Biomaterials
Volume 24, Issue 6 , March 2003, Pages 1111-1117

Effect of test frequency on the in vitro fatigue life of acrylic bone cement

Gladius Lewis^{, , a}, Si Janna^a and Michael Carroll<sup>b

a</sup> Department of Mechanical Engineering, The University of Memphis, Campus Box 526576, Memphis, TN 38152-3180, USA
^b Wright Medical Technology, Inc., 5677 Airline Road, Arlington, TN 38002, USA

Available online 19 December 2002.

1. Abstract

The goal of the present work was to test the hypothesis that test frequency, f, does not have a statistically significant effect on the in vitro fatigue life of an acrylic bone cement. Uniaxial constant-amplitude tension-compression fatigue tests were conducted on 12 sets of cements, covering three formulations with three very different viscosities, two different methods of mixing the cement constituents, and two values of f (1 and 10 Hz). The test results (number of fatigue stress cycles, N_f) were analyzed using the linearized form of the three-parameter Weibull equation, allowing the values of the Weibull mean (N_WM) to be determined for each set. Statistical analysis of the ln N_f data, together with an examination of the N_WM estimates, showed support for the hypothesis over the range of f used. The principal use and explanation of the present finding are presented.

Author Keywords: Acrylic bone cement; Test frequency; Fatigue life; Weibull equation

2. Article Outline

1. Introduction

2. Materials and methods

3. Results and discussion

4. Conclusion

Acknowledgements

References

3. 1. Introduction

Almost invariably, during most normal daily activities, the acrylic bone cement mantle in a cemented arthroplasty is subjected to irregular load-time histories. Furthermore, examination of cement mantles retrieved post-mortem from patients with cemented hip arthroplasties revealed fatigue cracks, even in those prostheses that were deemed "pain-free" [1]. Given these facts, it is not surprising that, in the in vitro evaluation of a bone cement material, determination of its fatigue performance is recognized to be a cornerstone. Over the years, research and development efforts in this field reflect this situation, spawning, in the process, a huge volume of literature [2, 3, 4, 5, 6 and 7] that has one key characteristic relevant to the present study. This is that in the myriad reports on the effect of an assortment of variables on the fatigue performance of a large number of cement formulations, certain variables have been extensively investigated—notably, mixing method [3 and 8] and reinforcing fillers [9]—but others have attracted very little systematic study. Among the latter variables is test frequency, f. To date, only two reports have appeared on this topic [10 and 11], both of them providing limited results. Information on the effect of f on a cement's fatigue performance is important from two perspectives. First, from a practical standpoint, knowledge of this effect would help in selecting the value of f to be used in tests aimed at expeditiously screening candidate cement formulations. Second, from a fundamentals standpoint, the impact of f on a cement's fatigue performance could provide insight into the fatigue mechanisms that are operational in the material.

The objective of the present study was to test the hypothesis that f does not have a statistically significant effect on the in vitro fatigue life of an acrylic bone cement. For this purpose, fatigue tests were conducted, in uniaxial constant-amplitude fully reversed tension-compression loading, on 12 sets of specimens fabricated from three commercially available cements (representing three different values of viscosities), two different mixing methods, and two values of f. All these features were carefully selected to reflect the spectrum of those that are relevant to cemented arthroplasties. The cements used were Orthoset^®1 (manufactured for Wright Medical Technology, Inc., Arlington, TN, USA) [OS1], Surgical Simplex^®P (Stryker Howmedica Osteonics, Rutherford, NJ, USA) [SSP], and Orthoset^®3 (Wright Medical) [OS3], which are classified as "high-" [12], "medium-" [13] and "low-viscosity" [12] formulations, respectively. All of these types of cements, as well as the mixing methods used—hand mixing and vacuum mixing—are employed clinically [14 and 15]. One of the two values of f used—1 Hz—is within the range of typical gait cycle frequencies [16]. It is realized that the other f value used—10 Hz—is unlikely to be seen in vivo, but it was selected because, it was argued, an investigation of frequency effect is best carried out over at least a decade of increase of f.

