Multiscale topology optimization of pelvic bone for combined walking and running gait cycles

References

• Allaire G, Jouve F, Toader A-M. 2004. Structural optimization using sensitivity analysis and a level-set method. Comput Phys. 194(1):363–393.
   Google Scholar
• Alsheghri A, Reznikov N, Piché N, McKee MD, Tamimi F, Song J. 2021. Optimization of 3D network topology for bioinspired design of stiff and lightweight bone-like structures. Mater Sci Eng C Mater Biol Appl. 123:112010.
   PubMed Web of Science ®Google Scholar
• Anderson AE, Peters CL, Tuttle BD, Weiss JA. 2005. Subject-specific finite element model of the pelvis: development, validation and sensitivity studies. J Biomech Eng. 127(3):364–373.
   PubMed Web of Science ®Google Scholar
• Andrade-Campos A, Ramos A, Simões JAO. 2012. A model of bone adaptation as a topology optimization process with contact. JBiSE. 05(05):229–244.
   Google Scholar
• Bagge M. 2000. A model of bone adaptation as an optimization process. J Biomech. 33(11):1349–1357.
   PubMed Web of Science ®Google Scholar
• Bergmann G, Deuretzbacher G, Heller M, Graichen F, Rohlmann A, Strauss J, Duda G. 2001. Hip contact forces and gait patterns from routine activities. J Biomech. 34(7):859–871.
   PubMed Web of Science ®Google Scholar
• Boyle C, Kim IY. 2011. Three-dimensional micro-level computational study of wolff’s law via trabecular bone remodeling in the human proximal femur using design space topology optimization. J Biomech. 44(5):935–942.
   PubMed Web of Science ®Google Scholar
• Challis VJ. 2010. A discrete level-set topology optimization code written in matlab. Struct Multidisc Optim. 41(3):453–464.
   Web of Science ®Google Scholar
• Challis VJ, Roberts AP, Grotowski JF, Zhang L-C, Sercombe TB. 2010. Prototypes for bone implant scaffolds designed via topology optimization and manufactured by solid freeform fabrication. Adv Eng Mater. 12(11):1106–1110.
   Web of Science ®Google Scholar
• Chen G, Pettet G, Pearcy M, McElwain D. 2007. Modelling external bone adaptation using evolutionary structural optimisation. Biomech Model Mechanobiol. 6(4):275–285.
   PubMed Web of Science ®Google Scholar
• Chen Y, Zhou S, Li Q. 2011. Microstructure design of biodegradable scaffold and its effect on tissue regeneration. Biomaterials. 32(22):5003–5014.
   PubMed Web of Science ®Google Scholar
• Cignoni P, Rocchini C, Scopigno R. 1998. Metro: measuring error on simplified surfaces. In: Computer Graphics Forum. Vol. 17. Wiley Online Library; p. 167–174.
   Google Scholar
• Coelho P, Fernandes P, Rodrigues H, Cardoso J, Guedes J. 2009. Numerical modeling of bone tissue adaptation—a hierarchical approach for bone apparent density and trabecular structure. J Biomech. 42(7):830–837.
   PubMed Web of Science ®Google Scholar
• Cowin S, Hegedus D. 1976. Bone remodeling i: theory of adaptive elasticity. J Elasticity. 6(3):313–326.
   Web of Science ®Google Scholar
• Cowin S, Moss-Salentijn L, Moss M. 1991. Candidates for the mechanosensory system in bone. J Biomech Eng. 113(2):191–197.
   PubMed Web of Science ®Google Scholar
• Cui M, Chen H, Zhou J. 2016. A level-set based multi-material topology optimization method using a reaction diffusion equation. Comput-Aided Des. 73:41–52.
   Web of Science ®Google Scholar
• Dalstra M, Huiskes R. 1995. Load transfer across the pelvic bone. J Biomech. 28(6):715–724.
