Measurement of Internal Implantation Strains in Analogue Bone Using DVC
Abstract
:1. Introduction
2. Materials and Methods
2.1. Analogue Bone
2.2. Customised Loading Rig
2.3. DVC Approach
2.4. FE Modelling
3. Results
3.1. Noise and Virtual Displacement Study
3.2. Implantation Force and Friction from Modelling
3.3. Localised Crushing
3.4. Internal Implantation Strains
3.4.1. Radial Direction
3.4.2. Hoop Direction
3.4.3. Axial Direction
3.5. Comparison with Modelling
3.5.1. Radial Direction
3.5.2. Hoop Direction
3.5.3. Axial Direction
4. Discussion
4.1. Experimental Protocol
- Identification of suitable DVC parameters. The subvolume size study indicated a size of 0.97 mm would be a suitable starting point for future DVC experiments involving similar geometries and structures. This was sufficiently sensitive to capture the most important radial and hoop strain signals, with spatial resolution to indicate the continuum-scale strain gradients.
- Lack of strain correlation close to implant–analogue bone interface. Regions of reduced confidence occurred close to the interface, between the implant and analogue bone, where largest strains were generated on implantation. However, regions of reduced strain correlation were not observed during the noise and virtual displacement study. It is likely that in these regions of reduced correlation the degradation was due to high strain caused by localised crushing of the cellular foam, visually observed in the CT scans (Figure 6), from which the analogue bone is made. Future work will need to be mindful of this constraint when cellular material is loaded beyond its elastic response. It is possible that texture on the surface of the implant could aid correlation by introducing a unique pattern.
- Rigid body motion and cone-beam artefact. Several of the axial strain fields contained an unusual feature—a wedge of negative strain—at either the top, the bottom, or both. The cause of this was likely due to a cone-beam artefact in two of the scans. The bottom wedge was generated by a cone-beam artefact on the reference scan, hence being present all the strain fields compared with the reference but none of those calculated sequentially. However, the wedge of negative strain at the top was due to a cone-beam artefact at the top of Scan 3; it was present in all strain fields calculated with the scan at the maximum displacement. The analogue bone’s positioning in the CT scanner changed during the implantation process, moving away from the bottom cone and into the top cone. DVC strain data should not be trusted in regions containing these unavoidable artefacts, so the experimental process could be improved to minimise their effects, for example by translating the scanner stage to correct the rigid body motion of the implant–foam construct.
- Scattering by implant tip. Banding of the strain fields was observed in the axial direction. This is likely to have occurred due to scatter at the implant tip, and where its section thickness changes between its hemispherical tip and hollow cylindrical body. These artefacts were not observed in the radial and hoop strain results, where the strain magnitude was an order of magnitude larger.
- Flexibility in custom loading rig. The difference between the target displacement and that actually achieved was small; rig flexibility resulted in an average achieved implantation of 2.9 mm per step, as opposed to the desired 3.0 mm—a difference of less than 5%. This suggests the custom design was sufficiently stiff for the purposes of this study.
4.2. Comparison of Fields Predicted and Measured
- FE results overestimated DVC strain magnitudes in all directions. The overestimation of the radial, hoop, and axial strains indicates a relaxation of the predicted strain. The likely cause is the local crushing of the cellular structure, which was not incorporated in the bilinear elastoplastic FE constitutive model. When polyurethane foams of the same density have been compressed in displacement control, stress relaxation has been observed in the plateau region of the stress curve [26,36]. Thus, localised crushing near the implant would be expected to reduce load transferred to the rest of the analogue bone, giving a gross reduction in strain. Visual inspection (Figure 6) demonstrated that local crushing was occurring during the tests. The machining of the cavity could have exacerbated the effect: milling of the internal diameter disrupts the cellular structure, and makes it more vulnerable to local collapse under load. Note the size of the foam cells and magnitude of radial displacement due to the interference (0.25 mm) are in the same order of magnitude.
- Point of transition from compressive to tensile axial strain on implant–analogue bone interface markedly deeper on FE predictions. In the measured axial strain field, the transition between compressive and tensile axial strain is close to the top of the analogue bone; in the FE simulation, this is much closer to the implant tip. The iteratively tuned coefficients of friction implemented in the FE model may be responsible. All are between 0.030 and 0.036, which is an order of magnitude lower than what would be expected [36,37]. The low tuned coefficient of friction arises from the larger radial compression generated in simulations than in the experiment, as the FE model did not capture localised crushing. Thus, the FE-predicted normal force at the implant–analogue bone interface is too high. To compensate, a small coefficient of friction must be employed to generate an axial load in the simulation to match the experimental measurement. This changes the predicted strain field, with the axial compression at the implant tip having a more significant role in resisting the axial load than frictional shear forces. In contrast, the experimental results suggest axial compression is generated over much of the implant–analogue bone interface. This makes sense, given the much higher coefficient of friction that will be present in reality.
