- Email: [email protected]
The effect of strain rate on the failure stress and toughness of bone of different mineral densities
Journal of Biomechanics 46 (2013) 2283–2287
Contents lists available at ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
The effect of strain rate on the failure stress and toughness of bone of different mineral densities R.J. Wallace n, P. Pankaj, A.H.R.W. Simpson The University of Edinburgh, Chancellor's Building, 49 Little France Crescent, Edinburgh, Eh16 4SB, UK
art ic l e i nf o
a b s t r a c t
Article history: Accepted 11 June 2013
The risk of low energy fracture of the bone increases with age and osteoporosis. This paper investigates the effect of strain rate and mineral level on the peak stress and toughness of whole ovine bones. 40 fresh ovine femurs were subjected to 3-point bending at high (17.14 s−1) and low (8.56 10−3 s−1) strain rates with or without a controlled amount of demineralisation. Mineral removal was achieved by ultrasonically assisted exposure in Ethylene diamine tetra-acetic acid (EDTA). The ultimate stress for whole bones of normal mineral content was 200 MPa at the high rate of strain and 149 MPa at the low rate of strain. With changes in bone mineral levels such as may occur in osteomalacia and osteoporosis, the change in toughness varied at different strain rates; a mean value of 3.7 71.4 MJ/m3 was obtained for the toughness of normal quality whole bone tested at slow loading rate and a reduction of approximately 25% was observed in the demineralised whole bone specimens at the slow loading rate (mean 2.8 70.9 MJ/m3). When tested at the high loading rate there was a negligible difference in the toughness between the two (2.0 70.6 MJ/m3) mineral levels. This indicated that there was a strain rate dependant effect for the mineral density, and that the removal of mineral alone did not explain all of the reduction in mechanical properties that occur with age or disease. Thus, the reduction in mechanical properties at high strain rates was likely to be due to other phenomena such as increased porosity or reduced collagen quality, rather than loss of mineral. With decreasing mineral levels, as measured by DEXA in clinical practice, the increased fracture risk is dependent on the velocity of the impact. Thus the estimates of increased fracture risk given clinically for a lower DEXA value should be different for high and low energy injuries. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Strain rate Demineralisation Toughness Stress
1. Introduction Bone is a hierarchical composite material and changes occur on multiple length scales that influence the mechanical properties of the whole bone. The risk of low energy fracture of the bone increases with age and osteoporosis. Martin (2003) and Van der Meulen et al. (2001) indicated that there are many factors that combine to give bone its overall quality. However, the onset of the effects of osteoporosis is determined by assessing the mineral content of the bone (Kanis, 1994). Shah et al. (1995) conducted bending tests on feline bone segments that had been demineralised to different degrees. However, these were tested with a machine crosshead speed of 10 mm/ min, which is considerably slower than that would be encountered in physiological activities such as walking. The viscoelastic response of demineralised bone was acknowledged in a study by Sasaki and
n
Corresponding author. Tel.: +131 242 6296; fax: +131 242 6534. E-mail address: [email protected] (R.J. Wallace).
0021-9290/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jbiomech.2013.06.010
Yoshikawa (1993) who investigated the stress relaxation of demineralised bone, but they used samples of bone machined from bovine femur rather than whole bones and tested these by cantilever bending. To date, no studies have investigated the effect of partially demineralised bone at traumatic loading rates. Therefore the aim of this research is to investigate the effect of partial mineral removal from bone to a clinically relevant level on the ultimate stress and the toughness at both low and fast strain rates. The strain rates in this study have been chosen to be representative of (i) the lower end of fractures classed as “low energy fractures”, i.e. those that could occur from a fall from a bed or chair or a fracture that occurs due to movement before the fall, which has been estimated to be just under 10% of elderly hip fractures (Cummings and Nevitt, 1989), (ii) those found to be representative of high energy fracture, such as the rates of strain that have been measured to occur in the lower limbs during a motor vehicle accident (Hansen, 2008). In particular, as bone is a viscoelastic multidimensional composite, we tested the hypothesis that alteration of the composition of this composite will have differing effects at different rates of strain.
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R.J. Wallace et al. / Journal of Biomechanics 46 (2013) 2283–2287
2. Methods
2.2. Demineralisation
A total of 40 femurs were harvested from freshly euthanized sheep. These were split equally between four testing groups according to testing speed and mineral content; fast-normal (FN), fast-demineralised (FD), slow-normal (SN), slowdemineralised (SD).
