Two-dimensional surrogate contact modeling for computationally efficient dynamic simulation of total knee replacements

Journal of Biomechanical Engineering

Volumn 131, Issue 4, 2009, Pages

  Lin, Yi Chung ^a   Haftka, Raphael T ^a   Queipo, Nestor V ^b   Fregly, Benjamin J ^c  

^a UNIVERSITY OF FLORIDA   (United States)

^b UNIVERSIDAD DEL ZULIA   (Venezuela)

^c University of Florida   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION TIME; COMPUTATIONAL EVALUATION; COMPUTATIONAL SPEED; COMPUTATIONALLY EFFICIENT; CONTACT ANALYSIS; CONTACT FORCES; CONTACT MODELING; CONTACT MODELS; CONTACT PROBLEM; DESIGN SENSITIVITY; DYNAMIC CONTACTS; DYNAMIC SIMULATION; DYNAMIC WEAR; ELASTIC FOUNDATION; FINITE ELEMENT MODELS; HIGHLY SENSITIVE; LIMITING FACTORS; MACHINE SETUP; MODELING TECHNIQUE; MONTE CARLO ANALYSIS; OPTIMIZATION STUDIES; PLANAR MOTION; RELATIVE POSE; SAMPLE POINT; SMALL VARIATIONS; SURROGATE MODEL; TOTAL KNEE REPLACEMENT; WEAR SIMULATION; WEAR VOLUME;

COMPUTER SIMULATION; END EFFECTORS; FINITE ELEMENT METHOD; IMPLANTS (SURGICAL); OPTIMIZATION; RAILROAD ROLLING STOCK; SPEED; STANDARDIZATION;

JOINT PROSTHESES;

ARTICLE; COMPUTER SIMULATION; GEOMETRY; MATHEMATICAL MODEL; MECHANICAL STRESS; MONTE CARLO METHOD; PREDICTION; TOTAL KNEE REPLACEMENT; BIOLOGICAL MODEL; BIOMECHANICS; EQUIPMENT; FINITE ELEMENT ANALYSIS; KNEE ARTHROPLASTY; KNEE PROSTHESIS; METHODOLOGY; SENSITIVITY AND SPECIFICITY; TIME;

ARTHROPLASTY, REPLACEMENT, KNEE; BIOMECHANICS; COMPUTER SIMULATION; EQUIPMENT FAILURE ANALYSIS; FINITE ELEMENT ANALYSIS; KNEE PROSTHESIS; MODELS, BIOLOGICAL; MONTE CARLO METHOD; SENSITIVITY AND SPECIFICITY; TIME FACTORS;

EID: 67049136615     PISSN: 01480731     EISSN: 15288951     Source Type: Journal    
DOI: 10.1115/1.3005152     Document Type: Article

References (60)