- Tensile radial strain predicted below the implant tip yet measured as compressive. Tensile strains (in the analogue bone) ahead of implant arise as an internal reaction to compressive radial strains generated in the region above. The filtering of measurements with correlation coefficients less than 0.9 has obscured this in the field measured using DVC. Thus, the difference between the measured and modelled fields is in the location of the region of tensile radial strain—it is further up in the experimental results. This again occurs as a consequence of the very low coefficients of friction in the simulation. As a result of the dominance of the region close to the implant tip in resisting the axial compression in the FE model, the tensile region of radial strain is shifted further down in the analogue bone.
4.3. Implications for Cementless Implants
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
- National Joint Registry. 14th Annual Report; National Joint Registry: Hemel Hempstead, UK, 2017. [Google Scholar]
- Khanuja, H.S.; Vakil, J.J.; Goddard, M.S.; Mont, M.A. Cementless Femoral Fixation in Total Hip Arthroplasty. J. Bone Jt. Surg. Am. 2011, 93, 500–509. [Google Scholar] [CrossRef]
- Ochsner, P.E. Osteointegration of orthopaedic devices. Semin. Immunopathol. 2011, 33, 245–256. [Google Scholar] [CrossRef] [PubMed]
- Brown, C.U.; Norman, T.L.; Kish, V.L.; Gruen, T.A.; Blaha, J.D. Time-dependent circumferential deformation of cortical bone upon internal radial loading. J. Biomech. Eng. 2002, 124, 456–461. [Google Scholar] [CrossRef] [PubMed]
- Cordey, J.; Gautier, E. Strain gauges used in the mechanical testing of bones Part I: Theoretical and technical aspects. Inj. Int. J. Care Inj. 1999, 30, S7–S13. [Google Scholar] [CrossRef]
- Cordey, J.; Gautier, E. Strain gauges used in the mechanical testing of bones Part II: “In vitro” and “in vivo” technique. Inj. Int. J. Care Inj. 1999, 30, S14–S20. [Google Scholar] [CrossRef]
- Dickinson, A.S.; Taylor, A.C.; Ozturk, H.; Browne, M. Experimental Validation of a Finite Element Model of the Proximal Femur Using Digital Image Correlation and a Composite Bone Model. J. Biomech. Eng. 2011, 133. [Google Scholar] [CrossRef]
- Dickinson, A.S.; Taylor, A.C.; Browne, M. The influence of acetabular cup material on pelvis cortex surface strains, measured using digital image correlation. J. Biomech. 2012, 45, 719–723. [Google Scholar] [CrossRef] [Green Version]
- Chanda, S.; Dickinson, A.; Gupta, S.; Browne, M. Full-field in vitro measurements and in silico predictions of strain shielding in the implanted femur after total hip arthroplasty. Proc. Inst. Mech. Eng. Part H 2015, 229, 549–559. [Google Scholar] [CrossRef] [Green Version]
- Luyckx, T.; Verstraete, M.; De Roo, K.; De Waele, W.; Bellemans, J.; Victor, J. Digital image correlation as a tool for three-dimensional strain analysis in human tendon tissue. J. Exp. Orthop. 2014, 1, 7. [Google Scholar] [CrossRef] [Green Version]
- Hoc, T.; Henry, L.; Verdier, M.; Aubry, D.; Sedel, L.; Meunier, A. Effect of microstructure on the mechanical properties of Haversian cortical bone. Bone 2006, 38, 466–474. [Google Scholar] [CrossRef]
- Sztefek, P.; Vanleene, M.; Olsson, R.; Collinson, R.; Pitsillides, A.A.; Shefelbine, S. Using digital image correlation to determine bone surface strains during loading and after adaptation of the mouse tibia. J. Biomech. 2010, 43, 599–605. [Google Scholar] [CrossRef] [PubMed]
- Bay, B.K.; Smith, T.S.; Fyhrie, D.P.; Saad, M. Digital volume correlation: Three-dimensional strain mapping using X-ray tomography. Exp. Mech. 1999, 39, 217–226. [Google Scholar] [CrossRef]