In order to examine the effects of the bone mineral on the bone properties, half of the bones were subjected to a standardised amount of demineralisation. The level of demineralisation was assessed using a calibrated step wedge in the radiographic image (Dawson et al., 2008) and mean values of 2.47 g/cm3 (7 0.42 SD) were found for the normal quality group and 1.86 g/cm3 ( 7 0.28 SD) for the demineralised group, representing a mean reduction of 25%. This mineral density reduction is representative of a density reduction that a 75 year old female may have undergone compared to her peak bone density (Kanis, 1994). To speed up the decalcification process, mineral was removed by ultrasonically assisted agitation in 10 M Ethylene diamine tetra-acetic acid (EDTA). This is a validated method that has been used in previous studies (Shah et al., 1995) and is commonly used as a means of preparation of bone samples for histology (Alers, 1999). It has been shown not to cause morphological deterioration of the tissue (Thorpe, 1963; Milan, 1981). Additionally, the ultrasonic agitation was thought to assist the removal of mineral from within the bone. The reduced grey level throughout the whole cross section of the bone on the microCT images confirmed that the mineral dissolution was not confined to the external surfaces. In order to ensure that the porosity was not altered during demineralisation, 8 sample fragments from 4 paired limbs (normal and demineralised) were scanned at a resolution of 4.8 mm. Analysis of these groups revealed mean porosities of 8.15% 73.13 SD and 7.88% 7 3.76 SD for the normal and demineralised specimens respectively, which represented no significant difference between the groups as found by a paired t-test with a p value of 0.924.
2.1. Testing The slow loading rate experiments were carried out on a commercially available mechanical testing machine, Zwick/Roell z005 (Zwick GmbH & Co, Ulm, Germany). Data capture was provided by TestXpert V9.01 (Zwick GmbH & Co, Ulm, Germany). This is the proprietary software for the Zwick and as such acted as both the data capture and the control system for the slow rate experiments. The bones were loaded in 3-point bending at a constant rate of 1 mm/s. This created an average strain rate in the bone of 8.56 10−3 s−1 ( 71.42 10−3 SD). The fast rate loading was applied in 3-point bending by a custom designed experimental set up. The final set up consisted of: a bespoke manufactured bone holder, an aluminium impact head, a dynamic force sensor (PCB 208C05 (PCB Piezotronics Inc. New York, USA)), a pneumatic actuator (Norgren PRA/18200/200) and a LabVIEW data capture system (National Instruments Corporation. Texas, USA) sampling at 100 kHz to monitor the loading. A Vision Research Phantom v7.1 monochromatic high speed camera (Vision Research Inc. New Jersey, USA) running at 25,000 fps and fitted with a Nikon 24–85 mm F2.8 lens was used to record the deformation at the high loading rate. The initial rate of displacement of the unloaded actuator was 3.6 m/s (70.2 m/s). As the mass of the actuator was constant, the initial energy imparted was comparable. The strain rate that was subsequently produced in the bone through bending was dependant on the stiffness of the bone; the normal bone quality specimens had a mean strain rate of 13.3 s−1(77.0 SD) and the demineralised group was found to have a mean strain rate of 20.9 s−1(77.7 SD). This gave an average strain rate of 17.14 s−1 (78.20 SD) for the fast loading rate experiments. Although the strain rates experienced by the bone in these tests varied significantly, even the minimum strain rate encountered in these experiments was three orders of magnitude greater than that found to occur during extreme physiological loading, such as up-hill running as found by Burr et al. (1996). During testing at both loading rates the bone was located on rounded supports of 10 mm diameter at either end and the load was applied via an aluminium cylinder with a diameter of 35 mm. The bone was positioned and the supports adjusted as required to ensure the supports were located consistently between samples. The area immediately distal to the lesser trochanter and the flat section of bone proximal to the posterior femoral condyles were chosen as this would ensure the supports were located consistently and on a section of bone that would prevent rotation of the bone during loading. The load was always applied equidistantly from the two supports. The experimental set up can be seen in Fig. 1. The second moment of area was derived at several cross sections along the length of the bone using images taken from post testing microCT scans. The second moment of area at either side of the fracture was averaged to provide a value for this property at the fracture site to be used when determining the stress. Peak stress was calculated using engineers bending theory using the bending moment due to peak force and the second moment of area derived as described above. Due to the low aspect ratio, the length of the tested span divided by the depth of a whole femur and the use of 3 point bending during testing it was required to account for deflection due to shear by using Timoshenko's bending theory. The normal (bending) strain was then calculated and used to plot a stress– strain curve. The toughness was found by from the area under the curve.
2.3. Data analysis The data was checked for normality before an analysis of variance (ANOVA) was performed with a Tukey simultaneous test to investigate the differences between the groups for statistical significance. A p-value equal to or less than 0.05 was taken to indicate a statistically significant difference.
3. Results The results from the experiments performed for this study are presented in Table 1 and Fig. 2. Statistically significant differences (p o0.05, ANOVA) were found between the fast loaded normal quality group and all the other groups when comparing the peak stress. No further statistical differences were found. Statistically significant differences (p o0.05, ANOVA) were found for the toughness at failure between the slow loaded, normal quality bones and both qualities of fast loaded bones. The results highlight the involvement of the mineral in preventing fracture from traumatic loading by demonstrating a decrease in peak stress when demineralised bone was loaded at a fast rate of strain. However, the very similar mean values and standard deviations for toughness for normal and low mineral levels at the high rate of strain was interesting as this implied that the mineral did not play a significant role in the toughening mechanism at rates of strain encountered in high velocity trauma.
4. Discussion 4.1. Tests at normal mineral levels Bones of normal density from healthy young adult animals were found to have a higher peak stress but a lower toughness when loaded at a fast strain rate. Table 1 Mean ( 7SD) of peak stress and failure toughness of tested bones.
Fig. 1. Experimental setup for fast loading rate tests. Bone shown wrapped in gauze to prevent dehydration prior to testing.
