Research Papers

Bio-Morphing of Progressive Pathologies in Haversian Cortical Bone

[+] Author and Article Information
É. Budyn1

Department of Mechanical Engineering,  University of Illinois at Chicago, 842 W. Taylor Street, Chicago, IL 60607ebudyn@uic.edu

J. Jonvaux

Department of Mechanical Engineering,  University of Illinois at Chicago, 842 W. Taylor Street, Chicago, IL 60607jjonva2@uic.edu

T. Hoc

Department of Mechanical Engineering,LTDS UMR 5513 — MSSMAT UMR 8579,Ecole Centrale de Lyon,36 Avenue Guy de Collongue,69134 Ecully Cedex, Francethierry.hoc@ec-lyon.fr


Corresponding author.

J. Appl. Mech 79(2), 021001 (Feb 09, 2012) (13 pages) doi:10.1115/1.4005533 History: Received July 30, 2010; Revised August 24, 2011; Posted January 25, 2012; Published February 09, 2012; Online February 09, 2012

We present an evolutionary microstructural model to study the mechanical behavior of pathological Haversian cortical bone in the framework of linear elasticity. The Haversian cortical bone includes Haversian canals, osteons, cement lines, and interstitial bone. The composite microstructure is built using a Monte Carlo (MC) algorithm and initially displays a healthy morphology, which then evolves to mimic bone progressive aging, due to osteoporosis or low remodeling. The MC algorithm incorporates bone macroscopic morphological components such as porosity and osteonal volume fraction, microscopic parameters such as osteonal and Haversian canal diameter distributions, and also pathological growth laws characteristic of aging diseases. The local mechanical properties are measured by nanoindentation and microextensometry. The microstructures are discretised by a finite element 3D model to calculate the evolving representative volume element of aging bone, the macroscopic elastic bulk properties and microscopic strain and stress fields. The macroscopic anisotropy and local strain of aging bone are compared to those of healthy tissue in order to understand how morphological changes affect bone failure.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

(a) Definitions of morphometric parameters in a transverse section of Haversian cortical bone; (b) schematic model of a transverse section of cortical bone showing additional morphometric parameters

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Figure 2

(a) Experimental and projected distributions of osteon and Haversian canal diameters in healthy and osteoporotic bone, respectively (primed variables relate to osteoporotic bone); (b) experimental distributions of osteon Young’s moduli measured by nanoindentation in the transverse plane ET and along the axis of the osteons EL

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Figure 3

(a) Dminc, Dmaxc, Dmino, and Dmaxo versus porosity for human specimens; (b) determination of evolutionary function α3

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Figure 4

Correlation coefficients between the projected diameter distribution and the numerical diameter distribution for all sets of microstructures of different sizes L for (a) decreased F'=45% and (b) increased P'=11.07%. The osteonal and Haversian canal diameters are presented.

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Figure 5

(a) Transverse boundary conditions, u¯2 is negative nonzero on the top, u¯2=0 on the bottom, u¯3=0 on the back lines (x2=x3=0) and (x3=0 and x2=L), u¯1=0 on the midpoints (black dots); (b) longitudinal boundary conditions, u¯3 is negative nonzero on the front, u¯3=0 on the back, u¯2=0 on the bottom lines (x2=x3=0) and (x3=t and x2=0), u¯1=0 on the midpoints (black dots)

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Figure 6

(a), (b) Macroscopic transverse Young’s moduli for decreased F′=45% and increased porosity P′=11.07% and (c), (d) macroscopic longitudinal Young’s moduli for decreased F′=45% and increased porosity P′=11.07% versus L. The mean and standard deviation are calculated for ETu¯,S and ELu¯,S.

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Figure 7

Comparison of transverse and longitudinal Young’s moduli based on surface and volume calculations (a) for low remodeling (F′=45%); (b) for osteoporosis (P′=11.07%)

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Figure 8

(a) Osteon percentage versus average Green-Lagrange strain GL22osteon=Ei22 of the osteons; (b) GL22osteon versus transverse Young’s modulus ET of RVE-size microstructures of healthy (H), low remodeling (LR), osteoporotic (O) and real bone (R); (c) GL22osteon versus Do; (d) GL22osteon versus Dc; (e) ΔGL22osteon versus Do; (f) ΔGL22osteon versus Dc

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Figure 9

Example of microstructure biomorphing calculation when porosity is tripled in the visualization algorithm

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Figure 10

Definition of the overlap coefficient γiB for osteon iB involving either (a) another osteon iB' or (b) the sample edge

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Figure 11

Biomorphing visualization in the case of bone low remodeling: (a), (b), (c) morphology evolution, (d), (e) E22 field; and in the case of osteoporosis: (h), (i), (j) morphology evolution, (f), (g) E22 field. The microstructures are of RVE size.



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