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Journal of Tribology | Volume 127 | Issue 4 | Research Paper
RESEARCH PAPERS

Elastohydrodynamic Lubrication Modeling of Artificial Hip Joints Under Steady-State Conditions

[+] Author and Article Information
F. C. Wang

School of Mechanical Engineering,  University of Leeds, Leeds LS2 9JT, UK

Z. M. Jin1

School of Mechanical Engineering,  University of Leeds, Leeds LS2 9JT, UKz.jin@leeds.ac.uk

1

Corresponding author.

J. Tribol 127(4), 729-739 (Mar 22, 2005) (11 pages) doi:10.1115/1.1924460 History: Received March 17, 2004; Revised March 22, 2005
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A general steady-state elastohydrodynamic lubrication model was developed for artificial hip joints, with particular reference to the effect of the anatomical position of the cup and the three-dimensional physiological loading and motion experienced during walking. Appropriate spherical coordinates and mesh grids were employed to facilitate the numerical solution. A specific hip implant employing an ultrahigh molecular-weight polyethylene acetabular cup against a metallic femoral head was chosen to demonstrate the general applicability of the lubrication model and the effects of both the cup inclination angle and the combined flexion-extension and internal-external rotation on the lubrication were analyzed.
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References

1
Paul, J. P., 1967, “Forces Transmitted by Joints in the Human Body,” "Proc. IMechE. on Lubrication and Wear in Living and Artificial Human Joints", Vol. 181 (3J)), pp. 8–15.
2
Ingham, E., and Fisher, J., 2005, “The Role of Macrophages in Osteolysis of Total Joint Replacement,” Biomaterials, 26 (11), pp. 1271–86.
3
Unsworth, A., Dowson, D., and Wright, V., 1975, “The Frictional Behaviour of Human Synovial Joints—Part II: Artificial Joints,” ASME J. Lubr. Technol., 97 (3), pp. 377–382.
4
Scholes, S. C., and Unsworth, A., 2000, “Comparison of Friction and Lubrication of Different Hip Prostheses,” Proc. Inst. Mech. Eng., Part H: J. Eng. Med., 214 (1), pp. 49–57.
5
Jin, Z. M., Medley, J. B., and Dowson, D., 2003, “Fluid Film Lubrication in Artificial Hip Joints,” "Proc. of 29th Leeds-Lyon Symp. on Tribology", pp. 237–256.
6
Goenka, P. K., 1980, “Effect of Surface Ellipticity on Dynamically Loaded Spherical and Cylindrical Joints and Bearings,” Ph.D. thesis, Cornell University, Ithaca, NY.
7
Goenka, P. K., and Booker, J. F., 1980, “Spherical Bearings: Static and Dynamic Analysis via the Finite Element Method,” ASME J. Lubr. Technol., 102 , pp. 308–319.
8
Kothari, M., Booker, J. F., and Bartel, D. L., 1995, “Analysis of Artificial Hip Joints as Spherical Bearings,” "Proc. of 21st Leeds-Lyon Symp. on Tribology", Leeds, pp. 93–98.
9
Ai, X. L., and Cheng, H. S., 1996, “Hydrodynamic Lubrication Analysis of Metallic Hip Joint,” Tribol. Trans., 39 (1), pp. 103–111.
10
Jin, Z. M., and Dowson, D., 1999, “A Full Numerical Analysis of Hydrodynamic Lubrication in Artificial Hip Joint Replacements Constructed from Hard Materials,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 213 (4), pp. 355–370.