4. 2. Materials and methods

All cement constituents were stored at ambient laboratory conditions (temperature: 21±1°C; relative humidity: 66.5±2.5%) prior to being mixed. A polymeric spatula was used to mix the cement constituents in a mixing bowl, either under ambient pressure (hand-mixing method) or in a commercially available vacuum chamber (Summit Medical Vacuum Mixing Bowl 550; Summit Medical Ltd., Bourton-on-the-Water, Gloucestershire, UK), with the evacuation pressure being 71.15±4.79 kPa (vacuum-mixing method), at about 1 beats⁻¹, for about 90 s, by which time a homogeneous dough (fluid cement) was obtained. This dough was then quickly but very carefully poured into a syringe, from which it was extruded into a silicone mold, with an interior cavity having the same nominal dimensions as the final specimen; that is, outer diameter=8.5 mm; diameter and length of waisted section=5.0 and 26.0 mm, respectively; transition radius=13.0 mm; and overall length=62.0 mm. After curing completely, in the ambient environment, the specimens were pushed out of the mold with a plunger. The cured specimens thus were of the dumbbell type (Fig. 1). The specimens were then very carefully examined visually for surface flaws, especially in the gage and transition sections. All specimens with any surface defects greater than 0.25 mm in diameter in any of the aforementioned sections were rejected and not tested. The remaining specimens were examined radiographically, and all specimens with internal defects greater than 0.5 mm in diameter in the gage section were rejected and not tested. The ratio of the total number of specimens rejected to the total number fabricated (RR) ranged from 43% for the hand-mixed SSP set to 8% for vacuum-mixed OS1 set.

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Fig. 1. Dimensioned drawing of the dumbbell-type fatigue test specimen.

For each cement set, all the accepted specimens were very lightly polished with 600 grit abrasive paper, cleaned, and then stored in ambient conditions for at least 48 h prior to the fatigue testing, which was conducted in ambient air using a custom-built servohydraulic universal materials testing machine. Each specimen was subjected to uniaxial constant-amplitude fully reversed (tensile-compressive) loading in a sinusoidal cyclic manner, with an amplitude of 15 MPa, at either f=1 or 10 Hz. The fatigue loading continued until the specimen failed (completely broke). The number of test specimens in each of the 12 sets varied from 8 (for SSP; hand mixed; 1 Hz) to 12 (for OS3; hand mixed; 10 Hz).

The fatigue test results, given as number of cycles-to-failure (N_f), were analyzed using the linearized format of the three-parameter Weibull relation, which is given by [17 and 18]

lnln[1/{1−P(Nf)}]=b ln(Nf−No)− b ln(Na−No),

(1)

where b is the Weibull slope or shape parameter, N_o is the Weibull minimum or guaranteed fatigue life, and N_a is the Weibull characteristic fatigue life.

Note that: (a) P(N_f) is the probability of fatigue fracture after N_f stress cycles, and is determined from the expression [17]

P(Nf)=M/(G+1.0),

(2)

where M is the failure rank number (that is, the rank assigned to an N_f result after all the N_f results are arranged in ascending order of magnitude) and G is the total number of specimens. Thus, M=1,2,3,…,G

(b) N_o is obtained from the vertical asymptote to a suitable plot of lnln[1/{1−P(N_f)}] versus ln N_f [17 and 18]; and

(c) the Weibull mean number of fatigue stress cycles (N_WM) is used as the index of the material's fatigue performance, with N_WM being given by [18]

NWM=No+(Na−No)Γ[1+1/b],

where Γ is the gamma function.

Thus, N_WM reflects the fact that fatigue performance is a function of both the magnitude of the fatigue life (i.e., N_a) and the variability or degree of scatter of the N_f results (i.e., b).

The size distribution of the polymer beads in the powder of each of the cements was determined using a commercially available particle counter/analyzer (Multisizer II; Coulter, Inc., Miami, FL, USA). The data were fed to a computer, in which software was used to plot the size-distribution diagram and calculate the overall mean diameter (D_m) of the particles.

