Shrinkage behaviors of dental composite restorations—The experimental–numerical hybrid analysis

Abstract

Objectives

To investigate the effects of light curing protocols on the shrinkage behaviors, contraction stress, and microleakage in composite restorations by an experimental–numerical hybrid analysis.

Methods

Three groups of human molars were collected to receive different light-curing protocols: vertical or oblique curing at regular intensity, and vertical curing at reduced intensity. For each tooth, the composite fillings were consecutively placed under unbonded and bonded states, and their shrinkage behaviors were examined with a digital image correlation (DIC) technique. The strains of the unbonded restorations were input into two finite element analysis (FEA) models with settings of the composite as either homogeneous or hardened along polymerization gradients. The preliminary solutions were verified by their individual deformations in the bonded restorations. The interfacial microleakage of restorations was also determined by micro-CT scanning and compared with the FEA results.

Results

The bonded restorations showed centripetal shrinkage patterns with greater downward displacements than their unbonded restorations. Vertical curing at regular intensity caused the greatest shrinkage strain, contraction stress, and microleakage among the three protocols. Low-intensity curing reduced overall shrinkage strain and displacements at cervical margin, but did not prevent the formation of microleakage. Oblique curing caused asymmetric shrinkage with the tooth-shielded side revealing less deformation. Setting the polymerization-dependent elastic moduli of the composite enhanced the reliability of FEA.

Significance

This hybrid analysis comprehensively examined the polymerization shrinkage behaviors. Both the light intensity and direction affect the shrinkages and contraction stress. Oblique curing decreases shrinkage due to the attenuated irradiation by tooth-shielding rather than modulations of shrinkage direction.

Introduction

Resin-base composites are the most popular restorative materials, and are used in a variety of dental applications. However, their shrinkage with polymerization can cause internal stresses and interfacial defects . Resin composites shrink centripetally toward the center at their unbounded state, and their free volumetric shrinkage primarily depends on their composition and degree of conversion (DC) . In dental cavities, the composites are bonded and constrained to develop various shrinkage patterns. The shrinkage behaviors are influenced by the material properties (elasticity and viscoelasticity) , light-curing conditions (light intensity, energy density, and direction) , filling techniques , and may reflect the reaction kinetics of polymerization . In general, these behaviors are the critical results of competition between the composite-tooth adhesion and contraction stress . Once the contraction stress exceeds the bond strength, interfacial separation or microleakage occurs at these weak-bonded areas. The influences of light curing protocols on both the shrinkage strain and build-up of contraction stress in composite restorations has been recognized in previous studies , and shown to be related to the occurrence of immediate or postoperative restorative failure .

Various approaches have been applied to assess the shrinkage behaviors and their dynamic changes in relation to polymerization kinetics, with the bonded disc method adopted in many investigations . A similar experimental setting has been also developed to plot the shrinkage profiles on flat composite materials by using a stylus-dial gauge system . However, the shrinkage behaviors in dental cavities are more complex than these extra-cavity measurements. The investigation of stress–strain kinetics is a difficult task, unless the measurements provide the spatially resolved information. The digital image correlation (DIC) method has recently been used to analyze the contraction behaviors of dental composites in either free shrinkage or restoration form. By comparing two images obtained at different states, the displacements and displacement gradients of certain points can be computed based on the assumptions of pattern matching on characterized subjects . The DIC-assisted measurements aid in assessing both the temporal and spatial dependence of shrinkage strain , and also demonstrate the global contraction fields of the composite restorations . Their results can also be input into numerical analysis to validate the simulations, via this approach the contraction stress is explored . The combination of DIC-experiment and numerical analysis enables the assessment of multiple influencing variables, and further evaluates their individual roles or interactions with regard to the shrinkage kinetics.

Finite element analysis (FEA) has become an valuable tool in examining the shrinkage deformations or the magnitude and distribution of contraction stresses . A virtual FEA simulation requires modeling the geometries, materials, and loading/boundary conditions. For the cases of polymerization shrinkage, the settings of the material property should consider the shrinkage strain of composites, their associated stiffness changes, and gradient polymerization at different depths of the restorations. The principal difficulty in studying the shrinkage behavior is that the polymerization process varies with the light-curing conditions, and is also modified by the complex anatomic configuration of composite restorations. The light irradiation is partially shielded by the surrounding tooth, while enamel and dentin allow different degrees of light transmittance. Accordingly, assignment of virtual shrinkage strain in FEA needs complicated examinations of the light penetration and DC when the curing regime changes. For most studies, assumptions are given to simplify the settings and make the solving process possible. In early 2-D FEA studies, Versluis et al. solved the proposition of shrinkage-stress analysis via comprehensive examinations of experimental parameters . By inputting measurements, including the gradient DC and shrinkages in the restorations, material properties of composites (the elastic modulus and Poisson’s ratio), light transmissions through tooth substances, the settings of the FEA were refined to simulate the polymerization reaction. Even with these complicated processes, the results did not completely correspond to the real situation, due to the lower impedance of irradiance by the sectioned tooth cusps. However, these studies did reveal the significance of the experimental data in increasing the accuracy of FEA.

