Technical Brief

A Genetic Algorithm Based Multi-Objective Shape Optimization Scheme for Cementless Femoral Implant

[+] Author and Article Information
Souptick Chanda, Dilip Kumar Pratihar

Department of Mechanical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur, West Bengal 721 302, India

Sanjay Gupta

Department of Mechanical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur, West Bengal 721 302, India
e-mail: sangupta@mech.iitkgp.ernet.in

1Corresponding author.

Manuscript received March 25, 2014; final manuscript received November 5, 2014; published online January 29, 2015. Assoc. Editor: David Corr.

J Biomech Eng 137(3), 034502 (Mar 01, 2015) (12 pages) Paper No: BIO-14-1136; doi: 10.1115/1.4029061 History: Received March 25, 2014; Revised November 05, 2014; Online January 29, 2015

The shape and geometry of femoral implant influence implant-induced periprosthetic bone resorption and implant-bone interface stresses, which are potential causes of aseptic loosening in cementless total hip arthroplasty (THA). Development of a shape optimization scheme is necessary to achieve a trade-off between these two conflicting objectives. The objective of this study was to develop a novel multi-objective custom-based shape optimization scheme for cementless femoral implant by integrating finite element (FE) analysis and a multi-objective genetic algorithm (GA). The FE model of a proximal femur was based on a subject-specific CT-scan dataset. Eighteen parameters describing the nature of four key sections of the implant were identified as design variables. Two objective functions, one based on implant-bone interface failure criterion, and the other based on resorbed proximal bone mass fraction (BMF), were formulated. The results predicted by the two objective functions were found to be contradictory; a reduction in the proximal bone resorption was accompanied by a greater chance of interface failure. The resorbed proximal BMF was found to be between 23% and 27% for the trade-off geometries as compared to ∼39% for a generic implant. Moreover, the overall chances of interface failure have been minimized for the optimal designs, compared to the generic implant. The adaptive bone remodeling was also found to be minimal for the optimally designed implants and, further with remodeling, the chances of interface debonding increased only marginally.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Kilgus, D. J., Shimaoka, E. E., Tipton, J. S., and Eberle, R. W., 1993, “Dual-Energy X-Ray Absorptiometry Measurement of Bone Mineral Density Around Porous-Coated Cementless Femoral Implants,” J. Bone Jt. Surg., Br. Vol., 75(2), pp. 279–287.
Kuiper, J. H., and Huiskes, R., 1997, “Mathematical Optimization of Elastic Properties: Application to Cementless Hip Stem Design,” ASME J. Biomech. Eng., 119(2), pp. 166–174. [CrossRef]
Ahnfelt, L., Herberts, P., Malchau, H., and Andersson, G. B. H., 1990, “Prognosis of Total Hip Replacement, a Swedish Multicenter Study of 4664 Revisions,” Acta Orthop. Scand., 238, pp. 1–26.
Kurtz, S., Ong, K., Lau, E., Mowat, F., and Halpern, M., 2007, “Projections of Primary and Revision Hip and Knee Arthroplasty in the United States From 2005 to 2030,” J. Bone Jt. Surg., Am. Vol., 89(4), pp. 780–785. [CrossRef]
Huiskes, R., and Boeklagen, R., 1988, “The Application of Numerical Shape Optimization to Artificial-Joint Design,” Computer Methods Bioengineering, 7th ed., Vol. 9, R. L.Spiker, and B. R.Simon, eds., ASME, NY, pp. 185–197.
Viceconti, M., Monti, L., Muccini, R., Bernakiewicz, M., and Toni, A., 2001, “Even a Thin Layer of Soft Tissue May Compromise the Primary Stability of Cementless Hip Stems,” Clin. Biomech., 16(9), pp. 765–775. [CrossRef]
Fraternali, F., Marino, A., Sayed, T. E., and Cioppa, A. D., 2011, “On the Structural Shape Optimization Through Variational Methods and Evolutionary Algorithms,” Mech. Adv. Mater. Struct., 18(4), pp. 225–243. [CrossRef]