Tests of significance of difference in the value of a named parameter (ln N_f or D_m) between pairs of the test sets were conducted using the Mann-Whitney method (
<0.05) and a commercially available software package (Microsoft Excel^TM 2000; Microsoft Corp., Redmond, WA, USA).

5. 3. Results and discussion

All the N_f data are presented in Table 1 and Fig. 2. Sample calculations for the estimation of the Weibull parameters for one set of these N_f results, to yield N_o, N_a, b, and N_WM, are presented in Table 2, Fig. 3 and Fig. 4. The values of all the Weibull parameters for all 12 test sets are presented in Table 3 and Fig. 5.

Table 1. The number of fatigue stress cycles (N_f) results for the 12 sets


OS1: Orthoset 1 cement; SSP: Surgical Simplex P cement; OS3: Orthoset 3 cement. HM: hand-mixed cement dough; VM: vacuum-mixed cement dough. Test frequency: 1 or 10 Hz.

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Fig. 2. Summary of the ln N_f results for all 12 sets of specimens.

Table 2. Sample calculations: Orthoset^®3; hand mixed; 10 Hz

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Fig. 3. Estimation diagram for minimum fatigue life, N_o: results for hand-mixed Orthoset^®3 specimens tested at 10 Hz.

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Fig. 4. The plot of Eq. (1): results for hand-mixed Orthoset^®3 specimens tested at 10 Hz.

Table 3. Summary of the three-parameter Weibull estimates

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Fig. 5. Summary of the ln N_WM estimates for all 12 sets of specimens.

Two trends from these results are recognized but are remarked upon only briefly because they are outside the ambit of the study's stated objective. First, regardless of the cement, vacuum mixing of its constituents leads to a specimen set with much lower value of RR (which reflects the smaller number of surface and internal defects) and a significantly higher fatigue life compared to the hand-mixed specimen set. This finding is consistent with results reported by previous workers for many cements [19, 20, 21 and 22]. Second, regardless of the mixing method used, the value of N_WM of the Simplex P set is lower than those of the Orthoset 1 and Orthoset 3 sets. It is suggested that this trend reflects the differences in the D_m for these cements—that for Simplex P is significantly smaller (determined to be 31.27±0.33
m) than for either Orthoset 1 (determined to be 41.75±0.23
m) or Orthoset 3 (determined to be 42.15±0.33
m). Recently, Ginebra et al. [23] showed that the fatigue crack propagation resistance of an acrylic bone cement is directly proportional to D_m. The present trends in the fatigue lives of Simplex P specimens, on the one hand, and Orthoset 1 and 3 specimens, on the other, are consistent with the finding of Ginebra et al. [23].

The present results reveal two clear trends that are central and germane to the study's stated objective. First, for a given combination of cement formulation and mixing method, an increase in f leads to an increase in fatigue life. This finding is in consonance with the results presented by previous workers [10 and 11]. Thus, when the N_f results for specimens of centrifuged Surgical Simplex P cement tested under sinusoidal tensile stress (0.3-20.0 MPa) in room-temperature air (24°C), as reported by Johnson et al. [10], were analyzed by the present workers using Eq. (1), N_o, N_a, and N_WM were determined to be 22026, 40561, and 39391, respectively, for f=1 Hz, while the corresponding estimates for f=10 Hz were 26903, 80861, and 80862. For specimens fabricated from hand-mixed Zimmer Low Viscosity Cement (Zimmer LVC) and CMW^TM3 cements, subjected to four-point bending with the applied loading having a sinusoidal waveform (R=0.1) in Ringer's solution at 37°C, Ishihara et al. [11] reported that "…the fatigue lives of both cements at 1 Hz are shorter by 1 to 2 orders of magnitude as compared with fatigue lives at 20 Hz… ." The second trend seen in the present results is that, for any combination of cement formulation and mixing method, the increase in fatigue life with increase in f is not statistically significant (Mann-Whitney test;
<0.05). In contrast, however, our Mann-Whitney (
<0.05) analysis of the N_f results reported by Johnson et al. [10] showed that the fatigue life at 10 Hz was statistically significantly longer than at 1 Hz. This result most likely reflects the fact that, while there was a small difference in the N_o estimates at these two values of f—as stated earlier—the scatter in the N_f results at f=10 Hz was considerably greater than at f=1 Hz (Estimates of b obtained from our analysis of these two sets of N_f results were 1.22 at f=1 Hz and 0.59 at f=10 Hz.) It is pointed out that Ishihara et al. [11] presented the N_f results in the format of a Wohler plot, with only a few data points shown for the results obtained at f=1 and 20 Hz. This format of presentation did not allow us to analyze the results for the statistical nature of the difference between the study sets.