11
Meyer, D. M., and Tichy, J. A., 1999, “Lubrication Model of an Artificial Hip Joint: Pressure Profile Versus Inclination Angle of the Acetabular Cup,” ASME J. Tribol., 121 (3), pp. 492–498.
12
Meyer, D. M., 2003, “Reynolds Equation for Spherical Bearings,” ASME J. Tribol.  [CrossRef], 125 (1), pp. 203–206.
13
Meyer, D. M., and Tichy, J. A., 2003, “3-D Model of a Total Hip Replacement in Vivo Providing Hydrodynamic Pressure and Film Thickness for Walking and Bicycling,” ASME J. Biomech. Eng.  [CrossRef], 125 (6), pp. 777–784.
14
Hamrock, B. J., and Dowson, D., 1978, “Elastohydrodynamic Lubrication of Elliptical Contacts for Materials of Low Elastic Modulus, I: Fully Flooded Conjunction,” ASME J. Lubr. Technol., 100 (2), pp. 236–245.
15
Medley, J. B., Chan, F. W., Krygier, J. J., and Bobyn, J. D., 1996, “Comparison of Alloys and Designs in Hip Simulator Study of Metal on Metal Implants,” Clin. Orthop. Relat. Res., 329 (Suppl.), pp. S148–S159.
16
Medley, J. B., Krygier, J. J., Bobyn, J. D., Chan, F. W., Lippincott, A., and Tanzer, M., 1997, “Kinematics of the MATCO Hip Simulator and Issues Related to Wear Testing of Metal-Metal Implants,” Proc. Inst. Mech. Eng., Part H: J. Eng. Med., 211 (1), pp. 89–100.
17
Jin, Z. M., Dowson, D., and Fisher, J., 1997, “Analysis of Fluid Film Lubrication in Artificial Hip Joint Replacements With Surfaces of High Elastic Modulus,” Proc. Inst. Mech. Eng., Part H: J. Eng. Med., 211 (3), pp. 247–256.
18
Jin, Z. M., 2000, “Elastohydrodynamic Lubrication of Circular Point Contact for a Compliant Layered Surface Bonded to a Rigid Substrate—Part 2 Numerical Results,” Proc. Inst. Mech. Eng., Part H: J. Eng. Med., 214 (3), pp. 281–289.
19
Jalali-Vahid, D., Jagatia, M., Jin, Z. M., and Dowson, D., 2000, “Elastohydrodynamic Lubrication Analysis of UHMWPE Hip Joint Replacements,” in Thinning Films and Tribological Interfaces, "Proc. of 26th Leeds-Lyon Symp. on Tribology", pp. 329–339.
20
Bartel, D. L., Burstein, A. H., Toda, M. D., and Edwards, D. L., 1985, “The Effect of Conformity and Plastic Thickness on Contact Stress in Metal-Backed Plastic Implants,” ASME J. Biomech. Eng., 107 , pp. 193–199.
21
Jagatia, M., and Jin, Z. M., 2001, “Elastohydrodynamic Lubrication of Metal-on-Metal Hip Prosthesis under Steady-State Entraining Motion,” Proc. Inst. Mech. Eng., Part H: J. Eng. Med., 215 (6), pp. 531–541.
22
Jagatia, M., and Jin, Z. M., 2002, “Analysis of Elastohydrodynamic Lubrication in a Novel Metal-on-Metal Hip Joint Replacement,” Proc. Inst. Mech. Eng., Part H: J. Eng. Med., 216 (3), pp. 185–193.
23
Udofia, I. J., and Jin, Z. M., 2003, “Elastohydrodynamic Lubrication Analysis of Metal-on-Metal Hip Resurfacing Prostheses,” J. Biomech., 36 (4), pp. 537–544.
24
Yew, A., Udofia, I. J., Jagatia, M., and Jin, Z. M., 2004, “Analysis of Elastohydrodynamic Lubrication in Mckee-Farrar Metal-on-Metal Hip Joint Replacements,” Proc. Inst. Mech. Eng., Part H: J. Eng. Med., In Press.
25
