CSF Pressure and Velocity in Obstructions of the Subarachnoid Spaces

Abstract

According to some theories, obstruction of CSF flow produces a pressure drop in the subarachnoid space in accordance with the Bernoulli theorem that explains the development of syringomyelia below the obstruction. However, Bernoulli's principle applies to inviscid stationary flow unlike CSF flow. Therefore, we performed a series of computational experiments to investigate the relationship between pressure drop, flow velocities, and obstructions under physiologic conditions. We created geometric models with dimensions approximating the spinal subarachnoid space with varying degrees of obstruction. Pressures and velocities for constant and oscillatory flow of a viscid fluid were calculated with the Navier-Stokes equations. Pressure and velocity along the length of the models were also calculated by the Bernoulli equation and compared with the results from the Navier-Stokes equations. In the models, fluid velocities and pressure gradients were approximately inversely proportional to the percentage of the channel that remained open. Pressure gradients increased minimally with 35% obstruction and with factors 1.4, 2.2 and 5.0 respectively with 60, 75 and 85% obstruction. Bernoulli's law underestimated pressure changes by at least a factor 2 and predicted a pressure increase downstream of the obstruction, which does not occur. For oscillatory flow the phase difference between pressure maxima and velocity maxima changed with the degree of obstruction. Inertia and viscosity which are not factored into the Bernoulli equation affect CSF flow. Obstruction of CSF flow in the cervical spinal canal increases pressure gradients and velocities and decreases the phase lag between pressure and velocity.

Effect of the Central Canal in the Spinal Cord on Fluid Movement within the Cord

“…Flow abnormalities in the Chiari I patient include flow jets and greater than normal CSF velocities in the foramen magnum and upper cervical spinal canal [1][2][3][4][5] . Flow resistance of the cervical spinal canal 6 and the relative amount of spinal canal obstruction 7 determine the CSF velocities in the spinal canal. The CSF velocities in the upper cervical spinal canal result from longitudinal pressure gradients during portions of the cardiac cycle.…”

Spinal Fluid Biomechanics and Imaging: An Update for Neuroradiologists

“…CSF oscillations are coupled to CSF pressure oscillations that, in the healthy adult, are approximately 90°out of phase with the velocity fluctuations. 2 Elastic properties of the tissues surrounding the subarachnoid space theoretically induce pressure waves, which to date are not fully characterized. 3 With contrast media or radionuclides in the spinal subarachnoid space, a slow convection of fluid is observed resulting from the continuous oscillation of CSF.…”

“…In the presence of obstruction, the phase difference narrows. 2 Pressure fluctuations in the CSF produce transient pressure waves and gradients in the spinal cord. In portions of the spinal cord with a persistent central canal, pressure on the external surface of the cord may produce radial pressure gradients in the cord.…”

Poro-elastic modeling of Syringomyelia – a systematic study of the effects of pia mater, central canal, median fissure, white and gray matter on pressure wave propagation and fluid movement within the cervical spinal cord

“…The modeling of CSF flow has been the subject of several computational studies in both patient-specific (Gupta et al 2009;Rutkowska et al 2012;Yiallourou et al 2012;Clarke et al 2013;Helgeland et al 2014) and idealized models (Loth et al 2001;Hentschel et al 2010;Linge et al 2011;Støverud et al 2013;Berselli et al 2014). These studies have demonstrated that the abnormal CSF velocities and pressures are related to abnormal anatomy of the CNS and that computational fluid dynamics capture the flow abnormalities and pressure dissociation observed clinically, although we remark that a comparison between CFD simulations and PC-MR has shown discrepancies (Yiallourou et al 2012).…”

“…The pressure dissociation is well explained by computational fluid dynamics (CFD), see, e.g. Støverud et al (2013). Prevailing theories therefore suggest that syringomyelia development is mechanically driven by abnormal fluid flow and significant pressure dissociation, and several biomechanical theories have been proposed along this mechanistic reasoning.…”