Khanoki, S. A., and Pasini, D., 2012, “Multiscale Design and Multiobjective Optimization of Orthopedic Hip Implants With Functionally Graded Cellular Material,” ASME J. Biomech. Eng., 134(3), p. 031004. [CrossRef]
Huiskes, R., and Boeklagen, R., 1989, “Mathematical Shape Optimization of Hip Prosthesis Design,” J. Biomech., 22(8–9), pp. 793–804. [CrossRef] [PubMed]
Katoozian, H., and Davy, D. T., 2000, “Effects of Loading Conditions and Objective Function on Three-Dimensional Shape Optimization of Femoral Components of Hip Endoprostheses,” Med. Eng. Phys., 22(4), pp. 243–251. [CrossRef] [PubMed]
Chang, P. B., Williams, B. J., Bhalla, K. S. B., Belknap, T. W., Santner, T. J., Notz, W. I., and Bartel, D. L., 2001, “Design and Analysis of Robust Total Joint Replacements: Finite Element Model Experiments With Environmental Variables,” ASME J. Biomech. Eng., 123(3), pp. 239–246. [CrossRef]
Kowalczyk, P., 2001, “Design Optimization of Cementless Femoral Hip Prostheses Using Finite Element Analysis,” ASME J. Biomech. Eng., 123(5), pp. 396–402. [CrossRef]
Fernandes, P. R., Folgado, J., and Ruben, R. B., 2004, “Shape Optimization of a Cementless Hip Stem for a Minimum of Interface Stress and Displacement,” Comput. Methods Biomech. Biomed. Eng., 7(1), pp. 51–61. [CrossRef]
Ishida, T., Nishimura, I., Tanino, H., Higa, M., Ito, H., and Mitamura, Y., 2011, “Use of a Genetic Algorithm for Multiobjective Design Optimization of the Femoral Stem of a Cemented Total Hip Arthroplasty,” Artif. Organs, 35(4), pp. 404–410. [CrossRef] [PubMed]
Ruben, R. B., Folgado, J., and Fernandes, P. R., 2012, “On the Optimal Shape of Hip Implants,” J. Biomech., 45(2), pp. 239–246. [CrossRef] [PubMed]
Weinans, H., Huiskes, R., van Rietbergen, B., Sumner, D. R., Turner, T. M., and Galante, J. O., 1993, “Adaptive Bone Remodelling Around Bonded Noncemented Total Hip Arthroplasty: A Comparison Between Animal Experiments and Computer Simulation,” J. Orthop. Res., 11(4), pp. 500–513. [CrossRef] [PubMed]
Ruben, R. B., Folgado, J., and Fernandes, P. R., 2007, “Three-Dimensional Shape Optimization of a Hip Prosthesis Using a Multicriteria Formulation,” Struct. Multidisc. Optim., 34(4), pp. 261–275. [CrossRef]
Sabatini, A. L., and Goswami, T., 2008, “Hip Implants VII: Finite Element Analysis and Optimization of Cross-Sections,” Mater. Des., 29(7), pp. 1438–1446. [CrossRef]
Viceconti, M., Bellingeri, L., Cristofolini, L., and Toni, A., 1997, “A Comparative Study on Different Methods of Automatic Mesh Generation of Human Femurs,” Med. Eng. Phys., 20(1), pp. 1–10. [CrossRef]
Fraldi, M., Esposito, L., Perrella, G., Cutolo, A., and Cowin, S., 2010, “Topological Optimization in Hip Prosthesis Design,” Biomech. Model. Mechanobiol., 9(4), pp. 389–402. [CrossRef] [PubMed]
Botkin, M. E., 1992, “Three-Dimensional Shape Optimization Using Fully Automatic Mesh Generation,” J. AIAA, 30(7), pp. 1932–1934. [CrossRef]
Haftka, R. T., and Grandhi, R. V., 1986, “Structural Shape Optimization—A Survey,” Comput. Methods Appl. Mech. Eng., 57(1), pp. 91–106. [CrossRef]
Viceconti, M., Davinelli, M., Taddei, F., and Cappello, A., 2004, “Automatic Generation of Accurate Subject Specific Bone Finite Element Models to Be Used in Clinical Studies,” J. Biomech., 37(10), pp. 1597–1605. [CrossRef] [PubMed]
Zannoni, C., Mantovani, R., and Viceconti, M., 1998, “Material Properties Assignment to Finite Element Models of Bone Structures: A New Method,” Med. Eng. Phys., 20(10), pp. 735–740. [CrossRef] [PubMed]
Taddei, F., Pancanti, A., and Viceconti, M., 2004, “An Improved Method for the Automatic Mapping of Computed Tomography Numbers Onto Finite Element Models,” Med. Eng. Phys., 26(1), pp. 61–69. [CrossRef] [PubMed]
Morgan, E. F., Bayraktar, H. H., and Keaveny, T. M., 2003, “Trabecular Bone Modulus-Density Relationships Depend on Anatomic Site,” J. Biomech., 36(7), pp. 897–904. [CrossRef] [PubMed]
