Cerebral hydrodynamics are at a most a third order system

The human body employs a sophisticated windkessel mechanism to dampen the arterial pulse entering the brain, thus ensuring the smooth flow of blood through the cerebral capillary bed. The energy from the arterial pulse is transferred to the cerebrospinal fluid (CSF), which pulses backwards and forwards across the foramen magnum. The dynamics associated with this system are complex and poorly understood. In an attempt to better understand the physiology, a number of researchers have constructed electrical analogue circuits to simulate the hydrodynamic behaviour of the brain. These generally consist of several low-pass filters. While such models have great potential, to date, they have met with only limited success. We suspect that this is in part due to a failure to identify the order of the model required to successfully capture the hydrodynamics of the brain. Here, we advance the hypothesis that the cerebral hydrodynamic system is at most a third order system, using evidence collected from the spectral eigen-system of the arterial, venous and CSF flows. Using singular spectrum analysis we computed the singular vectors for the measured arterial, venous and CSF flows from an individual. This revealed that the first singular vector contributes 67% of the observed variance; the first plus the second singular vectors contribute 96% of the variance; and sum of the first three singular vectors contribute more than 99.5% of the observed variance.