A theoretical unidirectional valve based on functional collapse of blood vessels in the penis

A model of a vessel exposed to external pressure was developed. Analytical derivation resulted in closed-form expressions describing pressure-flow relation in the vessel. These expressions describe a behavior of a unidirectional leaky valve. The vessel model was used to represent internal arteries and veins in the penis. Together with a compliant chamber representing the corpus cavernosum, the model demonstrates the valve action of the partially collapsed vessels during penile erection. This explains observations regarding arterial backflow during erectile contraction of the ischiocavernous muscles and demonstrates the differences in development of tumescence and rigidity.