Jalali-Vahid, D., and Jin, Z. M., 2002, “Transient Elastohydrodynamic Lubrication Analysis of UHMWPE Hip Joint Replacements,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 216 (4), pp. 409–420.
26
Jalali-Vahid, D., Jin, Z. M., and Dowson, D., 2003, “Elastohydrodynamic Lubrication Analysis of Hip Implants Under Transient Conditions,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 217 (7), pp. 767–777.
27
Saarri, H., Santavirta, S., Nordstrom, D., Paavolainen, P., and Konttinen, Y. T., 1993, “Hyaluronate in Total Hip Replacement,” J. Rheumatol., 20 (1), pp. 87–90.
28
Delecrin, J., Oka, M., Takahashi, S., Yamamuro, T., and Nakamura, T., 1994, “Changes in Joint Fluid After Total Arthroplasty,” Clin. Orthop. Relat. Res., 307 , pp. 240–249.
29
Yao, J. Q., Laurent, M. P., Johnson, T. S., Blanchard, C. R., and Crowinshield, R. D., 2003, “The Influence of Lubricant and Material on Polymer/CoCr Sliding Friction,” Wear, 255 , pp. 780–784.
30
Cooke, A. V., Dowson, D., and Wright, V., 1978, “The Rheology of Synovial Fluid and Some Potential Synthetic Lubricants for Degenerate Synovial Joints,” Eng. Med., 7 , pp. 66–72.
31
Jin, Z. M., Heng, S. M., Ng, H. W., and Auger, D. D., 1999, “An Axisymmetric Contact Model of Ultra High Molecular Weight Polyethylene Cups Against Metallic Femoral Heads for Artificial Hip Joint Replacements,” Proc. Inst. Mech. Eng., Part H: J. Eng. Med., 213 (4), pp. 317–327.
32
Mak, M. M., and Jin, Z. M., 2002, “Analysis of Contact Mechanics in Ceramic-on-Ceramic Hip Joint Replacements,” Proc. Inst. Mech. Eng., Part H: J. Eng. Med., 216 (4), pp. 231–236.
33
Jin, Z. M., Dowson, D., and Fisher, J., 1993, “Fluid Film Lubrication in Natural Hip Joints,” in "Thin Films in Tribology", Tribology Series D.Dowson, C.M.Taylor, and M.Godet, eds., Elsevier, Amsterdam, pp. 545–555.
34
Chan, F. W., Medley, J. B., Bobyn, J. D., and Krygier, J. J., 1998, “Numerical Analysis of Time-Varying Fluid Film Thickness in Metal-on-Metal Hip Implants in Simulator Tests,” in Alternative Bearing Surfaces in Total Joint Replacement, ASTM STP 1346 , J.J.Jacobs and T.L.Craig, eds., ASTM, pp. 111–128.
35
Roter, G. E., Medley, J. B., Bobyn, J. D., Krygier, J. J., and Chan, F. W., 2002, "Intermittent Motion: A Novel Simulator Protocol for the Wear of Metal-Metal Hip Implants", Tribology Series 40 , Elsevier, pp. 367–376.
36
Wang, D., 1994, “Elastohydrodynamic Lubrication of Point Contacts for Layers of Soft Solids and for ‘Monolithic’ Hard Materials in the Transient Bouncing Ball Problem,” Ph.D. thesis, University of Leeds.
37
Wang, F. C., and Jin, Z. M., 2004, “Prediction of Elastic Deformation of Acetabular Cup and Femoral Head for Lubrication Analysis of Artificial Hip Joints,” Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 218 , 283–291.
38
Bergmann, G., Deuretzbacher, G., Heller, M., Graichen, F., Rohlmann, A., Strauss, J., and Duda, G. N., 2001, “Hip Contact Forces and Gait Patterns from Routine Activities,” J. Biomech.  [CrossRef], 34 (7), pp. 859–871.
39
Hu, Y. Z., and Zhu, D., 2000, “A Full Numerical Solution to the Mixed Lubrication in Point Contacts,” ASME J. Tribol.  [CrossRef], 122 (1), pp. 1–9.

