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 stressrelaxation 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.

Remodeling by fibroblasts alters the rate-dependent mechanical properties of collagen

“…They are also key to understanding how myofibroblasts invade an infarct region [42, 43]. Additionally, these factors are central to healing of tendons, ligaments, and their bony attachments [44, 45, 46, 47, 48, 49, 50, 35]. In all of these, percolation phenomena involving formation of a continuous structural network are important, and variance is typically highest in conditions close to percolation [44].…”

“…Achieving this over 0.5 seconds is representative of strains in response to a brisk walking cadence and to stretching by the cardiovascular system. The stretch rate and prolonged monitoring were furthermore suitable for characterizing the temporal range of physiological responses [30, 35]. …”

Characterization of the mechanical properties of resected porcine organ tissue using optical fiber photoelastic polarimetry

“…This method provides material constants that can directly be compared between samples and measurements [16].…”

“…The predominant method for fitting loading-unloading curves within the biomaterials community is the Quasi-Linear Viscoelasticity (QLV) method [15][16][17]. This method provides material constants that can directly be compared between samples and measurements [16].…”

The fibrous cellular microenvironment, and how cells make sense of a tangled web

“…Using this approach, the continuum responses of the native tissue must be known under all possible loadings, and that understanding then defines the design criteria for tissue replacements. Seminal models in the field of biomechanics, such as the Y. C. Fung "quasilinear viscoelastic model" (8), draw upon continuum representations of tissues that account, under certain cases (9,10), for the ways that fibers and their solvent interact, but hide the fibrous nature of the tissue. Flory-type treatment of tissues such as polymers with prescribed orientation distributions, as established for musculoskeletal tissues by Lanir (11), Sacks and colleagues (12), and Zahalak and colleagues (13), are a mainstay of modeling of fibrous collagenous tissues and their attachments to bone (14,15).…”