- Email: [email protected]
Fracture and fatigue in osteocytes
journal of the mechanical behavior of biomedical materials 39 (2014) 231–237
Available online at www.sciencedirect.com
www.elsevier.com/locate/jmbbm
Fracture and fatigue in osteocytes Simone Mulargiaa,b, Clodagh Dooleya,c, Luca Cristofolinib, David Taylora,d,n a
Trinity Centre for Bioengineering, Trinity College Dublin, Dublin, Ireland Department of Industrial Engineering, University of Bologna, Bologna, Italy c Centre for Microscopy and Analysis, Trinity College Dublin, Dublin, Ireland d Department of Mechanical and Manufacturing Engineering, Trinity College Dublin, Dublin, Ireland b
art i cle i nfo
ab st rac t
Article history:
Fatigue is a common mode of mechanical failure which occurs when a material is
Received 13 June 2014
subjected to repeated cycles at a strain level less than that needed for monotonic fracture.
Received in revised form
Fatigue has been observed and measured in many different materials but, until recently,
22 July 2014
not in cells. We devised a novel experiment which allowed us to create both monotonic
Accepted 26 July 2014
failure and fatigue in the cellular processes of osteocytes within samples of bone (Dooley
Available online 4 August 2014
et al., European Cells and Materials 2014). In the present paper, we describe the results of
Keywords:
further experiments and a computer simulation, which has allowed us to estimate the
Fatigue
strain history of each sample tested and thus present, for the first time, strain/life data for
Cells
cells. Failure occurred during the first cycle at strains of 0.1–0.2; at lower strains failure
Osteocytes
occurred after a number of cycles which depended inversely on the applied strain range.
Strain
Scatter in the strain/life data was reduced when we allowed for the effects of mean stress
Failure
using the Smith–Watson–Topper parameter. We confirmed that aspects of our experimental method (the types of microcrack used and the testing of fresh versus frozen samples) did not affect the results. Such information is useful because many cell types, including the cellular processes of osteocytes, experience cyclic strain in vivo. & 2014 Elsevier Ltd. All rights reserved.
1.
Introduction
Engineers and materials scientists are very familiar with the term “fatigue”, which refers to the gradual failure of a material when it is subjected to cycles of strain, the largest value of which is not sufficient to cause failure if applied only once in so-called “monotonic” loading. In medical circles the word fatigue has a different meaning, and the failure of a tissue such as bone under cyclic loading is referred to as a “stress fracture”. Fatigue failures are divided into two groups – “low cycle fatigue” and “high cycle fatigue” – according to
the number of cycles to failure. Low cycle fatigue – the subject of the present paper – occurs when a material is loaded to a maximum strain which, in a monotonic test, would cause non-reversible behaviour such as plastic strain, microdamage or viscoelasticity over a significant proportion of the material volume. Damage accumulates quickly on each cycle leading to failure in a relatively small number of cycles. Fig. 1 shows typical test data (Boller and Seeger, 1987), in which the number of cycles to failure Nf is plotted as a function of the strain range Δε, defined as the difference between the maximum and minimum strain in the cycle. Data are usually
n Corresponding author at: Trinity Centre for Bioengineering, Trinity College Dublin, Dublin, Ireland. Tel.: þ353 1 8961703; fax: þ353 1 6795554. E-mail address: [email protected] (D. Taylor).
http://dx.doi.org/10.1016/j.jmbbm.2014.07.023 1751-6161/& 2014 Elsevier Ltd. All rights reserved.
232
journal of the mechanical behavior of biomedical materials 39 (2014) 231 –237
presented on a logarithmic plot and often fall approximately on a straight line, giving the following empirical relationship in which C and n are constants: Nf ¼
C Δεn
ð1Þ
It has been demonstrated that fatigue occurs in many different types of materials, including metals, ceramics, polymers and composites (Stephens and Fuchs, 2001; Hertzberg and Manson, 1980), and also in natural composite materials such as bone (Taylor, 1998) and wood (Salmi et al., 2012), but until very recently fatigue had not been detected in mammalian cells. Indeed, there are almost no published data on any kind of mechanical failure mode for cells. Exceptionally, the failure strain of the outer cell membrane (which consists of a bilayer of lipids) was measured at 0.02–0.03 (Nichol and Hutter, 1996). Failure of this membrane may not lead to total rupture of the cell, because the cell is also supported by a cytoskeleton and may be able to repair local membrane damage (Sheetz et al., 2006). Pipette aspiration has
Fig. 1 – Typical data from low-cycle fatigue testing, in this case for two metallic materials (Boller and Seeger, 1987). The number of cycles to failure is plotted logarithmically against the applied strain range.
been used to cause membrane rupture in red blood cells and thus estimate membrane strength (Rand, 1964). In summary, there is a lack of data in the literature reporting how much strain is needed to permanently rupture a cell, whether loaded monotonically or cyclically. This information is important because many types of cells experience cyclic strain. For example endothelial cells undergo strains of the order of 0.22 (Mofrad and Kamm, 2010) as a result of fluid shear. Cyclic strain levels of the order of 0.05 are necessary for the differentiation of various cell types (Mofrad and Kamm, 2010); the osteocyte network is ruptured in the vicinity of microdamaged bone (Colopy et al., 2004) and this rupture takes the form of fatigue failures of individual cellular processes (Dooley et al., 2014). Recently we devised an experiment which allowed us to carry out this type of testing on bone cells (osteocytes). Our method (Dooley et al., 2014) takes advantage of the fact that osteocytes live inside the bone matrix and are connected to each other via long, thin extensions of the cell body known as cellular processes (Fig. 2). We noticed that if there is a crack in the bone matrix, these processes can be seen passing across between the crack faces (Fig. 3). By applying forces to a sample of bone we were able to cause a crack to open and close, thus applying strain to the processes spanning it. Some processes failed immediately on the first loading cycle, whilst others failed after a number of cycles. We thus demonstrated the existence of fatigue failure in cellular processes, which are made from the same constituents as other parts of the cell membrane and cytoskeleton. However this experiment had some limitations. We were not able to quantify the applied strain because, though we could measure the opening displacement of the crack, we did not know the total length of the process, and processes are known to adhere to the bone matrix via focal adhesion points (McNamara et al., 2009), which will affect the distribution of strain along their lengths. We also had some concerns about some aspects of our methods for sample preparation. The work described in the present paper aimed to answer the following questions: (1) What are the strain levels at which monotonic rupture and low cycle fatigue failure occur? To answer this
Fig. 2 – Osteocytes are linked together in a network via numerous cellular processes: these images show examples of cells without (a) and with (b) the surrounding bone matrix (Klein-Nulend et al., 2005).