- Tozzi, G.; Zhang, Q.H.; Tong, J. Microdamage assessment of bone-cement interfaces under monotonic and cyclic compression. J. Biomech. 2014, 47, 3466–3474. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Tozzi, G.; Danesi, V.; Palanca, M.; Cristofolini, L. Elastic Full-Field Strain Analysis and Microdamage Progression in the Vertebral Body from Digital Volume Correlation. Strain 2016, 52, 446–455. [Google Scholar] [CrossRef] [Green Version]
- Danesi, V.; Tozzi, G.; Cristofolini, L. Application of digital volume correlation to study the efficacy of prophylactic vertebral augmentation. Clin. Biomech. 2016, 39, 14–24. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Basler, S.E.; Mueller, T.L.; Christen, D.; Wirth, A.J.; Muller, R.; van Lenthe, G.H. Towards validation of computational analyses of peri-implant displacements by means of experimentally obtained displacement maps. Comput. Method Biomech. 2011, 14, 165–174. [Google Scholar] [CrossRef] [PubMed]
- Du, J.; Lee, J.H.; Jang, A.T.; Gu, A.; Hossaini-Zadeh, M.; Prevost, R.; Curtis, D.A.; Ho, S.P. Biomechanics and strain mapping in bone as related to immediately-loaded dental implants. J. Biomech. 2015, 48, 3486–3494. [Google Scholar] [CrossRef] [Green Version]
- Joffre, T.; Isaksson, P.; Procter, P.; Persson, C. Trabecular deformations during screw pull-out: A micro-CT study of lapine bone. Biomech. Model. Mechan. 2017, 16, 1349–1359. [Google Scholar] [CrossRef]
- Le Cann, S.; Tudisco, E.; Perdikouri, C.; Belfrage, O.; Kaestner, A.; Hall, S.; Tagil, M.; Isaksson, H. Characterization of the bone-metal implant interface by Digital Volume Correlation of in-situ loading using neutron tomography. J. Mech. Behav. Biomed. 2017, 75, 271–278. [Google Scholar] [CrossRef]
- Sukjamsri, C.; Geraldes, D.M.; Gregory, T.; Ahmed, F.; Hollis, D.; Schenk, S.; Amis, A.; Emery, R.; Hansen, U. Digital volume correlation and micro-CT: An in-vitro technique for measuring full-field interface micromotion around polyethylene implants. J. Biomech. 2015, 48, 3447–3454. [Google Scholar] [CrossRef]
- Malfroy Camine, V.; Rudiger, H.A.; Pioletti, D.P.; Terrier, A. Full-field measurement of micromotion around a cementless femoral stem using micro-CT imaging and radiopaque markers. J. Biomech. 2016, 49, 4002–4008. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Cristofolini, L.; Viceconti, M.; Cappello, A.; Toni, A. Mechanical validation of whole bone composite femur models. J. Biomech. 1996, 29, 525–535. [Google Scholar] [CrossRef]
- Szivek, J.A.; Thomas, M.; Benjamin, J.B. Characterization of a Synthetic Foam as a Model for Human Cancellous Bone. J. Appl. Biomater. 1993, 4, 269–272. [Google Scholar] [CrossRef] [PubMed]
- Szivek, J.A.; Thompson, J.D.; Benjamin, J.B. Characterization of 3 Formulations of a Synthetic Foam as Models for a Range of Human Cancellous Bone Types. J. Appl. Biomater. 1995, 6, 125–128. [Google Scholar] [CrossRef]
- Thompson, M.S.; McCarthy, I.D.; Lidgren, L.; Ryd, L. Compressive and shear properties of commercially available polyurethane foams. J. Biomech. Eng. 2003, 125, 732–734. [Google Scholar] [CrossRef] [PubMed]
- Patel, P.S.D.; Shepherd, D.E.T.; Hukins, D.W.L. Compressive properties of commercially available polyurethane foams as mechanical models for osteoporotic human cancellous bone. BMC Musculoskel Dis. 2008, 9. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Calvert, K.L.; Trumble, K.P.; Webster, T.J.; Kirkpatrick, L.A. Characterization of commercial rigid polyurethane foams used as bone analogs for implant testing. J. Mater. Sci-Mater. Med. 2010, 21, 1453–1461. [Google Scholar] [CrossRef] [PubMed]
- Palissery, V.; Taylor, M.; Browne, M. Fatigue characterization of a polymer foam to use as a cancellous bone analog material in the assessment of orthopaedic devices. J. Mater. Sci-Mater. Med. 2004, 15, 61–67. [Google Scholar] [CrossRef]
- Berahmani, S.; Janssen, D.; van Kessel, S.; Wolfson, D.; de Waal Malefijt, M.; Buma, P.; Verdonschot, N. An experimental study to investigate biomechanical aspects of the initial stability of press-fit implants. J. Mech. Behav. Biomed. Mater. 2015, 42, 177–185. [Google Scholar] [CrossRef]
