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Research Papers

A Computational and Cellular Solids Approach to the Stiffness-Based Design of Bone Scaffolds

[+] Author and Article Information
J.A. Norato

A. J. Wagoner Johnson

Department of Mechanical Science and Engineering,  University of Illinois at Urbana-Champaign, Urbana, IL 61801ajwj@illinois.edu

It should be noted that the solution for Hertz contact between two perpendicular cylinders [48], does not agree with the results from the finite element model of Sec. 3, particularly for increasing overlap between layers.

J Biomech Eng 133(9), 091003 (Oct 04, 2011) (8 pages) doi:10.1115/1.4004994 History: Received February 09, 2011; Accepted September 05, 2011; Published October 04, 2011; Online October 04, 2011

We derive a cellular solids approach to the design of bone scaffolds for stiffness and pore size. Specifically, we focus on scaffolds made of stacked, alternating, orthogonal layers of hydroxyapatite rods, such as those obtained via micro-robotic deposition, and aim to determine the rod diameter, spacing and overlap required to obtain specified elastic moduli and pore size. To validate and calibrate the cellular solids model, we employ a finite element model and determine the effective scaffold moduli via numerical homogenization. In order to perform an efficient, automated execution of the numerical studies, we employ a geometry projection method so that analyses corresponding to different scaffold dimensions can be performed on a fixed, non-conforming mesh. Based on the developed model, we provide design charts to aid in the selection of rod diameter, spacing and overlap to be used in the robotic deposition to attain desired elastic moduli and pore size.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Scaffold fabricated by μ-RD

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Figure 3

Cylinder under applied concentrated loads

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Figure 4

Geometry measure calculation

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Figure 5

RVE geometry projection for d/L=0.5 and α=0.2

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Figure 6

Relative moduli versus d/l for several overlap fractions α, and for ν=0.25

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Figure 7

Porosity versus d/l for overlap fractions α=0.05 and α=0.45. Continuous lines denote the theoretical porosity; points represent the values obtained with the numerical simulation.

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Figure 8

Comparison between cellular solids model (continuous lines) and numerical results (points) for out-of-plane modulus, for various overlap fractions α and ν=0.25

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Figure 9

Effective moduli as a function of porosity for different overlap fracions α

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Figure 10

As-deposited rod spacing l̃ versus d/l for different nozzle gauges d̃. The points correspond to the pore sizes p  ∈  {300,400,…,1200}μm.

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