   PubMed Web of Science ®Google Scholar
• Dalstra M, Huiskes R, Odgaard A, Van Erning L. 1993. Mechanical and textural properties of pelvic trabecular bone. J Biomech. 26(4–5):523–535.
   PubMed Web of Science ®Google Scholar
• Dalstra M, Huiskes R, van Erning L. 1995. Development and validation of a three-dimensional finite element model of the pelvic bone. J Biomech Eng. 117(3):272–278.
   PubMed Web of Science ®Google Scholar
• Deaton JD, Grandhi RV. 2014. A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidisc Optim. 49(1):1–38.
   Web of Science ®Google Scholar
• Desai A, Mogra M, Sridhara S, Kumar K, Sesha G, Ananthasuresh G. 2021. Topological-derivative-based design of stiff fiber-reinforced structures with optimally oriented continuous fibers. Struct Multidisc Optim. 63(2):703–720.
   Web of Science ®Google Scholar
• Dostal WF, Andrews JG. 1981. A three-dimensional biomechanical model of hip musculature. J Biomech. 14(11):803–812.
   PubMed Web of Science ®Google Scholar
• Eswara Sai Kumar K, Rakshit S. 2020. Topology optimization of the hip bone for walking using multi-load approach. In: ASME International Mechanical Engineering Congress and Exposition, Vol. 84607. American Society of Mechanical Engineers; p. V012T12A013.
   Google Scholar
• Fedkiw SOR, Osher S. 2002. Level set methods and dynamic implicit surfaces. Surfaces. 44(77):685.
   Google Scholar
• Fernandes P, Folgado J, Jacobs C, Pellegrini V. 2002. A contact model with ingrowth control for bone remodelling around cementless stems. J Biomech. 35(2):167–176.
   PubMed Web of Science ®Google Scholar
• Fernandes P, Rodrigues H, Jacobs C. 1999. A model of bone adaptation using a global optimisation criterion based on the trajectorial theory of Wolff. Comput Methods Biomech Biomed Eng. 2(2):125–138.
   PubMedGoogle Scholar
• Folgado J, Fernandes PR, Guedes JM, Rodrigues HC. 2004. Evaluation of osteoporotic bone quality by a computational model for bone remodeling. Comput Struct. 82(17–19):1381–1388.
   Web of Science ®Google Scholar
• Fraldi M, Esposito L, Perrella G, Cutolo A, Cowin S. 2010. Topological optimization in hip prosthesis design. Biomech Model Mechanobiol. 9(4):389–402.
   PubMed Web of Science ®Google Scholar
• Fyhrie DP, Carter D. 1986. A unifying principle relating stress to trabecular bone morphology. J Orthop Res. 4(3):304–317.
   PubMed Web of Science ®Google Scholar
• Geraldes DM, Modenese L, Phillips AT. 2016. Consideration of multiple load cases is critical in modelling orthotropic bone adaptation in the femur. Biomech Model Mechanobiol. 15(5):1029–1042.
   PubMed Web of Science ®Google Scholar
• Giarmatzis G, Jonkers I, Wesseling M, Van Rossom S, Verschueren S. 2015. Loading of hip measured by hip contact forces at different speeds of walking and running. J Bone Miner Res. 30(8):1431–1440.
   PubMed Web of Science ®Google Scholar
• Goda I, Ganghoffer J-F, Czarnecki S, Czubacki R, Wawruch P. 2019. Topology optimization of bone using cubic material design and evolutionary methods based on internal remodeling. Mech Res Commun. 95:52–60.
   Web of Science ®Google Scholar
• Gonabadi H, Yadav A, Bull S. 2020. The effect of processing parameters on the mechanical characteristics of pla produced by a 3d fff printer. Int J Adv Manuf Technol. 111(3–4):695–709.
   Web of Science ®Google Scholar
• Guest JK, Prévost JH. 2006. Optimizing multifunctional materials: design of microstructures for maximized stiffness and fluid permeability. Int J Solids Struct. 43(22–23):7028–7047.
