Accelerated Fatigue Model for Predicting Composite Restoration Failure

Abstract

An empirical method is proposed to predict the clinical performance of resin composite dental restorations by using laboratory data derived from simple specimens subjected to chemical degradation and accelerated cyclic fatigue. Three resin composites were used to fill dentin disks (2-mm inner diameter, 5-mm outer diameter, and 2 mm thick) made from bovine incisor roots. The specimens (n = 30 per group) were aged with different durations of a low-pH challenge (0, 24, and 48 h under pH 4.5) before being subjected to diametral compression with either a monotonically increasing load (fast fracture) or a cyclic load with a continuously increasing amplitude (accelerated fatigue). The data from 1 material were used to establish the relationship between laboratory time (number of cycles) and clinical time to failure (years) via the respective survival probability curves. The temporal relationship was then used to predict the clinical rates of failure for restorations made of the other 2 materials, and the predictions were compared with the clinical data to assess their accuracy. Although there were significant differences in the fast fracture strength among the groups of materials or durations of chemical challenge, fatigue testing was much better at separating the groups. Linear relationships were found between the laboratory and clinical times to failure for the first material (R² = 0.90, 0.90, and 0.62 for the 0-, 24-, and 48-h low-pH groups, respectively). The clinical life of restorations made of the other 2 materials was best predicted with data from the 48-h low-pH groups. In conclusion, an accelerated fatigue model was successfully calibrated and applied to predict the clinical failure of resin composite restorations, and the predictions based on data obtained from chemically aged specimens provided the best agreement with clinical data.

Introduction

Resin composites are widely used for the restoration of anterior and posterior teeth because of their aesthetics, biocompatibility, and good mechanical properties (Demarco et al. 2013; Zhou et al. 2019). However, resin composite restorations have a relatively high failure rate (Kopperud et al. 2012), and their replacement takes up a large portion of a dentist’s working time, which places a heavy financial burden on the oral health care system (Nedeljkovic et al. 2020). Resin composite restorations fail mainly as a result of fracture or secondary caries, following degradation of the interface between the restoration and dental tissues caused by occlusal loading, hydrolysis, and bacterial challenge (Drummond 2008). Therefore, interfacial integrity is vital for the survival of resin composite restorations.

To ensure the longevity of dental restorations, the materials used for their construction should be assessed in a clinically representative manner. Although clinical studies are most accurate in determining the life span of dental restorations, they are time-consuming and require a large sample size, as the restorations are affected by many factors besides those related to the materials, such as the operator, defect size, and defect location (Askar et al. 2020). Thus, given the speed at which dental restorative materials are being developed and superseded, accurate and timely predictions of their clinical performance based on simpler and less time-consuming laboratory testing would be desirable.

Currently, a number of methods are utilized to assess the strength of resin composites and their interfaces with dental hard tissues. Among them, the microtensile bond strength test is considered relatively easy to perform, and the results are repeatable and appear to correlate well with clinical outcomes (Armstrong et al. 2017). Fracture toughness measured by the chevron-notched beam test has been found to correlate positively with microtensile bond strength and appears to be more reliable and less variable, but the test is more laborious and requires specific equipment (De Munck et al. 2013). These methods, however, give only static bond strength or fracture toughness, whose predictive power for long-term clinical performance is uncertain. The reason is that materials with the same initial fracture or bond strength may not degrade at the same rate under the same clinical challenges, which are usually cyclic in nature (Arola 2017). Even if the specimens are aged before testing, it is difficult to determine their equivalent clinical age. Thus, it is unlikely that measuring the static fracture/bond strength of dental restorative materials alone would be sufficient for lifetime prediction; cyclic fatigue tests should be used to provide more clinically representative assessment. In addition, clinical data should be used to calibrate the laboratory data for prediction purposes (Zhang et al. 2021).

To simulate the clinical situations, cyclic fatigue tests with a constant load amplitude based on that measured clinically could be applied to restored tooth specimens until failure (Studart et al. 2007; Yassini et al. 2016). However, even if loading is applied at a much higher frequency than that clinically, a prohibitively large number of cycles may still be required to fail the specimens. So, accelerated fatigue testing based on, for example, the step-stress method (Nelson 1980; Coelho et al. 2009) is preferred.

