title: Phase and amplitude of spontaneous retinal vein pulsations: An extended constant inflow and variable outflow model.
abstract: The constant inflow and variable outflow (CIVO) theory correctly predicts that spontaneous pulsation of the retinal veins will be visible close to the point where the vein exits the eye at the lamina cribrosa but will decrease rapidly in amplitude and become too small to see only a short distance upstream. However, the phase of vein oscillation relative to the oscillation of the intraocular pressure (IOP) predicted by CIVO has been unclear and controversial. We show that the CIVO model is indeterminate in predicting such phase relations. We propose a simple extension of the CIVO model that retains its basic equations but applies them to a larger domain that includes not only the intraocular (pre-laminar) portion of the vein but also the retrobulbar (post-laminar) portion of the vein behind the eye. We show that this extended CIVO model makes definite predictions about the phase of vein oscillation relative to the oscillation of IOP. This phase relationship is determined by the relative amplitude and phase of pulsations of the IOP and of the cerebrospinal fluid pressure (CSFP). If IOP and CSFP oscillate in phase, then the pre-laminar vein oscillates in phase with IOP when the amplitude of CSFP exceeds the amplitude of IOP but oscillates in counter phase with IOP when the amplitude of IOP exceeds that of CSFP. These relationships are modified when there is a phase difference between the oscillations of IOP and CSFP. When CSFP leads IOP, the phase of vein oscillation is advanced if the amplitude of CSFP exceeds that of IOP and is delayed if the amplitude of IOP exceeds that of CSFP. The result in each case is that maximum vein size occurs during the rising phase of IOP (ocular systole). We conclude that the driving force of vein oscillation is the difference between the oscillations of IOP and CSFP. The phase of this difference determines the phase relationships above. We show that additional delays in the phase of venous pulsation relative to that of IOP are induced by constriction of the vein within the lamina cribrosa and by recording the vein pulsations upstream from the lamina cribrosa. The amplitude of vein oscillation is proportional to the amplitude of the driving force and to the venous capacitance. Loss of spontaneous retinal vein pulsation with increase in mean CSFP is determined primarily by reduced venous capacitance. Increased amplitude of pulsation may occur when IOP is increased. It is the result of increased venous capacitance and possibly increased driving force of the pulsation. However, in chronic glaucoma the increase in capacitance may be counteracted by venous outflow obstruction, and the increase in driving force may be counteracted by reduced ocular blood flow. As a result retinal vein oscillation may be reduced in amplitude.
authors.affiliation: Department of Neurology, New York University School of Medicine, 240 East 38th Street, Suite 20-02, New York, NY 10016, USA. Electronic address: david.levine@nyumc.org.
authors.forename: David N
authors.initials: DN
authors.lastname: Levine
authors.affiliation: Institute for Theoretical Physics, University of Berne, CH-3012 Berne, Switzerland. Electronic address: h.bebie@bluewin.ch.
authors.forename: Hans
authors.initials: H
authors.lastname: Bebie
mesh_terms: D001783:Blood Flow Velocity; D003198:Computer Simulation; D005901:Glaucoma / Q000503:physiopathology; D006801:Humans; D019586:Intracranial Hypertension / Q000503:physiopathology; D007427:Intracranial Pressure; D007429:Intraocular Pressure; D008953:Models, Anatomic; D008955:Models, Cardiovascular; D011673:Pulsatile Flow; D012039:Regional Blood Flow; D012169:Retinal Vein / Q000033:anatomy & histology / Q000502:physiology*; D013997:Time Factors
keywords: Cerebrospinal fluid pressure pulsation; Constant inflow and variable outflow theory; Glaucoma; Increased intracranial pressure; Intraocular pressure pulsation; Mathematical modeling; Ocular hypertension; Retinal vein pulsation