Combined aging effects of strain and thermocycling on unload deflection modes of nickel-titanium closed-coil springs: An in-vitro comparative study
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1 ORIGINAL ARTICLE Combined aging effects of strain and thermocycling on unload deflection modes of nickel-titanium closed-coil springs: An in-vitro comparative study Gabriele Vidoni, a Giuseppe Perinetti, a Francesca Antoniolli, b Attilio Castaldo, c and Luca Contardo d Trieste, Italy Introduction: There are no reports on the aging effects of thermocycling of nickel-titanium (NiTi) based coil springs, and few studies have investigated their superelasticity phases in full. In this study, we compared the mechanical properties of NiTi-based closed-coil springs after the combined aging effects of prolonged strain and thermocycling, as a reflection of the clinical situation. Methods: Ninety NiTi-based closed-coil springs were used, 3 each of the following types: (1) Nitinol (3M Unitek, Monrovia, Calif), (2) Ni-Ti (Ormco, Glendora, Calif), and (3) RMO (Rocky Mountain Orthodontics, Denver, Colo); all had similar dimensions (length, 12 mm). In each sample group, 2 equal subgroups of 15 coil springs were extended by either % (to 18 mm) or % (to 3 mm), immersed in artificial saliva, and kept at 37 C for 45 days. All springs underwent sessions of thermocycles (1 minute long) from 5 Cto55 C on days 22 and 45. Unload deflection curves from both the % and % extensions (according to their strain subgroups) were recorded by using a universal testing machine before the strain (baseline) and at both 22 and 45 days, immediately after thermocycling. Results: At baseline, the loads exerted by the NiTi-based coil springs varied from 99.8 to gf for the RMO (% strain) and Ni-Ti (% strain) groups. Statistically significant, although small, differences were seen at each time point in both the % and % strain subgroups; generally, the highest and lowest values were recorded in the Ni-Ti and Nitinol groups (all, P \.1). Only the Nitinol coil-spring group showed an acceptable superelasticity phase. The strain and thermocycling did not dramatically change the deactivation forces of any coil springs. Conclusions: NiTibased closed-coil springs might not have a superelasticity phase, and prolonged strain and thermocycling do not produce clinically relevant alterations in their deactivation forces. (Am J Orthod Dentofacial Orthop 21;138:451-7) To obtain optimal orthodontic tooth movement (OTM), fine control of the forces exerted by the orthodontic appliances is required. 1 In particular, an in-vivo study 2 showed that, although the optimal force intensity still remains particularly subjective, a continuous and constant force always produces more efficient OTM compared with a discontinuous force. Therefore, orthodontic devices capable of From the Department of Biomedicine, School of Dentistry, University of Trieste, Trieste, Italy. a Resident, orthodontic program. b Research associate. c Professor. d Researcher. The authors report no commercial, proprietary, or financial interest in the products or companies described in this article. Reprint requests to: Giuseppe Perinetti, Struttura Complessa di Clinica Odontoiatrica e Stomatologica, Ospedale Maggiore, Via Stuparich 1, Trieste, Italy; , G.Perinetti@fmc.units.it. Submitted, February 9; revised and accepted, May /$36. Copyright Ó 21 by the American Association of Orthodontists. doi:1.116/j.ajodo exerting continuous and constant forces are more compatible with biologic OTM, as long as the intensity of the force itself is kept below certain thresholds. 1 Moreover, a continuous and light orthodontic force of 2 cn (about 2 gf) was recently reported to reduce biting pain, at least during the first week of OTM. 3 To obtain such constant forces, the use of nickeltitanium (NiTi) alloys was introduced in orthodontics. 4 NiTi alloys are characterized by 2 crystal structures: a martensitic phase and an austenitic phase; these have plastic and shape-memory properties, respectively. Transformation between the 2 phases is possible and can be induced by temperature changes in the transition temperature range (TTR). In this regard, it is important to have a TTR such that the NiTi alloy is in its austenitic phase when placed into the oral cavity. Mechanical stress has also been implied in this phase transformation. NiTi alloys in the austenitic phase also have the important mechanical property of superelasticity, according to which they exert relatively constant loads over a wide range of deflections
