Time-Harmonic Oscillations of a Poroelastic Body with an Application to Modelling the Spinal Cord

P. J. Harris () and J. Venton ()
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P. J. Harris: The University of Brighton
J. Venton: The National Physical Laboratory

Chapter Chapter 13 in Integral Methods in Science and Engineering, 2023, pp 155-164 from Springer

Abstract: Abstract The time-dependent flow of a liquid through a deforming poroelastic material can be modelled using a system of coupled time-dependant partial differential equations. One of the main problems with trying to find the numerical solution of these equations (subject to suitable initial and boundary conditions) is finding an accurate, stable and computationally efficient time-stepping method. However, if the boundary condition on the outer surface of the poroelastic structure have harmonic time dependence then the solution will have the same harmonic time dependence. By moving from the time domain to the frequency domain it is possible to transform the problem into a boundary value problem which is straight forward to solve using appropriate numerical method. The methods developed in this paper are used to determine the deformations of the spinal cord subject to a harmonic pressure loading on its outer surface. It will consider cases such when the cord has a region of oedema or a cavity (syrinx) that is characteristic of the condition syringomyelia.

Date: 2023
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DOI: 10.1007/978-3-031-34099-4_13

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