   Web of Science ®Google Scholar
• Hamner SR, Seth A, Delp SL. 2010. Muscle contributions to propulsion and support during running. J Biomech. 43(14):2709–2716.
   PubMed Web of Science ®Google Scholar
• Hao Z, Wan C, Gao X, Ji T. 2011. The effect of boundary condition on the biomechanics of a human pelvic joint under an axial compressive load: a three-dimensional finite element model. J Biomech Eng. 133(10):101006(1-9).
   PubMed Web of Science ®Google Scholar
• Harrigan TP, Hamilton JJ. 1993. Finite element simulation of adaptive bone remodelling: a stability criterion and a time stepping method. Int J Numer Meth Engng. 36(5):837–854.
   Web of Science ®Google Scholar
• Hollister SJ. 2005. Porous scaffold design for tissue engineering. Nat Mater. 4(7):518–524.
   PubMed Web of Science ®Google Scholar
• Hollister SJ, Brennan J, Kikuchi N. 1994. A homogenization sampling procedure for calculating trabecular bone effective stiffness and tissue level stress. J Biomech. 27(4):433–444.
   PubMed Web of Science ®Google Scholar
• Hollister SJ, Kikuchi N, Goldstein SA. 1993. Do bone ingrowth processes produce a globally optimized structure? J Biomech. 26(4–5):391–407.
   PubMed Web of Science ®Google Scholar
• Huiskes R, Ruimerman R, Van Lenthe GH, Janssen JD. 2000. Effects of mechanical forces on maintenance and adaptation of form in trabecular bone. Nature. 405(6787):704–706.
   PubMed Web of Science ®Google Scholar
• Huiskes R, Weinans H, Grootenboer H, Dalstra M, Fudala B, Slooff T. 1987. Adaptive bone-remodeling theory applied to prosthetic-design analysis. J Biomech. 20(11–12):1135–1150.
   PubMed Web of Science ®Google Scholar
• Huttenlocher DP, Klanderman GA, Rucklidge WJ. 1993. Comparing images using the hausdorff distance. IEEE Trans Pattern Anal Machine Intell. 15(9):850–863.
   Web of Science ®Google Scholar
• Iqbal T, Wang L, Li D, Dong E, Fan H, Fu J, Hu C. 2019. A general multi-objective topology optimization methodology developed for customized design of pelvic prostheses. Med Eng Phys. 69:8–16.
   PubMed Web of Science ®Google Scholar
• Jang IG, Kim IY. 2008. Computational study of Wolff’s law with trabecular architecture in the human proximal femur using topology optimization. J Biomech. 41(11):2353–2361.
   PubMed Web of Science ®Google Scholar
• Jang IG, Kim IY, Kwak BM. 2009. Analogy of strain energy density based bone-remodeling algorithm and structural topology optimization. J Biomech Eng. 131(1):011012(1-7).
   PubMed Web of Science ®Google Scholar
• Johansson MS, Korshøj M, Schnohr P, Marott JL, Prescott EIB, Søgaard K, Holtermann A. 2019. Time spent cycling, walking, running, standing and sedentary: a cross-sectional analysis of accelerometer-data from 1670 adults in the Copenhagen city heart study. BMC Public Health. 19(1):1–13.
   PubMed Web of Science ®Google Scholar
• Kang H, Lin C-Y, Hollister SJ. 2010. Topology optimization of three dimensional tissue engineering scaffold architectures for prescribed bulk modulus and diffusivity. Struct Multidiscipl Optim. 42(4):633–644.
   PubMed Web of Science ®Google Scholar
• Klarbring A, Torstenfelt B. 2010. Dynamical systems and topology optimization. Struct Multidisc Optim. 42(2):179–192.
   Web of Science ®Google Scholar
• Klarbring A, Torstenfelt B. 2012. Dynamical systems, SIMP, bone remodeling and time dependent loads. Struct Multidisc Optim. 45(3):359–366.
   Web of Science ®Google Scholar
• Kumar KES, Rakshit S. 2020a. Topology optimization of the hip bone for a few activities of daily living. Int J Adv Eng Sci Appl Math. 12(3–4):193–210.