1. Noble, P. C., Gordon, M. J., Weiss, J. M., Reddix, R. N., Conditt, M. A., and Mathis, K. B., 2005, "Does Total Knee Replacement Restore Normal Knee Function?," Clin. Orthop. Relat. Res., 431, pp. 157-165.
2. Mancuso, C. A., Sculco, T. P., Wickiewicz, T. L., Jones, E. C., Robbins, L., Warren, R. F., and Williams-Russo, P., 2001, "Patients' Expectations of Knee Surgery," J. Bone Jt. Surg., Am. Vol., 83A(7), pp. 1005-1012.
3. Weiss, J. M., Noble, P. C., Conditt, M. A., Kohl, H. W., Roberts, S., Cook, K. F., Gordon, M. J., and Mathis, K. B., 2002, "What Functional Activities Are Important to Patients With Knee Replacements?," Clin. Orthop. Relat. Res., 40(4), pp. 172-188.
4. Fregly, B. J., Sawyer, W. G., Harman, M. K., and Banks, S. A., 2005, "Computational Wear Prediction of a Total Knee Replacement From In Vivo Kinematics," J. Biomech., 38(2), pp. 305-314.
5. Giddings, V. L., Kurtz, S. M., and Edidin, A. A., 2001, "Total Knee Replacement Polyethylene Stresses During Loading in a Knee Simulator," ASME J. Tribol., 123(4), pp. 842-847.
6. Halloran, J. P., Petrella, A. J., and Rullkoetter, P. J., 2005, "Explicit Finite Element Modeling of Total Knee Replacement Mechanics," J. Biomech., 38(2), pp. 323-331.
7. Rawlinson, J. J., Furman, B. D., Li, S., Wright, T. M., and Bartel, D. L., 2006, "Retrieval, Experimental, and Computational Assessment of the Performance of Total Knee Replacements," J. Orthop. Res., 24(7), pp. 1384-1394.
8. Zhao, D., Sakoda, H., Sawyer, W. G., Banks, S. A., and Fregly, B. J., 2008, "Predicting Knee Replacement Damage in a Simulator Machine Using a Computational Model With a Consistent Wear Factor," ASME J. Biomech. Eng., 130(1), p. 011004.
9. Knight, L. A., Pal, S., Coleman, J. C., Bronson, F., Haider, H., Levine, D. L., Taylor, M., and Rullkoetter, P. J., 2007, "Comparison of Long-Term Numerical and Experimental Total Knee Replacement Wear During Simulated Gait Loading," J. Biomech., 40(7), pp. 1550-1558.
10. Halloran, J. P., Easley, S. K., Petrella, A. J., and Rullkoetter, P. J., 2005, "Comparison of Deformable and Elastic Foundation Finite Element Simulations for Predicting Knee Replacement Mechanics," ASME J. Biomech. Eng., 127(5), pp. 813-818.
11. Box, G. E. P., and Draper, N. R., 1987, "Empirical Model-Building and Response Surfaces," Applied Probability and Statistics (Wiley Series in Probability and Mathematical Statistics), Wiley, New York.
12. Khuri, A. I., and Cornell, J. A., 1996, Response Surfaces: Designs and Analyses, Statistics, Textbooks and Monographs, Dekker, New York.
13. Myers, R. H., and Montgomery, D. C., 1995, "Response Surface Methodology: Process and Product in Optimization Using Designed Experiments," Applied Probability and Statistics (Wiley Series in Probability and Statistics), Wiley, New York.
14. Jones, D. R., Schonlau, M., and Welch, W. J., 1998, "Efficient Global Optimization of Expensive Black-Box Functions," J. Global Optim., 13(4), pp. 455-492. (Pubitemid 128507405)
15. Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P., 1989, "Design and Analysis of Computer Experiments," Stat. Sci., 4(4), pp. 409-435.
16. Chen, S., Chng, E. S., and Alkadhimi, K., 1996, "Regularized Orthogonal Least Squares Algorithm for Constructing Radial Basis Function Networks," Int. J. Control, 64(5), pp. 829-837. (Pubitemid 126527191)
17. Wendland, H., 1995, "Piecewise Polynomial, Positive Definite and Compactly Supported Radial Basis Functions of Minimal Degree," Adv. Comput. Math., 4(1), pp. 389-396.
18. Wahba, G., 1987, "Spline Models for Observational Data," CBMS-NSF Regional Conference Series in Applied Mathematics, Based on a Series of Ten Lectures at Ohio State University at Columbus, Mar. 23-27, Society for Industrial and Applied Mathematics, Philadelphia, PA.
