A mathematical model for top-shelf vertigo: the role of sedimenting otoconia in BPPV.
Benign paroxysmal positional vertigo (BPPV) is a mechanical disorder of the vestibular system in which calcite particles called otoconia interfere with the mechanical functioning of the fluid-filled semicircular canals normally used to sense rotation. Using hydrodynamic models, we examine the two mechanisms proposed by the medical community for BPPV: cupulolithiasis, in which otoconia attach directly to the cupula (a sensory membrane), and canalithiasis, in which otoconia settle through the canals and exert a fluid pressure across the cupula. We utilize known hydrodynamic calculations and make reasonable geometric and physical approximations to derive an expression for the transcupular pressure DeltaPc exerted by a settling solid particle in canalithiasis. By tracking settling otoconia in a two-dimensional model geometry, the cupular volume displacement and associated eye response (nystagmus) can be calculated quantitatively. Several important features emerge: (1) a pressure amplification occurs as otoconia enter a narrowing duct; (2) an average-sized otoconium requires approximately 5 s to settle through the wide ampulla, where DeltaPc is not amplified, which suggests a mechanism for the observed latency of BPPV; and (3) an average-sized otoconium beginning below the center of the cupula can cause a volumetric cupular displacement on the order of 30 pL, with nystagmus of order 2 degrees/s, which is approximately the threshold for sensation. Larger cupular volume displacement and nystagmus could result from larger and/or multiple otoconia.
Squires
Todd M
TM
Departments of Applied and Computational Mathematics and Physics, California Institute of Technology, Pasadena, CA 91125, USA. tsquires@acm.caltech.edu
Weidman
Michael S
MS
Hain
Timothy C
TC
Stone
Howard A
HA
D002137:Calculi / Q000503:physiopathology; D007758:Ear, Inner / Q000503:physiopathology*; D006801:Humans; D008954:Models, Biological; D009759:Nystagmus, Pathologic / Q000209:etiology; D010037:Otolithic Membrane / Q000503:physiopathology*; D012665:Semicircular Canals / Q000503:physiopathology; D013997:Time Factors; D014717:Vertigo / Q000209:etiology* / Q000503:physiopathology