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The origin of retinal venous pulsations remains an open problem in physiology and medicine; so too, their exact relationship to intracranial pressure. This study takes a mathematical modeling approach to explore details of blood flow through the eye to reveal the mechanism of pulsations. The intravaginal, intraneural, and intraocular segments of the retinal arteries and veins are modeled as connected resistive-capacitive segments. The analysis incorporates two critical mechanical properties of these small blood vessels, not heretofore studied, which become significant under conditions of negative transmural pressures: (1) dramatically reduced compliance during flattening and (2) cross-sectional shape change as internal volume decreases. Intraocular pressure acting on these veins close to the optic disc normally creates fluctuating negative transmural pressure. The observed long diameters of these venous segments become wider during diastole as they empty and flatten and
narrower during systole as they refill with blood. Such visible pulsations occur only in models that include nonlinear compliance and constant-perimeter flattening. Further, the pulsations disappear when raised intracranial pressure, raised cavernous sinus pressure, or reduced arteriolar resistance elevates internal pressure in all retinal veins above the level of intraocular pressure. In this case transmural venous pressures are always positive, cross sectional shapes are circular, and compliance is greatly reduced. Then visible retinal venous pulsations disappear. Scenarios are suggested under which intracranial pressure can be estimated quantitatively from physical examination of retinal venous pulsations, if intraocular pressure is also measured.