1. Investigations on Bone Ingrowth on a Porous Coated Implant using Three-dimensional Finite Element Analysis and Mechano-regulatory Algorithm. Kaushik Mukherjee Sanjay Gupta Department of Mechanical Engineering Indian Institute of Technology Kharagpur July 2014

2. 2 Background A variety of acetabular cup designs rely on biological fixation

3. 3 Challenges and their Probable Solutions Three-dimensional arrangement of the beads FE Analysis of cast-in beaded Implant in a macroscale Physiological activity to be considered for the analysis Realistic physiological implant- bone relative displacement field Realistic physiological bone material properties Liu et al. (2008)

4. 4 Challenges and their Probable Solutions Three-dimensional arrangement of the beads FE Analysis of cast-in beaded Implant in a macroscale Physiological activity to be considered for the analysis Realistic physiological implant- bone relative displacement field Realistic physiological bone material properties Reconstruction of the beads from the image and porosity Microscale Model Eight load-steps of a Full walking cycle Mapping of displacement field Mapping of bone material properties

5. Development of 3D microscale FE model of cast-in beaded implant-bone interface BHR acetabular cup Cross-section of the Porocast bead 2 nd bead, from left, as read by Matlab Circle fitted through the points of the 2 nd bead 3-D microscale model of implant-bone interface Bone Granulation Tissue Implant Implant Bead Morrison (2006)

6. 6 Development of 3-D FE model based on CT-scan data (Ghosh et al. 2013)

7. 7 Bone material property distribution (Ghosh et al. 2013) Cancellous bone Apparent density vs. CT- grey value (HU) (linear calibration); ρ = 0.022 + 0.001038 HU Elastic modulus vs. apparent density (power law); E = 2017.3ρ 2.46 ; E in MPa,  in g·cm -3 An FE model of bone, where each bone element is assigned individual material properties, based on CT-grey value. Cortical bone, E = 17 GPa Dalstra and Huiskes (1995); Anderson et al. (2005)

8. 8 Applied Loading Conditions Hip-joint force Muscle force: 21 muscle forces Fixed constrains were applied at the pubis and the sacroiliac joint Dostal and Andrews (1981).; Dalstra and Huiskes (1995).; Crowninshield and Brand (1981); Bergmann et al. (1990) Applied loading conditions include eight phases of a normal walking cycle

9. 9 Submodelling Technique (a) Cut-boundaries (nodal displacements are transferred at the cut-boundaries from full model). Acetabular component Ghosh et al. (2013); Ghosh and Gupta (2014)

10. Mapping of Displacement Field and Bone Material Properties from Macroscale Model

11. Tissue differentiation algorithm: Phenomenological model Mechanoregulatory Tissue Algorithm Cell Proliferation Cell Migration Cell differentiation Extracellular Matrix generation and tissue formation is not explicitly modelled. Diffusion Constant (k): 0.1 mm 3 /day (Lacroix et al. 2002) (Lacroix and Prendergast 2002)

12. Predicted Tissue TypePrincipal Strain (%) Hydrostatic Pressure (MPa) Fibrous Tissue - >5 <-5 >0.15 >-0.15 Cartilage >15 <-15 <-0.15 Immature Bone-15 to 15≤-0.15 Mature Bone- 5 to 5-0.15 to 0.15 Mechanoregulatory Principle Single Phase Material Representation of Tissue Claes et al. (1999)

13. Iterative Update of Material Properties (Lacroix and Prendergast 2002): Homogenisation Principle (Lacroix and Prendergast 2000): Calculation of Mechanical Properties Prepared by Kaushik Mukherjee

14. Tissue phenotypeYoung’s modulus (MPa)Poisson’s Ratio Granulation tissue 10.167 Fibrous tissue 20.167 Cartilage 100.167 Immature bone 10000.3 Mature bone 60000.3 Material properties assigned to the tissues

15. Results: Microscale Simulation of Bone Ingrowth around Uncemented Implant Tissue Differentiation around the Acetabular Prosthesis after Attainment of Equilibrium Percentage Bone Ingrowth Implant-Bone Relative Displacement

16. 16 FE Predicted Implant-bone Relative Displacement: Realistic or Not ??? Experimental set upEquivalent FE Model R.Ghosh, Ph.D. Thesis, Indian Institute of Technology Kharagpur

17. 17 Anterior-posterior direction (LDS 1) FE Predicted Implant-bone Relative Displacement: Realistic or Not ??? R.Ghosh, Ph.D. Thesis, Indian Institute of Technology Kharagpur

18. 18 Superior-inferior direction (LDS 2) FE Predicted Implant-bone Relative Displacement: Realistic or Not ??? R.Ghosh, Ph.D. Thesis, Indian Institute of Technology Kharagpur

19. 19 Medial-lateral direction (LDS 3) FE Predicted Implant-bone Relative Displacement: Realistic or Not ??? R.Ghosh, Ph.D. Thesis, Indian Institute of Technology Kharagpur

20. 20 Results: Realistic or Not ??? Average Young’s modulus and, thereby, the stiffness of the tissue layer showed a steady progressive increase almost following the characteristic S- shape (Richardson et al. 1994, Isaksson et al. 2006). Time (days) Average Tissue Young’s Modulus Clinical Studies: Hanzlik & Day (2013): Titanium Acetabular Shell: 46±20% Bloebaum et al. (1997): Cancellous Structured Titanium: 84±9% Engh et al. (1993): Porous Coated Acetabular Implant: 33% Increase in implant-bone relative displacement promotes fibrous tissue formation and weak implant-bone interface (Haddad et al. 1987, Jasty et al. 1991, 1997, Engh et al. 1987, Bragdon et al. 2004 )

21. 21 Conclusions  The 3D FE microscale model of implant-bone interface is useful to gain an insight in the peri-prosthetic bone formation.  A novel methodology is developed to transfer the macroscale implant-bone relative displacement field to a 3D FE microscale model in order to apply physiological boundary condition to predict peri-prosthetic bone ingrowth.  Both debonded and bonded interface conditions predicted reduction in bone formation with an increase in implant-bone relative displacement. However, percentage of bone ingrowth predicted by debonded interface models were slightly higher compared to bonded interface models.  The bonded interface models, being less computationally expensive, seem to be very useful in multiscale analysis of peri-prosthetic bone ingrowth.

22. 22 Future Applications of this Methodology This methodology can be used to predict: Time-dependent bone formation across polar gap. Time-dependent localised bone ingrowth around any implant-bone interface. Time-dependent Spatial bone ingrowth around any implant-bone interface: interpolated from a number of localised bone ingrowth.

23. o Indian Institute of Technology Kharagpur o University of Southampton, UK. o UKIERI British Council Acknowledgements