For materials or their interfaces to fail, the load must exceed their strength. Clinically, the load has roughly a constant amplitude while the strength reduces with time due to material degradation. In accelerated fatigue, the load amplitude and hence the rate of degradation increase with time. This shortens the time to failure. On the basis of the diametral compression test (Carrera et al. 2016), our group has developed an accelerated fatigue test with a continuously increasing load (Li et al. 2017) and found it to be capable of more efficiently determining the fatigue parameters for the tooth-composite interface. The method can therefore potentially be used to assess resin composite systems in an accelerated yet clinically relevant manner. However, the synergistic effect of biochemical challenges (Li et al. 2014; Carrera et al. 2017; Zhu et al. 2017; Zhang et al. 2020), such as those posed by oral biofilms, on the degradation of the tooth-restoration interface has not yet been considered for this test method. Moreover, the question remains whether it is possible to accurately predict the clinical life of dental restorations with laboratory data.

In this study, the accelerated fatigue test with a continuously increasing load was applied to dentin composite specimens degraded by a low-pH environment for different durations. After calibration against clinical data for 1 of the tested restorative materials, the number of cycles to failure obtained was used to predict the clinical lifetimes of restorations made from the other restorative materials.

Materials and Methods

Theory

The survival probability (Ps) of specimens from a certain restorative material as a function of the number of loading cycles (N_c) could be obtained from a cyclic fatigue test. At the same time, Ps and the service time (t) of dental restorations of the same restorative material could be extracted from published clinical studies. It should be clear that Ps = f(t) and Ps = g(N_c) are monotonically decreasing functions. For the laboratory model to be predictive for any percentage of survival clinically, Ps = f(t) = g(N_c) or t = f^-1.g(N_c), with f^-1 being the inverse of f. It should be specified that f^-1.g is a monotonically increasing function relating t to N_c. The relationship between t and N_c for restorations made of this restorative material could then be obtained by plotting the corresponding values for these 2 variables against each other for different values of Ps (Fig. 1A). Assuming that this relationship between laboratory and clinical times applies to the other restorative materials, the clinical time to failure, t, for any dental restoration could be predicted from the number of cycles to failure, N_c, obtained from the laboratory tests. Note that no specific distribution shape or stress-life relation needs to be assumed.

Figure 1.

Temporal conversion and experimental setup. (A) Scheme for converting laboratory number of cycles to failure to clinical time to failure. (B) Dentin composite disc specimen (5-mm outer diameter, 2-mm inner diameter) in water-filled chamber under accelerated fatigue testing with diametral compression.

Sample Preparation

Dentin composite discs were prepared from bovine incisors (Li et al. 2014; Li et al. 2015; Carrera et al. 2016). The roots of these teeth were machined into cylinders of a 2-mm inner diameter and 5-mm outer diameter. The dentin cylinders were then randomly divided into 3 groups and filled with 1 of 3 resin composites: Herculite HRV (Kerr), Filtek Z100, and Filtek Z250 (3M ESPE), with the corresponding adhesives (Appendix Table). Prior to placing the resin composites, an etchant was applied to the inner surface of the cylinders. After 15 s, the etched surface was rinsed for 10 s with distilled water and blot dried with a mini-sponge. Two to 3 coats of adhesive were applied to the etched dentin surface for 15 s via gentle agitation with a fully saturated applicator immediately after blotting. The adhesive layer was gently air thinned for 5 s to evaporate the solvents before being light cured for 10 s. Then, the cylinders were filled with 1 of the aforementioned composites incrementally, with each increment being <2 mm thick, followed by 40 s of light curing with an Elipar S10 LED light-curing unit (3M ESPE) operated at 1,200 mW/cm². Finally, the filled dentin composite cylinders were cut into discs 2 mm thick (Fig. 1B) by using a diamond-blade cutter (Isomet; Buehler) at a speed of 60 cycles/min. The discs for each resin composite were then randomly divided into 3 subgroups (n = 30) and stored in 1) deionized water of pH 7 for 48 h, 2) lactic acid buffer of pH 4.5 for 24 h and then deionized water of pH 7 for 24 h, or 3) lactic acid buffer of pH = 4.5 for 48 h: all at 4 °C before fatigue testing.

