journal of the mechanical behavior of biomedical materials 46 (2015) 285–291
Available online at www.sciencedirect.com
www.elsevier.com/locate/jmbbm
Short Communication
Predicting composition–property relationships for glass ionomer cements: A multifactor central composite approach to material optimization Lauren Kiria, Daniel Boyda,b,n a b
Department of Applied Oral Sciences, Dalhousie University, 5981 University Avenue, Halifax, NS, Canada B3H 4R2 School of Biomedical Engineering, Dalhousie University, 5981 University Avenue, Halifax, NS, Canada B3H 4R2
art i cle i nfo
ab st rac t
Article history:
Adjusting powder–liquid ratio (P/L) and polyacrylic acid concentration (AC) has been documen-
Received 2 December 2014
ted as a means of tailoring the handling and mechanical properties of glass ionomer cements
Received in revised form
(GICs). This work implemented a novel approach in which the interactive effects of these two
6 February 2015
factors on three key GIC properties (working time, setting time, and compressive strength) were
Accepted 9 February 2015
investigated using a central composite design of experiments. Using nonlinear regression
Available online 19 February 2015
analysis, formulation–property relationships were derived for each property, which enabled
Keywords:
prediction of an optimal formulation (P/L and AC) through application of the desirability
Glass ionomer cement
approach. A novel aluminum free GIC was investigated, as this material may present the first
Bone cement
clinically viable GIC for use in injectable spinal applications, such as vertebroplasty. Ultimately,
Vertebroplasty
this study presents the first series of predictive regression models that explain the formulation-
Central composite designs
dependence of a GIC, and the first statistical method for optimizing both P/L and AC depending
Optimization
on user-defined inputs.
1.
Introduction
& 2015 Elsevier Ltd. All rights reserved.
systems comprising a basic glass powder and an aqueous solution of a polyalkenoic acid, usually polyacrylic acid (PAA).
Glass ionomer cements (GICs) are frequently deployed as luting,
Variation in the proportion of either component, as well as the
sealing and restorative materials in dental applications.
concentration of PAA have been shown to significantly affect
Recently, and arising directly (and in part), from their ability
the handling and mechanical properties of these materials.
to chemically bond to hydroxyapatite, GICs have been consid-
Consequently, adjusting these factors has been documented as
ered as a useful platform for the development of new materials
a means of tailoring GIC properties to accomplish a variety of
for orthopedic applications. With respect to the latter, alumi-
clinical objectives depending on the particular indication
num free GICs have been the focus of much attention (Dickey
(Fleming et al., 2003; Crisp et al., 1976, 1977). Through modifying the powder–liquid ratio (P/L) of traditional GICs, high viscosity/condensable GICs have been
et al., 2013; Boyd et al., 2008; Wren et al., 2010, 2012; Clarkin et al., 2010). GICs are generally supplied as two-component
n Corresponding author at: School of Biomedical Engineering, Dalhousie University, 5981 University Avenue, Halifax, NS, Canada B3H 4R2. Tel.: þ1 902 494 1686. E-mail addresses: [email protected] (L. Kiri), [email protected] (D. Boyd).
http://dx.doi.org/10.1016/j.jmbbm.2015.02.007 1751-6161/& 2015 Elsevier Ltd. All rights reserved.
286
journal of the mechanical behavior of biomedical materials 46 (2015) 285 –291
developed for atraumatic restorative treatment (ART) (Bonifácio et al., 2009). Increasing the proportion of reinforcing glass particles throughout the GIC matrix results in increased strength, making high-P/L GICs suitable restoratives, capable of resisting occlusal forces (Bonifácio et al., 2009). Unfortunately, such modifications enhance setting reactivity, increasing the speed of the neutralization reaction and compromising the handling of these materials (Bonifácio et al., 2009; Zahra et al., 2011). In fact, Billington et al. (1990) found that, in clinical practice, GIC restoratives are frequently mixed at P/Ls lower that those recommended by manufacturers to reduce viscosity in order to obtain a consistency that facilitates easier placement. Such modifications were found to result in a tradeoff with mechanical properties, highlighting the importance of establishing and utilizing a P/L that provides an optimal balance in properties for the intended application (Crisp et al., 1976; Billington et al., 1990; Zahra et al., 2011). Adjusting the PAA-to-water ratio of the aqueous acid component of GICs has also been investigated as a tailorability approach (Crisp et al., 1977; Boyd and Towler, 2005). The effects of acid concentration (AC) on GIC properties are complex, as both high and low ACs may suppress the setting process (Lohbauer, 2010). In the literature, higher ACs generally correlate with increased setting speed and strength, which are thought to result from increases in the reactivity of the neutralization reaction, a higher degree of matrix entanglement, or a combination (Boyd and Towler, 2005). However, high ACs are synonymous with low water contents, which may result in insufficient hydration to facilitate the reaction or inadequate metal cations for completion of the neutralization process (Lohbauer, 2010). Although manipulation of P/L and AC are heavily considered in the literature, an efficient and effective means of establishing optimal cement formulation (P/L–AC combination) has not been discussed. At present, investigations involving the effects of P/L and AC on GIC performance have been limited to one-variableat-a-time analyses (Clarkin et al., 2010; Crisp et al., 1976). Little is understood about the combined or interactive effects of these two factors, making derivation of an optimal formulation (i.e. a P/L–AC combination that provides the most desired balance in properties for an intended application) very challenging. This study aims to address the issue. Through implementing a central composite design of experiments (DOE) approach, P/L and AC may be adjusted concurrently, enabling optimization based on the responses of three critical material properties: working time (tw), setting time (ts), and compressive strength (CS) (Dickey et al., 2013). A novel aluminum free GIC formulation (DG209) was investigated, as this material is the first to provide sufficient tw (5–10 min) and CS (430 MPa) for injectable applications in the skeleton (e.g. vertebroplasty and kyphoplasty) (Dickey et al., 2013). Ultimately, this study provides the first set of predictive regression models that (1) describe the formulationdependence of GIC properties, and (2) enable optimization of P/L and AC based on user-defined property constraints.
