Modelling the time-dependent behaviour of brain tissue in torsion

As is the case for most biological soft tissues, brain tissue displays highly complex mechanical behaviour: it can accommodate finite deformations and its response to applied forces is markedly non-linear; it is incompressible and biphasic, consisting of a porous permeable solid matrix saturated with an interstitial fluid; it is structurally anisotropic and it exhibits isotropic, time-dependent mechanical behaviour. The latter is one of the most pronounced features of brain tissue, manifesting itself primarily through two distinct but coupled phenomena: poroelasticity and viscoelasticity. The viscoelastic response is associated with the deformation of the solid skeleton, whereas the movement of interstitial fluid through the solid skeleton gives rise to a poroelastic response. Since its coupled poro-viscoelastic behaviour remains only partially understood, brain tissue is typically modelled either as a biphasic poroelastic material or as a monophasic viscoelastic material. The main goal of this work is to use each of these approaches in turn to investigate how poroelastic and viscoelastic effects influence the mechanical behaviour of brain tissue under torsional loading, which is one of the most robust and reliable protocols for determining its material parameters. Using a biphasic poroelastic model developed within the general framework of mixture theory, we show for the first time computationally that poroelastic effects can significantly influence the torsional response of brain tissue, depending on the loading conditions and the choice of poroelastic material parameters. The sensitivity to these parameters is particularly relevant given the wide range of values reported in the literature. This highlights the need for robust and reliable testing protocols capable of providing a comprehensive and systematic characterisation of the porous behaviour of brain tissue, which is currently lacking in the literature. Treating brain tissue as a monophasic viscoelastic material, we combine computational and experimental methods to devise the first protocol for determining the viscoelastic material parameters in torsion. From the computational perspective, we develop a monophasic viscoelastic model based on the recently reappraised but largely unexploited modified quasi-linear viscoelastic model. Using a commercial rheometer, we perform ramp-and-hold relaxation tests in torsion on cylindrical brain samples prepared from freshly slaughtered ovine brains, which generates two independent datasets for the torque and normal force. We then use our proposed viscoelastic model to derive analytical expressions for the torque and normal force required to maintain the cylindrical samples in a state of torsion, which allow us to identify the complete set of viscoelastic material parameters through a simultaneous fit to the two datasets. Beyond advancing brain tissue's mechanical characterisation and validating the efficacy of the MQLV model, our results have broader implications. When coupled with bespoke finite element models, the estimated viscoelastic material parameters could enhance our understanding of slow progressing pathologies, such as tumour growth or neurodegeneration, and inform the development of improved in silico models for brain surgery planning and training. Our novel testing protocol also offers an efficient, robust and reliable method for determining the viscoelastic properties of brain tissue under much more rapid loading conditions, which are of crucial importance for modelling traumatic brain injury.

Funder

Research Ireland
University of Galway

Publisher

University of Galway

Rights

CC BY-NC-ND

cbn

Collections

University of Galway Theses (PhD Theses)