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 $\Delta P_c$ 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 five seconds to settle through the wide ampulla, where $\Delta P_c$ 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 $2^\circ$/s, which is approximately the threshold for sensation. Larger cupular volume displacement and nystagmus could result from larger and/or multiple otoconia.Comment: 15 pages, 5 Figures updated, to be published in J. Biomechanic

Receptive Field Inference with Localized Priors

The linear receptive field describes a mapping from sensory stimuli to a one-dimensional variable governing a neuron's spike response. However, traditional receptive field estimators such as the spike-triggered average converge slowly and often require large amounts of data. Bayesian methods seek to overcome this problem by biasing estimates towards solutions that are more likely a priori, typically those with small, smooth, or sparse coefficients. Here we introduce a novel Bayesian receptive field estimator designed to incorporate locality, a powerful form of prior information about receptive field structure. The key to our approach is a hierarchical receptive field model that flexibly adapts to localized structure in both spacetime and spatiotemporal frequency, using an inference method known as empirical Bayes. We refer to our method as automatic locality determination (ALD), and show that it can accurately recover various types of smooth, sparse, and localized receptive fields. We apply ALD to neural data from retinal ganglion cells and V1 simple cells, and find it achieves error rates several times lower than standard estimators. Thus, estimates of comparable accuracy can be achieved with substantially less data. Finally, we introduce a computationally efficient Markov Chain Monte Carlo (MCMC) algorithm for fully Bayesian inference under the ALD prior, yielding accurate Bayesian confidence intervals for small or noisy datasets

Treatment of vestibular disorders with weak asymmetric base-in prisms: An hypothesis with a focus on Ménière’s disease

BACKGROUND: Regular treatments of Ménière's disease (MD) vary largely, and no single satisfactory treatment exists. A complementary treatment popular among Dutch and Belgian patients involves eyeglasses with weak asymmetric base-in prisms, with a perceived high success rate. An explanatory mechanism is, however, lacking. OBJECTIVE: To speculate on a working mechanism explaining an effectiveness of weak asymmetric base-in prims in MD, based on available knowledge. METHODS: After describing the way these prisms are prescribed using a walking test and its effect reported on, we give an explanation of its underlying mechanism, based on the literature. RESULTS: The presumed effect can be explained by considering the typical star-like walking pattern in MD, induced by a drifting after-image comparable to the oculogyral illusion. Weak asymmetric base-in prisms can furthermore eliminate the conflict between a net vestibular angular velocity bias in the efferent signal controlling the VOR, and a net re-afferent ocular signal. CONCLUSIONS: The positive findings with these glasses reported on, the fact that the treatment itself is simple, low-cost, and socially acceptable, and the fact that an explanation is at hand, speak in favour of elaborating further on this treatment

Spatial orientation of the vestibular system: dependence of optokinetic after-nystagmus on gravity

1. Monkeys received optokinetic stimulation at 60 degrees/s about their yaw (animal vertical) and pitch (animal horizontal) axes, as well as about other head-centered axes in the coronal plane. The animals were upright or tilted in right-side-down positions with regard to gravity. The stimuli induced horizontal, vertical, and oblique optokinetic nystagmus (OKN). OKN was followed by optokinetic after-nystagmus (OKAN), which was recorded in darkness. 2. When monkeys were tilted, stimulation that generated horizontal or yaw axis eye velocity during OKN induced a vertical or pitch component of slow phase velocity during OKAN. This has been designated as "cross-coupling" of OKAN. Eigenvalues and eigenvectors associated with the system generating OKAN were found as a function of tilt. They were determined by use of the Levenberg-Marquardt algorithm to minimize the mean square error between the output of a model of OKAN and the data. 3. The eigenvector associated with yaw OKAN (yaw axis eigenvector) was maintained close to the spatial vertical regardless of the angle of tilt. The eigenvector associated with pitch OKAN (pitch axis eigenvector) was always aligned with the body axis. The data indicate that velocity storage can be modeled by a piecewise linear system, the structure of which is dependent on gravity and the yaw axis eigenvector, which tends to align with gravity. 4. Yaw axis eigenvectors were also determined by giving optokinetic stimulation about head-centered axes in the coronal plane with the animal in various angles of tilt. A technique using a spectral analysis of residuals was developed to estimate whether yaw and pitch OKAN slow phase velocities decayed concurrently at the same relative rate and over the same time course. The eigenvectors determined by this method were in agreement with those obtained by analyzing OKAN elicited by yaw OKN. 5. During yaw OKN with the animal in tilted positions, the mean vector of the ensuing nystagmus was closer to the body axis than to the spatial vertical. This suggests that there is suppression of the cross-coupled pitch component during OKN. The direction of the stimulus may be utilized to suppress components of velocity storage not coincident with the direction of stimulus motion. 6. There were similarities between the monkey eigenvectors and human perception of the spatial vertical, and the mean of eigenvectors for upward and downward eye velocities overlay human 1-g perceptual data.(ABSTRACT TRUNCATED AT 400 WORDS) </jats:p