   Web of Science ®Google Scholar
• Kumar KES, Rakshit S. 2020b. Topology optimization of the hip bone for gait cycle. Struct Multidisc Optim. 62(4):2035–2049.
   Web of Science ®Google Scholar
• Kumar KES, Rakshit S. 2022. Optimization based synthesis of pelvic structure for loads in running gait cycle. Sadhana. 47(118):47–118.
   Google Scholar
• Lin CY, Kikuchi N, Hollister SJ. 2004. A novel method for biomaterial scaffold internal architecture design to match bone elastic properties with desired porosity. J Biomech. 37(5):623–636.
   PubMed Web of Science ®Google Scholar
• Liu H, Wei P, Wang MY. 2022. Cpu parallel-based adaptive parameterized level set method for large-scale structural topology optimization. Struct Multidisc Optim. 65(1):30.
   Web of Science ®Google Scholar
• Liu H, Zong H, Shi T, Xia Q. 2020. M-vcut level set method for optimizing cellular structures. Comput Methods Appl Mech Eng. 367:113154.
   Web of Science ®Google Scholar
• Moussa A, Rahman S, Xu M, Tanzer M, Pasini D. 2020. Topology optimization of 3d-printed structurally porous cage for acetabular reinforcement in total hip arthroplasty. J Mech Behav Biomed Mater. 105:103705.
   PubMed Web of Science ®Google Scholar
• Mullender M, Huiskes R, Weinans H. 1994. A physiological approach to the simulation of bone remodeling as a self-organizational control process. J Biomech. 27(11):1389–1394.
   PubMed Web of Science ®Google Scholar
• Novotny AA, Feijóo RA, Taroco E, Padra C. 2003. Topological sensitivity analysis. Comput Methods Appl Mech Eng. 192(7–8):803–829.
   Web of Science ®Google Scholar
• Nowak M. 2006. Structural optimization system based on trabecular bone surface adaptation. Struct Multidisc Optim. 32(3):241–249.
   Web of Science ®Google Scholar
• Park J, Sutradhar A, Shah JJ, Paulino GH. 2018. Design of complex bone internal structure using topology optimization with perimeter control. Comput Biol Med. 94:74–84.
   PubMed Web of Science ®Google Scholar
• Phillips A, Pankaj P, Howie C, Usmani AS, Simpson A. 2007. Finite element modelling of the pelvis: inclusion of muscular and ligamentous boundary conditions. Med Eng Phys. 29(7):739–748.
   PubMed Web of Science ®Google Scholar
• Rahimizadeh A, Nourmohammadi Z, Arabnejad S, Tanzer M, Pasini D. 2018. Porous architected biomaterial for a tibial-knee implant with minimum bone resorption and bone-implant interface micromotion. J Mech Behav Biomed Mater. 78:465–479.
   PubMed Web of Science ®Google Scholar
• Rossi J-M, Wendling-Mansuy S. 2007. A topology optimization based model of bone adaptation. Comput Methods Biomech Biomed Engin. 10(6):419–427.
   PubMedGoogle Scholar
• Ruimerman R, Hilbers P, Van Rietbergen B, Huiskes R. 2005. A theoretical framework for strain-related trabecular bone maintenance and adaptation. J Biomech. 38(4):931–941.
   PubMed Web of Science ®Google Scholar
• Sethian JA. 1999. Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science. Vol. 3. USA: Cambridge University Press.
   Google Scholar
• Sturm S, Zhou S, Mai Y-W, Li Q. 2010. On stiffness of scaffolds for bone tissue engineering—a numerical study. J Biomech. 43(9):1738–1744.
   PubMed Web of Science ®Google Scholar
• Sutradhar A, Paulino GH, Miller MJ, Nguyen TH. 2010. Topological optimization for designing patient-specific large craniofacial segmental bone replacements. Proc Natl Acad Sci USA. 107(30):13222–13227.