Vail, T. P., Glisson, R. R., Koukoubis, T. D., and Guilak, F., 1998, “The Effect of Hip Stem Material Modulus on Surface Strain in Human Femora,” J. Biomech., 31(7), pp. 619–628. [CrossRef] [PubMed]
Martin, R. B., Burr, D. B., and Sharkey, N. A., 1998, Skeletal Tissue Mechanics, Springer, NY, pp. 137–166. [CrossRef]
Bergmann, G., Deuretzbacher, G., Heller, M., Graichen, F., Rohlmann, A., Strauss, J., and Duda, G., 2001, “Hip Contact Forces and Gait Patterns From Routine Activities,” J. Biomech., 34(7), pp. 859–871. [CrossRef] [PubMed]
Heller, M., Bergmann, G., Deuretzbacher, G., Durselen, L., Pohl, M., Claes, L., and Duda, G. N., 2001, “Musculo-Skeletal Loading Conditions at the Hip During Walking and Stair Climbing,” J. Biomech., 34(7), pp. 883–893. [CrossRef] [PubMed]
Taylor, M., 2006, “Finite Element Analysis of the Resurfaced Femoral Head,” Proc. Inst. Mech. Eng., Part H, 220(2), pp. 289–297. [CrossRef]
Duda, G. N., Brand, D., Freitag, S., Liersel, W., and Schneider, E., 1996, “Variability of Femoral Muscle Attachments,” J. Biomech., 29(9), pp. 1185–1190. [CrossRef] [PubMed]
Kuiper, J. H., 1993, “Numerical Optimization of Artificial Hip Joint Designs,” Ph.D. thesis, Nijmegen, The Netherlands.
Huiskes, R., Weinans, H., Grootenboer, H. J., Dalstra, M., Fudala, B., and Slooff, T. J., 1987, “Adaptive Bone-Remodelling Theory Applied to Prosthetic-Design Analysis,” J. Biomech., 20(11–12), pp. 1135–1150. [CrossRef] [PubMed]
Huiskes, R., Weinans, H., and van Rietbergen, B., 1992, “The Relationship Between Stress Shielding and Bone Resorption Around Total Hip Stems and the Effect of Flexible Materials,” Clin. Orthop. Relat. Res., 274, pp. 124–134. [CrossRef] [PubMed]
Huiskes, R., and van Rietbergen, B., 1995, “Preclinical Testing of Total Hip Stem: The Effects of Coating Placement,” Clin. Orthop. Relat. Res., 319, pp. 64–76. [CrossRef] [PubMed]
Ghosh, R., Mukherjee, K., and Gupta, S., 2013, “Bone Remodelling Around Uncemented Metallic and Ceramic Acetabular Components,” Proc. Inst. Mech. Eng., Part H, 227(5), pp. 490–502. [CrossRef]
Ghosh, R., and Gupta, S., 2014, “Bone Remodelling Around Cementless Composite Acetabular Components: The Effects of Implant Geometry and Implant-Bone Interfacial Conditions,” J. Mech. Behav. Biomed. Mater., 32, pp. 257–269. [CrossRef] [PubMed]
Hoffman, O., 1967, “The Brittle Strength of Orthotropic Materials,” J. Compos. Mater., 1(3), pp. 200–206. [CrossRef]
Pal, B., Gupta, S., and New, A. M. R., 2010, “Design Considerations for Ceramic Resurfaced Femoral Head: Effect of Interface Characteristics on Failure Mechanisms,” Comput. Methods Biomech. Biomed. Eng., 13(2), pp. 143–155. [CrossRef]
Kaplan, S. J., Hayes, W. C., and Stone, J. L., 1985, “Tensile Strength of Bovine Trabecular Bone,” J. Biomech., 18(9), pp. 723–727. [CrossRef] [PubMed]
Stone, J. L., Beaupré, G. S., and Hayes, W. C., 1983, “Multiaxial Strength Characteristics of Trabecular Bone,” J. Biomech., 16(9), pp. 743–752. [CrossRef] [PubMed]
Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T., 2002, “A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II,” IEEE Trans. Evol. Comput., 6(2), pp. 182–197. [CrossRef]
Deb, K., 2001, Multi-Objective Optimization Using Evolutionary Algorithms, 1st ed., ( Wiley-Interscience Series in Systems and Optimization), John Wiley & Sons Ltd, Baffins Lane, Chichester, West Sussex, England.
van Rietbergen, B., Huiskes, R., Weinans, H., Sumner, D. R., Turner, T. M., and Galante, J. O., 1993, “The Mechanism of Bone Remodelling and Resorption Around Press-Fitted THA Stems,” J. Biomech., 26(4–5), pp. 369–382. [CrossRef] [PubMed]
Pal, B., Gupta, S., and New, A., 2009, “A Numerical Study of Failure Mechanisms in the Cemented Resurfaced Femur: Effects of Interface Characteristics and Bone Remodelling,” Proc. Inst. Mech. Eng., Part H, 223(4), pp. 471–484. [CrossRef]