journal of the mechanical behavior of biomedical materials 39 (2014) 231 –237
233
Fig. 3 – SEM images of part of a microcrack in a bone sample, showing several cellular processes (thin white lines) passing across the crack. (A) This image was taken at the start of test: note the process indicated by the circle. (B) After a number of cycles this process has ruptured.
question we created a computer simulation of our experiment, using finite element analysis (FEA). (2) Are the results affected by tissue preservation methods? Previously we had used bone which had been frozen for storage. We carried out further tests using freshlyharvested bone. (3) Are the results identical when naturally-occurring cracks are used? In our previous work we artificially created cracks by applying forces to pre-notched samples. In the current work we used instead the microscopic cracks which are already present in vivo. This is of interest for obtaining a more general understanding of the role of osteocyte networks and their relationships to microdamage in bone.
2.
Methods and materials
2.1.
Experimental testing
The experimental methods were the same as reported previously (Dooley et al., 2014): what follows here is a brief description. The only differences were that in the present work the bone samples were fresh (rather than frozen), the loading axis was longitudinal to the bone axis (rather than transverse) and we used pre-existing microcracks (rather than inducing cracks to grow from notches). Fresh bovine tibiae were obtained from a meat producer (Keepac, Clonee, Ireland); samples were cut and ground into rectangular specimens with approximate dimensions 20 5 1 mm, the 20 mm length being parallel to the bone's axis. Because cracks tend to form during sample preparation, we used a heavy metal stain (Schaffler et al., 1994) which deposits lead and uranyl sulphide precipitates in the cracks; this allowed us to distinguish those cracks which had already formed in vivo when examining them in the scanning
electron microscope. We used only those cracks in the subsequent work. As in our previous study, the samples were fixed in 4% paraformaldehyde solution for 24 h at 4 1C and dried gradually using alcohol dehydration and critical point drying to minimise damage. Tests described previously (Dooley et al., 2014) established that this preparation protocol did not significantly affect the results. Axial loading was applied to the samples using an in situ straining stage (Deben, East Grinstead, UK) inside a scanning electron microscope (Tescan, BRNO, Czech Republic). Before applying any loads, a number of microcracks was identified and the processes crossing these cracks were counted and recorded (see Fig. 3 for an example of the images used). Processes can be distinguished from other features such as collagen fibres by their distinctive morphology: in our previous work (Hazenberg et al., 2006) we used phalloidin staining to confirm this. In total, 35 processes were studied. A compressive cyclic load was applied, varying from 180 N to 1 N, which corresponds to a stress cycle from 36 MPa to 0.2 MPa. Fatigue tests are normally carried out under cyclic tension, rather than compression; in this case the processes were already experiencing tension as a result of the opening of the crack which occurs during drying. Thus, by applying a compressive load we caused the crack to partially close, creating a cycle of strain between maximum and minimum levels which were both tensile. The time for each cycle was one minute; a total of 100 cycles was applied. Images were taken at maximum and minimum load; Image J software was used to measure the opening and closing of each crack at the location of each process, after each cycle, in a direction parallel to the long axis of the process. For those processes which failed (e.g. see Fig. 3) the number of cycles to failure was recorded.
2.2.
Computer simulation
A finite element model was created using ANSYS software to allow us to estimate the strain experienced by a cellular
234
journal of the mechanical behavior of biomedical materials 39 (2014) 231 –237
Fig. 4 – The finite element model of the test sample: this is a half-model, the plane of symmetry, being the front plane as shown here, contains two osteocytes linked by a process. In image (A) the crack is closed (see arrow): in (B) it has opened as a result of a tensile force applied to the ends of the sample.
process during crack opening and closing. Taking advantage of symmetry, a half model was created (see Fig. 4) including the bone sample, the crack and two osteocyte cells linked by a process passing across the crack. Bone was assumed to have Young's modulus values of 22 GPa and 12 GPa in the longitudinal and transverse directions respectively and a Poisson's ratio of 0.3 (Reilly and Burstein, 1975). No mechanical property data exist for osteocytes; we assumed a Young's modulus of 5.9 kPa and a Poisson's ratio of 0.39 based on data from osteoblasts (Kuznetsova et al., 2007). Since the Young's modulus is much less than that of bone, the chosen value will not have a significant effect on our predictions of strain for the process itself. Typical dimensions were used for osteocytes (diameter 10 μm) and processes (diameter 0.2 μm): the typical spacing between osteocyte centres was estimated to be 37 μm based on known data for the density of osteocytes in cortical bone (Mullender et al., 1996): as a result the total length of the process was 27 μm. Osteocytes and their processes are located within holes (lacunae) and channels (canaliculi) in the bone matrix. They fit snugly into these spaces but provide space for fluid to flow. They are attached to the bone at discreet points known as focal adhesions (McNamara et al., 2009). The nature of these adhesions is not well understood but there are some results in the literature for related cell types. For the strength of the adhesive bond we used a value of 7.96 Pa which was measured for osteoblast-like cells adhering to the surface of calciumcontaining borate glass which forms a calcium-phosphate
layer similar to the mineral found in bone (Wiederhorn et al., 2011). If the shear stress on the process/bone interface exceeded this value during the simulation then the interface condition was changed in the model to simulate debonding. The FE model was validated by comparing its predictions of stress near the crack tip and displacement of the crack faces, as a function of the applied load. Values of these parameters agreed with theoretical results (Janssen et al., 2002) to within 1%.
