Mathematical modelling of axonal microtubule bundles under dynamic torsion

doi:10.1007/s10483-018-2335-9

Abstract

Abstract:

Owing to its viscoelastic nature, axon exhibits a stress rate-dependent mechanical behavior. An extended tension-shear chain model with Kelvin-Voigt viscoelasticity is developed to illustrate the micromechanical behavior of the axon under dynamic torsional conditions. Theoretical closed-form expressions are derived to predict the deformation, stress transfer, and failure mechanism between microtubule (MT) and tau protein while the axon is sheared dynamically. The results obtained from the present analytical solutions demonstrate how the MT-tau interface length, spacing between the tau proteins, and loading rate affect the mechanical properties of axon. Moreover, it is found that the MTs are more prone to rupture due to the contributions from the viscoelastic effects. Under the torsional force, the MTs are so long that the stress concentrates at the loaded end where axonal MTs will break. This MT-tau protein dynamics model can help to understand the underlying pathology and molecular mechanisms of axonal injury. Additionally, the emphasis of this paper is on the micromechanical behavior of axon, whereas this theoretical model can be equally applicable to other soft or hard tissues, owning the similar fibrous structure.

Key words: optimal servo system, frequency dependent servo system, preview control system, diffuse axonal injury (DAI), tension-shear chain model, biocomposite, Kelvin-Voigt viscoelastic model, dynamic response, torsion

2010 MSC Number:

35E05
92B05

J. Y. WU, Hong YUAN, L. Y. LI. Mathematical modelling of axonal microtubule bundles under dynamic torsion. Applied Mathematics and Mechanics (English Edition), 2018, 39(6): 829-844.

TrendMD

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