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Minimization of polymerization shrinkage effects on composite resins by the control of irradiance during the photoactivation process

Abstract High levels of shrinkage stress caused by volumetric variations during the activation process are one of the main problems in the practical application of composite resins. Objective The aim of this study is to reduce the shrinkage stress and minimize the effects caused by composite resin volumetric variation due to the photopolymerization. In this way, this work proposes a systematic study to determine the optimal dimming function to be applied to light curing processes. Material and Methods The study was performed by applying mathematical techniques to the optimization of nonlinear objective functions. The effectiveness of the dimming function was evaluated by monitoring the polymerization shrinkage stress during the curing process of five brands/models of composites. This monitoring was performed on a universal testing machine using two steel bases coupled in the arms of the machine where the resin was inserted and polymerized. The quality of the composites cured by the proposed method was analyzed and compared with the conventional photoactivation method by experiments to determine their degree of conversion (DC). Absorbance measurements were performed using Fourier-transform infrared spectroscopy (FT-IR). A T-test was performed on DC results to compare the photoactivation techniques. We also used scanning electron microscopy (SEM) to analyze in-vitro the adhesion interface of the resin in human teeth. Results Our results showed that the use of the optimal dimming function, named as exponential, resulted in the significant reduction of the shrinkage stress (~36.88% ±6.56 when compared with the conventional method) without affecting the DC (t=0.86, p-value=0.44). The SEM analyses show that the proposed process can minimize or even eliminate adhesion failures between the tooth and the resin in dental restorations. Conclusion The results from this study can promote the improvement of the composite resin light curing process by the minimization of polymerization shrinkage effects, given an operational standardization of the photoactivation process.

Alternative light-activation protocols have been proposed to minimize the polymerization shrinkage effects 2,10, [17][18][19] . The soft-start techniques, for example, have been extensively studied. In this kind of photoactivation, the polymerization is started with low irradiance for a few seconds, followed by increased irradiance for the remaining period of light-activation.
This process advocated as an approach to reduce the shrinkage stress while maintaining proper degree of conversion (DC) of the composite 3 . However, there is no consensus about the time and irradiance parameters in the soft-start techniques. Therefore, in the literature, it is possible to find soft-start protocols with different values of irradiance and activation time, both for the initial phase of low irradiance and for the final phase of high irradiance 16 . In addition, this type of study is limited to the functions of conventional light curing devices, which do not allow continuous variation of the irradiance during the activation.
Our hypothesis is that it can be possible to determine an optimal curve of irradiance variation during the photoactivation, which will promote the reduction of the shrinkage stress without affecting the cured composites DC.
Considering the above, this project proposes a systematic study to optimize the dimming function in light curing processes. The study was performed by a mathematical approach to determine an optimal function for the irradiance modulation at the time domain. This function was incorporated in a light curing unit, developed by our research group, which can control the irradiance according to a mathematical function. The effectiveness of the optimal function was evaluated by monitoring the polymerization shrinkage stress during the curing process. The quality of the resins polymerized by the proposed method was experimentally analyzed to determine the conversion degree of the monomers into polymers. The interface adhesion between the teeth and resins was analyzed by scanning electron microscopy (SEM).

Materials and methods
This work has three major stages of development:  presented a logarithmic behavior, as illustrated in Figure 1(a). The graph showed that the resins were under an intensive stress in the initial seconds of the polymerization process, followed by stabilization, where the stress tends to become constant. This behavior shows that the composite contraction occurs at the beginning of the polymerization process.
The experimental data from the shrinkage stress can be fitted by a first order exponential decay function: (2) in which the determination coefficient is R 2 =0,99.
The mathematical optimization resulted in a minimization function with exponential behavior: where the parameters a, b and i 0 can be adjusted to attempt the manufacturers' recommendations for the  Figure 1(b) shows this exponential curve, which represents the theoretical optimal curve to minimize the effects of polymerization shrinkage. In this figure, the curve for the conventional method of photoactivation was inserted for comparison purposes.
By applying the exponential photoactivation method, new contraction stress patterns for the resins were obtained. Figure 2 shows comparative graphs of the shrinkage stress for the conventional and exponential photoactivation methods. By analyzing the standard deviation of the shrinkage stress quantification for the conventional and exponential photoactivation methods at the end of the monitoring experiment (300 s) and the T-test result for these values (Table 1), it can be concluded that the exponential method promoted a significant reduction of the shrinkage stress (~36.88% ±6.56) for all analyzed composites brand/models.

The result from T-test applied on DC values showed
there are no significant differences comparing the conventional and exponential photoactivation methods.
These results are also synthesized in Table 1.  In addition, note that we only have studied the effects of a function for irradiance modulation in a fixed activation time (35 seconds). Therefore, the conventional and exponential methods of photoactivation provide different total radiant exposure values, being 35 J/cm 2 for the conventional method and ~14 J/cm 2 for the exponential method. This implies that these two methods cannot be analyzed in terms of the Law of Reciprocity 12,20 , which we have considered as limitation of our study. Future works can be performed by varying the activation time for the exponential and/ or conventional methods, so that the photoactivation energy could be the same. Another proposal for future studies is to compare the exponential method with softstart techniques, which, as cited in the introduction, have been applied to minimize the polymerization shrinkage.
We still have considered as a limitation of our study the fact that the polymerization shrinkage may be associated with other not analyzed parameters, for example, intrinsic factors such as viscosity, monomers and fillers, and extrinsic factors such as temperature

Conclusions
The results obtained in this study showed that the control of irradiance during the photoactivation process by an optimized mathematical function is more efficient than the conventional technique for reducing the effects of polymerization shrinkage in composite resins. According to the DC results, the proposed photoactivation method does not cause damage to the cured resin, which is effective in converting monomers into polymers at the same level as for the conventional method. By the SEM analyses, we concluded that the exponential photoactivation method can reduce or eliminate the adhesion failure between the composite and the tooth.