A mathematical model for top-shelf vertigo: the role of sedimenting otoconia in BPPV

Abstract

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.

In vitro model of a semicircular canal: Design and validation of the model and its use for the study of canalithiasis

“…BPPV (also known as top-shelf vertigo) is the most common cause for vertigo syndromes in humans. BPPV due to canalithiasis has been studied theoretically and numerically by several authors (House and Honrubia, 2003;Rajguru et al, 2005;Squires et al, 2004;Obrist and Hegemann, 2008). Experiments investigating the physical mechanisms of BPPV on animal SCC have been presented Figure 1.…”

Task Analysis and Kinematic Design of a Novel Robotic Chair for the Management of Top-Shelf Vertigo

“…In particular, the otoconia is an irregularly shaped rigid particle which might stick to the SCC soft walls. Therefore: 1) Controlled inertial forces could be useful to break the particle-wall interaction (as reported in Squires et al (2004)); 2) A treatment strategy which prevents the otoconia from touching the SCC as the maneuver has started could increase the rate of success of non-invasive therapies. The next section further addresses this issue.…”

“…The nystagmus is evoked by the vestibular-ocular reflex (Raphan et al, 1979;Robinson, 1977) as a result of abnormal stimulation caused by the presence of otoconia within the interested canal. It is believed (Squires et al, 2004) that the size (and mass) of the otoconia dispersed within the SCC is proportional to the intensity of the nystagmus. Alike the treatment methodology, the diagnosis is carried out through a series of maneuvers called diagnostic maneuvers (DM) during which the doctor recognizes the existence and typology of nystagmus and decides which RM has to be used as treatment.…”

“…This is in contrast with (Squires et al, 2004) where a SCC with varying cross sectional area is considered; • The otoconium is considered as a sphere whose radius is negligible with respect to the SCC cross section; • The radius of the SCC cross section is negligible with respect to the curvature of the circular toroid (Squires et al, 2004). This assumption allows to consider the SCC as a straight circular cylinder when calculating the Stokes drag force acting on the particle.…”

“…However, a rough estimation of the particle trajectory is useful for verifying the effects of the maneuvers performed during BPPV therapy. A suitable compendium of the effects acting on the otoconium inside the SCC can be found in Obrist & Hegemann (2008) and Squires et al (2004).…”