Fractional Calculus as a New Perspective in the Viscoelastic Behaviour of the Intervertebral Disc

Abstract

The spinal column is the load-bearing structure of the human being along with its components, which together build a strong, resistant, and stable structure, but there are a few different pathologies from which it can suffer, such as herniated discs. The intervertebral disc acts as a shock absorber and ensures the spine’s great capacity to support high loads and different states of stress, thanks to its viscoelastic properties. Some studies have attempted to describe the viscoelastic behaviour of the intervertebral disc using classical rheological models, such as the Kelvin-Voigt, or multi-parameter models. Even if these models partially describe the viscoelastic response of disc, all viscoelastic characteristics are not fully captured. This article aims to present the current studies on the biomechanics of intervertebral disc and to introduce a new approach using the powerful mathematical tool of fractional calculus. With fractional rheological models, it could be possible to formulate a fractional law that can fully describe the viscoelastic behaviour of the intervertebral disc. This new approach could lead to a breakthrough in the study of herniated pathologies by understanding how the intervertebral disc is damaged and identifying strategies to deal with these pathological problems.