2 452 Vidoni et al American Journal of Orthodontics and Dentofacial Orthopedics October 21 Time points Spring subgroup (n = Baseline Strain + artificial saliva at 37 C 22 days 22 days 23 days Strain + artificial saliva at 37 C 45 days Thermocycling Thermocycling Fig 1. The study design. The same study design was used for each of the 6 subgroups: 3 closed-coil spring groups and 2 strains, at % and % of extension over the initial lengths, respectively. Among the available NiTi-based orthodontic devices are open-coil and closed-coil springs. These perform better than elastomeric chains in terms of load deflection responses to strain 6 and exposure to a simulated oral health environment. 7,8 Similar results were also obtained when comparing NiTi-based coil springs with stainless steel coil springs. 9 Many variables can affect force intensities produced by NiTi-based coil springs. These include the alloy, the wire and lumen diameters, the length of the springs, and the pitch angle of the coils Moreover, the forces exerted by NiTi-based coil springs can be rendered less predictable by both prolonged strain 6,7,1,13 and working temperature. 8,14-16 However, no data are available on the combined aging effects of prolonged strain and thermocycling on the unload deflection characteristics of such devices; this issue has not been addressed, even though the need for an investigation was stressed several years ago. 7,9 Although assumed to be characterized by a superelastic phase, the unloading deflection modes of different NiTi-based springs have not been investigated in full. Therefore, this study was designed to compare the performances of 3 commercially available, NiTi-based closed-coil springs after combined aging effects from prolonged strain and thermocycling, which should better resemble the oral environment conditions. Moreover, to fully show the properties of these NiTi-based closedcoil springs, we included analyses of both the load values exerted at discrete deflections and the deactivation forces. MATERIAL AND METHODS Ninety NiTi-based closed-coil springs were used, 3 of each of the following types: (1) Nitinol (code 146-, 3M Unitek, Monrovia, Calif), (2) Ni-Ti (code , Ormco, Glendora, Calif), and (3) RMO (code F321, Rocky Mountain Orthodontics, Denver, Colo). According to the manufacturers indications, all closed-coil springs had the wire diameters of.1 in (. mm), and the lumen diameter was.3 in (.76 mm), with a total length of each spring of 12 mm. The force exerted by these closed-coil springs was given by only 1 manufacturer as gf (Nitinol). All coil springs used in this study were selected at random from a large number of samples. The study design is illustrated in Figure 1. Each coilspring group was divided into 2 equal subgroups of 15 springs, which were subjected to prolonged and constant strain under an extension of either 6 mm (%) or 18 mm (%) over the initial length of 12 mm. Moreover, to simulate the aging that occurs in an oral environment, the coil springs of the 3 groups, and thus for both subgroups in each group, were kept in artificial saliva at 37 C and subjected to 2 sessions of thermocycling, on days 22 and 45 after the start of the strain. Curves of deactivation forces from both extension subgroups were recorded initially, before the start of the strain (baseline) and again on days 22 and 45, immediately after the thermocycling sessions. The coil springs in the % strain subgroups were never extended beyond this value. To hold the coil springs at % and % strain over the study period, a customized stainless steel jig was prepared. This jig included a base, onto which 3 arrays of 15 parallel posts were fixed. 6 The distances between the arrays were set to extend the coil springs to either % or % above their initial 12-mm length. After we carefully mounted the coil springs on the jig according to their strains, the whole jig and springs were immersed in the artificial saliva, 17 which contained 6.8 mmol/l sodium chloride, 5.4 mmol/l potassium chloride 5.4 mmol/l calcium chloride, 5. mmol/l monosodium phosphate,.21 mmol/l sodium sulfide, and 16.7 mmol/l urea. Each of the 2 thermocycling treatment sessions (days 22 and 45) included temperature cycles from 5 C to 55 C (Thermo Haake Willytech, SD Mechatronik, Feldkirchen-Westerham, Germany), with the springs cyclically immersed in each thermal bath for 3 seconds, with 2 seconds at air temperature between immersions, to reproduce temperature variations that can occur in the mouth when consuming cold and hot foods and beverages, 18 respectively.