2.
Materials and methods
2.1.
Glass synthesis
DG209 glass (composition: 0.36ZnO, 0.04SrO, 0.215SiO2, 0.215GeO2, 0.025ZnO2, 0.025Na2O, 0.12CaO) was synthesized using the rapid
quench method as detailed by Dickey et al. (2013). Briefly, appropriate amounts of each analytical grade reagent (Sigma-Aldrich Co., Oakville, Canada) were weighed out and mixed for 1 h in a mechanical mixer. The mixed powder was then packed into a 50 ml platinum crucible (Alfa Aesar, Ward Hill, USA), which was fired (1500710 1C, 1 h) in a high temperature furnace (Carbolite RHF 1600, Hope, UK), and then quenched into deionized water at room temperature. The resulting frit was dried overnight in a vacuum oven (100 1C), and then ground using a planetary ball mill (Pulversette 7, Fritsch, Germany) and sieved to yield a powder of o45 μm particle size. Glass powder was then annealed at 30 1C less than its glass transition temperature for 3 h and left to furnace cool.
2.2.
Glass transition temperature
Glass powder was analyzed using a differential scanning calorimeter (n¼ 3; Netzsch, STA 409 PC, Burlington, USA) to determine its glass transition temperature (Tg). Approximately thirty milligrams of glass powder was placed into stainless steel closed pans, while the reference pan was left empty. The samples were heated at 10 1C/min to a maximum temperature of 1000 1C. Netzsch Proteus Thermal Analysis software (5.2.0, Netzsch, Burlington, USA) was used to determine the Tg (point of inflection).
2.3.
Experimental design
A central composite DOE (Design Expert 8.0.4, Stat-Ease Inc.) was developed relating the effects of (a) P/L and (b) AC on tw, ts, and CS. A first-order design was augmented to a second-order design through the addition for face-centered star points, allowing for the approximation of curvature and thus utilization of response surface methods (Anderson and Whitcomb, 2005). The resulting design comprised 13 experimental runs representing different P/L–AC combinations, as outlined in Table 1. These discrete GIC formulations, herein referred to as design points, were determined based on previously established constraints for each factor (P/L between 1.0/1.0 and 2.0/1.0 w/w, and AC ranging 40–60 wt%) with four experimental runs set at the extreme vertices, four experiments at the axial-check points, and five replicates of the centroid (to test for lack of fit).
Table 1 – Summary of design points: P/L and AC. Design point
P/L
AC (wt%)
1 2 3 4 5 6 7 8 9 10 11 12 13
2.0/1.0 1.0/1.0 1.5/1.0 1.5/1.0 1.5/1.0 2.0/1.0 1.0/1.0 1.0/1.0 1.5/1.0 2.0/1.0 1.5/1.0 1.5/1.0 1.5/1.0
60 40 50 50 60 40 60 50 40 50 50 50 50
journal of the mechanical behavior of biomedical materials 46 (2015) 285 –291
2.4.
Cement preparation
For each design point, GICs were prepared through mixing synthesized glass powder and aqueous PAA, Mw ¼12,700 g/mol (Advanced Healthcare, Tonbridge, UK) on dental mixing pads with a dental spatula.
2.5.
Determination of working time and setting time
Both tw and ts were measured based on procedures defined in the literature (Dickey et al., 2013). The tw was measured in ambient air using a stopwatch, and was defined as the period of time from the start of mixing during which it was possible to manipulate the material without adversely affecting its properties. The ts was measured in a 37 1C room by filling an aluminum mold (10 mm 8 mm 5 mm) to excess, which was placed on an aluminum plate (75 mm 100 mm 8 mm) covered in aluminum foil. Sixty seconds prior to the cement's tw, a Gilmore needle (mass¼453 g, flat tip diameter¼ 1.1 mm) was placed onto the surface of the material. This process was repeated intermittently until the indenter tip failed to make a full circular impression in the cement when held for 5 s and viewed at 2 magnification. For each design point, both tw and ts measurements were preformed in triplicate.
2.6.
Determination of compressive strength
Compressive strength was also measured based on procedures outlined in the literature (Dickey et al., 2013). Stainless steel split ring molds (diameter¼ 4 mm, height¼ 6 mm) were filled to excess with cement, covered in acetate, clamped between two stainless steel plates, and incubated (37 1C, 1 h). After 1 h, the molds were dissembled, cement flash was removed, and the ends of the samples were ground flat using wet 800 grit silicon carbide paper. Cement samples were incubated in distilled water at 37 1C for 24 h under static conditions. The samples were removed from the incubation environment and immediately loaded using an Instron 3344 mechanical testing device (Instron, Norwood, USA; 2 kN load cell, 1 mm/min crosshead speed). Five samples for each design point were tested.
2.7.
Generation of models, optimization, and validation
The resulting tw, ts, and CS data were modeled using Scheffé multiple comparison equations and backward regression analysis to automatically determine significant model coefficients. The reduced polynomials were further analyzed by ANOVA and readjusted to show significant model terms. The desirability function approach was implemented to determine where the design space was optimal for a particular set of user-defined targets (design criteria). These design criteria were selected based on what has been defined as clinically desired for an injectable bone cement: between 5 and 10 min of tw, minimal ts, and a minimum of 30 MPa of CS (Heini and Berlemann, 2001). Using the model-predicted P/L and AC, DG209 was prepared as per Section 2.4 and tw, ts, and CS were measured as per Sections 2.5 and 2.6. The experimental measurements were compared to the model predictions to
287
assess the predictive power of the models and validate the properties of the derived optimal formulation.
2.8.
Statistical analysis
One-way analysis of variance (ANOVA) was used to compare tw, ts, and CS (Prism 6, GraphPad Software Inc., La Jolla, USA). The mean values of each measure were compared using the Tukey pots-hoc test, considering po0.05 as significant.
3.