Developing an investigation model by combining DIC and FEA could be an effective approach to investigate the shrinkage-stress states of composite restorations. Our previous work has shown that DIC supports observation of the shrinkage field, which facilitates the validation of FEA . Moreover, the measured shrinkage strain at different locations and under various restorative conditions can be extracted as the given material properties or initial conditions. The integration of the experimental and numerical methods is expected to solve complex proposition of polymerization with high accuracy, while avoiding uncertainty and complicated procedures in setting the constitutive conditions.

Numerous methods have been proposed to reduce or modulate the contraction stress and the associated marginal and interfacial failures, especially with regard to modifying the light-curing. The concept of guided polymerization shrinkage is based on the assumption that the contraction of the photo-activated composite is directed towards the light source . An alternative method was later proposed by placing the composite increments obliquely and polymerizing through the tooth walls, in order to minimize shrinkage and improve the adaptation of composites . The phenomenon of shrinkage toward the light source has been shown by several experimental analyses . However, some investigators considered that this technique worked due to the light impedance by the tooth rather than the alteration of shrinkage vectors . As a consequence of slow polymerization, relaxation of contraction stresses may occur to prevent the interfacial failure. In the last decade, there has been growing support for light irradiation at an initial low intensity or reduced rate, known as the “soft start” curing mode . Low irradiation energy during the start of polymerization may decrease post-gel shrinkage strain and stress, prevent the cusp deformation, and enhance the marginal integrity . The polymerization kinetics for these two approaches is difficult to assess in laboratory experiments, or simulate by an FEA without complicated settings. In this study, we thus attempted to develop a hybrid experimental–numerical model to examine the shrinkage strain and stress generated by different light-curing methods. The analytic results are then compared with a micro-CT examination of interfacial microleakage.

Materials and methods

The whole experimental scheme is composed of three parts: DIC measurement of shrinkage strain, FEA for contraction stress, and interface examination. The study design is shown in Fig. 1 . A box-shape class II cavity was restored with the composite consecutively in the unbonded and bonded states. The free shrinkage strain of the unbonded restoration was measured by DIC, and applied to set the shrinkage strain in FEA. After removal of the unbonded composite restoration, the cavity received adhesive treatment and restoration. The shrinkage deformations at the boundaries of bonded restorations were used to validate the results of FEA. Finally, the stress analysis of the verified FEA was compared with the interfacial microleakage of the real restorations. The details of the experiments are presented below.

Fig. 1
Illustration of the study design. The shrinkage strains were measured from unbonded cases for the setting of FEA, and the displacements from the bonded cases were used to validate the analytic results. The stress analysis resolved by FEA was compared with the analysis of interfacial bonding.

Measuring shrinkage strain of unbonded restorations by DIC

Twenty-four intact human third molars of similar sizes and morphologies, all extracted within one month, were used in this study. The study protocol was approved by the Institutional Review Board of National Cheng Kung University Hospital, Taiwan. Informed consent was obtained before collecting each tooth from patients. The teeth were mounted with their roots embedded in acrylic resin and long axes held vertically. For each tooth, a box-form cavity of 3 (W) × 3 (D) × 3 (H) mm was prepared on the mesial surface under water irrigation.

The light curing system used in this study was a quartz-tungsten-halogen light curing unit (Optilux 501, Kerr, USA). Two irradiation directions, vertical (90°) and oblique (45°), were chosen to test. A prior examination using the Marc device (BlueLight Analytics, NS, USA) indicated that oblique irradiation reduced the light intensity received by the restoration, and then the total light energy density (intensity × time) was affected. Accordingly, a third group was set as vertical irradiation but with light energy density equivalent to the oblique irradiation. The prepared teeth were divided into three groups (n = 8), as follows ( Fig. 2 ):

Fig. 2
Illustrations of the light curing regimes and shrinkage strain. (A) Groups V and R used the vertical irradiation. (A) Group O used the oblique direction irradiation. ε I , ε T , ε I1 , ε I2 , ε T1 , and ε T2 were the measured strains.

Group V: light irradiation orthogonal (90°) to the top surface of the restoration, with a light intensity of 500 mW/cm 2 for 40 s.

