Colloquium Christian Hellmich

Engineering Science and Mechanics as Key to the Mathematical Identification of "Universal" Patterns Pervading Mineralized Biological Tissues, and Beyond

When: Thursday 19 September 2013
Where: Ceres building, CE0.31, TU/e campus


According to the eminent Austro-American zoologist Rupert Riedl (1925-2005), "... the living world happens to be crowded by universal patterns of organization...". While Riedl, as "classical" biologist, typically took a descriptive approach to this issue, we ventured, over the last decade and in particular during the last few years, into an engineering science approach of mathematical nature, where we have indeed been succesful in identifying "universal" rules/patterns in structural biology and their mechanical consequences. A marjority of our investigations concerned mineralized biological tissues such as bones, for which we identified the following mathamatically cast rules: (I) In extracellular bone tissues across different organs from different animals/humans at different ages, mineral (hydroxyapatite) and collagen contents are not dandomly assgined to each other, but fulfill astonischingly precise cilinear relations1, which follow from rigorous evaluation of dehydration, demineralization, ashing, and de-organifying test data colected over a time period of more than 80 years of exeprimental research. Furthermore, (II) the distribution of mineral throughout the extracellular bone matrix of ultrastructure, i.e. its partitioning into the fibrillar and extrafibrillar spaces is governed by the on-average uniformity of hydroxyapatite concentration in the extracollagneneous space2, as was evidenced from chemical tests like the onse mentioned before, in combination with transmission electron micrographs. Before mineralication (as well as in unmineralized collageneous tissues such as tendon or cartilage), the fibrillar and extrafibrillar spaces again obey antother rule: (III) Upon hydration, the extrafibrillar space grows propertional to the fibrillar volumge gain due to accomodation of water in the intermolecular spaces3, as evidenced from dehydration and neutron diffraction test. Finally, (IV) mineralization of such tissues is driven by fluid-to-solid phase transformations in the extracollageneous sapce under closed thermodynamic conditions4, predicting precisely the volume losses which the tissues undergo during mineralization.
All these compositional and structural rules may serve as ideal input for multiscale mechanics models for the elasticity5, strength6, and creep7 of bone tissues; enabling various clinical applications, such as Computed Tomography (CT)-based Finite Element (FE) analysis for biomaterial design8.

The knowledge we gained in studying biological tissue, was also instrumental in driving forward the multiscale mechanics of wood9, ceramics10, and concrete11, materials that share quite some microstructural, chemical and mechanical features with bone.


1 Vuong, Hellmich, J Theor Biol 287, 115-130,2001.
2 Hellmich, Ulm, Biomech Model Mechanobiol 2; 21-36, 2003.
3 Morin, Hellmich, Henits, J Theor Biol 317, 384-393-2013.
4 Morin, Hellmich, J Theor Biol, DOI:10.1016/j.jtbi.2013.06.018,2013.
5 Fritsch, Hellmich, J Theor Biol 244: 597-620, 2007.
6 Fritsch, Hellmich, Dormieux, J Theor Biol 260: 230-252, 2009.
7 Eberhadsteiner, Hellmich, Scheiner, Comp Meth Biomech Biomed ENG DOI:10.1018/10255842,2012.670227, 2013.
8 Decajo, Komlec, Jaroszewicz, Sweiszkowski, Hellmich, J. Biomech 45, 1068-1075, 2012.
9 Bader, Hofstetter, Hellmich, Eberhardsteiner, Acta Mechanica 217, 75-100, 2011.
10 Fritsch, Hellmich, Young, J Appl Mech, DOI: 10.115/1.4007922, 2013.
11 Pichler, Hellmich, Cem Concr Res 41, 467-476,2011.