Results
The design space examined in this study results from the controlled variation of two cement components (P/L and AC), which enabled derivation of formulation–property relationships for a novel aluminum free GIC (DG209) such that the mixing ratios could be optimized for injectable spinal applications (Dickey et al., 2013). Table 2 outlines the general trends in tw, ts, and CS with regards to increasing P/L and AC, representing the range and magnitude of the measured properties across the design space. The wide ranges in tw, ts, and CS observed confirm the properties of DG209 may be tailored like conventional materials through altering P/L and AC. Using the backward regression method, significant model coefficients were automatically derived for each response. A second-order polynomial equation was fitted for the tw data; a power transformation (lambda¼0.75) was applied to the ts response, which then enabled second-order fitting; and a third-order polynomial equation was used to model the resulting CSs. Graphical representations of these models are provided in Fig. 1. The regression outputs and associated ANOVA for each model are provided in Table 3. All regression models and corresponding ANOVA showed high model adequacies and statistical significance since (i) the R2 adjusted and R2 predicted are within 0.20 of one another, (ii) the Prob4F values are less
Table 2 – General trends in tw, ts, and CS in response to increased P/L and increased AC. Factor adjustment
Material response
↑P/L
↓tw
↓ts
↑CSa ↑AC
↓tw
↑ts
↑CS
a
540–120 s, AC ¼ 40 wt% 450–120 s, AC ¼ 50 wt% 640–100 s, AC ¼ 60 wt% 700–140 s, AC ¼ 40 wt% 1940–310 s, AC ¼ 50 wt% 5220–720 s, AC ¼ 60 wt% 24–54 MPa, AC ¼50 wt% 28–53 MPa, AC ¼60 wt% 540–370 s, P/L¼ 1.0/1.0 250–180 s, P/L¼ 1.5/1.0 120–100 s, P/L¼ 2.0/1.0 700–5220 s, P/L¼ 1.0/1.0 280–1440 s, P/L¼ 1.5/1.0 140–720 s, P/L¼ 2.0/1.0 21–28 MPa, P/L¼1.0/1.0 26–45 MPa, P/L¼1.5/1.0 21–53 MPa, P/L¼2.0/1.0
No change in CS with↑P/L for AC ¼ 40 wt% (21 MPa).
288
journal of the mechanical behavior of biomedical materials 46 (2015) 285 –291
Fig. 1 – Three-dimensional contour plots showing the effect of varying P/L and AC on (a) tw (s), (b) ts (s), and (c) CS (MPa). Red circles indicate data points above the model; pink circles represent data points below the model. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
289
journal of the mechanical behavior of biomedical materials 46 (2015) 285 –291
Table 3 – Final regression equations and summarized ANOVA (CV: coefficient of variance; AP: adequate precision). Response
Regression models
R2
R2 adjusted
R2 predicted
Prob4F
CV (%)
tw
tw ¼ 1964.36 1297.29P/L 15.55ACþ7.40P/ L ACþ194.76P/L2 1/√ts ¼0.066þ0.098P/L 0.0033AC 0.00125P/ L ACþ0.0000336AC2 CS¼ 577 470P/L22.49ACþ18.75P/ L ACþ0.216AC2 0.175P/L AC2
0.9931
0.9897
0.9797
o0.0001
5.14
52.794
0.9978
0.9968
0.9893
o0.0001
2.47
110.634
0.9639
0.9381
0.6617
o0.0001
7.83
17.524
ts CS
than 0.05, (iii) the coefficients of variation (CV) are less than 10%, and (iv) the adequate precision (AP) values are greater than 4 (Kehoe et al., 2013). Given the high adequacy of the resulting models, the desirability objective function was implemented to predict a formulation that would provide 5–10 min of tw, minimal ts, and maximal CS with 30 MPa set as the minimum. Each condition was assigned equal importance (þþþ). Fig. 2 provides an overlay plot depicting the design space that identifies the optimal formulations based on these design criteria. The highlighted space represents the ranges in P/L and AC that provide 5–10 min tw, minimal ts, and at least 30 MPa of CS. The following formulation was predicted as optimal: P/ L ¼1.2/1.0 and AC¼ 56% as shown (Fig. 2). Table 4 provides a tabulated comparison of the predicted and measured behaviors of the optimal material formulation. The measured ts and CS showed no significant difference in comparison to what was predicted (ANOVA); however, the measured tw deviated significantly from the model's prediction.
4.
Discussion
Varying the P/L and AC of GICs is heavily considered in the literature as a method of tailoring cement properties (Lohbauer, 2010). Previous investigations involving the effects of altering GIC formulation have been limited to one-variableat-a-time analyses, which has prevented consideration of the combined and interactive effects of these two factors on the complex balance between handling and strength (Crisp et al., 1976; Billington et al., 1990; Zahra et al., 2011). The predictive regression models developed in this study may address this shortcoming through mathematically relating the effects of both P/L and AC on tw, ts, and CS, thereby providing an efficient and effective means of determining an optimal GIC formulation depending on user-defined inputs. The GIC examined in this study comprises the first aluminum free GIC that may provide both adequate handling and mechanical properties for injectable spinal applications (vertebroplasty and kyphoplasty) (Dickey et al., 2013). It is well accepted that aluminum must be removed from conventional GICs to render these materials biocompatible with bone (Dickey et al., 2013). Previous attempts to design aluminum free GICs for such applications have been unsuccessful, resulting in cements with insufficient time for injection (ca. 1–2 min) or inadequate strength (o30 MPa) (Boyd et al., 2008; Wren et al., 2010, 2012; Clarkin et al., 2010). Boyd and Towler (2005) reported the effects of varied AC on a zinc-based aluminum free GIC, demonstrating it was possible to adjust tw, ts, CS, and flexural strength in this fashion,
AP
Fig. 2 – Overlay plot showing the region that satisfies the design criteria and the P/L and AC identified as optimal; working time and setting time in s, compressive strength in MPa. Table 4 – Comparison of model generated predictions and experimental measurements using P/L ¼1.2/1.0 and AC¼ 56% (model generated optimal formulation). Property
Predicted
Experimental
tw (min:s) ts (min:s) CS (MPa)
5:10 33:20 32
3:40 34:00 28.5
although tw remained less than 3:38 min:s. Dickey et al. (2013) published the first set of germanium-inclusive aluminum free GICs with significant improvements in the handling-strength balance. This was an exciting advancement in the aluminum free GIC literature, as this publication presented the first series of aluminum free GICs with extended tw, without loss of strength. It was the objective of this study to investigate the effects of P/L and AC on this novel GIC composition (DG209), and to determine, using a DOE approach, the P/L–AC combination that provides the optimal balance in tw, ts, and CS for injectable spinal applications. As outlined in Fig. 1 and Table 2, the general trends observed for the tw and CS of DG209 are consistent with what has been reported in one-variable-at-a-time investigations involving conventional GICs; increases in both P/L and AC decreased tw and increased CS (Fleming et al., 2003; Dowling and Fleming, 2011). In general, increased P/L and AC are hypothesized to increase the reactivity of the setting material, explaining the observed decrease in tw (Boyd et al., 2008; Fleming et al., 2003). With regards to strength, higher P/Ls and ACs generally correlate with increased CS, presumably by