Accelerated Fatigue Test

Each specimen was put into a water-filled chamber at room temperature, as shown in Figure 1B, and mechanically tested with a universal testing system (MTS 858 MiniBionix II). Cyclic diametral compression with a sinusoidal load of 1 Hz and zero minimum value was used to test the specimens, with the maximum load increasing at a rate of 0.04 N/s. The load and the corresponding displacement were recorded throughout the test. When the displacement began to drift significantly from its projected value—that is, when the specimen began to behave nonlinearly following interfacial debonding (Li et al. 2015; Liet al. 2017)—the specimen was considered to have failed, and the corresponding number of cycles was chosen to be the number of cycles to failure. The specimens were ranked according to their number of cycles to failure and assigned with a probability of survival via the estimator i/(n + 1), where i is the rank of a specimen and n is the total number of specimens (Li et al. 2017).

Fast Fracture Test

Specimens made from the same resin composites and subjected to the same types of preconditioning were tested with fast fracture by using the setup shown in Figure 1B. The specimens were ranked according to their loads to failure and assigned with a probability of survival (Li et al. 2017).

Calibration with Clinical Data

Clinical data of class II restorations reported by Kopperud et al. (2012) were used to calibrate our laboratory data for the Herculite specimens as described in the Theory section. The times to failure for several values of survival probability were extracted from the graph with ImageJ (2012) and then plotted against the laboratory number of cycles to failure. The linear regressions obtained with the least squares method for the Herculite data from the different types of preconditioning were then used to predict the clinical times to failure for the Z100 and Z250 restorations, and the predictions were compared with clinical data (Kopperud et al. 2012).

Results

Fast Fracture Test

Figure 2 shows the survival probability curves as functions of the fast fracture load (represented by the nominal interfacial stress; Li et al. 2015) for the different groups of dentin composite discs. The low-pH storage reduced the survival probability of the specimens, especially those with a longer storage time (Table). For each material, the mean failure stress among the preconditions was not always significantly different. Over the 3 preconditions, the mean failure stress was 18.16, 16.92, and 20.63 MPa for Herculite, Z100, and Z250, respectively; the differences were statistically significant among the materials.

Figure 2.

Survival probability as a function of interfacial stress for the fast fracture test.

Table.

Failure Stress and Number of Cycles to Failure for Different Preconditions and Resin Composites.

	Herculite HRV			Filtek Z100			Filtek Z250
Precondition	Control	pH 4.5, 24 h	pH 4.5, 48 h	Control	pH 4.5, 24 h	pH 4.5, 48 h	Control	pH 4.5, 24 h	pH 4.5, 48 h
Failure stress, MPa
Precondition	18.94 ± 2.86	17.93 ± 2.57	17.62 ± 2.30	17.77 ± 2.48	16.46 ± 2.39	16.59 ± 3.34	21.70 ± 3.56	20.43 ± 3.46	19.76 ± 2.93
P valuea		0.1338	0.0427		0.0379	0.1202		0.1605	0.0222
Materialb	18.16 ± 2.57			16.92 ± 2.81			20.63 ± 3.35
No. of cycles
Precondition	6,209 ± 852	6,092 ± 874	5,642 ± 922	5,287 ± 714	5,018 ± 1,022	5,397 ± 944	7,001 ± 922	6,121 ± 814	6,196 ± 1,079
P valuea		0.6019	0.0163		0.2425	0.6105		0.0003	0.0034
Materialb	5,981 ± 907			5,232 ± 907			6,439 ± 1,016

Values are presented as mean ± SD.

^aCompared with control within group.

^bAll values in row are significantly different.

Accelerated Fatigue Test

Figure 3 shows the survival probability curves as functions of the number of cycles for the dentin composite discs under accelerated fatigue. Except for Z100, the low-pH storage (especially pH 4.5 for 48 h) clearly reduced the survival probability and mean number of cycles to failure of the specimens. For Z100, there were no statistically significant differences among the different preconditions (Table). The mean numbers of cycles to failure were 5,981, 5,232, and 6,439 for Herculite, Z100, and Z250, respectively; the differences were statistically significant among the materials.