Peak stress, sult (MPa) Toughness, T (MJ/m3)
FD
FN
SD
SN
141 717.6 2.0 70.6
2017 19.9 2.0 7 0.6
1367 23.9 2.8 7 0.9
1487 32.2 3.7 7 1.4
R.J. Wallace et al. / Journal of Biomechanics 46 (2013) 2283–2287
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Fig. 2. Box-plot of results for (a) stress and (b) toughness at failure.
Table 2 Testing methods used investigating effect of strain rate on mechanical properties of bone. Researcher
Species
Bone
Test type
Sample size
Strain rate range
Number of specimens
Crowninshield and Pope Crowninshield and Pope Wright McElhaney Hansen
Bovine Bovine Bovine Human Human
Tibia Tibia Femur Femur Femur
Tension Compressive Tension Compressive Compressive
12.7 28.6 1.5 (5 mm gauge) 12.7 28.6 1.5 (5 mm gauge) Necked sections 17.8 5.1 76 mm 3 2.4 7 mm gauge
0.01–200 s−1 0.01–200 s−1 5.3 10−4–237 s−1 1 10−3–1500 s−1 0.14–29 s−1
46 46 70 45 25
Several previous studies (Crowninshield and Pope, 1974; Hansen, 2008; McElhaney, 1966; Wright and Hayes, 1976) have examined the effects of loading rate on fracture of normal bone segments. The results from the current study for the normal bone quality experiments were compared with existing results in the literature (Table 2), but as none of the tests used exactly the same strain rates the values from the literature were interpolated for comparison. Hansen et al. (2008), consider that a strain rate on the bone of 25 s−1 provides an upper boundary for strain rates relevant to bone failures in traumatic events such as a motor vehicle accident, similar to the fast loading rate experiments conducted in this study (17.14 s−1 7 8.20 SD) The results of this comparison are presented in Figs. 3 and 4. Fig. 3 demonstrates that the numerical values of peak stress for normal bone are similar for all researchers. However, there is a larger degree of scatter in the numerical values found for toughness of normal bone (Fig. 4). As different testing methods were used by different authors it is perhaps more useful to compare the percentage differences between the properties found at the different strain rates. Table 3 compares the percentage change in peak stress and toughness of normal bone between high and low strain rates. The percentage changes in these properties found in this study are similar to the percentage changes found in previous studies (Figs. 3 and 4) Very close agreement was found when comparing peak stress between the strain rates of this study with the main body of literature. A larger amount of variation was found when comparing toughness. This is because other studies have used different sample types and loading methods—compressive, tensile or bending. The type of loading experienced by the bone will determine what failure value to use for predictive analysis.
Fig. 3. Stress at failure at high and low strain rates of this study compared to literature.
4.2. Testing at reduced mineral levels Previous studies have not examined the effect of reduced mineralisation on bone fracture at high strain rates. At high strain rates there was a significant difference in peak stress between
Fig. 4. Toughness at failure at high and low strain rates of this study compared to literature.
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R.J. Wallace et al. / Journal of Biomechanics 46 (2013) 2283–2287
Table 3 Percentage difference between high and low strain rate. Results from this study are compared with those from the literature. Property
This study
Mean existing data7 SD
Peak stress Toughness
36% 46%
38% 7 14% 35%7 12%
normal and demineralised bone; in contrast the toughness was similar. At low rates of strain there was no statistically significant differences between normal and demineralised bone, both for peak stress and toughness, though both these properties were found to be higher for normal bone. This finding implies that at the high rate of strain there is a method of energy absorption that is insensitive to mineral content. 4.3. Comparison with naturally occurring differences in mineralisation The results for the partially demineralised specimens were compared against values in the literature for bones with nonstandard/abnormal mineral levels. Examples of altered mineral level were found in juvenile bone, old bone and antler bone. Currey (1979) investigated the density and energy to fracture for a wide age range of bones. This work showed that the mineral level was minimal at both ends of the age range. However, the energy to fracture was maximal for the youngest specimens then decreased with age. It has been shown by Hansen (2008) and Vashishth and Tanner (2003), that microcracking is one of bones primary toughening mechanisms. It was proposed that the method of mineral removal used in this study may have altered the shape of the hydroxyapatite crystals in the bone, reducing the efficiency of microcrack initiation. The method of mineral removal was chelation of the calcium from the hydroxyapatite crystals in the bone matrix by exposure to EDTA. As this process occurs the fluid will effectively ‘erode' the crystals of mineral as it removes the calcium, smoothing the crystals as the mineral is leeched out of the bone. Yerramshetty (2008) and Akkus (2004) have shown that larger crystals of mineral will be stiffer and therefore more likely to be a cause of stress concentration and act as an initiation point for microcracking. This microcracking process would be less efficient with smaller crystals with smother edges, providing a possible explanation for the reduction in toughness observed with mineral removal when tested at slow rates of strain in these experiments. In addition to this, the reduction in the mineral at locations such as cement lines will also decrease the effectiveness of these locations in reducing crack propagation. Work by Currey (2002) has shown that there is a strong relationship between mineral content and fracture toughness, with the highly mineralised and very stiff ear bones providing little resistance to fracture and the low mineral deer antler providing a tough, fracture resistant material. Fracture toughness investigations in elk antler performed by Launey et al. (2010) have highlighted the structural differences between the non-loaded antler bone and long bones used for locomotion. In addition to a lower level of mineral, this material is shown to have smaller osteons and considerably smaller vascular channels. Furthermore, as well as the differences in size of these constructional elements, it has been shown by Skedros et al. (1995) that there is also a difference in the distribution of the mineral around these elements where the antler bone has highly mineralised regions surrounding these osteons compared to the thinly mineralised region, known as a cement line, which is found in structural bone. Cement lines are thought to play an important role in the fracture process,