290
journal of the mechanical behavior of biomedical materials 46 (2015) 285 –291
providing a higher concentration of reinforcing glass particles and through increasing the degree of matrix entanglement, respectively (Boyd et al., 2008; Fleming et al., 2003). Interestingly, the response modeled for ts deviated from the trends reported in the literature; increasing AC with constant P/L increased ts. This anomaly may result from the unique glass composition of DG209, which dictates the setting chemistry of the GIC, or from inadequate hydration to facilitate the neutralization reaction (Lohbauer, 2010). The resulting regression models and associated ANOVA showed high model adequacies for all three responses (Table 3). The CV was less than 10% for all responses, confirming reproducibility of the models, while the AP (range in the predicted responses in reference to the associated error) was satisfied for each model. With the exception of the R2 predicted value for CS, all R2 values exceeded 0.8, indicating significant regression models were realized. The relatively low R2 predicted value for the CS response may be indicative of an over-fit model. Ideally, response models should be as simple as possible, as complex models run risk of modeling insignificant variability (i.e. noise). Restricting the design space such that the CS response may be modeled as quadratic or eliminating outliers may improve the overall predictability (Anderson and Whitcomb, 2005). To identify the optimal formulation based on the requirements of a vertebroplasty cement (5–10 min tw, minimal ts, and 430 MPa CS), implementation of the desirability approach identified P/L¼1.2/1.0 and AC¼56 wt% as optimal (Fig. 2). When derived experimentally, the identified optimal formulation produced a cement with significantly lower tw (Table 4). This incongruity may result from the relatively low predictive power of the CS response (low R2 predicted ) or it may be an issue of robustness in the procedures used for data acquisition. Although the ISO procedures for dental materials are used extensively to approximate the clinical performance of acidbase cements, these standards have been subject of major criticism; mixing technique, environmental conditions, operator experience, and intra-operator factors (such as user fatigue) have all been identified as possible causes of variability (Fleming et al., 2012). Small changes in the inputted variables may result in big changes in the modeled responses, which may have significantly compromised the predictive power of the models. When looking at the overall design space (Fig. 1), it is apparent the centroid design point (P/L¼ 1.5/1.0 and AC¼50 wt%) yielded a significantly lower ts (10:40 min:s) and higher CS (39 MPa). However, the tw produced by this formulation (4:10 min:s) remained short of what is required for injectable skeletal applications (5–10 min). It appears that forcing the models to provide between 5–10 min of tw (i.e. increasing the importance of this property in the desirability function) significantly compromises ts and CS, highlighting the tradeoff in GIC properties. Small changes in the relative proportions of glass powder, PAA (dried), and water can significantly affect the balance in handling and strength. It is therefore crucial to understand the effects of altering cement formulation. The authors suggest the optimization approach presented in this study may be suitable for establishing appropriate P/L–AC combinations for other GICs, such that the materials may be tailored, in a predictable, controlled fashion, to meet the demands of a particular indication.
5.
Conclusion
This study presents the first set of regression models that may be used for predicting the formulation-dependence of tw, ts, and CS for a novel aluminum free GIC, DG209. The results presented confirm the tailorability of DG209 and demonstrate, for the first time, how DOE may be used to consider the combined effects of P/L and AC on GIC properties. The central composite design developed in this study may be an efficient and effective means for optimizing the properties of GICs through simple manipulations of P/L and AC.
Acknowledgments The authors would like to acknowledge the financial assistance of the Atlantic Canada Opportunities Agency (AIF Award 197820), and the Natural Sciences and Engineering Research Council of Canada (NSERC, 386022-2010) Discovery Program.
r e f e r e n c e s
Anderson, M., Whitcomb, P., 2005. RSM Simplified. CRC Press, Taylor and Francis Group, FL, USA. Billington, R., Williams, J., Pearson, G., 1990. Variation in powder/ liquid ratio of a restorative glass-ionomer cement used in dental practice. Br. Dent. J. 169 (6), 164–167. Bonifa´cio, C.C., Kleverlaan, C.J., Raggio, D.P., Werner, A., de Carvalho, R.C.R., van Amerongen, W.E., 2009. Physical– mechanical properties of glass ionomer cements indicated for atraumatic restorative treatment. Aust. Dent. J. 54 (3), 233–237, http://dx.doi.org/10.1111/j.1834-7819.2009.01125.x. Boyd, D., Towler, M., 2005. The processing, mechanical properties and bioactivity of zinc based glass ionomer cements. J. Mater. Sci. Mater. Med. 16 (9), 843–850. Boyd, D., Clarkin, O., Wren, A., Towler, M., 2008. Zinc-based glass polyalkenoate cements with improved setting times and mechanical properties. Acta Biomater. 4 (2), 425–431. Clarkin, O., Boyd, D., Towler, M., 2010. Strontium-based glass polyalkenoate cements for luting applications in the skeleton. J. Biomater. Appl. 24 (6), 483–502. Crisp, S., Lewis, B.G., Wilson, A.D., 1976. Characterization of glassionomer cements. 2. Effect of the powder: liquid ratio on the physical properties. J. Dent. 4 (6), 287–290, http://dx.doi.org/ 10.1016/S0300-5712(76)80008-5. Crisp, S., Lewis, B.G., Wilson, A.D., 1977. Characterization of glassionomer cements. 3. Effect of polyacid concentration on the physical properties. J. Dent. 5 (1), 51–56, http://dx.doi.org/10.1016/ S0300-5712(77)80025-0. Dickey, B., Kehoe, S., Boyd, D., 2013. Novel adaptations to zinc-silicate glass polyalkenoate cements: the unexpected influences of germanium based glasses on handling characteristics and mechanical properties. J. Mech. Behav. Biomed. Mater. 23, 8–21. Dowling, A., Fleming, G., 2011. The influence of poly(acrylic) acid number average molecular weight and concentration in solution on the compressive fracture strength and modulus of a glass-ionomer restorative. Dent. Mater. 27 (6), 535–543. Fleming, G., Farooq, A., Barralet, J., 2003. Influence of powder/ liquid mixing ratio on the performance of a restorative glassionomer dental cement. Biomaterials 24 (23), 4173–4179.