   PubMed Web of Science ®Google Scholar
• Takezawa A, Nishiwaki S, Kitamura M. 2010. Shape and topology optimization based on the phase field method and sensitivity analysis. Comput Phys. 229(7):2697–2718.
   Google Scholar
• Turbosquid. 2000. Turbosquid. https://www.turbosquid.com.
   Google Scholar
• Van Dijk NP, Maute K, Langelaar M, Van Keulen F. 2013. Level-set methods for structural topology optimization: a review. Struct Multidisc Optim. 48(3):437–472.
   Web of Science ®Google Scholar
• Wang Y, Kang Z. 2019. Concurrent two-scale topological design of multiple unit cells and structure using combined velocity field level set and density model. Comput Methods Appl Mech Eng. 347:340–364.
   Web of Science ®Google Scholar
• Wang S, Wang MY. 2006. Radial basis functions and level set method for structural topology optimization. Int J Numer Methods Eng. 65(12):2060–2090.
   Web of Science ®Google Scholar
• Wang MY, Wang X, Guo D. 2003. A level set method for structural topology optimization. Comput Methods Appl Mech Eng. 192(1–2):227–246.
   Web of Science ®Google Scholar
• Wang X, Xu S, Zhou S, Xu W, Leary M, Choong P, Qian M, Brandt M, Xie YM. 2016. Topological design and additive manufacturing of porous metals for bone scaffolds and orthopaedic implants: a review. Biomaterials. 83:127–141.
   PubMed Web of Science ®Google Scholar
• Wei P, Paulino GH. 2020. A parameterized level set method combined with polygonal finite elements in topology optimization. Struct Multidisc Optim. 61(5):1913–1928.
   Web of Science ®Google Scholar
• Weinans H, Huiskes R, Grootenboer H. 1992. The behavior of adaptive bone-remodeling simulation models. J Biomech. 25(12):1425–1441.
   PubMed Web of Science ®Google Scholar
• Wieding J, Wolf A, Bader R. 2014. Numerical optimization of open-porous bone scaffold structures to match the elastic properties of human cortical bone. J Mech Behav Biomed Mater. 37:56–68.
   PubMed Web of Science ®Google Scholar
• Wolff J. 1892. Das gesetz der transformation der knochen. A Hirshwald. 1:1–152.
   Google Scholar
• Wu J, Aage N, Westermann R, Sigmund O. 2018. Infill optimization for additive manufacturing—approaching bone-like porous structures. IEEE Trans Vis Comput Graph. 24(2):1127–1140.
   PubMed Web of Science ®Google Scholar
• Xinghua Z, He G, Dong Z, Bingzhao G. 2002. A study of the effect of non-linearities in the equation of bone remodeling. J Biomech. 35(7):951–960.
   PubMed Web of Science ®Google Scholar
• Yaghmaei M, Ghoddosian A, Khatibi MM. 2020. A filter-based level set topology optimization method using a 62-line MATLAB code. Struct Multidisc Optim. 62(2):1001–1018.
   Web of Science ®Google Scholar
• Yamada T, Izui K, Nishiwaki S, Takezawa A. 2010. A topology optimization method based on the level set method incorporating a fictitious interface energy. Comput Methods Appl Mech Eng. 199(45–48):2876–2891.
   Web of Science ®Google Scholar
• Yu C, Wang Q, Xia Z, Wang Y, Mei C, Liu Y. 2022. Multiscale topology optimization for graded cellular structures based on level set surface cutting. Struct Multidisc Optim. 65(1):32.
   Web of Science ®Google Scholar
• Zhang C, Wu T, Xu S, Liu J. 2023. Multiscale topology optimization for solid-lattice-void hybrid structures through an ordered multi-phase interpolation. Comput-Aided Des. 154:103424.
   Web of Science ®Google Scholar
• Zillober C. 2001. Global convergence of a nonlinear programming method using convex approximations. Numer Algorithms. 27(3):265–289.
   Web of Science ®Google Scholar