3 American Journal of Orthodontics and Dentofacial Orthopedics Vidoni et al 453 Volume 138, Number 4 Table. at discrete extensions of the coil-spring groups at the different strains and time points Strain Time point Nitinol Ni-Ti RMO % Baseline days days NS a b % Baseline * * * 22 days * * * 45 days * * * NS a c Data are presented as means 6 standard deviations of load deflections (gf) (n 5 15). Strain is presented as percentages relative to the extension over the initial lengths (12 mm) of the closed-coil springs. All pairwise comparisons between the groups at each time point and strain are statistically significant. NS, No statistically significant difference. Statistically significant difference between 45 days vs baseline and 22 days (a), 22 and 45 days vs baseline (b), and 45 days vs 22 days (c). *Statistically significant difference from the corresponding value at % strain. A universal testing machine (SUN, Galdabini, Cardano al Campo [VA], Italy) was used to measure the loads produced by the coil springs according to the distances the crossheads travelled (deflection rates) and the loads generated (deactivation forces) that were automatically recorded and plotted as x and y scatter plots. After each coil spring had been mounted on the crossheads of the testing machine by using a pair of hooks, they were extended to either % or % of their initial lengths (to 18 or 3 mm, respectively, according to their strain subgroup) at a rate of. mm per second. 7 Since only the force produced during deactivation of the extended spring is exerted by the spring in clinical situations, the analysis of the generated loads was conducted during the rebound cycle (deactivation), 19 when the springs were allowed to return to their original lengths at the same speed (with load recordings at every.1 mm of deflection). Moreover, the transfers from the customized stainless jig to the testing machine and back to the jig were carried out carefully to prevent any uncontrolled mechanical stress to the coil springs. Statistical analysis GraphPad Prism (version 5, GraphPad Software, La Jolla, Calif) and the Statistical Package for Social Sciences software (version 13., SPSS, Chicago, Ill) were used for data analysis. After testing for the normality of the data, parametric methods were used, including the Shapiro-Wilks test and Q-Q normality plots; the equality of variance among the data sets was also tested by using the Levene test. A 1-sample t test was run to evaluate the significance of the differences in the baseline load extensions of % and % in the 2 strain subgroups with the load deflection of gf reported by only 1 manufacturer. A 3-way analysis of variance (ANOVA) was performed to assess the differences in the load deflections at the discrete extensions of % and % over the initial length (in the % and % strain subgroups, respectively). The 3 factors in the ANOVA were the time point as a repeated factor, and the coil-spring group and the strain, as independent factors. Pairwise comparisons between the time points in each coil-spring groups and strains were performed by using the Bonferronicorrected paired-sample t test. The pairwise comparisons between the coil-spring groups at each time point and strain were performed by using the Bonferroni-corrected independent-sample t test. The same independent-sample t test was used to evaluate the significance of the differences in load deflections between the strains in each coil-spring group and at each time point. A P value less than.5 was used for rejection of the null hypothesis. To quantitatively describe the deactivation forces and to objectively identify nonlinear (superelasticity) ranges of activation in each coil-spring group, time point, and strain, the full data sets of the deactivation forces were fit by linear regression. Since the expected behavior for NiTi-based coil springs on deflection would be a rapid increase followed by a plateau phase (again, for superelasticity), segmental linear regression was used. For this function, 2 linear regressions were used to fit the data. The choice of the end point between the 2 regressions was based on the highest R 2 value achievable. If segmental linear regression showed an R 2 value below.99, alternative polynomial regressions were used to fit the data. RESULTS The loads at the discrete deflections of % and % in the subgroups are shown in the Table. At baseline, the loads exerted by the NiTi-based coil springs investigated here varied from 99.8 to gf for the RMO (% strain) and the Ni-Ti (% strain) types (Table). All loads were significantly different compared with the 1 manufacturer s reported gf (all at P \.1) for all coil-spring groups. For the load deflections at the 3-way ANOVA level, all time points, coil-spring groups, and strain factors yielded statistically significant differences in load deflections (F 2; , P \.1; F 2; , P\.1; and F 1; , P\.1, respectively).