Martin, R. B., 1972, “The Effect of Geometric Feedback in the Development of Osteoporosis,” J. Biomech., 5(5), pp. 447–455. [CrossRef] [PubMed]
He, J., and Yao, X., 2003, “Towards an Analytic Framework for Analysing the Computation Time of Evolutionary Algorithms,” Artif. Int., 145(1–2), pp. 59–97. [CrossRef]
Søballe, K., and Christensen, F., 1988, “Calcar Resorption After Total Hip Arthroplasty,” J. Arthrop., 3(2), pp. 103–107. [CrossRef]
Kröger, H., Venesmaa, P., Jurvelin, J., Miettinen, H., Suomalainen, O., and Alhava, E., 1998, “Bone Density at the Proximal Femur After Total Hip Arthroplasty,” Clin. Orthop. Relat. Res., 352, pp. 66–74. [PubMed]
Roth, A., Richartz, G., Sander, K., Sachse, A., Fuhrmann, R., Wagner, A., and Venbrocks, R. A., 2005, “Periprosthetic Bone Loss After Total Hip Endoprosthesis. Dependence on the Type of Prosthesis and Preoperative Bone Configuration,” Orthopade, 34(4), pp. 334–344. [CrossRef] [PubMed]
Ritter, M. A., and Fechtman, R. W., 1988, “Distal Cortical Hypertrophy Following Total Hip Arthroplasty,” J. Arthrop., 3(2), pp. 117–121. [CrossRef]
Sköldenberg, O. G., Boden, H. S., Salemyr, M. O., Ahl, T. E., and Adolphson, P. Y., 2006, “Peri-Prosthetic Proximal Bone Loss After Uncemented Hip Arthroplasty Is Related to Stem Size: DXA Measurements in 138 Patients Followed for 2–7 Years,” Acta Orthop., 77(3), pp. 386–392. [CrossRef] [PubMed]
Dorr, L. D., and Wan, Z., 1996, “Comparative Results of a Distal Modular Sleeve, Circumferential Coating, and Stiffness Relief Using the Anatomic Porous Replacement II,” J. Arthrop., 11(4), pp. 419–428. [CrossRef]
Vresilovic, E. J., Hozack, W. J., and Rothman, R. H., 1996, “Incidence of Thigh Pain After Uncemented Total Hip Arthroplasty as a Function of Femoral Stem Size,” J. Arthrop., 11(3), pp. 304–311. [CrossRef]
Kim, Y. H., Park, J. W., Kim, J. S., and Kang, J. S., 2014, “Long-Term Results and Bone Remodeling After THA With a Short, Metaphyseal-Fitting Anatomic Cementless Stem,” Clin. Orthop. Relat. Res., 472(3), pp. 943–950. [CrossRef] [PubMed]
Leali, A., and Fetto, J., 2007, “Promising Mid-Term Results of Total Hip Arthroplasties Using an Uncemented Lateral-Flare Hip Prosthesis: A Clinical and Radiographic Study,” Int. Orthop., 31(8), pp. 845–849. [CrossRef] [PubMed]
Abdul-Kadir, M. R., and Kamsah, N., 2009, “Interface Micromotion of Cementless Hip Stems in Simulated Hip Arthroplasty,” Am. J. Appl. Sci., 6(9), pp. 1682–1689. [CrossRef]
Hedia, H. S., Shabara, M. A. N., El-Midany, T. T., and Fouda, N., 2006, “Improved Design of Cementless Hip Stems Using Two-Dimensional Functionally Graded Materials,” J. Biomed. Mater. Res. B, 79(1), pp. 42–49. [CrossRef]
Yildiz, H., Chang, F. K., and Goodman, S., 1998, “Composite Hip Prosthesis Design. II. Simulation,” J. Biomed. Mater. Res., 39(1), pp. 102–119. [CrossRef] [PubMed]
Sakai, R., Itoman, M., and Mabuchi, K., 2006, “Assessments of Different Kinds of Stems by Experiments and FEM Analysis: Appropriate Stress Distribution on a Hip Prosthesis,” Clin. Biomech., 21(8), pp. 826–833. [CrossRef]
Bryan, J. M., Sumner, D. R., Hurwitz, D. E., Tompkins, G. S., Andriacchi, T. P., and Galante, J. O., 1996, “Altered Load History Affects Periprosthetic Bone Loss Following Cementless Total Hip Arthroplasty,” J. Orthop. Res., 14(5), pp. 762–768. [CrossRef] [PubMed]
Maurer, S. G., Baitner, A. C., and Di Cesare, P. E., 2000, “Reconstruction of the Failed Femoral Component and Proximal Femoral Bone Loss in Revision Hip Surgery,” Am. Acad. Orthop. Surg., 8(6), pp. 354–363.
Thomsen, M. N., Breusch, S. J., Aldinger, P. R., Görtz, W., Lahmer, A., Honl, M., Birke, A., and Nägerl, H., 2002, “Robotically-Milled Bone Cavities: A Comparison With Hand-Broaching in Different Types of Cementless Hip Stems,” Acta Orthop. Scand., 73(4), pp. 379–385. [CrossRef] [PubMed]