Figure 3.

Survival probability as a function of number of cycles for accelerated fatigue.

Conversion of Laboratory to Clinical Lifetime

The plots of clinical life span versus laboratory number of cycles to failure for Herculite can be well fitted with linear regression (Fig. 4A). The conversion equation given by the control group with storage at pH 7 has an R² of 0.90; that given by the group with storage at pH 4.5 for 24 h has an R² of 0.90; and that given by the group with storage at pH 4.5 for 48 h has an R² of 0.62.

Figure 4.

An empirical model for predicting the clinical performance of resin composite dental restorations with laboratory data. (A) Linear relationships between clinical life span and laboratory number of cycles to failure for Herculite. (B) Comparison between predicted and clinical survival probability curves for Z100 and Z250.

The different conversion equations from Figure 4A and the corresponding laboratory numbers of cycles to failure from the accelerated fatigue tests (Fig. 3) were then used to predict the clinical lifetimes of the Z100 and Z250 restorations. The predictions are compared with the clinical data in Figure 4B. For both materials, predictions based on data from the low-pH groups best match the clinical data.

Discussion

Resin composite restorations have a relatively high failure rate (Kopperud et al. 2012; Demarco et al. 2015). As a result, new restorative materials are being developed with the aim of improving the longevity of this class of restoration. While being the gold standard for assessing the performance of dental restorations, clinical studies are expensive, time-consuming, and difficult to conduct (Sarrett 2005; Lempel et al. 2015). Yet, laboratory tests, especially fast fracture tests, based on simple specimens could be limited in their predictive power even though they are cheaper, quicker, and easier to conduct (Armstrong et al. 2017).

In this study, an empirical method was proposed by using accelerated fatigue test data that were calibrated against clinical data (Kopperud et al. 2012) to predict the lifetimes of dental restorations. The specimen used was the dentin composite disc under cyclic diametral compression (Carrera et al. 2016; Li et al. 2017). Fast fracture tests were performed for comparison, and the specimens were stored in a low-pH solution before testing to simulate biochemical degradation caused by the oral environment.

The fast fracture test and the accelerated fatigue test gave the same ranking for the 3 material groups of specimens tested, with those of Z250 being the strongest or longest lasting, followed by those of Herculite and then Z100 (Table). The laboratory ranking agreed with that of the clinical study (Kopperud et al. 2012). However, the differences among the materials were not always statistically significant in the fast fracture test results, which were limited to the fast fracture loads. In contrast, with suitable calibration, the accelerated fatigue test could give relatively accurate predictions for the clinical survival probability of dental restorations as a function of time (Fig. 4B). Yet, the specimens needed to be preconditioned with a low-pH solution for the predictions to be accurate. This shows the importance of incorporating biochemical degradation in the laboratory testing of dental restorations. According to Zhang et al. (2020), the preconditions used were equivalent to 2 to 3 y of biochemical challenges under in situ oral conditions. Nevertheless, it should be pointed out that the linear regression for time conversion based on the 48-h low-pH data has the lowest R² value. This means that the corresponding predictions have the highest uncertainty.

Testing of the dentin rings and resin composites separately under the same storage conditions and mechanical loading did not produce any significant differences among the storage conditions for these monolithic specimens (results not presented). This strongly suggests that the reductions in the fast fracture load or the number of cycles to failure for the dentin composite discs were mainly due to interfacial degradation (Li et al. 2014; Carrera et al. 2017; Zhu et al. 2017).

Clinically, the majority of failure among resin composite restorations is caused by secondary caries (Kopperud et al. 2012), which requires, as a prerequisite, the opening of the tooth-restoration interface to allow the invasion of bacteria. Compared with occlusal loading, which normally occurs only during mastication, bacterial challenge is more frequent due to the ever-present dental plaque. Therefore, it is reasonable to assume that, clinically, secondary caries would occur not long after interfacial opening, whereas for fracture to occur, a longer duration of mechanical loading, in vitro and in vivo, would be required beyond interfacial opening. This may explain why the majority of clinical failure observed was due to secondary caries. This also justifies equating interfacial failure in the accelerated fatigue test, identified by the emergence of nonlinear mechanical behavior of the specimen, with its gross failure.