4 454 Vidoni et al American Journal of Orthodontics and Dentofacial Orthopedics October 21 % strain % strain A Nitinol B Nitinol Baseline 22 days 45 days C Ni-Ti D Ni-Ti E RMO F RMO Fig 2. Deactivation forces of the coil-spring groups at the different strains and time points. Also, among the 2-way and 3-way interactions, all reached statistically significant levels (at least P \.5; results not shown). In the pairwise comparisons in both strains, no significant differences were seen between the time points for the Nitinol group (Table). In contrast, for the Ni-Ti group, the load deflections recorded at 45 days were significantly lower compared with the corresponding baseline and 22-day values in both the % and % strains (Table). For the RMO group, the load deflections recorded at both days 22 and 45 were greater than the corresponding baseline values for the % strain (Table). Also, in the % strain, the load deflection recorded at 45 days was significantly lower than the corresponding value at 22 days. Moreover, in the pairwise comparisons between the coil-spring groups, the load deflections showed statistically significant differences at each time point at both % and % strains, generally with the greatest and lowest values recorded in the Ni-Ti and Nitinol groups, respectively (all at least P\.5; Table). All load deflections recorded at the % strain were significantly greater than the corresponding values recorded at the % strain (Table). The curves of the deactivation forces of the coilspring groups are shown in Figure 2, in relation to time and strain. Generally, the Nitinol and RMO groups showed similar behaviors between the strains at each time point and among the time points in each strain. All data can be fitted to segmental linear regression, with R 2 always above.991 (Fig 2, A, B, E, and F). In contrast, the Ni-Ti coil-spring groups showed notably different
5 American Journal of Orthodontics and Dentofacial Orthopedics Vidoni et al 455 Volume 138, Number 4 behavior according to the strain, with the % and % strain subgroup data fitted to segmental linear regressions (Fig 2, C) and third-order functions (Fig 2, D), respectively (all with R 2 above.996). Moreover, in the same % strain subgroup, an evident change in loads was seen among the time points (Fig 2, D). Only the Nitinol group showed a superelasticity phase, which started from the maximum strain recorded (at % or %) to less than about 5% (about.5 mm of 12 mm) of residual extension, with only a modest decrease in the loads seen across the full range of deflection. In contrast, the other 2 coil-spring groups showed no superelasticity phase of activation under any experimental condition. With the % strain subgroup of the Ni-Ti coil spring (Fig 2, C) and the RMO coil springs in both strain subgroups (Fig 2, E and F), almost proportional phases of activation were seen. In the Ni-Ti coil springs, the % strain subgroup had mixed behavior, with a progressive decay in the deactivation forces from baseline to 45 days. DISCUSSION In this in-vitro comparative study, we investigated the aging effects of a combination of 2 levels of prolonged strains with thermocycling on the performance of Nitinol, Ni-Ti, and RMO coil springs; we analyzed the load values at % and % of strain over the initial lengths, and the deactivation forces, recorded at baseline and after 22 and 45 days of strain and thermal treatments. To better reproduce the oral environment, the coil springs were kept in artificial saliva throughout this study period, and thermocycling was performed twice, on days 22 and 45. Surprisingly, only the Nitinol group had an acceptable superelasticity phase, which was not significantly altered after the strain and thermocycling. Because dimensional variables can affect force levels produced by coil springs, 1-13 in our study, springs with the same wire and lumen diameters and the same lengths were included. As a consequence, the pitch angle of the coils of the 3 types of springs (although not reported by the manufacturers) can be considered similar. Nevertheless, the variability among the coil springs might still derive from the concept that the springs are subjected to their winding as an additional manufacturing procedure, 2 and that forces applied to springs also include torsional and tensional components, in addition to bending forces. For this reason, the load exerted by the NiTi coil springs would be expected to be less predictable that those from NiTi archwires, and results obtained from archwires cannot be fully extended to coil springs. Moreover, differences in the alloy compositions and the TTRs also influence the resultant forces. 5,21 Specifically, for the coil springs investigated here, no data concerning the exact alloy compositions were included in the accompanying information from the manufacturers. Information was also lacking concerning the forces to be expected from these springs; the manufacturer stated only for the Nitinol coil springs that this was gf. With the Ni-Ti coil springs, this was reported as medium force ; for the RMO coil springs, this was not mentioned at all. At the same time, only for the Nitinol coil springs was an indication of the maximaum extension given: up to about 3% (36 mm) of the initial length. With this in mind, the 2 strains of % and % over the initial lengths were included in this study to overcome this lack of information. No data on the curves of the deactivation forces, or on the TTRs of the alloys, were provided by any manufacturer. This reinforces a previous report that stressed the unsatisfactory levels of information supplied by manufacturers. 