3.
Results
Fig. 5 shows examples of the variation of displacement δ during a test for two of the processes examined, one of which failed after three cycles whilst the other did not fail after 100 cycles. The initial displacement represents the opening of the crack at that point before any compressive load was applied. Cycling the load between 180 N and 1 N caused δ to vary, but the increase and decrease of δ at a given point did not necessarily follow exactly the cycles of applied load, owing to local irregularities in the crack shape and variations in the angle at which a process crossed a crack. For the same reason the amount of displacement experienced by a process, and its variation during load cycling, changed considerably from place to place along the crack front. There were also changes in the mean strain, which showed slight increases and decreases initially, though these changes tended to level
journal of the mechanical behavior of biomedical materials 39 (2014) 231 –237
Fig. 5 – Typical test data, showing displacement measured across the crack faces at the location of each process, at the start of the test (0 N) and for each cycle of load thereafter (max load 180 N, min load 1 N). Two processes are shown: one failed after 3 cycles, whilst the other remained unfailed for 100 cycles (here only the first few cycles and last few cycles are shown).
tentative line to indicate the trend of the data. Accurate curve fitting would not be appropriate given that most of the data lie in the region 1–4 cycles (and show significant scatter) and the line should, in theory, pass above the data for the unfailed samples. In the computer simulation, a force was first applied to cause crack face opening, simulating the starting condition for the experiments. This loading caused failure of the adhesive bond between the cellular process and the bone in regions close to the crack faces where the local shear stress exceeded the adhesive strength. This was implemented in the model by changing the interface condition for the relevant nodes, allowing us to define a “free length”, being the length over which the cellular process was not bonded to the bone. The strain in the process could then be calculated by dividing the measured displacement by this free length. The total length of the process in the model was 27 μm: we found that for crack opening displacements in the range 1–5 μm (which were the values measured experimentally) the free length f (in microns) varied in a linear manner with displacement δ according to the following equation: f ¼ 1:14δ þ 16:3
4.
Fig. 6 – Test results showing the number of cycles to failure for individual processes as a function of cyclic displacement range (“Natural Cracks”) along with data reported previously (Dooley et al., 2014) (“Induced Cracks”). Also included is a point and scatter band representing the 25 unfailed processes.
out after the first few cycles; this was probably due to local creep in the bone matrix. For the purpose of presenting the results we calculated the average cyclic displacement range for each process. This is shown in Fig. 6 as a function of the number of cycles to failure. The data generated in the present work is labelled “Natural Cracks”; also included on the figure are the data from our previous work (Dooley et al., 2014), which are labelled “Induced Cracks” because in those experiments we created cracks artificially in the samples as explained above. Eight processes were monitored in those tests. In the present work, a total of 35 processes were observed, of which 10 failed either on the first cycle or subsequent cycles, and the remaining 25 did not fail after 100 cycles. The results for these unfailed processes are included in Fig. 6, along with a
235
ð2Þ
Discussion
The results shown in Fig. 6 confirm our previous findings that osteocyte processes can experience fatigue failure. The number of cycles to failure which we were able to record is admittedly very small, ranging from 1 to 8, but these fatigue failures happened at applied displacements which were considerably less than those needed for monotonic failure, i.e. failure on the first cycle. All tests below 0.1 μm gave no failures up to 100 cycles, implying a reduction in the slope of the line which also seen in other materials (Boller and Seeger, 1987). It would be very interesting to extend this data to larger numbers of cycles, but currently this would not be possible with our equipment owing to the difficulty of measuring smaller cyclic displacements with the necessary accuracy. Fig. 7 shows the same data, converted into cyclic strain range values using our FE results. This is the first time that strain/life data, of the kind commonly collected for engineering materials, has been presented for cells. Failure on the first cycle occurred at strains in the range 0.1–0.2, with fatigue failure occurring for strain ranges as low as 0.007. Following the normal convention for fatigue analysis we have drawn a straight line through this data: this gives a value of 0.75 for the exponent n in Eq. (1) which describes the dependence of fatigue life on applied strain. The general trend of the results is quite similar to those for typical metallic materials: in the example shown in Fig. 1 the overall strain levels are larger, but the value of n, being 0.98, is quite similar. As noted above, one of the limitations of these experiments was that the mean strain tended to vary from sample to sample, and within a sample during cycling. It is well known that mean strain affects fatigue behaviour: higher mean strain results in smaller numbers of cycles to failure, though the effect is different in different materials. A number
236
journal of the mechanical behavior of biomedical materials 39 (2014) 231 –237
Fig. 7 – Estimated cyclic strain range plotted against cycles to failure for all failed processes.
Fig. 8 – Allowing for mean strain by plotting the SWT parameter, which tends to reduce the scatter.