Figures

Grahic Jump Location
+Ball-in-socket lubrication models for artificial hip joints: (a) full anatomical model with the three-dimensional load and velocity components, (b) simplified anatomical model with the vertical load and the flexion/extension, (c) simplified anatomical model with the load and motion resolved into the cup coordinates, and (d) simple model for a horizontally positioned cup with the vertical load and the flexion/extension.
View Large  |  Save Figure  |  Download Slide (.ppt)
Ball-in-socket lubrication models for artificial hip joints: (a) full anatomical model with the three-dimensional load and velocity components, (b) simplified anatomical model with the vertical load and the flexion/extension, (c) simplified anatomical model with the load and motion resolved into the cup coordinates, and (d) simple model for a horizontally positioned cup with the vertical load and the flexion/extension.
Figure 1

Ball-in-socket lubrication models for artificial hip joints: (a) full anatomical model with the three-dimensional load and velocity components, (b) simplified anatomical model with the vertical load and the flexion/extension, (c) simplified anatomical model with the load and motion resolved into the cup coordinates, and (d) simple model for a horizontally positioned cup with the vertical load and the flexion/extension.

Grahic Jump Location
+(a,b) Two spherical coordinates and correspondiong mesh grids, with z-axis being always aligned with the pole of the spherical coordinates
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(a,b) Two spherical coordinates and correspondiong mesh grids, with z-axis being always aligned with the pole of the spherical coordinates
Figure 2

(a,b) Two spherical coordinates and correspondiong mesh grids, with z-axis being always aligned with the pole of the spherical coordinates

Grahic Jump Location
+Comparison of the predicted film contours and/or profiles (a) and pressure distributions (b) for the simple ball-in-socket model shown in Fig. 1 (horizontally positioned cup) under a fixed-horizontal angular velocity of 2rad∕s around the medial-lateral axis and a fixed vertical load of 2500N between two different spherical coordinates and mesh grids shown in Fig. 2(ωz=2rad∕s) and Fig. 2(ωx=−2rad∕s). Comparison of the predicted minimum (c) and central (d) film thicknesses for the simple ball-in-socket model shown in Fig. 1 (horizontally positioned cup) under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis and different vertical loads between two different spherical coordinates and mesh grids shown in Fig. 2(ωz=2rad∕s) and Fig. 2(ωx=−2rad∕s).
View Large  |  Save Figure  |  Download Slide (.ppt)
Comparison of the predicted film contours and/or profiles (a) and pressure distributions (b) for the simple ball-in-socket model shown in Fig. 1 (horizontally positioned cup) under a fixed-horizontal angular velocity of 2rad∕s around the medial-lateral axis and a fixed vertical load of 2500N between two different spherical coordinates and mesh grids shown in Fig. 2(ωz=2rad∕s) and Fig. 2(ωx=−2rad∕s). Comparison of the predicted minimum (c) and central (d) film thicknesses for the simple ball-in-socket model shown in Fig. 1 (horizontally positioned cup) under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis and different vertical loads between two different spherical coordinates and mesh grids shown in Fig. 2(ωz=2rad∕s) and Fig. 2(ωx=−2rad∕s).
Figure 3

Comparison of the predicted film contours and/or profiles (a) and pressure distributions (b) for the simple ball-in-socket model shown in Fig. 1 (horizontally positioned cup) under a fixed-horizontal angular velocity of 2rad∕s around the medial-lateral axis and a fixed vertical load of 2500N between two different spherical coordinates and mesh grids shown in Fig. 2(ωz=2rad∕s) and Fig. 2(ωx=−2rad∕s). Comparison of the predicted minimum (c) and central (d) film thicknesses for the simple ball-in-socket model shown in Fig. 1 (horizontally positioned cup) under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis and different vertical loads between two different spherical coordinates and mesh grids shown in Fig. 2(ωz=2rad∕s) and Fig. 2(ωx=−2rad∕s).

Grahic Jump Location
+Comparison of the predicted film contours/profiles (a) and pressure distributions (b) between the two different lubrication models shown in Figs.  1, 1 using the mesh grid shown in Fig. 2 under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis, a fixed cup inclination angle of 45deg, and a fixed vertical load of 2500N. Comparison of the predicted minimum film thickness between the two different lubrication models shown in Figs.  1, 1 using the mesh grid shown in Fig. 2 under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis, a fixed cup inclination angle of 45deg, and different vertical loads.
View Large  |  Save Figure  |  Download Slide (.ppt)
Comparison of the predicted film contours/profiles (a) and pressure distributions (b) between the two different lubrication models shown in Figs.  1, 1 using the mesh grid shown in Fig. 2 under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis, a fixed cup inclination angle of 45deg, and a fixed vertical load of 2500N. Comparison of the predicted minimum film thickness between the two different lubrication models shown in Figs.  1, 1 using the mesh grid shown in Fig. 2 under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis, a fixed cup inclination angle of 45deg, and different vertical loads.
Figure 4