The Z100 specimens had the lowest mean fracture load and mean fatigue life, and their results were not sensitive to the storage condition. A plausible explanation lies in the high polymerization shrinkage stress that Z100 could generate (Li et al. 2011), which may have led to extensive interfacial debonding in the specimens following curing. The subsequent storage in a low-pH solution probably did not cause further significant interfacial degradation that could affect the results of the mechanical tests.

The Herculite specimens appeared to be more resistant to the chemical challenge than those of Z250, as a longer storage time was required to reduce the former’s mean fatigue life. The difference in resistance against chemical degradation was attributed to the different adhesives used to prepare the specimens (Appendix Table).

Ideally, in vitro biochemical and mechanical aging of the interface should proceed concurrently at speeds that reflect their relative rates of clinical degradation; that is, their rates of degradation should be synchronized (Zhang et al. 2020; Zhang et al. 2021). This means that after a particular duration or number of cycles of testing, the mechanical and biochemical loads should have accumulated their respective degrees of damage as would be expected clinically for the equivalent service time. The fact that specimens subjected to the most severe precondition gave the best life predictions indicates that, clinically, interfacial degradation due to biochemical challenges possibly occurs at a much faster rate than that due to mechanical fatigue, at least for the class II restorations, the results of which we used to calibrate our laboratory data. Thus, the use of sequential aging in this study was perhaps justified.

The calibration of the in vitro data, or the determination of the temporal conversion equation (Fig. 4A), could be done by using data from any of the 3 materials tested. Indeed, since there were no significant differences in the results among the storage conditions for the Z100 specimens, it would be simpler to use the Z100 data to determine the temporal conversion equation: the calibration would produce more or less the same equation for all 3 storage conditions.

In this study, we used the dentin composite disc under cyclic diametral compression to simulate an actual restoration under occlusal loading. It may be possible to use other mechanical tests, such as the microtensile test or microbend test, to produce the in vitro data for lifetime prediction, and it would be interesting to see if they can produce accurate predictions. We also used a linear increase in load amplitude with the number of cycles; it is possible that a nonlinear increase in load would be more appropriate.

The clinical data used to calibrate the laboratory data were based on class II restorations of Herculite (Kopperud et al. 2012). Therefore, the predictions made are expected to be applicable only to class II restorations of other materials. To predict the lifetime of other types of restoration, clinical data of the appropriate restoration type should be used for calibration. Furthermore, the proposed method has been tested against just 1 set of clinical data (Kopperud et al. 2012), which covered a maximum of approximately 50% of failure at 4.6 y. The method should therefore be tested against more clinical results to establish its general validity.

Another limitation of the current study was the lack of explicit consideration of failure through secondary caries. However, this would require the chemical or even bacterial challenge to be applied concurrently with the mechanical loading, with the latter (which took much less time to perform) slowed down to synchronize with the former (Zhang et al. 2021). Also, the tests would need to be interrupted periodically to allow the specimens to be examined for caries (demineralization) development.

As an alternative to the empirical method proposed here, a stress analysis could be performed for the restoration in question to determine the amplitude of the failure-causing stresses (Li et al. 2015). These could then be compared against the stress-life curves of the materials or tooth-restoration interface to predict the lifetime of the restoration. However, the stress amplitudes used to construct the stress-life curves of dental materials and their interfaces are usually much higher than those experienced by the restored teeth clinically. As a result, considerable extrapolation is needed in using the stress-life curves for lifetime predictions, which will inevitably contain much uncertainty.

In conclusion, an accelerated fatigue model was successfully calibrated and applied to predict the clinical failure of resin composite restorations, and the predictions based on laboratory data obtained with chemically aged specimens provided the best agreement with clinical data.

Author Contributions

B. Yang, contributed to data analysis and interpretation, drafted the manuscript; W. Aregawi, contributed to data acquisition and analysis, critically revised the manuscript; R. Chen, contributed to data acquisition, critically revised the manuscript; L. Zhang, Y. Wang, contributed to data design, critically revised the manuscript; A.S.L. Fok, contributed to conception and design, data interpretation, drafted and critically revised the manuscript.