of different theoretical models exist to predict the effect of mean stress and strain (Ince and Glinka, 2011). We employed a commonly-used approach: the Smith–Topper–Watson (SWT) parameter (Boller and Seeger, 1987) which, when expressed in terms of mean strain εm and strain range Δε, can be written: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð3Þ PðSWTÞ ¼ ð2Δε þ εm Þ2Δε Fig. 8 shows the data replotted using the SWT parameter. Comparing Figs. 6–8 one can observe a reduction in the amount of scatter: to quantify this we fitted a straight regression line to the date on these log/log plots and calculated the R2 value, which increased from 0.363 when displacement was used (Fig. 6) to 0.562 for strain (Fig. 7) to 0.774 for the SWT parameter (Fig. 8), showing the advantage in taking account of both cyclic strain and mean strain. Some scatter remains, especially at high strain levels where, owing to the relatively flat slope of the line, a small change in strain causes a large change in Nf. This variability in individual results is not unusual even for engineering materials: in our case some of the scatter will be caused by inaccuracy in our
method of estimating strain, particularly our assumption that the length of the process (i.e. the distance between osteoctyes) is constant. Whatever the method of displaying the data, it is clear that there is no significant difference between the present results and those obtained in our previous study. To confirm this we carried out a T-test, comparing the two groups (Natural Cracks and Induced Cracks) in terms of the SWT parameter, normalised in each case by the mean value for a given number of cycles. The resulting p value for an unpaired, two tailed T-test was p ¼0.48. Strictly speaking a more rigorous analysis, with more data, would be necessary to prove similarity, but the present result certainly indicates that no significant difference can be detected between these two groups. Thus, the use of previously-frozen bone samples does not appear to affect the fatigue behaviour of the osteocytes, nor does the use of induced cracks as opposed to naturally-occurring cracks. Both types of crack tend to form parallel to the osteons and therefore are oriented approximately parallel to the longitudinal axis of the bone, though for microcracks the orientation with respect to the bone axis varies by as much as 301 (Taylor and Lee, 1998). In our previous work using induced cracks we loaded the bone in tension perpendicular to the longitudinal axis, so that the angle between the loading axis and the crack plane was always 901. In the present study we used a more physiological type of loading, applying compression parallel to the longitudinal axis. As a result the angle between the microcrack and the load axis varied, being typically about 201. This will give rise to shear as well as compression across the crack faces, to a degree which varies from place to place along the crack front because the cracks are not completely straight and planar. However, this did not affect our results because we measured crack opening local to each individual process, which given its long, thin shape can only experience tensile strain and not shear strain. Another type of long-term failure mode experienced by materials is creep. It's very likely that the cell membrane and cytoskeleton experience creep, but it's unlikely that the processes which we tested are failing in this way. The initial application of strain to the process is here caused by the opening of the crack which occurs during drying, a process which takes several hours. Under such conditions creep will cause a reduction in stress in the material over time, so creep failures rarely occur under conditions of constant applied strain. Thus any processes which have not failed before cycling commences are unlikely to fail by creep during the cyclic testing. There were a number of limitations to this study. Some of these, related to the fact that we tested dried and fixed samples in the vacuum environment of an SEM, were addressed in our previous paper (Dooley et al., 2014). We were able to compare our in situ SEM results with various other test results and also to compare cracks formed at various stages from in vivo onwards, providing evidence that the fatigue failure characteristics of the processes in our test was the same as for processes in vivo. Two aspects of our previous protocol, i.e. the use of induced cracks and frozen samples, had given cause for concern in the previous work; this has now been successfully addressed here. A remaining
journal of the mechanical behavior of biomedical materials 39 (2014) 231 –237
significant limitation is the relatively small number of cycles to failure that can be examined: this could only be overcome by developing a way to measure smaller cyclic displacements, below 0.1 μm. We hope that our efforts will stimulate others to investigate the monotonic and cyclic strength of cells, which we believe is an important area of mechanobiology research. Within these limitations, we have been able to present, for the first time, data showing the strain levels at which monotonic and cyclic failure occurs. In relation to the other research questions which we posed, we can confirm that changes to the test protocol, specifically the use of natural rather than artificial cracks and the preservation of the samples by freezing, do not affect our results. These results may be useful in understanding how the osteocyte network responds to mechanical damage. Previously we have hypothesised that the failure of cellular processes which span cracks might form part of a signalling pathway enabling osteocytes to detect microcracks and cause them to be repaired, preventing stress fractures from occurring (Taylor et al., 2003, 2007). Osteocytes would certainly be able to detect the rupture of their processes (which form an integral part of the cell body) and being mechanosensors they would be able to sense the increased cyclic strain of a process spanning a crack. There is evidence that osteocytes in the vicinity of microdamage undergo changes including apoptosis and altered production of cytokines such as RANK and OPG which are implicated in bone remodelling (Kennedy et al., 2012; Mulcahy et al., 2011). There are many other cell types which experience cyclic strain as part of their normal environment, including blood cells and endothelial cells, which might usefully be investigated as well.
r e f e r e n c e s
Boller, C., Seeger, T., 1987. Materials Data for Cyclic Loading. Elsevier, Amsterdam. Colopy, S.A., Benz-Dean, J., Barrett, J.G., Sample, S.J., Lu, Y., Danova, N.A., Kalscheur, V.L., Vanderby, J., Markel, M.D., Muir, P., 2004. Response of the osteocyte syncytium adjacent to and distant from linear microcracks during adaptation to cyclic fatigue loading. Bone 35, 881–891. Dooley, C., Cafferky, D., Lee, T.C., Taylor, D., 2014. Fatigue failure of osteocyte cellular processes: implications for the repair of bone. Eur. Cells Mater 27, 39–49. Hazenberg, J.G., Freeley, M., Foran, E., Lee, T.C., Taylor, D., 2006. Microdamage: a cell transducing mechanism based on ruptured osteocyte processes. J. Biomech. 39, 2096–2103. Hertzberg, R.W., Manson, J.A., 1980. Fatigue of Engineering Plastics. Academic Press, London. Ince, A., Glinka, G., 2011. A modification of Morrow and SmithWatson-Topper mean stress correction models. Fatigue Fract. Eng. Mater. Struct. 34, 854–867.
