Fibrillar organization in tendons: A pattern revealed by percolation

DOS SANTOS, D. A., PONSSA, M. L., TULLI, M.J., ABDALA, V.

Network Biology

: International Academy of Ecology and Environmental Sciences

Lugar: Hong Kong ; Año: 2014 vol. 4 p. 31 - 46

2220­8879

Since the tendon is composed by collagen fibrils of various sizes connected between them through molecular cross-links, it sounds logical to model it via a heterogeneous network of fibrils. Using cross sectional images, that network is operatively inferred from the respective Gabriel graph of the fibril mass centers. We focus on network percolation characteristics under an ordered activation of fibrils (progressive recruitment going from the smallest to the largest fibril). Analyses of percolation were carried out on a repository of images of digital flexor  tendons  obtained  from  samples  of  lizards  and  frogs.  Observed  percolation  thresholds  were  compared against  values  derived  from  hypothetical  scenarios  of  random  activation  of  nodes.  Strikingly,  we  found  a significant delay for the occurrence of percolation in actual data. We interpret this finding as the consequence of  some  non-random  packing  of  fibrillar  units  into  a  size-constrained  geometric  pattern.  We  erect  an  ideal geometric  model  of  balanced  interspersion  of  polymorphic  units  that  accounts  for  the  delayed  percolating instance. We also address the circumstance of being percolation curves  mirrored by the empirical curves of stress-strain obtained from the same studied tendons. By virtue of this isomorphism, we hypothesize that the inflection  points  of  both  curves  are  different  quantitative  manifestations  of  a  common  transitional  process during mechanical load transference.