NANOINDENTATION OF BONE - Nanoindentation with Biological Applications - page 216

( G 0 ), increased with decreased Hansen's solubility parameter, the viscous
creep increased. A poroelastic analysis of the same data set revealed that
bone's intrinsic permeability increased with increasing values of the
solubility parameter. 148 Correlation of these results to the fundamental
porosity length scale indicated that a characteristic pore size of 1.6

nanometers describes the intrinsic permeability of water in bone at the
scale of the collagen-apatite interactions. While such analyses are
simplified and preliminary in nature, they demonstrate the applicability
of nanoindentation for the exploration of time-dependent and molecular-
level interactions in bone.
Analysis of viscoelasticity in bone is well within the reach of
available analytical tools. In particular, approaches for analysis of
polymers with viscous behavior are well-developed 46,141,143-146,149 and
applicable to the study of biological tissues - including bone. 47,48,66,147
Such analytical formulations are ideal for the analysis of local variations
in tissue properties. These analytical methods are easily applied and can
provide insight into the viscous behavior at the tissue-level of bone.
Finally, such analyses may add to our ability to better understand many
research and clinical problems.

3.4 . Finite element modeling

Finite element analysis (FEA) has been commonly used to analyze
nanoindentation of various engineered materials, however application to
bone is complicated by its heterogeneous composition and structure.
Most finite element models assume bone is elastic-perfectly plastic,
homogenous, and isotropic, and thus fail to capture bone's true
mechanical response at the tissue-level. Alternatively, several models
have investigated bone's complicated structure by modeling bone as a
two-phase composite: organic and inorganic. These analyses have
employed standard composites theory and modeled bone as a particle or
rod-reinforced matrix. 132,150 The mineral volume fraction of normal bone
generally ranges from 0.35 to 0.5, yet over this small range the modulus
of bone ranges widely. 127,148 As such, the modulus of bone cannot be
simply predicted by knowledge of the mineral volume fraction of
bone. 132