The vestibular membranes of the cochlea and saccule are subject to two simultaneous constraints as they deform in endolymphatic hydrops. Boundary tethers impose a bulge-type constraint during pressure-induced transverse membrane displacement, while inherent elasticity imposes a stretch-type constraint during stress-induced longitudinal membrane distention.
The aim of this study is to reconcile the effect of these dual constraints on membrane deformation. It is hypothesized that it is the interaction of these constraints that determines whether a stable membrane configuration can be achieved or progression to endolymphatic hydrops will occur.
Reissner's membrane was modeled as a flat elastic ribbon that was bound along its lateral edges and subject to trans-mural pressure. The bulge and stretch constraints on membrane deformation were formulated mathematically. A graphic solution of the constraint functions was used to examine the nature of the interaction and determine how pressure and elasticity influence the hydropic process.
The graphic analysis shows how bulge and stretch phenomena interact to achieve an equilibrium point that satisfies both physical requirements. Nominal values of pressure and elasticity are projected to result in a stable membrane equilibrium in the precritical zone with the modest isolated increases in either parameter alone compatible with stability. However, a sufficiently large increase in either pressure or elasticity alone can constitute a single hit mechanism to exceed the critical point and destabilize the membrane. Moreover, simultaneous modest increases in both pressure and elasticity, neither of which would be sufficient in its own right, can be additive and constitute a double hit mechanism to destabilize the membranes as well. Finally, extreme values of pressure and elasticity that fail to intersect imply that no solution is feasible and that the affected membranes will fail immediately.
Sufficiently large increases in either endolymphatic pressure or membrane elasticity alone can destabilize the membranes and constitute single hit mechanisms for inducing hydrops. Combined moderate increases in both trans-mural pressure and membrane elasticity can also destabilize the membranes and constitute a double hit mechanism for hydrops induction.
College of Physicians and Surgeons, Columbia University, New York City, New York
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Source of Funding: None.
The authors disclose no conflicts of interest.