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Fleming, G., Dowling, A., Addison, O., 2012. The crushing truth about glass ionomer restoratives: exposing the standard of the standard. J. Dent. 40 (3), 181–188. Heini, P., Berlemann, U., 2001. Bone substitutes in vertebroplasty. Eur. Spine J. 10 (2), S205–S213. Kehoe, S., Langman, M., Werner Zwanziger, U., Abraham, R., Boyd, D., 2013. Mixture designs to assess composition–structure–property relationships in SiO2–CaO–ZnO–La2O3–TiO2–MgO–SrO–Na2O glasses: potential materials for embolization. J. Biomater. Appl. 28 (3), 416–433. Lohbauer, U., 2010. Dental glass ionomer cements as permanent filling materials? Properties, limitations and future trends. Materials 3, 76–96.
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Available online at www.sciencedirect.com
www.elsevier.com/locate/jmbbm
Short Communication
Predicting composition–property relationships for glass ionomer cements: A multifactor central composite approach to material optimization Lauren Kiria, Daniel Boyda,b,n a b
Department of Applied Oral Sciences, Dalhousie University, 5981 University Avenue, Halifax, NS, Canada B3H 4R2 School of Biomedical Engineering, Dalhousie University, 5981 University Avenue, Halifax, NS, Canada B3H 4R2
art i cle i nfo
ab st rac t
Article history:
Adjusting powder–liquid ratio (P/L) and polyacrylic acid concentration (AC) has been documen-
Received 2 December 2014
ted as a means of tailoring the handling and mechanical properties of glass ionomer cements
Received in revised form
(GICs). This work implemented a novel approach in which the interactive effects of these two
6 February 2015
factors on three key GIC properties (working time, setting time, and compressive strength) were
Accepted 9 February 2015
investigated using a central composite design of experiments. Using nonlinear regression
Available online 19 February 2015
analysis, formulation–property relationships were derived for each property, which enabled
Keywords:
prediction of an optimal formulation (P/L and AC) through application of the desirability
Glass ionomer cement
approach. A novel aluminum free GIC was investigated, as this material may present the first
Bone cement
clinically viable GIC for use in injectable spinal applications, such as vertebroplasty. Ultimately,
Vertebroplasty
this study presents the first series of predictive regression models that explain the formulation-
Central composite designs
dependence of a GIC, and the first statistical method for optimizing both P/L and AC depending
Optimization
on user-defined inputs.
1.
Introduction
& 2015 Elsevier Ltd. All rights reserved.
systems comprising a basic glass powder and an aqueous solution of a polyalkenoic acid, usually polyacrylic acid (PAA).
Glass ionomer cements (GICs) are frequently deployed as luting,
Variation in the proportion of either component, as well as the
sealing and restorative materials in dental applications.
concentration of PAA have been shown to significantly affect
Recently, and arising directly (and in part), from their ability
the handling and mechanical properties of these materials.
to chemically bond to hydroxyapatite, GICs have been consid-
Consequently, adjusting these factors has been documented as
ered as a useful platform for the development of new materials
a means of tailoring GIC properties to accomplish a variety of
for orthopedic applications. With respect to the latter, alumi-
clinical objectives depending on the particular indication
num free GICs have been the focus of much attention (Dickey
(Fleming et al., 2003; Crisp et al., 1976, 1977). Through modifying the powder–liquid ratio (P/L) of traditional GICs, high viscosity/condensable GICs have been
et al., 2013; Boyd et al., 2008; Wren et al., 2010, 2012; Clarkin et al., 2010). GICs are generally supplied as two-component
n Corresponding author at: School of Biomedical Engineering, Dalhousie University, 5981 University Avenue, Halifax, NS, Canada B3H 4R2. Tel.: þ1 902 494 1686. E-mail addresses: [email protected] (L. Kiri), [email protected] (D. Boyd).
http://dx.doi.org/10.1016/j.jmbbm.2015.02.007 1751-6161/& 2015 Elsevier Ltd. All rights reserved.