22 In spite of the similar dimensions of the NiTi-based coil springs, the actual forces exerted by these appeared to vary greatly across the manufacturers, as well as between the degrees of strain at the extensions of % and % of the initial lengths of these NiTi-based coil springs (see baseline values in the Table). In the literature, there are reports of both increases 8 and decreases 9 in forces delivered by NiTi coil springs after prolonged incubation at 37 C. However, although these previous studies used constant incubation temperatures, our investigation also used thermocycling of the coil springs to better reproduce the oral environment. Interestingly, no statistically significant effects were noted for either Nitinol coil-spring subgroups. In contrast, variations in the load at discrete deflections after the treatments were seen mainly in the % strain subgroups, with the Ni-Ti and RMO coil springs undergoing a slight decrease and a slight increase, respectively (Table). However, although statistically significant, these differences will probably not have clinical relevance, as was suggested previously. 7 Considering that the changes in the load values on thermocycling and strains in NiTibased coil springs are well known to be particularly low compared with those of stainless steel coils 7 and polyurethane elastics, 6,7 our data would thus favor the use of these NiTi-based devices. In addition to the loads exerted by the NiTi-based coil springs when extended to discrete lengths (% and % over the initial length), further useful information can be derived by an analysis of the corresponding curves of the deactivation forces. This is because, in clinical practice, NiTi-based coil springs exert forces during relaxation, as the teeth move. As a consequence, it is also important for NiTi-based orthodontic devices to have
6 456 Vidoni et al American Journal of Orthodontics and Dentofacial Orthopedics October 21 a superelasticity phase, which is necessary to deliver a constant force that is the most biologically compatible. 1,2 Despite this consideration, few previous studies have reported on load deflection modes 7,12,13,19 or investigated the linear ranges of deflection rates; 1 all other studies in the literature were limited to analyses of load values at discrete deflections. 6,8,9,14 Moreover, in the studies that included analysis of load deflection modes, 7,1,12,13,19 the discrimination between the linear and nonlinear (superelasticity) phases was not based on quantitative and objective methodologies. In this study, we investigated the superelasticity phases of these coil springs using a segmental linear regression model, the fitting of which with the actual data sets was tested according to the R 2 values. Only the Nitinol coil-spring group showed an acceptable superelasticity phase of activation from the maximum extensions (for both the % and % groups) to about 5% (about.5 mm) of residual extension (Fig 2, A and B). A similar superelasticity phase with a fairly constant load was reported for NiTi-alloy archwires. 21 On the contrary, the Ni-Ti and RMO coil-spring groups did not show a superelasticity phase of activation (Fig 2, C-F). These particularly variable behaviors among the coil springs investigated were potentially due to differences in their alloy compositions. In this regard, future studies are warranted to fully elucidate the role of alloy composition in determining the deactivation forces of orthodontic devices based on NiTi. At % strain, the Ni-Ti coil-spring group also failed to satisfactorily fit the segmental linear regression model, with a third-order polynomial curve better resembling the load behavior (Fig 2, D). Because this was the situation only when the springs were subjected to % strain (compare Fig 1, C and D), this strain was most likely beyond the optimal range of activation of these Ni-Ti coil springs. Thus, with the exception of this coil-spring subgroup, the effects produced by thermocycling and prolonged strain would probably be of minor clinical relevance in terms of the deactivation forces. This aspect is even less relevant if compared with the high variability seen in the loads exerted by the Ni-Ti and RMO coil-spring groups during relaxation (Fig 2, C and D). Whereas it is well known that NiTi-based orthodontic devices can deliver a continuous force during treatment, 23 in our study, only the Nitinol coil springs showed an acceptable constant load over a wide range of deactivations, up to an extension of % of the initial length. In contrast, the other coil springs in this study showed dramatically different load values depending on the length of activation, which would result in a suboptimal level of the control of the force delivered during treatment. Therefore, in these latter 2 cases, not only would the knowledge of the force delivered when the coil spring is put in place be imprecise, but also its delivery would decrease as the teeth move. From a clinical point of view, to achieve more efficient OTM, the force used should be not only continuous, but also not too great. 