Rosenthall, L., Bobyn, J. D., and Tanzer, M., 1999, “Bone Densitometry: Influence of Prosthetic Design and Hydroxyapatite Coating on Regional Adaptive Bone Remodeling,” Int. Orthop., 23(6), pp. 325–329. [CrossRef] [PubMed]
Sandiford, N., Doctor, C., Rajaratnam, S. S., Ahmed, S., East, D. J., Miles, K., Butler-Manuel, A., and Shepperd, J. A., 2013, “Primary Total Hip Replacement With a Furlong Fully Hydroxyapatite-Coated Titanium Alloy Femoral Component: Results at a Minimum Follow-Up of 20 Years,” Bone Jt. J., 95-B(4), pp. 467–471. [CrossRef]
Shetty, A. A., Slack, R., Tindall, A., James, K. D., and Rand, C., 2005, “Results of a Hydroxyapatite-Coated (Furlong) Total Hip Replacement: A 13- to 15-year Follow-Up,” J. Bone Jt. Surg. [Br], 87(8), pp. 1050–1054. [CrossRef]
Singh, S., Trikha, S. P., and Edge, A. J., 2004, “Hydroxyapatite Ceramic Coated Femoral Stems in Young Patients: A Prospective Ten-Year Study,” J. Bone Jt. Surg. [Br], 86-B(8), pp. 1118–1123. [CrossRef]
ten Broeke, R. H. M., Tarala, M., Arts, J. J., Janssen, D. W., Verdonschot, N., and Geesink, R. G. T., 2014, “Improving Peri-Prosthetic Bone Adaptation Around Cementless Hip Stems: A Clinical and Finite Element Study,” Med. Eng. Phys., 36(3), pp. 345–353. [CrossRef] [PubMed]
Baca, V., Horak, Z., Mikulenka, P., and Dzupa, V., 2008, “Comparison of an Inhomogeneous Orthotropic and Isotropic Material Models Used for FE Analyses,” Med. Eng. Phys., 30(7), pp. 924–930. [CrossRef] [PubMed]
Peng, L., Bai, J., Zeng, X., and Zhou, Y., 2006, “Comparison of Isotropic and Orthotropic Material Property Assignments on Femoral Finite Element Models Under Two Loading Conditions,” Med. Eng. Phys., 28(3), pp. 227–233. [CrossRef] [PubMed]
Huiskes, R., 1990, “The Various Stress Patterns of Press-Fit, Ingrown, and Cemented Femoral Stems,” Clin. Orthop., 261, pp. 27–38. [CrossRef]
Engh, C. A., and Bobyn, J. D., 1988, “The Influence of Stem Size and Extent of Porous Coating on Femoral Bone Resorption After Primary Cementless Hip Arthroplasty,” Clin. Orthop., 231, pp. 7–28. [CrossRef]
Gupta, S., Pal, B., and New, A. M. R., 2010, “The Effects of Interfacial Conditions and Stem Length on Potential Failure Mechanisms in the Uncemented Resurfaced Femur,” Anal. Biomed. Eng., 38(6), pp. 2107–2120. [CrossRef]
Wu, L. D., Hahne, H. J., and Hassenpflug, J., 2004, “The Dimensional Accuracy of Preparation of Femoral Cavity in Cementless Total Hip Arthroplasty,” J. Zheijiang Univ. Sci., 5(10), pp. 1270–1278. [CrossRef]
Howard, J. L., Hui, A. J., Bourne, R. B., McCalden, R. W., McDonald, S. J., and Rorabeck, C. H., 2004, “A Quantitative Analysis of Bone Support Comparing Cementless Tapered and Distal Fixation Total Hip Replacement,” J. Arthrop., 19(3), pp. 266–273. [CrossRef]
Mann, K. A., Bartel, D. L., Wright, T. M., and Ingraffea, A. R., 1991, “Mechanical Characteristics of the Stem-Cement Interface,” J. Orthop. Res., 9(6), pp. 798–808. [CrossRef] [PubMed]
Viceconti, M., Muccini, R., Bernakiewicz, M., Baleani, M., and Cristofolini, L., 2000, “Large-Sliding Contact Elements Accurately Predict Levels of Bone-Implant Micromotion Relevant to Osseointegration,” J. Biomech., 33(12), pp. 1611–1618. [CrossRef] [PubMed]
Viceconti, M., Brusi, G., Pancanti, A., and Cristofolini, L., 2006, “Primary Stability of an Anatomical Cementless Hip Stem: A Statistical Analysis,” J. Biomech., 39(7), pp. 1169–1179. [CrossRef] [PubMed]
Araujo, A. B., Travison, T. G., Harris, S. S., Holick, M. F., Turner, A. K., and McKinlay, J. B., 2007, “Race/Ethnic Differences in Bone Mineral Density in Men,” Osteoporos. Int., 18(7), pp. 943–953. [CrossRef] [PubMed]
Bryan, R., Mohan, P. S., Hopkins, A., Galloway, F., Taylor, M., and Nair, P. B., 2010, “Statistical Modelling of the Whole Human Femur Incorporating Geometric and Material Properties,” Med. Eng. Phys., 32(1), pp. 57–65. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 1

