Modeling fluid–structure interactions between cerebro-spinal fluid and the spinal cord

The spinal cord (SC) is a tissue composed of white and gray matter that is permeated by capillary blood, venular blood and cerebrospinal fluid (CSF). It is surrounded by an annular cavity, called the subarachnoid space (SAS), within which the CSF exhibits a pulsatile laminar flow. Insights into the functioning of cerebrospinal fluid are expected to reveal the pathogenesis of severe neurological diseases – such as syringomyelia – involving the formation of fluid-filled cavities (syrinxes) in the spinal cord. A fully analytical fluid–structure interaction model, based on the Multiple Network Porous Elastic Theory, is here proposed. The spinal cord is regarded as a deformable porous medium permeated by different fluids, while a pulsatile flow in the subarachnoid space is taken into account. By virtue of the slender body approximation, the mathematical model allows to analytically solve the space–time structure of the CSF flow field, the displacements in the spinal cord, and the pressures of the fluids inside the cord. The results are consistent with data reported in literature and with some numerical simulations. A sensitivity analysis shows that the deviation from the physiological values of the Young modulus, the capillary pressures at the SC–SAS interface and the permeability of blood networks can lead to a great increase in the CSF fluxes across the spinal cord. These findings bring new insights into the factors that affect CSF exchange, and they may support hypotheses which attribute syrinx formation to an abnormal exchange of cerebrospinal fluid between the SAS and the spinal cord.