Mathematical Model of the Cupula-Endolymph System with Morphological Parameters for the Axolotl (Ambystoma tigrinum) Semicircular Canals~!2008-03-27~!2008-06-23~!2008-08-26~!

Abstract

By combining mathematical methods with the morphological analysis of the semicircular canals of the axolotl (Ambystoma tigrinum), a system of differential equations describing the mechanical coupling in the semicircular canals was obtained. The coefficients of this system have an explicit physiological meaning that allows for the introduction of morphological and dynamical parameters directly into the differential equations. The cupula of the semicircular canals was modeled both as a piston and as a membrane (diaphragm like), and the duct canals as toroids with two main regions: i) the semicircular canal duct and, ii) a larger diameter region corresponding to the ampulla and the utricle. The endolymph motion was described by the Navier-Stokes equations. The analysis of the model demonstrated that cupular behavior dynamics under periodic stimulation is equivalent in both the piston and the membrane cupular models, thus a general model in which the detailed cupular structure is not relevant was derived.

Vortical flow in the utricle and the ampulla: a computational study on the fluid dynamics of the vestibular system

“…Therefore, the simulations were repeated for several values of K leading to values of τ c from 4.2 to 104 s. These values are motivated by data reported in Grant and Van Buskirk (1976), Rabbitt et al (2009), Selva et al (2009). The resulting cupula volume displacements V (t) are plotted in 1996;Ifediba et al 2007;Obrist 2008;Vega et al 2008). The volumetric displacement V is approximately proportional to the angular velocityα of the head.…”

“…For head movements within this frequency (ω) range, the cupula displacement V (to be defined later) is proportional and in phase with the angular velocitẏ α of the head in the plane of the SCC (V andα indicate the respective Laplace-transformed variables). Several models of increasing complexity have been proposed to relate the values of τ c , τ s , and G to the actual anatomy and physics of the SCCs (Van Buskirk et al 1976;Pardoe and Haughton 1979;Bernard 1982;Oman et al 1987;Rabbitt and Damiano 1992;Damiano and Rabbitt 1996;Ifediba et al 2007;Obrist 2008;Vega et al 2008). All these models lead qualitatively to similar results.…”

Vestibular prosthesis: from basic research to clinics

“…Most authors have used a linear or sigmoidal transfer function to code the gyroscope output as a frequency-modulated output ( Gong and Merfeld, 2002 ; Della Santina et al, 2005 , 2007 ; Töreyin and Bhatti, 2013 ; Perez-Fornos et al, 2014 ; Boutros et al, 2016 ; van de Berg et al, 2017a ). A neuromimetic mathematical model to code the gyroscope or accelerometer output into a series of frequency-modulated pulses has been proposed ( Sadovnichy et al, 2007 ; Vega et al, 2008 , 2016 ; Alexandrov et al, 2014 ). Theoretical analyses using this model reproduce the afferent activity in response to linear or angular accelerations (mechanical coupling differs for both), predicting the complex behavior of afferent neurons, including repetitive spike discharge.…”

An angular acceleration sensor inspired by the vestibular system with a fully circular fluid-channel and thermal read-out

“…To find a solution for the fluid velocity-profile v(r,t), we assume a harmonic flow with a parabolic profile [9,10]:…”