A discrete spectral analysis for determining quasi-linear viscoelastic properties of biological materials

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.