19. Girosi, F., 1998, "An Equivalence Between Sparse Approximation and Support Vector Machines," Neural Comput., 10(6), pp. 1455-1480. (Pubitemid 128464285)
20. Vapnik, V. N., Statistical Learning Theory, Wiley, New York.
21. Cox, S. E., Haftka, R. T., Baker, C. A., Grossman, B., Mason, W. H., and Watson, L. T., 2001, "A Comparison of Global Optimization Methods for the Design of a High-Speed Civil Transport," J. Global Optim., 21(4), pp. 415-433.
22. Koch, P. N., Simpson, T. W., Allen, J. K., and Mistree, F., 1999, "Statistical Approximations for Multidisciplinary Design Optimization: The Problem of Size," J. Aircr., 36(1), pp. 275-286.
23. Liu, B., Haftka, R. T., and Akgun, M. A., 2000, "Two-Level Composite Wing Structural Optimization Using Response Surfaces," Struct. Multidiscip. Optim., 20(2), pp. 87-96.
24. Queipo, N. V., Haftka, R. T., Shyy, W., Goel, T., Vaidyanathan, R., and Tucker, P. K., 2005, "Surrogate-Based Analysis and Optimization," Prog. Aerosp. Sci., 41(1), pp. 1-28.
25. Queipo, N. V., Pintos, S., Rincon, N., Contreras, N., and Colmenares, J., 2002, "Surrogate Modeling-Based Optimization for the Integration of Static and Dynamic Data Into a Reservoir Description," J. Pet. Sci. Eng., 35(3-4), pp. 167-181.
26. Wang, G. G., and Shan, S., 2007, "Review of Metamodeling Techniques in Support of Engineering Design Optimization," ASME J. Mech. Des., 129(4), pp. 370-380.
27. Bouzid, A. H., De Technologie Superieure, E., and Champliaud, H., 1998, "On the Use of Dual Kriging Interpolation for the Evaluation of the Gasket Stress Distribution in Bolted Joints," Proceedings of the ASME Pressure Vessels and Piping Conference, Vol. 457, pp. 77-83.
28. Chang, P. B., Williams, B. J., Santner, T. J., Notz, W. I., and Bartel, D. L., 1999, "Robust Optimization of Total Joint Replacements Incorporating Environmental Variables," ASME J. Biomech. Eng., 121(3), pp. 304-310.
29. Lin, Y. C., Farr, J., Carter, K., and Fregly, B. J., 2006, "Response Surface Optimization for Joint Contact Model Evaluation," J. Appl. Biomech., 22(2), pp. 120-130.
30. An, K. N., Himenso, S., Tsumura, H., Kawai, T., and Chao, E. Y. S., 1990, "Pressure Distribution on Articular Surfaces: Application to Joint Stability Analysis," J. Biomech., 23(10), pp. 1013-1020.
31. Blankevoort, L., Kuiper, J. H., Huiskes, R., and Grootenboer, H. J., 1991, "Articular Contact in a Three-Dimensional Model of the Knee," J. Biomech., 24(11), pp. 1019-1031.
32. Fregly, B. J., Bei, Y. H., and Sylvester, M. E., 2003, "Experimental Evaluation of an Elastic Foundation Model to Predict Contact Pressures in Knee Replacements," J. Biomech., 36(11), pp. 1659-1668.
33. Li, G. A., Sakamoto, M., and Chao, E. Y. S., 1997, "A Comparison of Different Methods in Predicting Static Pressure Distribution in Articulating Joints," J. Biomech., 30(6), pp. 635-638.
34. Pandy, M. G., Sasaki, K., and Kim, S., 1998, "A Three-Dimensional Musculoskeletal Model of the Human Knee Joint. Part 1: Theoretical Construct," Comput. Methods Biomech. Biomed. Eng., 1(2), pp. 87-108.
35. Walker, P. S., Blunn, G. W., Broome, D. R., Perry, J., Watkins, A., Sathasivam, S., Dewar, M. E., and Paul, J. P., 1997, "A Knee Simulating Machine for Performance Evaluation of Total Knee Replacements," J. Biomech., 30(1), pp. 83-89.
36. Desjardins, J. D., Walker, P. S., Haider, H., and Perry, J., 2000, "The Use of a Force-Controlled Dynamic Knee Simulator to Quantify the Mechanical Performance of Total Knee Replacement Designs During Functional Activity," J. Biomech., 33(10), pp. 1231-1242.
37. Hammersley, J. M., 1960, "Related Problems .3. Monte-Carlo Methods for Solving Multivariable Problems," Ann. N.Y. Acad. Sci., 86(3), pp. 844-874.
38. Diwekar, U. M., 2003, Introduction to Applied Optimization, Springer, New York.
39. Kalagnanam, J. R., and Diwekar, U. M., 1997, "An Efficient Sampling Technique for Off-Line Quality Control," Technometrics, 39(3), pp. 308-319.
