PONSSA Maria Laura
Fibrillar organization in tendons: A pattern revealed by percolation
DOS SANTOS, D. A., PONSSA, M. L., TULLI, M.J., ABDALA, V.
: International Academy of Ecology and Environmental Sciences
Lugar: Hong Kong ; Año: 2014 vol. 4 p. 31 - 31
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.