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journal of the mechanical behavior of biomedical materials 46 (2015) 285 –291
developed for atraumatic restorative treatment (ART) (Bonifácio et al., 2009). Increasing the proportion of reinforcing glass particles throughout the GIC matrix results in increased strength, making high-P/L GICs suitable restoratives, capable of resisting occlusal forces (Bonifácio et al., 2009). Unfortunately, such modifications enhance setting reactivity, increasing the speed of the neutralization reaction and compromising the handling of these materials (Bonifácio et al., 2009; Zahra et al., 2011). In fact, Billington et al. (1990) found that, in clinical practice, GIC restoratives are frequently mixed at P/Ls lower that those recommended by manufacturers to reduce viscosity in order to obtain a consistency that facilitates easier placement. Such modifications were found to result in a tradeoff with mechanical properties, highlighting the importance of establishing and utilizing a P/L that provides an optimal balance in properties for the intended application (Crisp et al., 1976; Billington et al., 1990; Zahra et al., 2011). Adjusting the PAA-to-water ratio of the aqueous acid component of GICs has also been investigated as a tailorability approach (Crisp et al., 1977; Boyd and Towler, 2005). The effects of acid concentration (AC) on GIC properties are complex, as both high and low ACs may suppress the setting process (Lohbauer, 2010). In the literature, higher ACs generally correlate with increased setting speed and strength, which are thought to result from increases in the reactivity of the neutralization reaction, a higher degree of matrix entanglement, or a combination (Boyd and Towler, 2005). However, high ACs are synonymous with low water contents, which may result in insufficient hydration to facilitate the reaction or inadequate metal cations for completion of the neutralization process (Lohbauer, 2010). Although manipulation of P/L and AC are heavily considered in the literature, an efficient and effective means of establishing optimal cement formulation (P/L–AC combination) has not been discussed. At present, investigations involving the effects of P/L and AC on GIC performance have been limited to one-variableat-a-time analyses (Clarkin et al., 2010; Crisp et al., 1976). Little is understood about the combined or interactive effects of these two factors, making derivation of an optimal formulation (i.e. a P/L–AC combination that provides the most desired balance in properties for an intended application) very challenging. This study aims to address the issue. Through implementing a central composite design of experiments (DOE) approach, P/L and AC may be adjusted concurrently, enabling optimization based on the responses of three critical material properties: working time (tw), setting time (ts), and compressive strength (CS) (Dickey et al., 2013). A novel aluminum free GIC formulation (DG209) was investigated, as this material is the first to provide sufficient tw (5–10 min) and CS (430 MPa) for injectable applications in the skeleton (e.g. vertebroplasty and kyphoplasty) (Dickey et al., 2013). Ultimately, this study provides the first set of predictive regression models that (1) describe the formulationdependence of GIC properties, and (2) enable optimization of P/L and AC based on user-defined property constraints.
2.
Materials and methods
2.1.
Glass synthesis
DG209 glass (composition: 0.36ZnO, 0.04SrO, 0.215SiO2, 0.215GeO2, 0.025ZnO2, 0.025Na2O, 0.12CaO) was synthesized using the rapid
quench method as detailed by Dickey et al. (2013). Briefly, appropriate amounts of each analytical grade reagent (Sigma-Aldrich Co., Oakville, Canada) were weighed out and mixed for 1 h in a mechanical mixer. The mixed powder was then packed into a 50 ml platinum crucible (Alfa Aesar, Ward Hill, USA), which was fired (1500710 1C, 1 h) in a high temperature furnace (Carbolite RHF 1600, Hope, UK), and then quenched into deionized water at room temperature. The resulting frit was dried overnight in a vacuum oven (100 1C), and then ground using a planetary ball mill (Pulversette 7, Fritsch, Germany) and sieved to yield a powder of o45 μm particle size. Glass powder was then annealed at 30 1C less than its glass transition temperature for 3 h and left to furnace cool.
2.2.
Glass transition temperature
Glass powder was analyzed using a differential scanning calorimeter (n¼ 3; Netzsch, STA 409 PC, Burlington, USA) to determine its glass transition temperature (Tg). Approximately thirty milligrams of glass powder was placed into stainless steel closed pans, while the reference pan was left empty. The samples were heated at 10 1C/min to a maximum temperature of 1000 1C. Netzsch Proteus Thermal Analysis software (5.2.0, Netzsch, Burlington, USA) was used to determine the Tg (point of inflection).
2.3.
Experimental design
A central composite DOE (Design Expert 8.0.4, Stat-Ease Inc.) was developed relating the effects of (a) P/L and (b) AC on tw, ts, and CS. A first-order design was augmented to a second-order design through the addition for face-centered star points, allowing for the approximation of curvature and thus utilization of response surface methods (Anderson and Whitcomb, 2005). The resulting design comprised 13 experimental runs representing different P/L–AC combinations, as outlined in Table 1. These discrete GIC formulations, herein referred to as design points, were determined based on previously established constraints for each factor (P/L between 1.0/1.0 and 2.0/1.0 w/w, and AC ranging 40–60 wt%) with four experimental runs set at the extreme vertices, four experiments at the axial-check points, and five replicates of the centroid (to test for lack of fit).
Table 1 – Summary of design points: P/L and AC. Design point
P/L
AC (wt%)
1 2 3 4 5 6 7 8 9 10 11 12 13
2.0/1.0 1.0/1.0 1.5/1.0 1.5/1.0 1.5/1.0 2.0/1.0 1.0/1.0 1.0/1.0 1.5/1.0 2.0/1.0 1.5/1.0 1.5/1.0 1.5/1.0
60 40 50 50 60 40 60 50 40 50 50 50 50
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2.4.
Cement preparation
For each design point, GICs were prepared through mixing synthesized glass powder and aqueous PAA, Mw ¼12,700 g/mol (Advanced Healthcare, Tonbridge, UK) on dental mixing pads with a dental spatula.
2.5.
Determination of working time and setting time
Both tw and ts were measured based on procedures defined in the literature (Dickey et al., 2013). The tw was measured in ambient air using a stopwatch, and was defined as the period of time from the start of mixing during which it was possible to manipulate the material without adversely affecting its properties. The ts was measured in a 37 1C room by filling an aluminum mold (10 mm 8 mm 5 mm) to excess, which was placed on an aluminum plate (75 mm 100 mm 8 mm) covered in aluminum foil. Sixty seconds prior to the cement's tw, a Gilmore needle (mass¼453 g, flat tip diameter¼ 1.1 mm) was placed onto the surface of the material. This process was repeated intermittently until the indenter tip failed to make a full circular impression in the cement when held for 5 s and viewed at 2 magnification. For each design point, both tw and ts measurements were preformed in triplicate.
2.6.