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Janssen, M., Zuidema, J., Wanhill, R., 2002. Fracture Mechanics. Spon Press, London, UK. Kennedy, O.D., Herman, B.C., Laudier, D.M., Majeska, R.J., Sun, H.B., Schaffler, M.B., 2012. Activation of resorption in fatigue-loaded bone involves both apoptosis and active pro-osteoclastogenic signaling by distinct osteocyte populations. Bone 50, 1115–1122. Klein-Nulend, J., Bacabac, R.G., Mullender, M.G., 2005. Mechanobiology of bone tissue. Pathol. Biol. 53, 576–580. Kuznetsova, T.G., Starodubtseva, M.N., Yegorenkov, N.I., Chizhik, S.A., Zhdanov, R.I., 2007. Atomic Force Microscopy Probing of Cell Elasticity. Micron 38, 824–833. McNamara, L.M., Majeska, R.J., Weinbaum, S., Friedrich, V., Schaffler, M.B., 2009. Attachment of osteocyte cell processes to the bone matrix. Anat. Rec. 292, 355–363. Mofrad, R.K., Kamm, R.D., 2010. Cellular Mechanotransduction. Cambridge University Press, Cambridge, UK. Mulcahy, L.E., Taylor, D., Lee, T.C., Duffy, G.P., 2011. RANKL and OPG activity is regulated by injury size in networks of osteocyte-like cells. Bone 48, 182–188. Mullender, M.G., Huiskes, R., Versleyen, H., Buma, P., 1996. Osteocyte density and histomorphometric parameters in cancellous bone of the proximal femur in five mammalian species. J. Orthop. Res. 14, 972–979. Nichol, J.A., Hutter, O.F., 1996. Tensile strength and dilatational elasticity of giant sarcolemmal vesicles shed from rabbit muscle. J. Physiol. 493, 187–198. Rand, R.P., 1964. Mechanical properties of the red cell membrane. II. Viscoelastic 4, 303–316. Reilly, D.T., Burstein, A.H., 1975. The elastic and ultimate properties of compact bone tissue. J. Biomech. 8, 393–405. Salmi, A., Montonen, R., Salminen, L.I., Suuronen, J.P., Serimaa, R., Haeggstrom, E., 2012. Cyclic impulsive compression loading along the radial and tangential wood directions causes localized fatigue. J. Appl. Phys. 112. Schaffler, M.B., Pitchford, W.C., Choi, K., Riddle, J.M., 1994. Examination of compact bone microdamage using backscattered electron microscopy. Bone 15, 483–488. Sheetz, M.P., Sable, J.E., H-G. Dobereiner,H.G., 2006. Continuous Membrane-cytoskeleton Adhesion Requires Continuous Accommodation to Lipid and Cytoskeleton Dynamics. 35, 417434. Ref Type: Serial (Book, Monograph). Stephens, R.I., Fuchs, H.O., 2001. Metal Fatigue in Engineering. Wiley, New York. Taylor, D., 1998. Fatigue of bone and bones: an analysis based on stressed volume. J. Orthop. Res. 16, 163–169. Taylor, D., Hazenberg, J.G., Lee, T.C., 2003. The cellular transducer in damage-stimulated bone remodelling: a theoretical investigation using fracture mechanics. J. Theor. Biol. 225, 65–75. Taylor, D., Hazenberg, J.G., Lee, T.C., 2007. Living with cracks: damage and repair in human bone. Nat. Mater. 2, 263–268. Taylor, D., Lee, T.C., 1998. Measuring the shape and size of microcracks in bone. J. Biomech. 31, 1177–1180. Wiederhorn, S.M., Chae, Y.H., Simon, J., Cahn, J., Deng, Y., Day, D., 2011. Cell adhesion to borate glasses by colloidal probe microscopy. Acta Biomater. 7, 2256–2263.
Available online at www.sciencedirect.com
www.elsevier.com/locate/jmbbm
Fracture and fatigue in osteocytes Simone Mulargiaa,b, Clodagh Dooleya,c, Luca Cristofolinib, David Taylora,d,n a
Trinity Centre for Bioengineering, Trinity College Dublin, Dublin, Ireland Department of Industrial Engineering, University of Bologna, Bologna, Italy c Centre for Microscopy and Analysis, Trinity College Dublin, Dublin, Ireland d Department of Mechanical and Manufacturing Engineering, Trinity College Dublin, Dublin, Ireland b
art i cle i nfo
ab st rac t
Article history:
Fatigue is a common mode of mechanical failure which occurs when a material is
Received 13 June 2014
subjected to repeated cycles at a strain level less than that needed for monotonic fracture.
Received in revised form
Fatigue has been observed and measured in many different materials but, until recently,
22 July 2014
not in cells. We devised a novel experiment which allowed us to create both monotonic
Accepted 26 July 2014
failure and fatigue in the cellular processes of osteocytes within samples of bone (Dooley
Available online 4 August 2014
et al., European Cells and Materials 2014). In the present paper, we describe the results of
Keywords:
further experiments and a computer simulation, which has allowed us to estimate the
Fatigue
strain history of each sample tested and thus present, for the first time, strain/life data for
Cells
cells. Failure occurred during the first cycle at strains of 0.1–0.2; at lower strains failure
Osteocytes
occurred after a number of cycles which depended inversely on the applied strain range.
Strain
Scatter in the strain/life data was reduced when we allowed for the effects of mean stress
Failure
using the Smith–Watson–Topper parameter. We confirmed that aspects of our experimental method (the types of microcrack used and the testing of fresh versus frozen samples) did not affect the results. Such information is useful because many cell types, including the cellular processes of osteocytes, experience cyclic strain in vivo. & 2014 Elsevier Ltd. All rights reserved.
1.
Introduction
Engineers and materials scientists are very familiar with the term “fatigue”, which refers to the gradual failure of a material when it is subjected to cycles of strain, the largest value of which is not sufficient to cause failure if applied only once in so-called “monotonic” loading. In medical circles the word fatigue has a different meaning, and the failure of a tissue such as bone under cyclic loading is referred to as a “stress fracture”. Fatigue failures are divided into two groups – “low cycle fatigue” and “high cycle fatigue” – according to
the number of cycles to failure. Low cycle fatigue – the subject of the present paper – occurs when a material is loaded to a maximum strain which, in a monotonic test, would cause non-reversible behaviour such as plastic strain, microdamage or viscoelasticity over a significant proportion of the material volume. Damage accumulates quickly on each cycle leading to failure in a relatively small number of cycles. Fig. 1 shows typical test data (Boller and Seeger, 1987), in which the number of cycles to failure Nf is plotted as a function of the strain range Δε, defined as the difference between the maximum and minimum strain in the cycle. Data are usually
n Corresponding author at: Trinity Centre for Bioengineering, Trinity College Dublin, Dublin, Ireland. Tel.: þ353 1 8961703; fax: þ353 1 6795554. E-mail address: [email protected] (D. Taylor).
http://dx.doi.org/10.1016/j.jmbbm.2014.07.023 1751-6161/& 2014 Elsevier Ltd. All rights reserved.