As explained earlier, the cement formulations and mixing methods used in the present work were purposely selected. Consequently, if the test results support the working hypothesis—that f does not exert a statistically significant effect on a cement's fatigue performance—then that conclusion may have generality. In fact, the present results do support the hypothesis. In that case, it is recommended that when in vitro fatigue testing of candidate sets of bone cement formulations is to be performed for the purposes of screening them, such testing should be carried out at 10 Hz. Clearly, this will expedite the evaluation compared to case when the test frequency is, say, 1 or 2 Hz, as has been used in other studies [8, 9 and 24].

Two possible explanations for the increase in fatigue life with increase in f are now presented. The first is that, bone cement being viscoelastic, with an increase in f there is a decrease in its strain at an initiating pore in a specimen [25]; this inhibits crack initiation and, hence, results in an increase in fatigue life. A corollary of this reason is that the strain intensity factor at an advancing crack tip in the cement specimen decreases with an increase in f, leading to a drop in crack growth rate [26] and, hence, an increase in fatigue life. The second possibility is that an increase in f results in a temperature rise at the advancing crack tip in the cement specimen, leading to a reduction in the size of the plastic zone and, hence, the strain intensity factor [27].

Compared to the two previous studies on the subject of the effect of f on a cement's fatigue life [10 and 11], the present study has two principal attractions. First, in the present study, specimens were fabricated using three different cement formulations and two different mixing methods. Johnson et al. [10] used only one formulation and mixing method; namely, Surgical Simplex P mixed using centrifugation at 2500 rpm for 0.5 min. Ishihara et al. [11] used two different formulations (Zimmer LVC and CMW3) and one mixing method ("… in accord with instructions contained in each company's operation manual."). Second, the present N_f results were statistically analyzed for determining the nature of the difference between pairs of test sets. In contrast, in both Johnson et al. [10] and Ishihara et al. [11] studies, no such analysis was reported, although the latter workers still asserted that, from their results, there was "… a clear indication that an influence of frequency on fatigue lives exists."

It is realized that the cement mantle in an arthroplasty is subjected to a complex stress system and that, usually, fatigue cracks initiate and propagate under tensile stresses [28]. These facts notwithstanding, fully reversed (tensile-compressive) loading was used in the present work because this type of loading yields the most conservative estimate of a material's fatigue performance [28].

The present study has one main limitation. This is that the stress level used (15 MPa) is higher than the levels which, reportedly, the cement experiences in vivo. For normal joint loading, the normal tensile stress levels in the cement mantle in a hip arthroplasty have been put at between 3 and 11 MPa [2]. However, it is unlikely that tests conducted at lower stress levels would show a trend different from that reported here. This is because a decrease in fatigue life with an increase in f is likely to result if, at the test stress level, failure is due to thermal softening, occurring consequently upon temperature increase in the specimen as f increases. In fact, this phenomenon is likely to play an important role in the fatigue life at stress levels greater than 15 MPa. Notwithstanding the point expounded upon above, at this juncture, there is insufficient information that will allow any comments to be made as to the validity of the present finding over a wide range of test stress levels. Future research should explore this issue.