Group O: oblique light irradiation. The light guide was tilted 45° to irradiate from the buccal cusp, with a light intensity of 500 mW/cm 2 for 40 s.

Group R: reduced intensity curing. The light irradiation was orthogonal (90°) to the restoration and at a light intensity of 300 mW/cm 2 for 40 s.

The light energy densities for Groups V, O, and R were confirmed by the Marc device as approximately 20, 12, and 12 J/cm 2 , respectively.

The free shrinkage of the composite in the cavity was first measured at an unbonded state. The cavity surfaces were coated with a thin layer of vaseline gel (Petroleum Jelly, Pure) to allow free shrinkage of the composite. The tooth was secured on a jig with the cavity facing an image acquisition system composed of an optic microscope (Zoom microscope ML-Z07545D, Moritex Inc., Japan) and a CCD (MTV-12V1E, Mintron, Co., 640 × 480 pixels). A microhybrid composite Filtek Z250 (3M/ESPE, St. Paul, MN, USA) was filled into the cavity in one increment, then the tooth with the restoration was sprayed with black paint to generate the speckle pattern needed for surface characterization. The specimen and image acquisition system were placed on an optical shockproof table to prevent vibration. First, the unpolymerized composite was photographed as the reference image. After light irradiation with its specific protocol, the composite was photographed again to generate the deformed images. A DIC program, Vic-2D (Correlated Solutions, West Columbia, SC, USA), was used to analyze the free shrinkage strain on the composite restoration surfaces. In the DIC analysis, the subset was set as 41 × 41 pixels. The sub-pixel precision and calculation time were optimized by applying an interpolation 6-tap nonlinear filter. The calibration work for the DIC system, surface patterning method, and the analytic conditions are described in our previous work , which demonstrated an error of 5.75 ± 0.64% for displacement that is 1–5 μm.

To express the direction and magnitude of shrinkage displacements, a virtual plane X–Y coordinate system was defined on the restoration surfaces, with the origin set at the joint of lingual and gingival walls ( Fig. 3 A). The FEA was planned to simulate the polymerization shrinkage by a heat transfer analysis. The shrinkages were assumed as the volumetric changes caused by temperature decreases, which varied along with curing protocols and locations in the restoration. The polymerization under different light curing protocols was simulated by setting different temperatures at the irradiation and termination regions. For the unbonded restorations of groups V and R, the gradient polymerization is a function of cavity depth. The shrinkage strains on the top surface (Y = 3) and cavity floor (Y = 0) were thus measured and nominated as ε I (irradiation region) and ε T (termination region), respectively ( Fig. 2 A). Group O presented a different polymerization pattern with the irradiated region located around the buccoocclual edge and progressing in a 45° direction. This obliquely gradient polymerization was simulated by setting two different initiation strains at two boundaries: ε I1 at the buccal half of the top surface and ε I2 at the top half of the buccal wall ( Fig. 2 B). Similarly, two termination strains, ε T1 and ε T2, were set at the bottom half of the lingual wall and at the lingual half of the bottom surface, respectively. These strain values were used for the assumption of shrinkage in their corresponding FEA models.

Fig. 3
Displacement plots of the polymerized restorations. An X–Y coordinate system was set to denote the horizontal and vertical shrinkage patterns. (A) Unbonded cases, and (B) bonded cases. The white arrows indicate the shrinkage vectors at 500× magnification.

Shrinkage displacement measurements of bonded restorations

After DIC measurement, the unbonded composite material was removed from the cavity. The cavity surfaces were cleaned with 75% ethanol and thoroughly rinsed with water, and the teeth were further soaked in water overnight for residual stress relaxation. Before the second restoration, the teeth were gently dried. All the cavity surfaces were etched with 37% phosphoric acid for 15 s, then water-rinsed for 10 s and air-dried. The cavities were serially treated with the Adper Scotchbond™ Multipurpose system (3M-ESPE) according to the manufacturer’s instructions, light-cured for 10 s, and then filled with the same composite Filtek Z250. The second DIC measurements of the restorations were performed as in the unbounded restorations. For the validation of the FEA, the shrinkage displacements at the free occlusal surfaces, two axial margins, and the cervical margins were collected and compared to the analytic results.

A quantitative analysis and comparison of the displacements among the three groups was also performed. The X- and Y-direction displacements, denoted as u and v, of all points on the unbonded and bonded restorations were collected and analyzed.