acting as both potential crack initiation sites and as features to arrest crack propagation (Yeni and Norman, 2000). Therefore, differences in this feature would be expected to contribute towards differences in fracture properties It has been demonstrated by Zioupos (2008) that there is a reduction in microcracking that occurs with increasing strain rate. The results presented in this study show that there was no significant difference in toughness between the two mineral levels when tested at the high strain rate in spite of higher peak stress. The slow loaded normal bones demonstrated a statistically significant higher toughness than the fast loaded normal bones, despite having a statistically significant lower peak stress, suggesting that the toughening mechanism, which occurs due to the formation of microcracks, is more effective at low than at high rates of strain. Augat and Schorlemmer (2006) showed that pore size increased with age and that there was a significant reduction in the strength of bone with pore size, and researchers such as Donaldson (2011) have shown that there was a strong correlation between the mechanical properties and porosity; the age of the samples alone was found to be far less predictive than the porosity. This implies that both porosity and mineral content are important aspects of bone quality and should be considered when determining fracture risk. Of the material changes that occur to bone during the aging process, such as reduced mineral content, altered microstructure (porosity), build-up of microcracks and changes to the collagen, this study can only directly assess the effect of the partial removal of mineral; the porosity for normal and demineralised samples was found to remain unchanged.
5. Conclusions A reduction in the mineral content results in a decrease in strength of the bone but not in toughness at fast, traumatic rates of strain. When tested at a slow rate of strain there was minimal change in the peak stress but a reduction in toughness with reduced mineral content, possibly due to a reduction in microcrack formation provided by the presence of mineral. Significance:
With decreasing mineral levels, as measured by DEXA in
clinical practice, the increased fracture risk is dependent on the velocity of the impact. Thus the increased fracture risk predicted with a lower DEXA value will be different for high and low energy injuries. With changes in bone mineral levels as may occur in osteomalacia and osteoporosis, the change in toughness varies at different strain rates; values are provided that can be used in future fracture prediction models.
Conflict of interest There were no conflicts of interest in the research or presentation of this paper.
Acknowledgements The Vision Research high speed camera was loaned for this research by the EPSRC Equipment Loan Pool. References Akkus, O., Adar, F., et al., 2004. Age-related changes in physicochemical properties of mineral crystals are related to impaired mechanical function of cortical bone. Bone 34 (3), 443–453.
R.J. Wallace et al. / Journal of Biomechanics 46 (2013) 2283–2287
Alers, J.C., Krijtenburg, P.-J., et al., 1999. Effect of bone decalcification procedures on DNA in situ hybridization and comparative genomic hybridization: EDTA is highly preferable to a routinely used acid decalcifier. Journal of Histochemistry and Cytochemistry 47 (5), 703–709. Augat, P., Schorlemmer, S., 2006. The role of cortical bone and its microstructure in bone strength. Age Ageing 35 (Suppl. 2), ii27–ii31. Burr, D.B., et al., 1996. In vivo measurement of human tibial strains during vigorous activity. Bone 18 (5), 405–410. Bruce Martin, R., 2003. Fatigue damage, remodeling, and the minimization of skeletal weight. Journal of Theoretical Biology 220 (2), 271–276. Crowninshield, R., Pope, M., 1974. The response of compact bone in tension at various strain rates. Annals of Biomedical Engineering 2 (2), 217–225. Cummings, S.R., Nevitt, M.C., 1989. A hypothesis: the causes of hip fractures. Journal of Gerontology l44 (4), M107–111. Currey, J.D., 1979. Changes in the impact energy absorption of bone with age. Journal of Biomechanics 12 (6), 459–465 467–469. Currey, J.D., 2002. Bones: Structure and Mechanics. Princeton University Press, N.J.; Oxford p. c2002. Dawson, S.P., Muir, A.Y., Simpson A.H.R.W., 2008. Quantitative density information with computed radiography. 2nd Joint Meeting of the British Orthopaedic Research Society and BoneResearch Society, 23–25 June 2008. Manchester, England. Donaldson, F.E., Pankaj, P., et al., 2011. Relating age and micro-architecture with apparent-level elastic constants: a micro-finite element study of female cortical bone from the anterior femoral midshaft. Proceedings of the Institution of Mechanical Engineers H225 (6), 585–596. Hansen, U., Zioupos, P., et al., 2008. The effect of strain rate on the mechanical properties of human cortical bone. Journal of Biomechanical Engineering 130 (1), 011011–011018. Kanis, J.A., Melton, L.J., et al., 1994. The diagnosis of osteoporosis. Journal of Bone and Mineral Research 9 (8), 1137–1141. Launey, M.E., Chen, P.Y., et al., 2010. Mechanistic aspects of the fracture toughness of elk antler bone. Acta Biomaterialia 6 (4), 1505–1514.
