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Dominik Obrist
Institute of Fluid Dynamics, ETH Zurich Sonneggstr. 3, 8092 Zurich, Switzerland

Stefan Hegemann
Department of Otorhinolaryngology, University Hospital Zurich Frauenklinikstr. 24, 8091 Zurich, Switzerland


Particulate flow in the semicircular canals of the inner ear is suspected to be the most common cause for vertigo. This pathologic condition is known as benign paroxysmal positional vertigo (BPPV). We propose an analytical model for this flow configuration which consists of an equation for the fluid flow and of an equation of motion for the particles including the appropriate Stokes drag and gravitational forces. A modal analysis of the linearized equations suggests a reduced-order model for BPPV constructed from the two least stable modes. A Stokes number, formed with the eigenvalues of these two modes, is shown to be an important parameter in BPPV. We derive explicit expressions that connect the particle and canal properties directly to the onset, strength and duration of the vertigo.