[Modern trends in mathematical modeling of the hemispheric channels functions].

The review deals with new trends in modeling the vestibular function of the hemispheric channels (HC) involved in the head angular movements. The trends were spurred by the growing significance of computers in both mathematical modeling and direct simulation of the HC structure and processes, and conditions of experiments. Literature analysis reveals the following trends in the CH modeling: 1) reconstruction, 2) micromodeling, 3) integral modeling, 4) simulation (imitation), and 5) alternative modeling.

Effect of difference of cupula and endolymph densities on the dynamics of semicircular canal.

The effect of different densities of a cupula and endolymph on the dynamics of the semicircular canals is considered within the framework of a simplified one-dimensional mathematical model where the canal is approximated by a torus. If the densities are equal, the model is represented by Steinhausen's phenomenological equation. The difference of densities results in the complex dynamics of the cupulo-endolymphatic system, and leads to a dependence on the orientation of both the gravity vector relative to the canal plane and the axis of rotation, as well as on the distance between the axis of rotation and the center of the semicircular canal.

The model of cupular dynamics in the case of the difference of the cupula and endolymph densities.

The function of semicircular canals (SC) is based on the precise equality of densities of the cupula and endolymph. Otherwise the information provided by SC would depend on the orientation of both the gravity vector relative to canal plane and the axis of rotation. It would also depend on the distance between the axis of rotation and the center of the SC.

The distribution of otolith polarization vectors in mammals: comparison between model predictions and single cell recordings.

The transformation of head-movements into neural signals represents a multi-stage process. It depends on orientation and movement of the head, the geometry and mechanics of the vestibular sensors, and the ensuing processing of the peripheral vestibular signals. While this process is well understood for the semicircular canals, where each canal transduces the angular velocity in the corresponding canal plane, the contributions of the individual otoliths, our linear acceleration sensors, are still under debate.

[Modeling of the Otolith's structure and functions].

Physical and chemical processes of the transformation of mechanic stimuli into nerve signals in the otolith responsible for gravity and linear accelerations perception are of interest of equally biologists and experts in aerospace medicine. A severe experimental difficulty is the small size of the otolith and, therefore, mathematical and computer modeling has become a powerful tool for examination of the otolith organs. Most of the above processes are spatially distributed; consequently, spatial distribution models will provide the exact description of the existing biological structures and processes.

Feedback hypothesis and the effects of altered gravity on formation and function of gravireceptors of mollusks and fish.

Popular hypothesis based on the idea of simple feedback mechanism that correlates gravity level and weight of test mass cannot explain the variety of the effects of altered gravity on development and function of gravireceptors. The reaction of organisms to the change of gravity depends on the gravisensitivity of the physical and chemical processes corresponding to specific phases of development and may have no relation to any feedback mechanisms of compensation of altered weight of the test mass. The present work analyzes the hypothesis of feedback and shows the ambiguity of possible effects of the altered gravity on formation and function of gravireceptors basing on the data from mollusks and fish.

On generation of statoconia in gravireceptors of mollusks.

Two models of development of statoconia in the statocyst of mollusks, based on the experimental data [Hearing Res. 49 (1990) 63; Hearing Res. 109 (1997) 125; Hearing Res.

Models of the mechanical sensitivity and growth of otoliths in fish.

It has been suggested that, in the fish, the change of otolith mass during development under altered gravity conditions and the growth of otoliths in normal conditions, are determined by feedback between otolith dynamics and the processes that regulate otolith growth. The hypothesis originates from an oscillator model of the otolith in which otolith mass is one of the parameters. However, the validity of this hypothesis is not obvious and has not been experimentally verified.

New model of hair cell bundle functioning in otoliths.

Transformation of the mechanical input in the chain: acceleration of otolithic membrane (OM)-displacement of the OM gel layer -deflection of hair cell bundle (HCB) -deformation of the system of tip-links- formation of temporal pattern of polarization was studied using simplified analytical models of these stages of conversion of mechanical stimulus into the HCB electrical response. The process of transformation of information in this chain was considered for two extreme cases of OM gel-HCB interaction: 1) the HCBs exactly follow the gel displacement; 2) stiff stereocilia and weak surrounding gel allow the relative motion of the bundle with regard to the gel. The analysis of a simplified model of cell polarization based on threshold triggering of the HCB tip-links allows to hypothesize that spatially nonhomogeneous HCB structure with a set of stereocilia of varying heights is designed to perceive spatially nonhomogeneous gel displacements caused by external acceleration.

Mass and mechanical sensitivity of otoliths.

It has been suggested that the changes of otolith mass during the otolith development in altered gravity conditions as well as the growth of otoliths in fishes in normal conditions are determined by the feedback between the otolith dynamics and the processes that regulate otolith growth. This hypothesis originates from the pendulum model of an otolith (de Vries, 1950), in which otolith mass is a parameters. The validity of this hypothesis is tested by comparing the pendulum model with a simplified spatially distributed model of an otolith.

Qualitative model of otolith-ocular asymmetry in vertical eccentric rotation experiments.

Today, investigation of the vestibulo-ocular reactions is a mainstream method of studying the vestibular asymmetry. Analysis of experimental data requires a model of otolith-ocular interaction. The proposed model is based on the literary data concerning measurements of ocular counter-rotation (OCR) and luminous line rotation (LLR) in experiments with eccentric rotation carried out by Wetzig et al.

Model of statoconia accumulation in gravireceptors of mollusks.

