Multiscale Elastic Models of Collagen Bio-structures: From Cross-Linked Molecules to Soft Tissues
Mechanics of collagen bio-structures at different scales (nano, micro, and macro) is addressed, aiming to describe multiscale mechanisms affecting the constitutive response of soft collagen-rich tissues. Single-scale elastic models of collagen molecules,
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Abstract Mechanics of collagen bio-structures at different scales (nano, micro, and macro) is addressed, aiming to describe multiscale mechanisms affecting the constitutive response of soft collagen-rich tissues. Single-scale elastic models of collagen molecules, fibrils, and crimped fibers are presented and integrated by means of consistent inter-scale relationships and homogenization arguments. In this way, a unique modeling framework based on a structural multiscale approach is obtained, which allows to analyze the macroscale mechanical behavior of soft collagenous tissues. It accounts for the dominant mechanisms at lower scales without introducing phenomenological descriptions. Comparisons between numerical results obtained via present model and the available experimental data in the case of tendons and aortic walls prove present multiscale approach to be effective in capturing the deep link between histology and mechanics, opening to the possibility of developing patient-specific diagnostic and clinical tools.
1 Introduction Soft tissues are throughout the whole human body and they include tendons, ligaments, skin, fibrous tissues, muscles and blood vessels. They link, support, and are part of other bio-structures and organs, playing a key role in the biomechanics
M. Marino (&) G. Vairo Department of Civil Engineering and Computer Science, University of Rome ‘‘Tor Vergata’’, via del Politecnico 1, 00133 Rome, Italy e-mail: [email protected] G. Vairo e-mail: [email protected]
Stud Mechanobiol Tissue Eng Biomater (2013) 14: 73–102 DOI: 10.1007/8415_2012_154 Springer-Verlag Berlin Heidelberg 2012 Published Online: 5 October 2012
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of many body systems (e.g., musculo-skeletal, cardiovascular) [1]. Collagen, elastin and ground substance are the main constituents of the extracellular matrix in soft tissues, and their arrangement significantly affect the tissue mechanical response. For instance, stiffness and strength features in soft tissues mainly depend on the arrangement and the amount of collagen, which is organized in agreement with a precise hierarchical multiscale scheme [2]. Since the fundamental mechanical role of collagen, soft tissues are usually referred to as collagenous tissues. The structured organization of soft tissues, and thereby their mechanical behavior, is highly related to the biochemical processes occurring within them [2]. In fact, altered tissue response in disease (e.g., aneurism, keratoconus, arthofibrosis) arises from pathological tissue remodeling, inducing unphysiological histology and biochemical composition. Typical disorders, such as tissue hyper-extensibility or weakness, can be associated with alterations at different scales [3–7]: in content of tissue constituents, in shape of collagen fibers, in collagen genetic pattern, in density of inter-molecular cross-links. Nevertheless, available non-invasive techniques do not allow to measure directly a number of important histological, mechanical, and biochemical properties of collagenou
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