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McElhaney, J.H., 1966. Dynamic response of bone and muscle tissue. Journal of Applied Physiology 21 (4), 1231–1236. Milan, L., Trachtenberg, M.C., 1981. Ultrasonic decalcification of bone. American Journal of Surgical Pathology 5 (6), 573–580. Sasaki, N., Yoshikawa, M., 1993. Stress relaxation in native and EDTA-treated bone as a function of mineral content. Journal of Biomechanics 26 (1), 77–83. Shah, K., Goh, J., et al., 1995. Effect of decalcification on bone mineral content and bending strength of feline femur. Calcified Tissue International 56 (1), 78–82. Skedros, J.G., Bloebaum RD, D.P., 1995. Hypermineralized peripheral lamellae in primary osteons of deer antler: potential functional analogues of cement lines in mammalian secondary bone. Journal of Bone and Mineral Research 10 (Suppl. 1), S441. Thorpe, E.J., Bellomy, B.B., et al., 1963. Ultrasonic decalcification of bone: an experimental and clinical study. Journal of Bone and Joint Surgery 45 (6), 1257–1259. van der Meulen, M.C.H., Jepsen, K.J., et al., 2001. Understanding bone strength: size isn't everything. Bone 29 (2), 101–104. Vashishth, D., Tanner, K.E., et al., 2003. Experimental validation of a microcrackingbased toughening mechanism for cortical bone. Journal of Biomechanics 36 (1), 121–124. Wright, T., Hayes, W., 1976. Tensile testing of bone over a wide range of strain rates: effects of strain rate, microstructure and density. Medical and Biological Engineering and Computing 14 (6), 671–680. Yeni, Y.N., Norman, T.L., 2000. Calculation of porosity and osteonal cement line effects on the effective fracture toughness of cortical bone in longitudinal crack growth. Journal of Biomedical Materials Research 51 (3), 504–509. Yerramshetty, J.S., Akkus, O., 2008. The associations between mineral crystallinity and the mechanical properties of human cortical bone. Bone 42 (3), 476–482. Zioupos, P., Hansen, U., et al., 2008. Microcracking damage and the fracture process in relation to strain rate in human cortical bone tensile failure. Journal of Biomechanics 41 (14), 2932.
Contents lists available at ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
The effect of strain rate on the failure stress and toughness of bone of different mineral densities R.J. Wallace n, P. Pankaj, A.H.R.W. Simpson The University of Edinburgh, Chancellor's Building, 49 Little France Crescent, Edinburgh, Eh16 4SB, UK
art ic l e i nf o
a b s t r a c t
Article history: Accepted 11 June 2013
The risk of low energy fracture of the bone increases with age and osteoporosis. This paper investigates the effect of strain rate and mineral level on the peak stress and toughness of whole ovine bones. 40 fresh ovine femurs were subjected to 3-point bending at high (17.14 s−1) and low (8.56 10−3 s−1) strain rates with or without a controlled amount of demineralisation. Mineral removal was achieved by ultrasonically assisted exposure in Ethylene diamine tetra-acetic acid (EDTA). The ultimate stress for whole bones of normal mineral content was 200 MPa at the high rate of strain and 149 MPa at the low rate of strain. With changes in bone mineral levels such as may occur in osteomalacia and osteoporosis, the change in toughness varied at different strain rates; a mean value of 3.7 71.4 MJ/m3 was obtained for the toughness of normal quality whole bone tested at slow loading rate and a reduction of approximately 25% was observed in the demineralised whole bone specimens at the slow loading rate (mean 2.8 70.9 MJ/m3). When tested at the high loading rate there was a negligible difference in the toughness between the two (2.0 70.6 MJ/m3) mineral levels. This indicated that there was a strain rate dependant effect for the mineral density, and that the removal of mineral alone did not explain all of the reduction in mechanical properties that occur with age or disease. Thus, the reduction in mechanical properties at high strain rates was likely to be due to other phenomena such as increased porosity or reduced collagen quality, rather than loss of mineral. With decreasing mineral levels, as measured by DEXA in clinical practice, the increased fracture risk is dependent on the velocity of the impact. Thus the estimates of increased fracture risk given clinically for a lower DEXA value should be different for high and low energy injuries. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Strain rate Demineralisation Toughness Stress
1. Introduction Bone is a hierarchical composite material and changes occur on multiple length scales that influence the mechanical properties of the whole bone. The risk of low energy fracture of the bone increases with age and osteoporosis. Martin (2003) and Van der Meulen et al. (2001) indicated that there are many factors that combine to give bone its overall quality. However, the onset of the effects of osteoporosis is determined by assessing the mineral content of the bone (Kanis, 1994). Shah et al. (1995) conducted bending tests on feline bone segments that had been demineralised to different degrees. However, these were tested with a machine crosshead speed of 10 mm/ min, which is considerably slower than that would be encountered in physiological activities such as walking. The viscoelastic response of demineralised bone was acknowledged in a study by Sasaki and
n
Corresponding author. Tel.: +131 242 6296; fax: +131 242 6534. E-mail address: [email protected] (R.J. Wallace).
