A model of fluid injection into the spinal disc

This paper presents an analytical model of the stress–strain response of intervertebral disc to fluid injection. The disc has nonlinear properties and collagen fibres play a significant role in sustaining strain. Each fibre is modeled as a flexible, helical string inclined at ∼30° to the horizontal plane. The tensile stress in the fibres is obtained from a nonlinear stress–strain law that has been determined by experiment. An asymptotic approximation of the model equations based on the ratio of the fluid injected to the initial volume of fluid in the disc is developed and its solution obtained. Some quantitative predictions are made by considering a hypothetical value of the amount of fluid injected and some material values of discs at different levels of the spine. Numerical simulations show that the model compare reasonably well with some experimental observations for discs of the lumbar region.