Numerical simulations of the pulsating flow of cerebrospinal fluid flow in the cervical spinal canal of a Chiari patient

The flow of cerebrospinal fluid (CSF) in a patient-specific model of the subarachnoid space in a Chiari I patient was investigated using numerical simulations. The pulsating CSF flow was modeled using a time-varying velocity pulse based on peak velocity measurements (diastole and systole) derived from a selection of patients with Chiari I malformation. The present study introduces the general definition of the Reynolds number to provide a measure of CSF flow instability to give an estimate of the possibility of turbulence occurring in CSF flow. This was motivated by the fact that the combination of pulsating flow and the geometric complexity of the spinal canal may result in local Reynolds numbers that are significantly higher than the commonly used global measure such that flow instabilities may develop into turbulent flow in these regions. The local Reynolds number was used in combination with derived statistics to characterize the flow. The results revealed the existence of both local unstable regions and local regions with velocity fluctuations similar in magnitude to what is observed in fully turbulent flows. The results also indicated that the fluctuations were not self-sustained turbulence, but rather flow instabilities that may develop into turbulence. The case considered was therefore believed to represent a CSF flow close to transition.