0021-9290/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jbiomech.2013.06.010
Yoshikawa (1993) who investigated the stress relaxation of demineralised bone, but they used samples of bone machined from bovine femur rather than whole bones and tested these by cantilever bending. To date, no studies have investigated the effect of partially demineralised bone at traumatic loading rates. Therefore the aim of this research is to investigate the effect of partial mineral removal from bone to a clinically relevant level on the ultimate stress and the toughness at both low and fast strain rates. The strain rates in this study have been chosen to be representative of (i) the lower end of fractures classed as “low energy fractures”, i.e. those that could occur from a fall from a bed or chair or a fracture that occurs due to movement before the fall, which has been estimated to be just under 10% of elderly hip fractures (Cummings and Nevitt, 1989), (ii) those found to be representative of high energy fracture, such as the rates of strain that have been measured to occur in the lower limbs during a motor vehicle accident (Hansen, 2008). In particular, as bone is a viscoelastic multidimensional composite, we tested the hypothesis that alteration of the composition of this composite will have differing effects at different rates of strain.
2284
R.J. Wallace et al. / Journal of Biomechanics 46 (2013) 2283–2287
2. Methods
2.2. Demineralisation
A total of 40 femurs were harvested from freshly euthanized sheep. These were split equally between four testing groups according to testing speed and mineral content; fast-normal (FN), fast-demineralised (FD), slow-normal (SN), slowdemineralised (SD).
In order to examine the effects of the bone mineral on the bone properties, half of the bones were subjected to a standardised amount of demineralisation. The level of demineralisation was assessed using a calibrated step wedge in the radiographic image (Dawson et al., 2008) and mean values of 2.47 g/cm3 (7 0.42 SD) were found for the normal quality group and 1.86 g/cm3 ( 7 0.28 SD) for the demineralised group, representing a mean reduction of 25%. This mineral density reduction is representative of a density reduction that a 75 year old female may have undergone compared to her peak bone density (Kanis, 1994). To speed up the decalcification process, mineral was removed by ultrasonically assisted agitation in 10 M Ethylene diamine tetra-acetic acid (EDTA). This is a validated method that has been used in previous studies (Shah et al., 1995) and is commonly used as a means of preparation of bone samples for histology (Alers, 1999). It has been shown not to cause morphological deterioration of the tissue (Thorpe, 1963; Milan, 1981). Additionally, the ultrasonic agitation was thought to assist the removal of mineral from within the bone. The reduced grey level throughout the whole cross section of the bone on the microCT images confirmed that the mineral dissolution was not confined to the external surfaces. In order to ensure that the porosity was not altered during demineralisation, 8 sample fragments from 4 paired limbs (normal and demineralised) were scanned at a resolution of 4.8 mm. Analysis of these groups revealed mean porosities of 8.15% 73.13 SD and 7.88% 7 3.76 SD for the normal and demineralised specimens respectively, which represented no significant difference between the groups as found by a paired t-test with a p value of 0.924.
2.1. Testing The slow loading rate experiments were carried out on a commercially available mechanical testing machine, Zwick/Roell z005 (Zwick GmbH & Co, Ulm, Germany). Data capture was provided by TestXpert V9.01 (Zwick GmbH & Co, Ulm, Germany). This is the proprietary software for the Zwick and as such acted as both the data capture and the control system for the slow rate experiments. The bones were loaded in 3-point bending at a constant rate of 1 mm/s. This created an average strain rate in the bone of 8.56 10−3 s−1 ( 71.42 10−3 SD). The fast rate loading was applied in 3-point bending by a custom designed experimental set up. The final set up consisted of: a bespoke manufactured bone holder, an aluminium impact head, a dynamic force sensor (PCB 208C05 (PCB Piezotronics Inc. New York, USA)), a pneumatic actuator (Norgren PRA/18200/200) and a LabVIEW data capture system (National Instruments Corporation. Texas, USA) sampling at 100 kHz to monitor the loading. A Vision Research Phantom v7.1 monochromatic high speed camera (Vision Research Inc. New Jersey, USA) running at 25,000 fps and fitted with a Nikon 24–85 mm F2.8 lens was used to record the deformation at the high loading rate. The initial rate of displacement of the unloaded actuator was 3.6 m/s (70.2 m/s). As the mass of the actuator was constant, the initial energy imparted was comparable. The strain rate that was subsequently produced in the bone through bending was dependant on the stiffness of the bone; the normal bone quality specimens had a mean strain rate of 13.3 s−1(77.0 SD) and the demineralised group was found to have a mean strain rate of 20.9 s−1(77.7 SD). This gave an average strain rate of 17.14 s−1 (78.20 SD) for the fast loading rate experiments. Although the strain rates experienced by the bone in these tests varied significantly, even the minimum strain rate encountered in these experiments was three orders of magnitude greater than that found to occur during extreme physiological loading, such as up-hill running as found by Burr et al. (1996). During testing at both loading rates the bone was located on rounded supports of 10 mm diameter at either end and the load was applied via an aluminium cylinder with a diameter of 35 mm. The bone was positioned and the supports adjusted as required to ensure the supports were located consistently between samples. The area immediately distal to the lesser trochanter and the flat section of bone proximal to the posterior femoral condyles were chosen as this would ensure the supports were located consistently and on a section of bone that would prevent rotation of the bone during loading. The load was always applied equidistantly from the two supports. The experimental set up can be seen in Fig. 1. The second moment of area was derived at several cross sections along the length of the bone using images taken from post testing microCT scans. The second moment of area at either side of the fracture was averaged to provide a value for this property at the fracture site to be used when determining the stress. Peak stress was calculated using engineers bending theory using the bending moment due to peak force and the second moment of area derived as described above. Due to the low aspect ratio, the length of the tested span divided by the depth of a whole femur and the use of 3 point bending during testing it was required to account for deflection due to shear by using Timoshenko's bending theory. The normal (bending) strain was then calculated and used to plot a stress– strain curve. The toughness was found by from the area under the curve.
