Random field assessment of nanoscopic inhomogeneity of bone.
Bone quality is significantly correlated with the inhomogeneous distribution of material and ultrastructural properties (e.g., modulus and mineralization) of the tissue. Current techniques for quantifying inhomogeneity consist of descriptive statistics such as mean, standard deviation and coefficient of variation. However, these parameters do not describe the spatial variations of bone properties. The objective of this study was to develop a novel statistical method to characterize and quantitatively describe the spatial variation of bone properties at ultrastructural levels. To do so, a random field defined by an exponential covariance function was used to represent the spatial uncertainty of elastic modulus by delineating the correlation of the modulus at different locations in bone lamellae. The correlation length, a characteristic parameter of the covariance function, was employed to estimate the fluctuation of the elastic modulus in the random field. Using this approach, two distribution maps of the elastic modulus within bone lamellae were generated using simulation and compared with those obtained experimentally by a combination of atomic force microscopy and nanoindentation techniques. The simulation-generated maps of elastic modulus were in close agreement with the experimental ones, thus validating the random field approach in defining the inhomogeneity of elastic modulus in lamellae of bone. Indeed, generation of such random fields will facilitate multi-scale modeling of bone in more pragmatic details.
Dong
X Neil
XN
Department of Mechanical Engineering, University of Texas at San Antonio, San Antonio, TX 78249, USA.
Luo
Qing
Q
Sparkman
Daniel M
DM
Millwater
Harry R
HR
Wang
Xiaodu
X
D000818:Animals; D001842:Bone and Bones / Q000033:anatomy & histology* / Q000502:physiology; D002417:Cattle; D055119:Elastic Modulus / Q000502:physiology; D008953:Models, Anatomic; D036103:Nanotechnology / Q000379:methods*
J Biomech. 2006;39(12):2282-94
16144702
J Biomech. 2009 Feb 9;42(3):202-9
19058806
J Biomech. 1984;17(5):349-61
6736070
Ultrasonics. 1996 Dec;34(8):777-83
9010460
Bone. 2009 Dec;45(6):1034-43
19679206
Bone. 2008 Apr;42(4):775-87
18234577
Bone. 2008 Jun;42(6):1184-92
18378204
J Biomech. 1992 Apr;25(4):359-68
1583015
Bone. 2007 May;40(5):1308-19
17337263
Nat Mater. 2007 Jun;6(6):454-62
17515917
J Biomech. 2007;40(6):1211-8
16934818