Comparison of the predicted film contours/profiles (a) and pressure distributions (b) between the two different lubrication models shown in Figs.  1, 1 using the mesh grid shown in Fig. 2 under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis, a fixed cup inclination angle of 45deg, and a fixed vertical load of 2500N. Comparison of the predicted minimum film thickness between the two different lubrication models shown in Figs.  1, 1 using the mesh grid shown in Fig. 2 under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis, a fixed cup inclination angle of 45deg, and different vertical loads.

Grahic Jump Location
+Comparison of the predicted film contours and/or profiles (a) and pressure distributions (b) between different cup inclination angles using the simplified anatomical lubrication model shown in Fig. 1 and the mesh grid shown in Fig. 2 under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis and a fixed vertical load of 350N. (c) Comparison of the predicted minimum film thickness for different cup inclination angles using the simplified anatomical lubrication model shown in Fig. 1 and the mesh grid shown in Fig. 2 under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis and a fixed vertical load of 350N.
View Large  |  Save Figure  |  Download Slide (.ppt)
Comparison of the predicted film contours and/or profiles (a) and pressure distributions (b) between different cup inclination angles using the simplified anatomical lubrication model shown in Fig. 1 and the mesh grid shown in Fig. 2 under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis and a fixed vertical load of 350N. (c) Comparison of the predicted minimum film thickness for different cup inclination angles using the simplified anatomical lubrication model shown in Fig. 1 and the mesh grid shown in Fig. 2 under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis and a fixed vertical load of 350N.
Figure 5

Comparison of the predicted film contours and/or profiles (a) and pressure distributions (b) between different cup inclination angles using the simplified anatomical lubrication model shown in Fig. 1 and the mesh grid shown in Fig. 2 under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis and a fixed vertical load of 350N. (c) Comparison of the predicted minimum film thickness for different cup inclination angles using the simplified anatomical lubrication model shown in Fig. 1 and the mesh grid shown in Fig. 2 under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis and a fixed vertical load of 350N.

Grahic Jump Location
+Comparison of the predicted minimum film thickness between two different cup inclination angles of 0 and 45deg using the simplified anatomical lubrication model shown in Fig. 1 and the mesh grid shown in Fig. 2 under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis and different vertical loads
View Large  |  Save Figure  |  Download Slide (.ppt)
Comparison of the predicted minimum film thickness between two different cup inclination angles of 0 and 45deg using the simplified anatomical lubrication model shown in Fig. 1 and the mesh grid shown in Fig. 2 under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis and different vertical loads
Figure 6

Comparison of the predicted minimum film thickness between two different cup inclination angles of 0 and 45deg using the simplified anatomical lubrication model shown in Fig. 1 and the mesh grid shown in Fig. 2 under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis and different vertical loads

Grahic Jump Location
+Effect of the internal-external rotation around the vertical axis on the predicted film contours and/or profiles (a) and pressure distributions (b) using the lubrication model shown in Fig. 1 for a cup inclined at 45deg and the mesh grid in Fig. 2 under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis and a fixed vertical load of 2500N.
View Large  |  Save Figure  |  Download Slide (.ppt)
Effect of the internal-external rotation around the vertical axis on the predicted film contours and/or profiles (a) and pressure distributions (b) using the lubrication model shown in Fig. 1 for a cup inclined at 45deg and the mesh grid in Fig. 2 under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis and a fixed vertical load of 2500N.
Figure 7

Effect of the internal-external rotation around the vertical axis on the predicted film contours and/or profiles (a) and pressure distributions (b) using the lubrication model shown in Fig. 1 for a cup inclined at 45deg and the mesh grid in Fig. 2 under a fixed horizontal angular velocity of 2rad∕s around the medial-lateral axis and a fixed vertical load of 2500N.

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