2.3. Data analysis The data was checked for normality before an analysis of variance (ANOVA) was performed with a Tukey simultaneous test to investigate the differences between the groups for statistical significance. A p-value equal to or less than 0.05 was taken to indicate a statistically significant difference.
3. Results The results from the experiments performed for this study are presented in Table 1 and Fig. 2. Statistically significant differences (p o0.05, ANOVA) were found between the fast loaded normal quality group and all the other groups when comparing the peak stress. No further statistical differences were found. Statistically significant differences (p o0.05, ANOVA) were found for the toughness at failure between the slow loaded, normal quality bones and both qualities of fast loaded bones. The results highlight the involvement of the mineral in preventing fracture from traumatic loading by demonstrating a decrease in peak stress when demineralised bone was loaded at a fast rate of strain. However, the very similar mean values and standard deviations for toughness for normal and low mineral levels at the high rate of strain was interesting as this implied that the mineral did not play a significant role in the toughening mechanism at rates of strain encountered in high velocity trauma.
4. Discussion 4.1. Tests at normal mineral levels Bones of normal density from healthy young adult animals were found to have a higher peak stress but a lower toughness when loaded at a fast strain rate. Table 1 Mean ( 7SD) of peak stress and failure toughness of tested bones.
Fig. 1. Experimental setup for fast loading rate tests. Bone shown wrapped in gauze to prevent dehydration prior to testing.
Peak stress, sult (MPa) Toughness, T (MJ/m3)
FD
FN
SD
SN
141 717.6 2.0 70.6
2017 19.9 2.0 7 0.6
1367 23.9 2.8 7 0.9
1487 32.2 3.7 7 1.4
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Fig. 2. Box-plot of results for (a) stress and (b) toughness at failure.
Table 2 Testing methods used investigating effect of strain rate on mechanical properties of bone. Researcher
Species
Bone
Test type
Sample size
Strain rate range
Number of specimens
Crowninshield and Pope Crowninshield and Pope Wright McElhaney Hansen
Bovine Bovine Bovine Human Human
Tibia Tibia Femur Femur Femur
Tension Compressive Tension Compressive Compressive
12.7 28.6 1.5 (5 mm gauge) 12.7 28.6 1.5 (5 mm gauge) Necked sections 17.8 5.1 76 mm 3 2.4 7 mm gauge
0.01–200 s−1 0.01–200 s−1 5.3 10−4–237 s−1 1 10−3–1500 s−1 0.14–29 s−1
46 46 70 45 25
Several previous studies (Crowninshield and Pope, 1974; Hansen, 2008; McElhaney, 1966; Wright and Hayes, 1976) have examined the effects of loading rate on fracture of normal bone segments. The results from the current study for the normal bone quality experiments were compared with existing results in the literature (Table 2), but as none of the tests used exactly the same strain rates the values from the literature were interpolated for comparison. Hansen et al. (2008), consider that a strain rate on the bone of 25 s−1 provides an upper boundary for strain rates relevant to bone failures in traumatic events such as a motor vehicle accident, similar to the fast loading rate experiments conducted in this study (17.14 s−1 7 8.20 SD) The results of this comparison are presented in Figs. 3 and 4. Fig. 3 demonstrates that the numerical values of peak stress for normal bone are similar for all researchers. However, there is a larger degree of scatter in the numerical values found for toughness of normal bone (Fig. 4). As different testing methods were used by different authors it is perhaps more useful to compare the percentage differences between the properties found at the different strain rates. Table 3 compares the percentage change in peak stress and toughness of normal bone between high and low strain rates. The percentage changes in these properties found in this study are similar to the percentage changes found in previous studies (Figs. 3 and 4) Very close agreement was found when comparing peak stress between the strain rates of this study with the main body of literature. A larger amount of variation was found when comparing toughness. This is because other studies have used different sample types and loading methods—compressive, tensile or bending. The type of loading experienced by the bone will determine what failure value to use for predictive analysis.
Fig. 3. Stress at failure at high and low strain rates of this study compared to literature.
4.2. Testing at reduced mineral levels Previous studies have not examined the effect of reduced mineralisation on bone fracture at high strain rates. At high strain rates there was a significant difference in peak stress between
Fig. 4. Toughness at failure at high and low strain rates of this study compared to literature.
