Collagen fiber bundles are important constituent parts of biological soft tissues, such as tendons, blood vessels and skin. The single collagen fibers within a bundle have a certain crimp that determines the bundle's stretching characteristic, which is of particular interest in mechanobiology. A thorough understanding of the complex interrelations between mechanical factors and the associated biological responses may help to improve diagnostics, which allow disease and injury to be treated earlier. We present a method to obtain the relative stretching characteristics (RSC) of collagen (fibrous) bundles based on the analysis of microscopic tissue images. We show, how the orientation statistics of local orientations in a bundle can be directly related to the RSC. The von Mises distribution (VMD) - a circular probability distribution is used to describe the 2D orientation statistics. The k parameter of the VMD is used to obtain the mean stretching and the probability density function (PDF) of the bundles' RSC is identified.
[1]
T. Sellaro,et al.
Effects of collagen orientation on the medium-term fatigue response of heart valve biomaterials
,
2003
.
[2]
William H. Press,et al.
Numerical recipes in C
,
2002
.
[3]
S. R. Jammalamadaka,et al.
Topics in Circular Statistics
,
2001
.
[4]
Eero P. Simoncelli,et al.
Optimally Rotation-Equivariant Directional Derivative Kernels
,
1997,
CAIP.
[5]
J. Lemaître,et al.
Handbook of materials behavior models
,
2001
.
[6]
P. Peebles.
Probability, Random Variables and Random Signal Principles
,
1993
.
[7]
H. Bischof,et al.
Structure Analysis of Collagen Fibers Based on Microscopic Images
,
2003
.
[8]
M. Epstein,et al.
Cardiovascular Solid Mechanics: Cells, Tissues, and Organs
,
2002
.