For constant IOP (setting
A I = 0 mm Hg), the model prediction of the channel constriction in the eye compartment (region I) is illustrated as the solid line in
Figure 2a as a function of time over a complete period of ICP oscillation (
Fig. 2a, dashed line), with a mean IOP of
P I = 18.0 mm Hg and a mean ICP of
P III = 0 mm Hg. For these parameter values, the wall of the vessel in compartment I exhibited a small amplitude oscillation of a frequency identical to that of the ICP but a quarter cycle out of phase (
Fig. 2a, dashed line). However, when the mean IOP was increased to
P I = 18.5 mm Hg, the vessel wall in compartment I exhibited a transient violent oscillation of much higher frequency than that of the ICP pulsation (
Fig. 2b), consistent with the onset of RVP in the vein at the optic disc. The critical value of IOP where onset was observed is a function of ICP but also the RBF,
Q, the vein diameter
d and the vessel tension
T. The dependency on each of these parameters is explored in the
Supplementary Material. Briefly, in the range of
Q, considered the onset, IOP varied by approximately 3.8 mm Hg; in the range of
d, the onset IOP varied by approximately 6 mm Hg. In the examples shown in
Figure 2, the vessel wall in compartment III oscillated with small amplitude in phase with the external force; as
P III was further increased, the model predicted the onset of vigorous high-frequency oscillations in compartment III (evident in
Supplementary Fig. S5). As these vigorous oscillations grew in amplitude, they qualitatively resembled “slamming” oscillations reported using similar models,
19,20 where the vein becomes highly constricted at one or more points over a period, but the walls are prevented from making contact due to the inertia of the flow in the downstream segments.