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Table 3 Percentage difference between high and low strain rate. Results from this study are compared with those from the literature. Property
This study
Mean existing data7 SD
Peak stress Toughness
36% 46%
38% 7 14% 35%7 12%
normal and demineralised bone; in contrast the toughness was similar. At low rates of strain there was no statistically significant differences between normal and demineralised bone, both for peak stress and toughness, though both these properties were found to be higher for normal bone. This finding implies that at the high rate of strain there is a method of energy absorption that is insensitive to mineral content. 4.3. Comparison with naturally occurring differences in mineralisation The results for the partially demineralised specimens were compared against values in the literature for bones with nonstandard/abnormal mineral levels. Examples of altered mineral level were found in juvenile bone, old bone and antler bone. Currey (1979) investigated the density and energy to fracture for a wide age range of bones. This work showed that the mineral level was minimal at both ends of the age range. However, the energy to fracture was maximal for the youngest specimens then decreased with age. It has been shown by Hansen (2008) and Vashishth and Tanner (2003), that microcracking is one of bones primary toughening mechanisms. It was proposed that the method of mineral removal used in this study may have altered the shape of the hydroxyapatite crystals in the bone, reducing the efficiency of microcrack initiation. The method of mineral removal was chelation of the calcium from the hydroxyapatite crystals in the bone matrix by exposure to EDTA. As this process occurs the fluid will effectively ‘erode' the crystals of mineral as it removes the calcium, smoothing the crystals as the mineral is leeched out of the bone. Yerramshetty (2008) and Akkus (2004) have shown that larger crystals of mineral will be stiffer and therefore more likely to be a cause of stress concentration and act as an initiation point for microcracking. This microcracking process would be less efficient with smaller crystals with smother edges, providing a possible explanation for the reduction in toughness observed with mineral removal when tested at slow rates of strain in these experiments. In addition to this, the reduction in the mineral at locations such as cement lines will also decrease the effectiveness of these locations in reducing crack propagation. Work by Currey (2002) has shown that there is a strong relationship between mineral content and fracture toughness, with the highly mineralised and very stiff ear bones providing little resistance to fracture and the low mineral deer antler providing a tough, fracture resistant material. Fracture toughness investigations in elk antler performed by Launey et al. (2010) have highlighted the structural differences between the non-loaded antler bone and long bones used for locomotion. In addition to a lower level of mineral, this material is shown to have smaller osteons and considerably smaller vascular channels. Furthermore, as well as the differences in size of these constructional elements, it has been shown by Skedros et al. (1995) that there is also a difference in the distribution of the mineral around these elements where the antler bone has highly mineralised regions surrounding these osteons compared to the thinly mineralised region, known as a cement line, which is found in structural bone. Cement lines are thought to play an important role in the fracture process,
acting as both potential crack initiation sites and as features to arrest crack propagation (Yeni and Norman, 2000). Therefore, differences in this feature would be expected to contribute towards differences in fracture properties It has been demonstrated by Zioupos (2008) that there is a reduction in microcracking that occurs with increasing strain rate. The results presented in this study show that there was no significant difference in toughness between the two mineral levels when tested at the high strain rate in spite of higher peak stress. The slow loaded normal bones demonstrated a statistically significant higher toughness than the fast loaded normal bones, despite having a statistically significant lower peak stress, suggesting that the toughening mechanism, which occurs due to the formation of microcracks, is more effective at low than at high rates of strain. Augat and Schorlemmer (2006) showed that pore size increased with age and that there was a significant reduction in the strength of bone with pore size, and researchers such as Donaldson (2011) have shown that there was a strong correlation between the mechanical properties and porosity; the age of the samples alone was found to be far less predictive than the porosity. This implies that both porosity and mineral content are important aspects of bone quality and should be considered when determining fracture risk. Of the material changes that occur to bone during the aging process, such as reduced mineral content, altered microstructure (porosity), build-up of microcracks and changes to the collagen, this study can only directly assess the effect of the partial removal of mineral; the porosity for normal and demineralised samples was found to remain unchanged.
5. Conclusions A reduction in the mineral content results in a decrease in strength of the bone but not in toughness at fast, traumatic rates of strain. When tested at a slow rate of strain there was minimal change in the peak stress but a reduction in toughness with reduced mineral content, possibly due to a reduction in microcrack formation provided by the presence of mineral. Significance:
With decreasing mineral levels, as measured by DEXA in
clinical practice, the increased fracture risk is dependent on the velocity of the impact. Thus the increased fracture risk predicted with a lower DEXA value will be different for high and low energy injuries. With changes in bone mineral levels as may occur in osteomalacia and osteoporosis, the change in toughness varies at different strain rates; values are provided that can be used in future fracture prediction models.
Conflict of interest There were no conflicts of interest in the research or presentation of this paper.
Acknowledgements The Vision Research high speed camera was loaned for this research by the EPSRC Equipment Loan Pool. References Akkus, O., Adar, F., et al., 2004. Age-related changes in physicochemical properties of mineral crystals are related to impaired mechanical function of cortical bone. Bone 34 (3), 443–453.
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