It is reiterated that the present results characterize the bone cement materials under controlled and specific test conditions. In other words, these results may not reflect the in vivo performance of the cements, which may be affected by a host of factors, such as surgical technique, method of preparation of the intrameduallary bone canal, implant design, and patient activity pattern.

6. 4. Conclusion

The main conclusion of this study is that the results obtained provide support for the working hypothesis, that is, test frequency (over the range used) does not exert a statistically significant effect on the fatigue life of the cements tested.

7. Acknowledgements

The authors are very grateful to Wright Medical Technology for providing supplies of the Orthoset^®1 and Orthoset^®3 cements and performance of some of the fatigue tests, and to Mr. Andy Hardison, Department of Biomedical Engineering, The University of Memphis, for performing the particle size analysis of the cement powders.

8. References

1. M. Jasty, W.J. Maloney, C.R. Bragdon, D.O. O'Connor, T. Haire and W.H. Harris , The initiation of failure in cemented femoral components of hip arthroplasties. J Bone Jt Surg 73-B (1991), pp. 551-558. Abstract-MEDLINE | Abstract-EMBASE  

2. W. Krause and R.S. Mathis , Fatigue properties of acrylic bone cement: review of the literature. J Biomed Mater Res (Appl Biomater) 22 A1 (1988), pp. 37-53. Abstract-MEDLINE | Abstract-EMBASE  

3. W. Krause, L.W. Grimes and R.S. Mathis , Fatigue testing of acrylic bone cements: statistical concepts and proposed methodology. J Biomed Mater Res (Appl Biomater) 22 A2 (1988), pp. 179-190. Abstract-MEDLINE | Abstract-EMBASE  

4. W. Krause, R.S. Mathis and L.W. Grimes , Fatigue properties of acrylic bone cement: S-N, P-N, and P-S-N data. J Biomed Mater Res (Appl Biomater) 22 A3 (1988), pp. 221-244. Abstract-MEDLINE | Abstract-EMBASE  

5. G. Lewis , Properties of acrylic bone cement: state-of-the-art review. J Biomed Mater Res (Appl Biomater) 38 (1997), pp. 155-182. Abstract-MEDLINE | Abstract-EMBASE | Abstract-Compendex   | Full Text via CrossRef

6. G. Lewis and J.S. Nyman , Toward standardization of methods of determination of fracture properties of acrylic bone cement and statistical analysis of test results. J Biomed Mater Res (Appl Mater.) 53 (2000), pp. 748-768. Abstract-MEDLINE | Abstract-Compendex | Abstract-EMBASE   | Full Text via CrossRef

7. B.P. Murphy and P.J. Prendergast , On the magnitude and variability of the fatigue strength of acrylic bone cement. Int J Fatigue 22 (2000), pp. 855-864. SummaryPlus | Full Text + Links | PDF (2498 K)

8. G. Lewis , Effect of two variables on the fatigue performance of acrylic bone cement: mixing method and viscosity. Bio-Med Mater Eng 9 (1999), pp. 197-207. Abstract-MEDLINE | Abstract-EMBASE  

9. Y.K. Kim and H.K. Yasuda , Improvement of fatigue properties of poly (methyl methacrylate) bone cement by means of plasma surface treatment. J Biomed Mater Res (Appl Biomater) 48 (1999), pp. 135-142.

10. J.A. Johnson, J.W. Provan, J.J. Krygier, K.H. Chan and J. Miller , Fatigue of acrylic bone cement-effect of frequency and environment. J Biomed Mater Res 23 (1989), pp. 819-831. Abstract-MEDLINE | Abstract-EMBASE | Abstract-Compendex  

11. Ishihara S, McEvily AJ, Goshima, Kanekasu K, Nara T. On fatigue lifetimes and fatigue crack growth behavior of bone cement. J Mater Sci Mater Med 2000;11:661-6.

