ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

Fig. 1. Experimental data from uniaxial tensile tests on rabbit skin from Lanir and Fung (1972) and the
corresponding theoretical values (continuous lines) calculated after identification of the constitutive
parameters. Conceptualisation of the shear interactions occurring between two tropocollagen molecules as
they are subjected to tension along their main axis. The molecular representation for tropocollagen is
obtained from the Protein Data Bank file 1QSU.pdb (www.pdb.org): crystal structure of the triplehelical
collagen-like peptide C, (PRO-HYP-GLY)4-GLU-LYS-GLY(PRO-HYP-GLY)5 [17].
The stiffness of entropic molecular chains can be estimated by using the simple
following formula Lp= EI / K q where EI represents the bending stiffness of the
chain. By assuming that a molecular chain is contained within a cylindrical volume of
radius R and that it exhibits homogeneous structural properties, the Young’s modulus
4
of the molecular chain can be deduced as E = 4 LpK q / pR
[1] . Numerical optimisation
of the constitutive parameters leads to 22 and 65 nm persistence lengths for the two
families of type I collagen. If one assumes a molecular radius of 0.8 nm one obtains
equivalent Young’s moduli of 293 and 865 MPa. These values lie within one order of
magnitude less of what has been determined experimentally [18] and trough
computational modelling studies (see Gautieri et al. [19]). However, Sun et al. [18]
estimated the Young’s modulus of collagen molecules to range between 350 MPa and
12 GPa. In the same way that the macroscopic stiffness of collagenous tissues is much
lower than that of individual collagen fibrils and microfibrils because of length scale
effects, the Young’s modulus of microfibrils is significantly lower than that of
individual tropocollagen molecules.
8. CONCLUSION
A meso/microstructurally motivated multi-scale model of skin featuring experimentally
measurable mesoscopic biophysical parameters has been developed. The nondissipative
formulation is able to faithfully capture the multi-axial properties of rabbit
skin whilst accounting for fibre-to-matrix/fibre interactions. This is a first step toward
more realistic constitutive models that will include transport and plastic phenomena.
8. ACKNOWLEDGEMENTS
Experimental data
· Fibre family 1 r = 0.998
·
Fibre family 2 r = 0.997
Financial support from EPSRC [Grant EP/F034296/1] and the University of
Southampton is gratefully acknowledged.