Extended Willis circle model to explain clinical observations in periorbital arterial flow.

A fluid-dynamic model of the circle of Willis and its periorbital links with the external carotid arteries has been established and tested. It is based on anatomic data and takes Doppler measurements as flow input conditions. The model explains, on fluid-dynamic grounds, the clinical observations of periorbital reverse flow and arrival pulse time delay. It also obtains the velocity and pressure pulse at any point of the studied area. This allows the comparison between the normal or healthy condition and the flow distribution when an internal carotid is externally or pathologically occluded. Several combinations of the communicating artery sizes are explored to obtain the reduced cerebral flow. The combination of the communicating diameters can lead to insufficient irrigation which can be hydrodynamically assessed. No other physiological response is included, and the results must be considered as a minimum assured. These results show the need for a common evaluation of the alternative paths and explain some paradoxes found in literature.