The kinetics of formation and accumulation of statoconia are different for Aplysia californica and Biomphalaria glabrata. In Aplysia californica, the fast growth of statoconia number occurs after the critical size (approximately 45 micrometers) of statocyst is reached; then the increase of statoconia number is proceeding with the nonmonotonic rate during the life of an animal. In Biomphalaria the growth of statoconia number occurs only in the initial phase.

Simulation and interpretation of experiments with otoliths.

The function of otolith as a gravisensor comprises a sequence of different physical and chemical processes, which experimental investigation is difficult or unfeasible. To understand the relationship between the input and output in otolith organ, certain assumptions concerning the mechanisms of transformation of information on the inner, intermediate stages have to be made. Their validity has to be tested by comparison of the properties of output characteristics, which follow from these assumptions, with experimental data.

The influence of the HGMF on mass-charge transfer in gravisensing cells.

The present work is focused on the influence of the high-gradient-magnetic field (HGMF) on spatial distribution of ion fluxes along the roots (a), cytoplasmic streaming (b), and the processes of plant cell growth connected with intracellular mass and charge transfer (c).

[Sensitivity and parameters of the otolith as a spatially distributed system].

Comparison of the de Vries pendulum and spatially distributed otolith models allowed physical interpretation of the pendulum model parameters and determination of the influence of otolith structure on its mechanical sensitivity when otolith dynamics is represented by a parallel displacement relative to the receptor surface. Proof was obtained that in this case otolith dynamics is independent of total mass, and mechanic sensitivity is not proportional to size of the organ. Possible explanations of the effects of changed dynamics conditions on otolith parameters in the fish are discussed.

Otoliths as biomechanical gravisensors.

This paper analyzes experimental data related to the reaction of otolith afferents in response to acceleration (Fernandez and Goldberg, 1976). It considers the assumptions that were the basis of the interpretation of the stimulus-response characteristics of afferents proposed by Fernandez and Goldberg. Comparing these experimental data with the results of modeling the otolith structures of vertebrates indicates that some peculiarities of the neural responses may be explained by the spatial dependence of the material parameters of the otolithic membrane across its thickness and within the volume of the membrane corresponding to the terminal field.

Models of otolithic membrane-hair cell bundle interaction.

Transformation of the mechanical input in the chain: acceleration of otolithic membrane (OM)-displacement of the OM gel layer-deflection of hair cell bundle (HCB)-formation of the temporal pattern of polarization was studied using simplified analytical models of these stages of conversion of mechanical stimulus into the HCB electrical response. The dynamic behavior of an OM was modeled by a homogeneous viscoelastic (Kelvin-Voight body) model of the OM. Two alternative models of an 'HCB-surrounding gel' interaction corresponding to different types of the HCB were considered: (1) a model of stereocilia tip-link deformation in the case when the HCBs passively follow the gel deformation and (2) a model in which the tip-link dynamics is determined by an 'HCB-viscous fluid' interaction.

[Modeling of the structure and mechanics of the otolith membrane].

Behavior of otoliths of mammals against static (gravitation and changed pressure in the surrounding endolymph) and dynamic loads was surveyed using analytic and computerized (the finite difference method) models of the otolith membrane (OM). It was presumed that OM consists of gel-like and otoconial layers differing in mechanic and thickness. Comparison with available experimental data allowed to assess magnitudes of mechanic parameters of the gel-like layer responsible for OM interaction with the receptor hair cells (Yung's module for the layer is 1-10 N/m2 with the viscosity in the order of 1 poise), the characteristic times of otolith dynamics (T2 approximately 0.

Models of the dynamics of otolithic membrane and hair cell bundle mechanics.

Dynamic behavior of an otolithic membrane (OM) was studied analytically using simplified homogeneous viscoelastic (Kelvin-Voight body) model of the OM. The OM was represented by a thin plate attached to a macular plane. Viscoelastic properties of the OM determine the specific times (T(1) and T(2)) and frequency-dependent behavior of the local displacements of the membrane caused by the inertial time-dependent forces.

Finite element modeling of the 3D otolith structure.

A 3D finite element model (FEM) of the mammalian utricular otolith corresponding to spatial structure, shape and size of the otolith from the guinea pig was developed. The otolithic membrane (OM) was considered as consisting of gel and otoconial layers. The macular surface was approximated as a plane.

The effects of HGMFs on the plant gravisensing system.

High Gradient Magnetic Fields (HGMFs) offer new opportunities for studying the gravitropic system of plants. However, it is necessary to analyze the influence that HGMF can have on cellular processes and structures that may not be related to amyloplasts displacement. This paper considers possible HGMF effects on plants, which may accompany HGMF stimulation of amyloplasts and contribute to the mechanisms of the HGMF-induced curvature.

Theoretical considerations of plant gravisensing.

The mechanisms proposed to explain gravity sensing can be divided into two groups, "statolith" and "non-statolith" mechanisms. The traditional estimates of the plausibility of these mechanisms are based on the analysis of the signal-to-noise ratio. The existing data indicate that the problem of plant gravisensing may be related to the general problem of the detection of weak signals in mechanoreceptors.

Mathematical model of the evolution of statoconia.

A mathematical model of the evolution of statoconia in statocysts of freshwater snails based on the analysis of experimental data [Wiederhold et al., 1990; Pedrozo et al., 1996; Gao et al.

[The imitation of the effects of otolith-ocular asymmetry by eccentric rotation].

Today, investigation of the vestibuloocular reactions is the mainstream method of studying the vestibular asymmetry. Analysis of experimental data requires a model of otolith-ocular interaction. The proposed model is based on the literary data concerning measurements of ocular counter-rotation (OCR) and luminous line rotation (LLR) in experiments with eccentric rotation.