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Research Papers

Physically Realizable Three-Dimensional Bone Prosthesis Design With Interpolated Microstructures

[+] Author and Article Information
Andrew D. Cramer

School of Mathematics and Physics,
The University of Queensland,
Brisbane QLD 4072, Australia
e-mail: a.cramer@uq.edu.au

Vivien J. Challis

School of Mathematics and Physics,
The University of Queensland,
Brisbane QLD 4072, Australia
e-mail: vchallis@maths.uq.edu.au

Anthony P. Roberts

School of Mathematics and Physics,
The University of Queensland,
Brisbane QLD 4072, Australia
e-mail: apr@maths.uq.edu.au

Manuscript received June 13, 2016; final manuscript received November 29, 2016; published online January 24, 2017. Assoc. Editor: Kristen Billiar.

J Biomech Eng 139(3), 031013 (Jan 24, 2017) (8 pages) Paper No: BIO-16-1254; doi: 10.1115/1.4035481 History: Received June 13, 2016; Revised November 29, 2016

We present a new approach to designing three-dimensional, physically realizable porous femoral implants with spatially varying microstructures and effective material properties. We optimize over a simplified design domain to reduce shear stress at the bone-prosthetic interface with a constraint on the bone resorption measured using strain energy. This combination of objective and constraint aims to reduce implant failure and allows a detailed study of the implant designs obtained with a range of microstructure sets and parameters. The microstructure sets are either specified directly or constructed using shape interpolation between a finite number of microstructures optimized for multifunctional characteristics. We demonstrate that designs using varying microstructures outperform designs with a homogeneous microstructure for this femoral implant problem. Further, the choice of microstructure set has an impact on the objective values achieved and on the optimized implant designs. A proof-of-concept metal prototype fabricated via selective laser melting (SLM) demonstrates the manufacturability of designs obtained with our approach.

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Figures

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Fig. 1

Visualization of the microstructure sets used. Base cells shown at volume fractions of 10%, 30%, 50%, 70%, and 90%. The front octant has been removed to show internal structure. The right most picture visualizes directional dependence of the Young's modulus (E) for the 50% volume fraction microstructure as a fraction of the base material Young's modulus (E0). The axes in the lower left corner indicate orientation of all subfigures. (a) microstructure set A, (b) microstructure set B, (c) microstructure set C, and (d) microstructure set D.

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Fig. 2

Schematics of the domains used for the femoral implant problem. (a) Orthographic schematic of the idealized design domain, with proximal torsion and fixed distal boundary conditions shown, (b) Isometric sketch of ideal domain, (c) 2D slice of rasterized ideal domain (top right quarter only), (d) Isometric sketch of domain with collar added, and (e) 2D slice of rasterized domain with collar (top right quarter only).

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Fig. 3

Prosthetic designs displaying volume fraction, ρ. Slices taken from the back of the prosthesis to the front with the torque forcing clockwise in the page (i.e., torque axis is out of page). All designs shown have a base material with Young's modulus 60 GPa. Black is bone, white is void (a) m = 1, microstructure set A, (b) m = 1, microstructure set C, and (c) m = 2, microstructure set C. Note the filament-like structures with microstructure set A.

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Fig. 4

Stress distributions across the interface Π for: m = 1, microstructure set A (a) homogeneous and (b) inhomogeneous; m = 1, microstructure set C (c) homogeneous and (d) inhomogeneous; m = 2, microstructure set C (e) homogeneous and (f) inhomogeneous. An angle of 0 corresponds to the part of Π where y = 0, x > 0. Stress values have been truncated to the range [103, 106], however, some extreme values are outside this. Vertical striations are an artifact of the discretization. Note the reduction in shear stress concentrated at the proximal end (top) from the homogeneous ((b), (d), and (f)) to the inhomogeneous ((a), (c), and (e)) and the further reduction from the m = 1 case (c) to the m = 2 case (e).

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Fig. 5

Shear stress averaged on circles around the interface surface Π. Microstructure set C with a 60 GPa base material.

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Fig. 6

(a) Two renders of a potential design with microstructure cells 2.86 mm across, the left has one quadrant removed to show internal structure, the right is unmodified. (b) Two renders of a design similar to (a) with microstructure cells that are 800 μm across, giving pores at a scale relevant for bone in-growth [23,24]. (c) and (d) Photographs of the design in (a) manufactured using selective laser melting (SLM) [18].

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