Parametric scheme for evolution of key sections of the implant: ellipse (p = 2) to superellipse (p > 2)

Grahic Jump Location
Fig. 2

Design parameters used in the study: (a) eighteen design variables characterizing four key sections of the implant and (b) initial implant model based on a collarless TriLock (DePuy) prosthesis

Grahic Jump Location
Fig. 3

Probable shapes of the implant key sections: a comparison between the two parameterization schemes

Grahic Jump Location
Fig. 4

Finite element model of the implanted femur subjected to musculoskeletal loading conditions of normal walking and stair climbing. Finer mesh density was used at the implant-bone interface as indicated in the sectional view of the FE model. For magnitude of loading, see Table 1.

Grahic Jump Location
Fig. 11

A comparison of bone resorption in the proximal femur for different implants. The plots (a), (b), (c), and (d) correspond to immediate postoperative bone density distribution for OSG-1, OSG-2, OSG-3, and initial stem, respectively. The plots (e), (f), (g), and (h) correspond to bone density distribution after bone remodeling for OSG-1, OSG-2, OSG-3, and initial stem, respectively. Negative sign indicates bone resorption and the number indicates average reduction in bone density. Gray-scale variations represent bone density ranges in g cm−3.

Grahic Jump Location
Fig. 10

A probability plot of the initial and optimal geometries (OSGs) based on local failure values (FL) obtained along implant-bone interface

Grahic Jump Location
Fig. 9

The distribution of local failure values (FL) obtained along the posterior and anterior parts of implant-bone interface, respectively, of (a) initial model, (b) OSG-1, (c) OSG-2, and (d) OSG-3

Grahic Jump Location
Fig. 8

Three OSGs with four key transverse sections: (a) OSG-1, (b) OSG-2, and (c) OSG-3

Grahic Jump Location
Fig. 7

Pareto-optimal front of solutions: proximal resorbed BMF (%) versus global interface failure. The encircled markers indicate three dominant trade-off stem geometries which correspond to stem profiles OSG-1, OSG-2, and OSG-3, respectively.

Grahic Jump Location
Fig. 6

A scatter plot of the feasible solutions with the direction of optimization indicated by arrowheads

Grahic Jump Location
Fig. 5

A schematic representation of the optimization procedure



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In