Determination of compressive strength
Compressive strength was also measured based on procedures outlined in the literature (Dickey et al., 2013). Stainless steel split ring molds (diameter¼ 4 mm, height¼ 6 mm) were filled to excess with cement, covered in acetate, clamped between two stainless steel plates, and incubated (37 1C, 1 h). After 1 h, the molds were dissembled, cement flash was removed, and the ends of the samples were ground flat using wet 800 grit silicon carbide paper. Cement samples were incubated in distilled water at 37 1C for 24 h under static conditions. The samples were removed from the incubation environment and immediately loaded using an Instron 3344 mechanical testing device (Instron, Norwood, USA; 2 kN load cell, 1 mm/min crosshead speed). Five samples for each design point were tested.
2.7.
Generation of models, optimization, and validation
The resulting tw, ts, and CS data were modeled using Scheffé multiple comparison equations and backward regression analysis to automatically determine significant model coefficients. The reduced polynomials were further analyzed by ANOVA and readjusted to show significant model terms. The desirability function approach was implemented to determine where the design space was optimal for a particular set of user-defined targets (design criteria). These design criteria were selected based on what has been defined as clinically desired for an injectable bone cement: between 5 and 10 min of tw, minimal ts, and a minimum of 30 MPa of CS (Heini and Berlemann, 2001). Using the model-predicted P/L and AC, DG209 was prepared as per Section 2.4 and tw, ts, and CS were measured as per Sections 2.5 and 2.6. The experimental measurements were compared to the model predictions to
287
assess the predictive power of the models and validate the properties of the derived optimal formulation.
2.8.
Statistical analysis
One-way analysis of variance (ANOVA) was used to compare tw, ts, and CS (Prism 6, GraphPad Software Inc., La Jolla, USA). The mean values of each measure were compared using the Tukey pots-hoc test, considering po0.05 as significant.
3.
Results
The design space examined in this study results from the controlled variation of two cement components (P/L and AC), which enabled derivation of formulation–property relationships for a novel aluminum free GIC (DG209) such that the mixing ratios could be optimized for injectable spinal applications (Dickey et al., 2013). Table 2 outlines the general trends in tw, ts, and CS with regards to increasing P/L and AC, representing the range and magnitude of the measured properties across the design space. The wide ranges in tw, ts, and CS observed confirm the properties of DG209 may be tailored like conventional materials through altering P/L and AC. Using the backward regression method, significant model coefficients were automatically derived for each response. A second-order polynomial equation was fitted for the tw data; a power transformation (lambda¼0.75) was applied to the ts response, which then enabled second-order fitting; and a third-order polynomial equation was used to model the resulting CSs. Graphical representations of these models are provided in Fig. 1. The regression outputs and associated ANOVA for each model are provided in Table 3. All regression models and corresponding ANOVA showed high model adequacies and statistical significance since (i) the R2 adjusted and R2 predicted are within 0.20 of one another, (ii) the Prob4F values are less
Table 2 – General trends in tw, ts, and CS in response to increased P/L and increased AC. Factor adjustment
Material response
↑P/L
↓tw
↓ts
↑CSa ↑AC
↓tw
↑ts
↑CS
a
540–120 s, AC ¼ 40 wt% 450–120 s, AC ¼ 50 wt% 640–100 s, AC ¼ 60 wt% 700–140 s, AC ¼ 40 wt% 1940–310 s, AC ¼ 50 wt% 5220–720 s, AC ¼ 60 wt% 24–54 MPa, AC ¼50 wt% 28–53 MPa, AC ¼60 wt% 540–370 s, P/L¼ 1.0/1.0 250–180 s, P/L¼ 1.5/1.0 120–100 s, P/L¼ 2.0/1.0 700–5220 s, P/L¼ 1.0/1.0 280–1440 s, P/L¼ 1.5/1.0 140–720 s, P/L¼ 2.0/1.0 21–28 MPa, P/L¼1.0/1.0 26–45 MPa, P/L¼1.5/1.0 21–53 MPa, P/L¼2.0/1.0
No change in CS with↑P/L for AC ¼ 40 wt% (21 MPa).
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Fig. 1 – Three-dimensional contour plots showing the effect of varying P/L and AC on (a) tw (s), (b) ts (s), and (c) CS (MPa). Red circles indicate data points above the model; pink circles represent data points below the model. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Table 3 – Final regression equations and summarized ANOVA (CV: coefficient of variance; AP: adequate precision). Response
Regression models
R2
R2 adjusted
R2 predicted
Prob4F
CV (%)
tw
tw ¼ 1964.36 1297.29P/L 15.55ACþ7.40P/ L ACþ194.76P/L2 1/√ts ¼0.066þ0.098P/L 0.0033AC 0.00125P/ L ACþ0.0000336AC2 CS¼ 577 470P/L22.49ACþ18.75P/ L ACþ0.216AC2 0.175P/L AC2
0.9931
0.9897
0.9797
o0.0001
5.14
52.794
0.9978
0.9968
0.9893
o0.0001
2.47
110.634
0.9639
0.9381
0.6617
o0.0001
7.83
17.524
ts CS
than 0.05, (iii) the coefficients of variation (CV) are less than 10%, and (iv) the adequate precision (AP) values are greater than 4 (Kehoe et al., 2013). Given the high adequacy of the resulting models, the desirability objective function was implemented to predict a formulation that would provide 5–10 min of tw, minimal ts, and maximal CS with 30 MPa set as the minimum. Each condition was assigned equal importance (þþþ). Fig. 2 provides an overlay plot depicting the design space that identifies the optimal formulations based on these design criteria. The highlighted space represents the ranges in P/L and AC that provide 5–10 min tw, minimal ts, and at least 30 MPa of CS. The following formulation was predicted as optimal: P/ L ¼1.2/1.0 and AC¼ 56% as shown (Fig. 2). Table 4 provides a tabulated comparison of the predicted and measured behaviors of the optimal material formulation. The measured ts and CS showed no significant difference in comparison to what was predicted (ANOVA); however, the measured tw deviated significantly from the model's prediction.
4.