40. Fregly, B. J., Banks, S. A., D'lima, D. D., and Colwell, C. W., Jr., 2008, "Sensitivity of Knee Replacement Contact Calculations to Kinematic Measurement Errors," J. Orthop. Res., 26(9), pp. 1173-1179.
41. Cressie, N., 1992, "Statistics for Spatial Data," Terra Nova, 4(5), pp. 613-617.
42. Gupta, A., Ding, Y., Xu, L., and Reinikainen, T., 2006, "Optimal Parameter Selection for Electronic Packaging Using Sequential Computer Simulations," ASME J. Manuf. Sci. Eng., 128(3), pp. 705-715.
43. Lophaven, S. N., Nielsen, H. B., and Søndergaard, J., 2002, "Dace - A Matlab Kriging Toolbox," Technical Report No. IMM-TR-2002-13, Informatics and Mathematical Modelling, Technical University of Denmark.
44. Johnson, K. L., 1987, Contact Mechanics, Cambridge University Press, Cambridge.
45. Archard, J. F., and Hirst, W., 1956, "The Wear of Metals Under Unlubricated Conditions," Proc. R. Soc. London, Ser. A, 236(1206), pp. 397-410.
46. Fisher, J., Dowson, D., Hamdzah, H., and Lee, H. L., 1994, "The Effect of Sliding Velocity on the Friction and Wear of Uhmwpe for Use in Total Artificial Joints," Wear, 175(1-2), pp. 219-225.
47. Kane, T. R., and Levinson, D. A., 1985, Dynamics, Theory and Applications (Series in Mechanical Engineering), McGraw-Hill, New York.
48. Daffertshofer, A., Lamoth, C. J. C., Meijer, O. G., and Beek, P. J., 2004, "PCA in Studying Coordination and Variability: A Tutorial," Clin. Biomech., 19(4), pp. 415-428.
49. Valero-Cuevas, F. J., Johanson, M. E., and Towles, J. D., 2003, "Towards a Realistic Biomechanical Model of the Thumb: The Choice of Kinematic Description May Be More Critical Than the Solution Method or the Variability/ Uncertainty of Musculoskeletal Parameters," J. Biomech., 36(7), pp. 1019-1030.
50. Bei, Y. H., and Fregly, B. J., 2004, "Multibody Dynamic Simulation of Knee Contact Mechanics," Med. Eng. Phys., 26(9), pp. 777-789.
51. Laz, P. J., Pal, S., Halloran, J. P., Petrella, A. J., and Rullkoetter, P. J., 2006, "Probabilistic Finite Element Prediction of Knee Wear Simulator Mechanics," J. Biomech., 39(12), pp. 2303-2310.
52. Wu, Y. T., Millwater, H. R., and Cruse, T. A., 1990, "Advanced Probabilistic Structural-Analysis Method for Implicit Performance Functions," AIAA J., 28(9), pp. 1663-1669.
53. Jin, R., Chen, W., and Simpson, T. W., 2001, "Comparative Studies of Metamodelling Techniques Under Multiple Modelling Criteria," Struct. Multidiscip. Optim., 23(1), pp. 1-13. (Pubitemid 34271934)
54. Simpson, T. W., Peplinski, J. D., Koch, P. N., and Allen, J. K., 2001, "Metamodels for Computer-Based Engineering Design: Survey and Recommendations," Eng. Comput., 17(2), pp. 129-150.
55. Bai, B., Baez, J., Testa, N. N., and Kummer, F. J., 2000, "Effect of Posterior Cut Angle on Tibial Component Loading," J. Arthroplasty, 15(7), pp. 916-920.
56. Blunn, G. W., Walker, P. S., Joshi, A., and Hardinge, K., 1991, "The Dominance of Cyclic Sliding in Producing Wear in Total Knee Replacements," Clin. Orthop. Relat. Res., 273, pp. 253-260.
57. Kawanabe, K., Clarke, I. C., Tamura, J., Akagi, M., Good, V. D., Williams, P. A., and Yamamoto, K., 2001, "Effects of a-P Translation and Rotation on the Wear of Uhmwpe in a Total Knee Joint Simulator," J. Biomed. Mater. Res., 54(3), pp. 400-406.
58. Barnett, P. I., Fisher, J., Auger, D. D., Stone, M. H., and Ingham, E., 2001, "Comparison of Wear in a Total Knee Replacement Under Different Kinematic Conditions," J. Mater. Sci.: Mater. Med., 12(10-12), 1039-1042.
59. D'lima, D. D., Hermida, J. C., Chen, P. C., and Colwell, C. W., 2001, "Polyethylene Wear and Variations in Knee Kinematics," Clin. Orthop. Relat. Res., 392, pp. 124-130.
60. Johnson, T. S., Laurent, M. P., Yao, J. Q., and Gilbertson, L. N., 2001, "The Effect of Displacement Control Input Parameters on Tibiofemoral Prosthetic Knee Wear," Wear, 250, pp. 222-226.