232
journal of the mechanical behavior of biomedical materials 39 (2014) 231 –237
presented on a logarithmic plot and often fall approximately on a straight line, giving the following empirical relationship in which C and n are constants: Nf ¼
C Δεn
ð1Þ
It has been demonstrated that fatigue occurs in many different types of materials, including metals, ceramics, polymers and composites (Stephens and Fuchs, 2001; Hertzberg and Manson, 1980), and also in natural composite materials such as bone (Taylor, 1998) and wood (Salmi et al., 2012), but until very recently fatigue had not been detected in mammalian cells. Indeed, there are almost no published data on any kind of mechanical failure mode for cells. Exceptionally, the failure strain of the outer cell membrane (which consists of a bilayer of lipids) was measured at 0.02–0.03 (Nichol and Hutter, 1996). Failure of this membrane may not lead to total rupture of the cell, because the cell is also supported by a cytoskeleton and may be able to repair local membrane damage (Sheetz et al., 2006). Pipette aspiration has
Fig. 1 – Typical data from low-cycle fatigue testing, in this case for two metallic materials (Boller and Seeger, 1987). The number of cycles to failure is plotted logarithmically against the applied strain range.
been used to cause membrane rupture in red blood cells and thus estimate membrane strength (Rand, 1964). In summary, there is a lack of data in the literature reporting how much strain is needed to permanently rupture a cell, whether loaded monotonically or cyclically. This information is important because many types of cells experience cyclic strain. For example endothelial cells undergo strains of the order of 0.22 (Mofrad and Kamm, 2010) as a result of fluid shear. Cyclic strain levels of the order of 0.05 are necessary for the differentiation of various cell types (Mofrad and Kamm, 2010); the osteocyte network is ruptured in the vicinity of microdamaged bone (Colopy et al., 2004) and this rupture takes the form of fatigue failures of individual cellular processes (Dooley et al., 2014). Recently we devised an experiment which allowed us to carry out this type of testing on bone cells (osteocytes). Our method (Dooley et al., 2014) takes advantage of the fact that osteocytes live inside the bone matrix and are connected to each other via long, thin extensions of the cell body known as cellular processes (Fig. 2). We noticed that if there is a crack in the bone matrix, these processes can be seen passing across between the crack faces (Fig. 3). By applying forces to a sample of bone we were able to cause a crack to open and close, thus applying strain to the processes spanning it. Some processes failed immediately on the first loading cycle, whilst others failed after a number of cycles. We thus demonstrated the existence of fatigue failure in cellular processes, which are made from the same constituents as other parts of the cell membrane and cytoskeleton. However this experiment had some limitations. We were not able to quantify the applied strain because, though we could measure the opening displacement of the crack, we did not know the total length of the process, and processes are known to adhere to the bone matrix via focal adhesion points (McNamara et al., 2009), which will affect the distribution of strain along their lengths. We also had some concerns about some aspects of our methods for sample preparation. The work described in the present paper aimed to answer the following questions: (1) What are the strain levels at which monotonic rupture and low cycle fatigue failure occur? To answer this
Fig. 2 – Osteocytes are linked together in a network via numerous cellular processes: these images show examples of cells without (a) and with (b) the surrounding bone matrix (Klein-Nulend et al., 2005).
journal of the mechanical behavior of biomedical materials 39 (2014) 231 –237
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Fig. 3 – SEM images of part of a microcrack in a bone sample, showing several cellular processes (thin white lines) passing across the crack. (A) This image was taken at the start of test: note the process indicated by the circle. (B) After a number of cycles this process has ruptured.
question we created a computer simulation of our experiment, using finite element analysis (FEA). (2) Are the results affected by tissue preservation methods? Previously we had used bone which had been frozen for storage. We carried out further tests using freshlyharvested bone. (3) Are the results identical when naturally-occurring cracks are used? In our previous work we artificially created cracks by applying forces to pre-notched samples. In the current work we used instead the microscopic cracks which are already present in vivo. This is of interest for obtaining a more general understanding of the role of osteocyte networks and their relationships to microdamage in bone.
2.
Methods and materials
2.1.
Experimental testing
The experimental methods were the same as reported previously (Dooley et al., 2014): what follows here is a brief description. The only differences were that in the present work the bone samples were fresh (rather than frozen), the loading axis was longitudinal to the bone axis (rather than transverse) and we used pre-existing microcracks (rather than inducing cracks to grow from notches). Fresh bovine tibiae were obtained from a meat producer (Keepac, Clonee, Ireland); samples were cut and ground into rectangular specimens with approximate dimensions 20 5 1 mm, the 20 mm length being parallel to the bone's axis. Because cracks tend to form during sample preparation, we used a heavy metal stain (Schaffler et al., 1994) which deposits lead and uranyl sulphide precipitates in the cracks; this allowed us to distinguish those cracks which had already formed in vivo when examining them in the scanning
electron microscope. We used only those cracks in the subsequent work. As in our previous study, the samples were fixed in 4% paraformaldehyde solution for 24 h at 4 1C and dried gradually using alcohol dehydration and critical point drying to minimise damage. Tests described previously (Dooley et al., 2014) established that this preparation protocol did not significantly affect the results. Axial loading was applied to the samples using an in situ straining stage (Deben, East Grinstead, UK) inside a scanning electron microscope (Tescan, BRNO, Czech Republic). Before applying any loads, a number of microcracks was identified and the processes crossing these cracks were counted and recorded (see Fig. 3 for an example of the images used). Processes can be distinguished from other features such as collagen fibres by their distinctive morphology: in our previous work (Hazenberg et al., 2006) we used phalloidin staining to confirm this. In total, 35 processes were studied. A compressive cyclic load was applied, varying from 180 N to 1 N, which corresponds to a stress cycle from 36 MPa to 0.2 MPa. Fatigue tests are normally carried out under cyclic tension, rather than compression; in this case the processes were already experiencing tension as a result of the opening of the crack which occurs during drying. Thus, by applying a compressive load we caused the crack to partially close, creating a cycle of strain between maximum and minimum levels which were both tensile. The time for each cycle was one minute; a total of 100 cycles was applied. Images were taken at maximum and minimum load; Image J software was used to measure the opening and closing of each crack at the location of each process, after each cycle, in a direction parallel to the long axis of the process. For those processes which failed (e.g. see Fig. 3) the number of cycles to failure was recorded.