Discussion
Varying the P/L and AC of GICs is heavily considered in the literature as a method of tailoring cement properties (Lohbauer, 2010). Previous investigations involving the effects of altering GIC formulation have been limited to one-variableat-a-time analyses, which has prevented consideration of the combined and interactive effects of these two factors on the complex balance between handling and strength (Crisp et al., 1976; Billington et al., 1990; Zahra et al., 2011). The predictive regression models developed in this study may address this shortcoming through mathematically relating the effects of both P/L and AC on tw, ts, and CS, thereby providing an efficient and effective means of determining an optimal GIC formulation depending on user-defined inputs. The GIC examined in this study comprises the first aluminum free GIC that may provide both adequate handling and mechanical properties for injectable spinal applications (vertebroplasty and kyphoplasty) (Dickey et al., 2013). It is well accepted that aluminum must be removed from conventional GICs to render these materials biocompatible with bone (Dickey et al., 2013). Previous attempts to design aluminum free GICs for such applications have been unsuccessful, resulting in cements with insufficient time for injection (ca. 1–2 min) or inadequate strength (o30 MPa) (Boyd et al., 2008; Wren et al., 2010, 2012; Clarkin et al., 2010). Boyd and Towler (2005) reported the effects of varied AC on a zinc-based aluminum free GIC, demonstrating it was possible to adjust tw, ts, CS, and flexural strength in this fashion,
AP
Fig. 2 – Overlay plot showing the region that satisfies the design criteria and the P/L and AC identified as optimal; working time and setting time in s, compressive strength in MPa. Table 4 – Comparison of model generated predictions and experimental measurements using P/L ¼1.2/1.0 and AC¼ 56% (model generated optimal formulation). Property
Predicted
Experimental
tw (min:s) ts (min:s) CS (MPa)
5:10 33:20 32
3:40 34:00 28.5
although tw remained less than 3:38 min:s. Dickey et al. (2013) published the first set of germanium-inclusive aluminum free GICs with significant improvements in the handling-strength balance. This was an exciting advancement in the aluminum free GIC literature, as this publication presented the first series of aluminum free GICs with extended tw, without loss of strength. It was the objective of this study to investigate the effects of P/L and AC on this novel GIC composition (DG209), and to determine, using a DOE approach, the P/L–AC combination that provides the optimal balance in tw, ts, and CS for injectable spinal applications. As outlined in Fig. 1 and Table 2, the general trends observed for the tw and CS of DG209 are consistent with what has been reported in one-variable-at-a-time investigations involving conventional GICs; increases in both P/L and AC decreased tw and increased CS (Fleming et al., 2003; Dowling and Fleming, 2011). In general, increased P/L and AC are hypothesized to increase the reactivity of the setting material, explaining the observed decrease in tw (Boyd et al., 2008; Fleming et al., 2003). With regards to strength, higher P/Ls and ACs generally correlate with increased CS, presumably by
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providing a higher concentration of reinforcing glass particles and through increasing the degree of matrix entanglement, respectively (Boyd et al., 2008; Fleming et al., 2003). Interestingly, the response modeled for ts deviated from the trends reported in the literature; increasing AC with constant P/L increased ts. This anomaly may result from the unique glass composition of DG209, which dictates the setting chemistry of the GIC, or from inadequate hydration to facilitate the neutralization reaction (Lohbauer, 2010). The resulting regression models and associated ANOVA showed high model adequacies for all three responses (Table 3). The CV was less than 10% for all responses, confirming reproducibility of the models, while the AP (range in the predicted responses in reference to the associated error) was satisfied for each model. With the exception of the R2 predicted value for CS, all R2 values exceeded 0.8, indicating significant regression models were realized. The relatively low R2 predicted value for the CS response may be indicative of an over-fit model. Ideally, response models should be as simple as possible, as complex models run risk of modeling insignificant variability (i.e. noise). Restricting the design space such that the CS response may be modeled as quadratic or eliminating outliers may improve the overall predictability (Anderson and Whitcomb, 2005). To identify the optimal formulation based on the requirements of a vertebroplasty cement (5–10 min tw, minimal ts, and 430 MPa CS), implementation of the desirability approach identified P/L¼1.2/1.0 and AC¼56 wt% as optimal (Fig. 2). When derived experimentally, the identified optimal formulation produced a cement with significantly lower tw (Table 4). This incongruity may result from the relatively low predictive power of the CS response (low R2 predicted ) or it may be an issue of robustness in the procedures used for data acquisition. Although the ISO procedures for dental materials are used extensively to approximate the clinical performance of acidbase cements, these standards have been subject of major criticism; mixing technique, environmental conditions, operator experience, and intra-operator factors (such as user fatigue) have all been identified as possible causes of variability (Fleming et al., 2012). Small changes in the inputted variables may result in big changes in the modeled responses, which may have significantly compromised the predictive power of the models. When looking at the overall design space (Fig. 1), it is apparent the centroid design point (P/L¼ 1.5/1.0 and AC¼50 wt%) yielded a significantly lower ts (10:40 min:s) and higher CS (39 MPa). However, the tw produced by this formulation (4:10 min:s) remained short of what is required for injectable skeletal applications (5–10 min). It appears that forcing the models to provide between 5–10 min of tw (i.e. increasing the importance of this property in the desirability function) significantly compromises ts and CS, highlighting the tradeoff in GIC properties. Small changes in the relative proportions of glass powder, PAA (dried), and water can significantly affect the balance in handling and strength. It is therefore crucial to understand the effects of altering cement formulation. The authors suggest the optimization approach presented in this study may be suitable for establishing appropriate P/L–AC combinations for other GICs, such that the materials may be tailored, in a predictable, controlled fashion, to meet the demands of a particular indication.
5.
Conclusion
This study presents the first set of regression models that may be used for predicting the formulation-dependence of tw, ts, and CS for a novel aluminum free GIC, DG209. The results presented confirm the tailorability of DG209 and demonstrate, for the first time, how DOE may be used to consider the combined effects of P/L and AC on GIC properties. The central composite design developed in this study may be an efficient and effective means for optimizing the properties of GICs through simple manipulations of P/L and AC.
Acknowledgments The authors would like to acknowledge the financial assistance of the Atlantic Canada Opportunities Agency (AIF Award 197820), and the Natural Sciences and Engineering Research Council of Canada (NSERC, 386022-2010) Discovery Program.
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