1 Therefore, to achieve such a predictable continuous force for optimal OTM, a NiTi-based coil spring with a superelasticity phase exerting light forces (\ gf) would potentially be best used in combination with a system characterized by differential friction 24 among the teeth that need to be anchored (high friction) or moved (low friction). These data suggest that, although NiTi-based closed-coil springs can be used in the oral cavity for prolonged periods of time with no significant alterations in their mechanical properties, the correct choice of NiTibased springs appears to be crucial for the optimization of OTM. Also, for this correct choice to be made possible, manufacturers should provide more information about their coil springs, with particular reference to their curves of deactivation forces. CONCLUSIONS This in-vitro study showed the following with these commercially available NiTi-based closed coil springs. 1. At both the % and % strains, the Ni-Ti coil springs exerted the highest loads. 2. Only the Nitinol coil springs showed the superelasticity phase. 3. Thermocycling did not appear to produce particular changes in the mechanical properties of any coil springs. 4. Only the RMO coil springs underwent clinically relevant changes in the deactivation forces with the % strain. We thank Christopher Paul Berrie for his critical appraisal of this manuscript. REFERENCES 1. Krishnan V, Davidovitch Z. Cellular, molecular, and tissue-level reactions to orthodontic force. Am J Orthod Dentofacial Orthop 6;129:469.e van Leeuwen EJ, Maltha JC, Kuijpers-Jagtman AM. Tooth movement with light continuous and discontinuous forces in beagle dogs. Eur J Oral Sci 1999;17: Ogura M, Kamimura H, Al-Kalaly A, Nagayama K, Taira K, Nagata J, et al. Pain intensity during the first 7 days following the application of light and heavy continuous forces. Eur J Orthod 9;31: Andreasen GF, Hilleman TB. An evaluation of 55 cobalt substituted Nitinol wire for use in orthodontics. J Am Dent Assoc 1971;82:
7 American Journal of Orthodontics and Dentofacial Orthopedics Vidoni et al 457 Volume 138, Number 4 5. Santoro M, Nicolay OF, Cangialosi TJ. Pseudoelasticity and thermoelasticity of nickel-titanium alloys: a clinically oriented review. Part I: temperature transitional ranges. Am J Orthod Dentofacial Orthop 1;119: Santos AC, Tortamano A, Naccarato SR, Dominguez- Rodriguez GC, Vigorito JW. An in vitro comparison of the force decay generated by different commercially available elastomeric chains and NiTi closed coil springs. Braz Oral Res 7;21: Han S, Quick DC. Nickel-titanium spring properties in a simulated oral environment. Angle Orthod 1993;63: Nattrass C, Ireland AJ, Sherriff M. The effect of environmental factors on elastomeric chain and nickel titanium coil springs. Eur J Orthod 1998;2: Angolkar PV, Arnold JV, Nanda RS, Duncanson MG Jr. Force degradation of closed coil springs: an in vitro evaluation. Am J Orthod Dentofacial Orthop 1992;12: Boshart BF, Currier GF, Nanda RS, Duncanson MG Jr. Loaddeflection rate measurements of activated open and closed coil springs. Angle Orthod 199;6: Chaconas SJ, Caputo AA, Harvey K. Orthodontic force characteristics of open coil springs. Am J Orthod 1984;85: Miura F, Mogi M, Ohura Y, Karibe M. The super-elastic Japanese NiTi alloy wire for use in orthodontics. Part III. Studies on the Japanese NiTi alloy coil springs. Am J Orthod Dentofacial Orthop 1988;94: Manhartsberger C, Seidenbusch W. Force delivery of Ni-Ti coil springs. Am J Orthod Dentofacial Orthop 1996;19: Barwart O. The effect of temperature change on the load value of Japanese NiTi coil springs in the superelastic range. Am J Orthod Dentofacial Orthop 1996;11: Tripolt H, Burstone CJ, Bantleon P, Manschiebel W. Force characteristics of nickel-titanium tension coil springs. Am J Orthod Dentofacial Orthop 1999;115: Schneevoigt R, Haase A, Eckardt VL, Harzer W, Bourauel C. Laboratory analysis of superelastic NiTi compression springs. Med Eng Phys 1999;21: Johansson BI, Lucas LC, Lemons JE. Corrosion of copper, nickel, and gold dental casting alloys: an in vitro and in vivo study. J Biomed Mater Res 1989;23: De Munck J, Van Landuyt K, Coutinho E, Poitevin A, Peumans M, Lambrechts P, et al. Micro-tensile bond strength of adhesives bonded to Class-I cavity-bottom dentin after thermocycling. Dent Mater 5;21: von Fraunhofer JA, Bonds PW, Johnson BE. Force generation by orthodontic coil springs. Angle Orthod 1993;63: Lopez I, Goldberg J, Burstone CJ. Bending characteristics of nitinol wire. Am J Orthod 1979;: Santoro M, Nicolay OF, Cangialosi TJ. Pseudoelasticity and thermoelasticity of nickel-titanium alloys: a clinically oriented review. Part II: deactivation forces. Am J Orthod Dentofacial Orthop 1;119: Melsen B, Topp LF, Melsen HM, Terp S. Force system developed from closed coil springs. Eur J Orthod 1994;16: Kapila S, Sachdeva R. Mechanical properties and clinical applications of orthodontic wires. Am J Orthod Dentofacial Orthop 1989; 96: Perinetti G. The friction concept must acknowledge the biology of tooth movement. Am J Orthod Dentofacial Orthop 8;134:
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