2.2.
Computer simulation
A finite element model was created using ANSYS software to allow us to estimate the strain experienced by a cellular
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Fig. 4 – The finite element model of the test sample: this is a half-model, the plane of symmetry, being the front plane as shown here, contains two osteocytes linked by a process. In image (A) the crack is closed (see arrow): in (B) it has opened as a result of a tensile force applied to the ends of the sample.
process during crack opening and closing. Taking advantage of symmetry, a half model was created (see Fig. 4) including the bone sample, the crack and two osteocyte cells linked by a process passing across the crack. Bone was assumed to have Young's modulus values of 22 GPa and 12 GPa in the longitudinal and transverse directions respectively and a Poisson's ratio of 0.3 (Reilly and Burstein, 1975). No mechanical property data exist for osteocytes; we assumed a Young's modulus of 5.9 kPa and a Poisson's ratio of 0.39 based on data from osteoblasts (Kuznetsova et al., 2007). Since the Young's modulus is much less than that of bone, the chosen value will not have a significant effect on our predictions of strain for the process itself. Typical dimensions were used for osteocytes (diameter 10 μm) and processes (diameter 0.2 μm): the typical spacing between osteocyte centres was estimated to be 37 μm based on known data for the density of osteocytes in cortical bone (Mullender et al., 1996): as a result the total length of the process was 27 μm. Osteocytes and their processes are located within holes (lacunae) and channels (canaliculi) in the bone matrix. They fit snugly into these spaces but provide space for fluid to flow. They are attached to the bone at discreet points known as focal adhesions (McNamara et al., 2009). The nature of these adhesions is not well understood but there are some results in the literature for related cell types. For the strength of the adhesive bond we used a value of 7.96 Pa which was measured for osteoblast-like cells adhering to the surface of calciumcontaining borate glass which forms a calcium-phosphate
layer similar to the mineral found in bone (Wiederhorn et al., 2011). If the shear stress on the process/bone interface exceeded this value during the simulation then the interface condition was changed in the model to simulate debonding. The FE model was validated by comparing its predictions of stress near the crack tip and displacement of the crack faces, as a function of the applied load. Values of these parameters agreed with theoretical results (Janssen et al., 2002) to within 1%.
3.
Results
Fig. 5 shows examples of the variation of displacement δ during a test for two of the processes examined, one of which failed after three cycles whilst the other did not fail after 100 cycles. The initial displacement represents the opening of the crack at that point before any compressive load was applied. Cycling the load between 180 N and 1 N caused δ to vary, but the increase and decrease of δ at a given point did not necessarily follow exactly the cycles of applied load, owing to local irregularities in the crack shape and variations in the angle at which a process crossed a crack. For the same reason the amount of displacement experienced by a process, and its variation during load cycling, changed considerably from place to place along the crack front. There were also changes in the mean strain, which showed slight increases and decreases initially, though these changes tended to level
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Fig. 5 – Typical test data, showing displacement measured across the crack faces at the location of each process, at the start of the test (0 N) and for each cycle of load thereafter (max load 180 N, min load 1 N). Two processes are shown: one failed after 3 cycles, whilst the other remained unfailed for 100 cycles (here only the first few cycles and last few cycles are shown).
tentative line to indicate the trend of the data. Accurate curve fitting would not be appropriate given that most of the data lie in the region 1–4 cycles (and show significant scatter) and the line should, in theory, pass above the data for the unfailed samples. In the computer simulation, a force was first applied to cause crack face opening, simulating the starting condition for the experiments. This loading caused failure of the adhesive bond between the cellular process and the bone in regions close to the crack faces where the local shear stress exceeded the adhesive strength. This was implemented in the model by changing the interface condition for the relevant nodes, allowing us to define a “free length”, being the length over which the cellular process was not bonded to the bone. The strain in the process could then be calculated by dividing the measured displacement by this free length. The total length of the process in the model was 27 μm: we found that for crack opening displacements in the range 1–5 μm (which were the values measured experimentally) the free length f (in microns) varied in a linear manner with displacement δ according to the following equation: f ¼ 1:14δ þ 16:3
4.
Fig. 6 – Test results showing the number of cycles to failure for individual processes as a function of cyclic displacement range (“Natural Cracks”) along with data reported previously (Dooley et al., 2014) (“Induced Cracks”). Also included is a point and scatter band representing the 25 unfailed processes.
out after the first few cycles; this was probably due to local creep in the bone matrix. For the purpose of presenting the results we calculated the average cyclic displacement range for each process. This is shown in Fig. 6 as a function of the number of cycles to failure. The data generated in the present work is labelled “Natural Cracks”; also included on the figure are the data from our previous work (Dooley et al., 2014), which are labelled “Induced Cracks” because in those experiments we created cracks artificially in the samples as explained above. Eight processes were monitored in those tests. In the present work, a total of 35 processes were observed, of which 10 failed either on the first cycle or subsequent cycles, and the remaining 25 did not fail after 100 cycles. The results for these unfailed processes are included in Fig. 6, along with a
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ð2Þ
Discussion
The results shown in Fig. 6 confirm our previous findings that osteocyte processes can experience fatigue failure. The number of cycles to failure which we were able to record is admittedly very small, ranging from 1 to 8, but these fatigue failures happened at applied displacements which were considerably less than those needed for monotonic failure, i.e. failure on the first cycle. All tests below 0.1 μm gave no failures up to 100 cycles, implying a reduction in the slope of the line which also seen in other materials (Boller and Seeger, 1987). It would be very interesting to extend this data to larger numbers of cycles, but currently this would not be possible with our equipment owing to the difficulty of measuring smaller cyclic displacements with the necessary accuracy. Fig. 7 shows the same data, converted into cyclic strain range values using our FE results. This is the first time that strain/life data, of the kind commonly collected for engineering materials, has been presented for cells. Failure on the first cycle occurred at strains in the range 0.1–0.2, with fatigue failure occurring for strain ranges as low as 0.007. Following the normal convention for fatigue analysis we have drawn a straight line through this data: this gives a value of 0.75 for the exponent n in Eq. (1) which describes the dependence of fatigue life on applied strain. The general trend of the results is quite similar to those for typical metallic materials: in the example shown in Fig. 1 the overall strain levels are larger, but the value of n, being 0.98, is quite similar. As noted above, one of the limitations of these experiments was that the mean strain tended to vary from sample to sample, and within a sample during cycling. It is well known that mean strain affects fatigue behaviour: higher mean strain results in smaller numbers of cycles to failure, though the effect is different in different materials. A number
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Fig. 7 – Estimated cyclic strain range plotted against cycles to failure for all failed processes.