FEA of composite polymerization shrinkage

An intact human mandibular molar of average size in the DIC experiments was used to generate the finite element model. The tooth was scanned by a micro-CT (SkyScan 1076, SkyScan, Belgium) with a resolution of 9 μm to construct the tooth model. The outer contour and inner tooth structures were defined by setting the gray level thresholds in an image processing software (Mimics 10.01, Materialize NV, Belgium). Subsequently, the 3D solid tooth model, with multiple components of enamel, dentin, and pulp, was reconstructed by Solidworks 2008 SP4.0 drafting software (Dassault Systemes, USA). A simulated restoration of the same size as the dental restoration was generated on the solid model. This model was auto-meshed to 4-node tetrahedral elements of 0.4 mm by ANSYS 13 (ANSYS Inc., Canonsburg, PA).

The tooth substances of enamel, dentin, and pulp were assumed to be homogenous, isotropic, and linear elastic to simplify the property settings. The FEA was solved in two models (FEA1 and FEA2) by inputting the elastic properties of the resin composites differently. Our previous study has examined the mechanical properties of the Z250 composite using a nanoindentation test, and established the elastic modulus as the function of cavity depth . Accordingly, the elastic modulus in FEA1 was set as homogeneous at the average value (14800 MPa), while FEA2 applied local DC-dependent elastic modulus. The analytic results of the two models were verified by DIC measurements of bonded cases. All the material properties used in the FEA are listed in Table 1 .

Table 1
Mechanical properties applied in the FEA model.
Young’s modulus (MPa) Poisson’s ratio Thermal conductivity (W/(m °C)) c
Enamel 84100 a 0.3 0.001
Dentin 18600 a 0.31 0.001
Pulp 2 a 0.45 0.001
Composite FEA1: 14,800 b 0.33 0.1
FEA2: 16,000 as Δ T = −1 (DC = 100%), 14,000 as Δ T = −0.6 (DC = 60%)

a Ref. .

b Ref. .

c Arbitrary setting for the low thermal conductivities of tooth structures.

The boundary condition was set as fixation of the exterior root surfaces 2 mm below the crown portion in all directions. The interfacial conditions between two neighboring structures were assumed as bonded. To solve the FEA, a thermal expansion module in structural mechanics was used to simulate polymerization shrinkage. The thermal strain during the temperature change is governed by the following equation:

ε = α· Δ T

where ε is the strain, α is the coefficient of thermal expansion, and ΔT is the change in temperature. When the thermal strain is replaced by the polymerization shrinkage strain ε polymerization , the governing equation is as follows:

ε polymerization = α p · ΔT

The coefficient of thermal expansion α p was assigned as 0.5% °C −1 , which is the free linear shrinkage of Z250 composite . Δ T is the equivalent temperature change determined from the DIC measurements in three experimental groups. After setting the local temperature changes on the irradiation and termination regions, the thermal conduction resulted in various gradient temperature distributions. The ANSYS solver generated the solutions of strain and stress. The displacements obtained from the bonded restorations were used to verify the results of two FEA models. The von Mises stress was examined for the equivalent stress states. The maximum principal stress and shear stress were also inspected for the peak tensile and shear stress values at the restoration and tooth entities.

Interfacial adhesion analysis

The effects of light curing on the interfacial microleakage were examined by using micro-CT scanning of the bonded restorations. After DIC measurements, these teeth were stored in water for 24 h. The teeth were scanned at a resolution of 9 μm. For each tooth, ten equidistant buccolingual sectional images were chosen to locate and quantify the areas of microleakage. Microleakage was defined as the interfacial areas with gray levels lower than the tooth structure and composite in the x-ray images. A home-made program was developed to select the region of microleakage, and also to measure these areas.

Materials and methods

The whole experimental scheme is composed of three parts: DIC measurement of shrinkage strain, FEA for contraction stress, and interface examination. The study design is shown in Fig. 1 . A box-shape class II cavity was restored with the composite consecutively in the unbonded and bonded states. The free shrinkage strain of the unbonded restoration was measured by DIC, and applied to set the shrinkage strain in FEA. After removal of the unbonded composite restoration, the cavity received adhesive treatment and restoration. The shrinkage deformations at the boundaries of bonded restorations were used to validate the results of FEA. Finally, the stress analysis of the verified FEA was compared with the interfacial microleakage of the real restorations. The details of the experiments are presented below.

Fig. 1
Illustration of the study design. The shrinkage strains were measured from unbonded cases for the setting of FEA, and the displacements from the bonded cases were used to validate the analytic results. The stress analysis resolved by FEA was compared with the analysis of interfacial bonding.

