title: A discrete spectral analysis for determining quasi-linear viscoelastic properties of biological materials.
abstract: The viscoelastic behaviour of a biological material is central to its functioning and is an indicator of its health. The Fung quasi-linear viscoelastic (QLV) model, a standard tool for characterizing biological materials, provides excellent fits to most stress-relaxation data by imposing a simple form upon a material's temporal relaxation spectrum. However, model identification is challenging because the Fung QLV model's 'box'-shaped relaxation spectrum, predominant in biomechanics applications, can provide an excellent fit even when it is not a reasonable representation of a material's relaxation spectrum. Here, we present a robust and simple discrete approach for identifying a material's temporal relaxation spectrum from stress-relaxation data in an unbiased way. Our 'discrete QLV' (DQLV) approach identifies ranges of time constants over which the Fung QLV model's typical box spectrum provides an accurate representation of a particular material's temporal relaxation spectrum, and is effective at providing a fit to this model. The DQLV spectrum also reveals when other forms or discrete time constants are more suitable than a box spectrum. After validating the approach against idealized and noisy data, we applied the methods to analyse medial collateral ligament stress-relaxation data and identify the strengths and weaknesses of an optimal Fung QLV fit.
authors.affiliation: Department of Mechanical Engineering and Materials Science, School of Engineering and Applied Science, Washington University in St Louis, St Louis, MO 63130, USA.
authors.forename: Behzad
authors.initials: B
authors.lastname: Babaei
authors.affiliation: Musculoskeletal Research Center, Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA 15219, USA.
authors.forename: Steven D
authors.initials: SD
authors.lastname: Abramowitch
authors.affiliation: Department of Mechanical Engineering and Materials Science, School of Engineering and Applied Science, Washington University in St Louis, St Louis, MO 63130, USA Department of Biochemistry and Molecular Biophysics, School of Medicine, Washington University in St Louis, St Louis, MO 63110, USA.
authors.forename: Elliot L
authors.initials: EL
authors.lastname: Elson
authors.affiliation: Department of Mechanical Engineering and Materials Science, School of Engineering and Applied Science, Washington University in St Louis, St Louis, MO 63130, USA Department of Orthopaedic Surgery, School of Medicine, Washington University in St Louis, St Louis, MO 63110, USA.
authors.forename: Stavros
authors.initials: S
authors.lastname: Thomopoulos
authors.affiliation: Department of Mechanical Engineering and Materials Science, School of Engineering and Applied Science, Washington University in St Louis, St Louis, MO 63130, USA Department of Neurological Surgery, School of Medicine, Washington University in St Louis, St Louis, MO 63110, USA genin@wustl.edu.
authors.forename: Guy M
authors.initials: GM
authors.lastname: Genin
mesh_terms: D000818:Animals; D004548:Elasticity; D006801:Humans; D008954:Models, Biological
keywords: ligament; quasi-linear viscoelasticity; spectral analysis; stress–relaxation