Fig. 8 – Allowing for mean strain by plotting the SWT parameter, which tends to reduce the scatter.
of different theoretical models exist to predict the effect of mean stress and strain (Ince and Glinka, 2011). We employed a commonly-used approach: the Smith–Topper–Watson (SWT) parameter (Boller and Seeger, 1987) which, when expressed in terms of mean strain εm and strain range Δε, can be written: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð3Þ PðSWTÞ ¼ ð2Δε þ εm Þ2Δε Fig. 8 shows the data replotted using the SWT parameter. Comparing Figs. 6–8 one can observe a reduction in the amount of scatter: to quantify this we fitted a straight regression line to the date on these log/log plots and calculated the R2 value, which increased from 0.363 when displacement was used (Fig. 6) to 0.562 for strain (Fig. 7) to 0.774 for the SWT parameter (Fig. 8), showing the advantage in taking account of both cyclic strain and mean strain. Some scatter remains, especially at high strain levels where, owing to the relatively flat slope of the line, a small change in strain causes a large change in Nf. This variability in individual results is not unusual even for engineering materials: in our case some of the scatter will be caused by inaccuracy in our
method of estimating strain, particularly our assumption that the length of the process (i.e. the distance between osteoctyes) is constant. Whatever the method of displaying the data, it is clear that there is no significant difference between the present results and those obtained in our previous study. To confirm this we carried out a T-test, comparing the two groups (Natural Cracks and Induced Cracks) in terms of the SWT parameter, normalised in each case by the mean value for a given number of cycles. The resulting p value for an unpaired, two tailed T-test was p ¼0.48. Strictly speaking a more rigorous analysis, with more data, would be necessary to prove similarity, but the present result certainly indicates that no significant difference can be detected between these two groups. Thus, the use of previously-frozen bone samples does not appear to affect the fatigue behaviour of the osteocytes, nor does the use of induced cracks as opposed to naturally-occurring cracks. Both types of crack tend to form parallel to the osteons and therefore are oriented approximately parallel to the longitudinal axis of the bone, though for microcracks the orientation with respect to the bone axis varies by as much as 301 (Taylor and Lee, 1998). In our previous work using induced cracks we loaded the bone in tension perpendicular to the longitudinal axis, so that the angle between the loading axis and the crack plane was always 901. In the present study we used a more physiological type of loading, applying compression parallel to the longitudinal axis. As a result the angle between the microcrack and the load axis varied, being typically about 201. This will give rise to shear as well as compression across the crack faces, to a degree which varies from place to place along the crack front because the cracks are not completely straight and planar. However, this did not affect our results because we measured crack opening local to each individual process, which given its long, thin shape can only experience tensile strain and not shear strain. Another type of long-term failure mode experienced by materials is creep. It's very likely that the cell membrane and cytoskeleton experience creep, but it's unlikely that the processes which we tested are failing in this way. The initial application of strain to the process is here caused by the opening of the crack which occurs during drying, a process which takes several hours. Under such conditions creep will cause a reduction in stress in the material over time, so creep failures rarely occur under conditions of constant applied strain. Thus any processes which have not failed before cycling commences are unlikely to fail by creep during the cyclic testing. There were a number of limitations to this study. Some of these, related to the fact that we tested dried and fixed samples in the vacuum environment of an SEM, were addressed in our previous paper (Dooley et al., 2014). We were able to compare our in situ SEM results with various other test results and also to compare cracks formed at various stages from in vivo onwards, providing evidence that the fatigue failure characteristics of the processes in our test was the same as for processes in vivo. Two aspects of our previous protocol, i.e. the use of induced cracks and frozen samples, had given cause for concern in the previous work; this has now been successfully addressed here. A remaining
journal of the mechanical behavior of biomedical materials 39 (2014) 231 –237
significant limitation is the relatively small number of cycles to failure that can be examined: this could only be overcome by developing a way to measure smaller cyclic displacements, below 0.1 μm. We hope that our efforts will stimulate others to investigate the monotonic and cyclic strength of cells, which we believe is an important area of mechanobiology research. Within these limitations, we have been able to present, for the first time, data showing the strain levels at which monotonic and cyclic failure occurs. In relation to the other research questions which we posed, we can confirm that changes to the test protocol, specifically the use of natural rather than artificial cracks and the preservation of the samples by freezing, do not affect our results. These results may be useful in understanding how the osteocyte network responds to mechanical damage. Previously we have hypothesised that the failure of cellular processes which span cracks might form part of a signalling pathway enabling osteocytes to detect microcracks and cause them to be repaired, preventing stress fractures from occurring (Taylor et al., 2003, 2007). Osteocytes would certainly be able to detect the rupture of their processes (which form an integral part of the cell body) and being mechanosensors they would be able to sense the increased cyclic strain of a process spanning a crack. There is evidence that osteocytes in the vicinity of microdamage undergo changes including apoptosis and altered production of cytokines such as RANK and OPG which are implicated in bone remodelling (Kennedy et al., 2012; Mulcahy et al., 2011). There are many other cell types which experience cyclic strain as part of their normal environment, including blood cells and endothelial cells, which might usefully be investigated as well.
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