Measuring shrinkage strain of unbonded restorations by DIC

Twenty-four intact human third molars of similar sizes and morphologies, all extracted within one month, were used in this study. The study protocol was approved by the Institutional Review Board of National Cheng Kung University Hospital, Taiwan. Informed consent was obtained before collecting each tooth from patients. The teeth were mounted with their roots embedded in acrylic resin and long axes held vertically. For each tooth, a box-form cavity of 3 (W) × 3 (D) × 3 (H) mm was prepared on the mesial surface under water irrigation.

The light curing system used in this study was a quartz-tungsten-halogen light curing unit (Optilux 501, Kerr, USA). Two irradiation directions, vertical (90°) and oblique (45°), were chosen to test. A prior examination using the Marc device (BlueLight Analytics, NS, USA) indicated that oblique irradiation reduced the light intensity received by the restoration, and then the total light energy density (intensity × time) was affected. Accordingly, a third group was set as vertical irradiation but with light energy density equivalent to the oblique irradiation. The prepared teeth were divided into three groups (n = 8), as follows ( Fig. 2 ):

Fig. 2
Illustrations of the light curing regimes and shrinkage strain. (A) Groups V and R used the vertical irradiation. (A) Group O used the oblique direction irradiation. ε I , ε T , ε I1 , ε I2 , ε T1 , and ε T2 were the measured strains.

Group V: light irradiation orthogonal (90°) to the top surface of the restoration, with a light intensity of 500 mW/cm 2 for 40 s.

Group O: oblique light irradiation. The light guide was tilted 45° to irradiate from the buccal cusp, with a light intensity of 500 mW/cm 2 for 40 s.

Group R: reduced intensity curing. The light irradiation was orthogonal (90°) to the restoration and at a light intensity of 300 mW/cm 2 for 40 s.

The light energy densities for Groups V, O, and R were confirmed by the Marc device as approximately 20, 12, and 12 J/cm 2 , respectively.

The free shrinkage of the composite in the cavity was first measured at an unbonded state. The cavity surfaces were coated with a thin layer of vaseline gel (Petroleum Jelly, Pure) to allow free shrinkage of the composite. The tooth was secured on a jig with the cavity facing an image acquisition system composed of an optic microscope (Zoom microscope ML-Z07545D, Moritex Inc., Japan) and a CCD (MTV-12V1E, Mintron, Co., 640 × 480 pixels). A microhybrid composite Filtek Z250 (3M/ESPE, St. Paul, MN, USA) was filled into the cavity in one increment, then the tooth with the restoration was sprayed with black paint to generate the speckle pattern needed for surface characterization. The specimen and image acquisition system were placed on an optical shockproof table to prevent vibration. First, the unpolymerized composite was photographed as the reference image. After light irradiation with its specific protocol, the composite was photographed again to generate the deformed images. A DIC program, Vic-2D (Correlated Solutions, West Columbia, SC, USA), was used to analyze the free shrinkage strain on the composite restoration surfaces. In the DIC analysis, the subset was set as 41 × 41 pixels. The sub-pixel precision and calculation time were optimized by applying an interpolation 6-tap nonlinear filter. The calibration work for the DIC system, surface patterning method, and the analytic conditions are described in our previous work , which demonstrated an error of 5.75 ± 0.64% for displacement that is 1–5 μm.

To express the direction and magnitude of shrinkage displacements, a virtual plane X–Y coordinate system was defined on the restoration surfaces, with the origin set at the joint of lingual and gingival walls ( Fig. 3 A). The FEA was planned to simulate the polymerization shrinkage by a heat transfer analysis. The shrinkages were assumed as the volumetric changes caused by temperature decreases, which varied along with curing protocols and locations in the restoration. The polymerization under different light curing protocols was simulated by setting different temperatures at the irradiation and termination regions. For the unbonded restorations of groups V and R, the gradient polymerization is a function of cavity depth. The shrinkage strains on the top surface (Y = 3) and cavity floor (Y = 0) were thus measured and nominated as ε I (irradiation region) and ε T (termination region), respectively ( Fig. 2 A). Group O presented a different polymerization pattern with the irradiated region located around the buccoocclual edge and progressing in a 45° direction. This obliquely gradient polymerization was simulated by setting two different initiation strains at two boundaries: ε I1 at the buccal half of the top surface and ε I2 at the top half of the buccal wall ( Fig. 2 B). Similarly, two termination strains, ε T1 and ε T2, were set at the bottom half of the lingual wall and at the lingual half of the bottom surface, respectively. These strain values were used for the assumption of shrinkage in their corresponding FEA models.

Nov 23, 2017 | Posted by in Dental Materials | Comments Off on Shrinkage behaviors of dental composite restorations—The experimental–numerical hybrid analysis
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