A mathematical model of the formation of output information in a biosensor of angular acceleration is presented. The functional and numerical parameters of the model have been determined by results of experiments made in 2001–2008. A comparison with the mathematical model of J. M. Goldberg and C. Fernandez (1971) describing the change in spike frequency of the primary afferent neuron spikes in response to an angular acceleration of the head as it turns around a vertical axis is carried out.

In this work we present a mathematical model of the informative process of the biosensor of angular acceleration (vestibular system in the inner ear). The functional and numerical parameters of the model have been identified by physiological and morphological experiments in the inner ear of amphibians and mammals. The model developed is a compartmental-type model in which we considered all the stages of the sensory activation process in the biosensor of angular acceleration. We performed a comparative analysis between our model and the mathematical model of Fernandez and Goldberg (1971), in which they described the change of the firing frequency of primary afferent neurons in response to the angular acceleration of the head about the vertical axis. The comparative analysis of both models indicates that our model more appropriately reproduce the fast responses of the vestibular system than Fernandez and Goldberg model; in addition, the parameters used in our model have physiological meaning.

Advances in electronics open the possibility for developing appliances simulating the vestibular system operation. To contribute for the developing and testing of this appliances, we have developed a mathematical model of the generation of the information output from the vestibular mechanoreceptor. For this, we have considered five compartments: mechano-electrical transduction, adaptation of transduction, hair cell ionic currents, synaptic transmission, and afferent neuron discharge. The adaptation of the transducer mechanism as an intrinsic control mechanism was also considered. The numerical parameters of the model were obtained from experiments that were done in the inner ear of the rat. The results of the numerical analysis of the model showed that the mathematical modelling of the output from the vestibular mechanoreceptor may be used to construct an encoder system for artificial sensors (eg: vibrational gyroscope) contributing to the development of a reliable vestibular prosthesis prototype.

A mathematical model of the system composed of two sensors, the semicircular canal and the sacculus, is suggested. The model is described by three lines of blocks, each line of which has the following structure: a biomechanical block, a mechanoelectrical transduction mechanism, and a block describing the hair cell ionic currents and membrane potential dynamics. The response of this system to various stimuli (head rotation under gravity and falling) is investigated. Identification of the model parameters was done with the experimental data obtained for the axolotl (Ambystoma tigrinum) at the Institute of Physiology, Autonomous University of Puebla, Mexico. Comparative analysis of the semicircular canal and sacculus membrane potentials is presented.

A mathematical model of the output generation of the vestibular mechanoreceptor is presented. The model consider the series of events in the vestibular end organs that lead to the activation of the afferent neurons in the vestibular nerve and the generation of the afferent impulses. We have considered five compartments: mechano-electrical transduction, adaptation of transduction, hair cell ionic currents, synaptic transmission, and afferent neuron discharge. The numerical parameters of the model were obtained from experiments that were done in the inner ear of the rat. The results of the numerical analysis of the model showed that the mathematical modelling of the output from the vestibular mechanoreceptor may be used to construct an encoder system for artificial sensors (e.g.: vibrational gyroscope) contributing to the development of a reliable vestibular prosthesis prototype. This model can be used as the basis for the mathematical modelling of the vestibular sensors.