Network Biology, 2014, 4(2): 31-46
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Fibrillar organization in tendons: A pattern revealed by percolation characteristics of the respective geometric network

Daniel Andres Dos Santos1 , Maria Laura Ponssa2, Maria Jose Tulli2, Virginia Abdala1,2,3
1Instituto de Biodiversidad Neotropical, Facultad de Ciencias Naturales e Instituto Miguel Lillo, Universidad Nacional de Tucuman - CONICET. Horco Molle S/N, Yerba Buena, Tucuman, Argentina
2Instituto de Herpetologia, Fundacion Miguel Lillo-CONICET. Miguel Lillo 251, San Miguel de Tucuman, Tucuman, Argentina
3Catedra de Biologia General, Facultad de Ciencias Naturales e IML, Universidad Nacional de Tucuman. Miguel Lillo 251, San Miguel de Tucuman, Tucuman, Argentina

Received 7 January 2014;Accepted 10 February 2014;Published online 1 June 2014

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.

Keywords percolation;collagen;fibril network;interspersion;pattern recognition.

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