- Schindelin, J.; Arganda-Carreras, I.; Frise, E.; Kaynig, V.; Longair, M.; Pietzsch, T.; Preibisch, S.; Rueden, C.; Saalfeld, S.; Schmid, B.; et al. Fiji: An open-source platform for biological-image analysis. Nat. Methods 2012, 9, 676–682. [Google Scholar] [CrossRef] [Green Version]
- Gillard, F.; Boardman, R.; Mavrogordato, M.; Hollis, D.; Sinclair, I.; Pierron, F.; Browne, M. The application of digital volume correlation (DVC) to study the microstructural behaviour of trabecular bone during compression. J. Mech. Behav. Biomed. 2014, 29, 480–499. [Google Scholar] [CrossRef] [PubMed]
- Palanca, M.; Tozzi, G.; Cristofolini, L.; Viceconti, M.; Dall’Ara, E. Three-Dimensional Local Measurements of Bone Strain and Displacement: Comparison of Three Digital Volume Correlation Approaches. J. Biomech. Eng. 2015, 137. [Google Scholar] [CrossRef] [PubMed]
- Madi, K.; Tozzi, G.; Zhang, Q.H.; Tong, J.; Cossey, A.; Au, A.; Hollis, D.; Hild, F. Computation of full-field displacements in a scaffold implant using digital volume correlation and finite element analysis. Med. Eng. Phys. 2013, 35, 1298–1312. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Hamilton, A.R.; Thomsen, O.T.; Madaleno, L.A.O.; Jensen, L.R.; Rauhe, J.C.M.; Pyrz, R. Evaluation of the anisotropic mechanical properties of reinforced polyurethane foams. Compos. Sci. Technol. 2013, 87, 210–217. [Google Scholar] [CrossRef] [Green Version]
- Jin, H.; Lu, W.Y.; Scheffel, S.; Hinnerichs, T.D.; Neilsen, M.K. Full-field characterization of mechanical behavior of polyurethane foams. Int J. Solids Struct. 2007, 44, 6930–6944. [Google Scholar] [CrossRef] [Green Version]
- Damm, N.B.; Morlock, M.M.; Bishop, N.E. Friction coefficient and effective interference at the implant-bone interface. J. Biomech. 2015, 48, 3517–3521. [Google Scholar] [CrossRef]
- Le Cann, S.; Tudisco, E.; Tagil, M.; Hall, S.A.; Isaksson, H. Bone Damage Evolution Around Integrated Metal Screws Using X-Ray Tomography - in situ Pullout and Digital Volume Correlation. Front. Bioeng. Biotechnol. 2020, 8, 934. [Google Scholar] [CrossRef]
- The Dataset Supporting the Conclusions of This Article Is Available in the University of Southampton Repository. Available online: https://doi.org/10.5258/SOTON/D1547 (accessed on 11 September 2020).
Foaming Direction Modulus (Ez) | Transverse Direction Modulus (Ex, Ey) | Shear Modulus (Gxz, Gyz) | Shear Modulus (Gxy) | Foaming Direction Poisson’s Ratio (νxy) | Transverse Direction Poisson’s Ratio (νxy) |
---|---|---|---|---|---|
505 MPa | 357 MPa | 187 MPa | 137 MPa | 0.33 | 0.28 |
Load Step | Incremental Displacement (mm) | Total Displacement (mm) | Incremental Load (N) | Total Load (N) | Coefficient of Friction |
---|---|---|---|---|---|
0 | 1.5 | 1.5 | 120 | 120 | 0.036 |
1 | 2.8 | 4.3 | 80 | 200 | 0.030 |
2 | 2.8 | 7.1 | 80 | 280 | 0.031 |
3 | 3.0 | 10.1 | 80 | 360 | 0.035 |
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Marter, A.; Burson-Thomas, C.; Dickinson, A.; Rankin, K.; Mavrogordato, M.; Pierron, F.; Browne, M. Measurement of Internal Implantation Strains in Analogue Bone Using DVC. Materials 2020, 13, 4050. https://doi.org/10.3390/ma13184050
Marter A, Burson-Thomas C, Dickinson A, Rankin K, Mavrogordato M, Pierron F, Browne M. Measurement of Internal Implantation Strains in Analogue Bone Using DVC. Materials. 2020; 13(18):4050. https://doi.org/10.3390/ma13184050
Chicago/Turabian StyleMarter, Alexander, Charles Burson-Thomas, Alexander Dickinson, Kathryn Rankin, Mark Mavrogordato, Fabrice Pierron, and Martin Browne. 2020. "Measurement of Internal Implantation Strains in Analogue Bone Using DVC" Materials 13, no. 18: 4050. https://doi.org/10.3390/ma13184050