12. Orthoset^®1 Radiopaque Bone Cement and Orthoset^®3 Radiopaque Bone Cement product brochures, Wright Medical Technology, Arlington, TN, USA, July 1998.

13. K.-.D. Kuhn Bone cements: up-to-date comparison of physical and chemical properties of commercial materials, Springer, Berlin (2000).

14. L.I. Havelin, B. Espehaug, S.M. Vollset and L.B. Engesaeter , The effect of the type of cement on early revision of Charnley total hip prostheses. J Bone Jt Surg 77-A (1995), pp. 1543-1550. Abstract-MEDLINE | Abstract-EMBASE  

15. Malchau H, Herberts P. Prognosis of total hip replacement, revision and re-revision rate in THR: a revision-risk study of 148,359 primary operations. Scientific Exhibition Presented at the 65th Annual Meeting of the American Academy of Orthopaedic Surgeons, New Orleans, LA, USA, February 19-23, 1998.

16. G. Bergmann, G. Deuretzbacher, M. Heller, F. Graichen, A. Rohlmann, J. Strauss and G.N. Duda , Hip contact forces and gait patterns from routine activities. J Biomech 34 (2001), pp. 859-871. SummaryPlus | Full Text + Links | PDF (1035 K)

17. N.A.J. Hastings and J.B. Peacock Statistical distributions, Butterworth Ltd., London (1975).

18. J.E. Shigley and C.R. Mischke Mechanical engineering design (6th ed.),, McGraw-Hill, New York (2001).

19. R.L. Wixson, E.P. Lautenschlager and M.A. Novak , Vacuum mixing of acrylic bone cement. J Arthroplasty 2 (1987), pp. 141-149. Abstract-MEDLINE  

20. Healey RM, Perona P, DiMaio F, Allen JJ, Coutts RD. A technique for assessing acrylic bone cement porosity and fatigue life. In: Transactions of the 44th Annual Meeting of the Orthopaedic Research Society, New Orleans, LA, USA, March 16-19, 1998. p. 422.

21. G. Lewis , Effect of mixing method and storage temperature of cement constituents on the fatigue and porosity of acrylic bone cement. J Biomed Mater Res (Appl Biomater) 48 (1999), pp. 143-149. Abstract-Compendex | Abstract-EMBASE | Abstract-MEDLINE   | Full Text via CrossRef

22. G. Lewis , Relative roles of cement molecular weight and mixing method on the fatigue performance of acrylic bone cement: Simplex P versus Osteopal. J Biomed Mater Res (Appl Biomater) 53 (2000), pp. 119-130. Abstract-MEDLINE | Abstract-Compendex | Abstract-EMBASE   | Full Text via CrossRef

23. Ginebra MP, Morejon L, Delgado JA, Manero JM, Gil FJ, Artola A, Goni I, Garruchaga M, Vazquez B, San Roman J, Planell JA. Effect of size distribution of the PMMA beads on the fatigue crack propagation of acrylic bone cements. In: Transactions of the 16th European Conference on Biomaterials, London, UK, September 12-14, 2001.

24. Cooke FW, Friis EA, Kumar B, Graber CD, Blake DJ, McQueen DA. Endurance limit and fatigue strength of PMMA cement. In: Transactions of the 25th Annual Meeting of the Society for Biomaterials, Providence, RI, USA, April 28-May 2, 1999. p. 97.

25. Y.F. Chou and C.T. Sun , Modelling of the frequency effect on fatigue crack propagation in PMMA. Eng Fract Mech 17 (1983), pp. 17-26. Abstract

26. S. Arad, J.C. Radon and I.E. Culver , Fatigue crack propagation in polymethylmethacrylate: The effect of loading frequency. J Mech Eng Sci 14 (1972), pp. 328-334. Abstract-Compendex  

27. R.W. Hertzberg and J.A. Manson Fatigue of engineering plastics, Academic Press, New York (1980).

28. N.A. Dowling Mechanical behavior of materials (2nd ed ed.),, Prentice-Hall, Upper Saddle Creek, NJ (1999).

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