth substance and ceramics (~11 to 17-6/°C).[26] These properties may explain the frequent observation of ceramic and/or silver amalgam restoration fracture rather than debonding of restoration commonly noted with composite resin restorations.

The incorporation of dynamic loading, along with the effect of thermal loading within FEA analysis, would have provided a better indication of the performance of these restorative materials, which accounts for the limitation of this study. The stress distribution within the normal unrestored tooth would have added value in the interpretation of the result. Future studies should take into consideration these factors and restoration-tooth interfaces. This study considered not-so extensive cavity preparation as the reference tooth structure loss, which can be expanded to include extensive loss of tooth structure as in mesio-occluso-distal tooth preparations.

CONCLUSION

Taking into consideration the failure criterion and stress values, ceramic inlays and silver amalgam are able to restore the biomechanical properties compared to direct composite restorations. Silver amalgam has to be considered as a direct restorative material in high load-bearing areas unless esthetics is a factor. Indirect composite inlay should be preferred over direct composite resin when economical factor and esthetics has a role in restoration decision making. Every effort has to be made to use restorative materials with minimum tooth restorative interfaces and with high elastic modulus to limit the transfer of critical tensile stresses onto the tooth structure. Future studies employing stabilized and improved hybrid layer (biomimetic remineralization) of direct resin composite have to be compared with these restorations.

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.