Constitutive Modeling of the Microstructure of Arterial Walls Including Collagen Cross-Linking
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Extended Bio
Gerhard A. Holzapfel is a world-leading figure in biomechanics, currently serving as Professor and Head of the Institute of Biomechanics at Graz University of Technology (TUG), Austria. He also holds appointments as Adjunct Professor at the Norwegian University of Science and Technology (NTNU) in Trondheim and Visiting Professor at the University of Glasgow. From 2004 to 2013, he was Professor of Biomechanics at the Royal Institute of Technology (KTH) in Stockholm.
Following a PhD in Mechanical Engineering from Graz, Professor Holzapfel was awarded an Erwin Schrödinger Scholarship, enabling him to conduct research at Stanford University. He achieved his Habilitation at TU Vienna in 1996 and was the recipient of Austria’s prestigious START Award in 1997. Over subsequent decades, he has led pioneering work in computational biomechanics, including as Head of the Computational Biomechanics research group at TUG (1998–2004).
Professor Holzapfel has received numerous accolades, including the Erwin Schrödinger Prize of the Austrian Academy of Sciences (2011), listings among “The World’s Most Influential Scientific Minds” (Thomson Reuters, 2014), the William Prager Medal and Warner T. Koiter Medal (2021), an honorary doctorate from École des Mines de Saint-Étienne (2024), and election to the U.S. National Academy of Engineering (2025). In 2024, he was awarded a prestigious Synergy Grant from the European Research Council (ERC).
His research spans experimental and computational biomechanics and mechanobiology, with a particular focus on soft biological tissues and the cardiovascular system in both health and disease. His expertise includes nonlinear continuum mechanics, constitutive modelling, growth and remodeling, imaging and image-based modeling, and the mechanics of therapeutic interventions such as angioplasty and stenting.
Professor Holzapfel is the author of the widely adopted graduate textbook Nonlinear Solid Mechanics (Wiley), has co-edited seven additional books, and contributed chapters to over 30 volumes. He has published more than 300 peer-reviewed journal articles. He is also the co-founder and co-editor of the journal Biomechanics and Modeling in Mechanobiology (Springer). His work has been funded by numerous national and international agencies, including the Austrian Science Fund, NIH, the European Commission, and industry collaborators.
Abstract
Nowadays, the 3D ultrastructure of a fibrous tissue can be reconstructed in order to visualize the complex nanoscale arrangement of collagen fibrils including neighboring proteoglycans even in the stretched loaded state [1]. In particular, experimental data of collagen fibers in human artery layers have shown that the f ibers are not symmetrically dispersed [2]. In addition, it is known that collagen f ibers are cross-linked and the density of cross-links in arterial tissues has a stiffening effect on the associated mechanical response. A first attempt to characterize this effect on the elastic response is presented and the influence of the cross-link density on the mechanical behavior in uniaxial tension is shown [3]. A recently developed extension of the model that accounts for dispersed fibers connected by randomly distributed cross-links is outlined [4]. A simple shear test focusing on the sign of the normal stress perpendicular to the shear planes (Poynting effect) is analyzed. In [5] it was experimentally observed that, in contrast to rubber, semi-flexible biopolymer gels show a tendency to approach the top and bottom faces under simple shear. This so-called negative Poynting effect and its connection with the cross-links as well as the fiber and crosslink dispersion is also examined.
References
[1]A. Pukaluk et al.: An ultrastructural 3D reconstruction method for observing the arrangement of collagen fibrils and proteoglycans in the human aortic wall under mechanical load. Acta Biomaterialia, 141:300-314, 2022.
[2] G.A. Holzapfel et al.: Modelling non-symmetric collagen fibre dispersion in arterial walls. Journal of the Royal Society Interface, 12:20150188, 2015.
[3] G.A. Holzapfel and R.W. Ogden: An arterial constitutive model accounting for collagen content and cross-linking. Journal of the Mechanics and Physics of Solids, 136:103682, 2020.
[4] S. Teichtmeister and G.A. Holzapfel: A constitutive model for fibrous tissues with cross-linked collagen fibers including dispersion – with an analysis of the Poynting effect. Journal of the Mechanics and Physics of Solids, 164:104911, 2022.
[5] P.A. Janmey et al.: Negative normal stress in semiflexible biopolymer gels. Nature Materials, 6:48–51, 2007.