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We propose a noninvasive method to estimate the time constant. The calculation of this factor permits us to understand the pressure variations of the inner ear and also predict the behavior of the flow resistance of the cochlear aqueduct. A set of mathematical relationships incorporating the intralabyrinthine pressure, the intracranial pressure, and the time constant was applied. The modeling process describes the hydrodynamic effects of the cerebrospinal fluid in the intralabyrinthine fluid space, where the input and output of the created model are, respectively, the sinusoidal variation of the respiration signal and the distortion product of otoacoustic emissions. The obtained results were compared with those obtained by different invasive techniques. A long time constant was detected each time when the intracranial pressure increased; this phenomenon is related to the role of the cochlear aqueduct described elsewhere. The interpretation of this model has revealed the ability of these predictions to provide a greater precision for hydrodynamic variation of the inner ear, consequently the variation of the dynamic process of the cerebrospinal fluid.

The intracranial pressure (ICP) has been shown to influence the perilymphatic pressure [

Densert et al. have investigated the inner ear pressure by measuring a time constant for pressure release [

In this context, the aim of our work was to estimate under hydrodynamic conditions, the variation of the time constant

Our technique is based on the transmission of infrasonic pressure waves from cerebrospinal to intralabyrinthine fluids through the human cochlear aqueduct [

All experiments were performed on young, healthy volunteers with normal-hearing of both genders (4 males, 4 females, age ranging from 22 to 32). Volunteers were instructed not to swallow, to keep reasonably quiet and breathe naturally. They were placed on a tilting table enabling three postures: up-right, supine flat on their back on a horizontal plane, and finally head down

To estimate the time constant

The following diagram shows the methodology of how the time constant is estimated. The infrasonic waves of the ICP and ILP were filtered from the thoracic and DPOAE signals; each infrasonic wave was between (0.166 Hz, 0.5 Hz), noticed that the reference [

Based on the work of Gopen et al. [

Model system. (a) Mechanical system. (b) Equivalent electrical circuit of the model.

This model has been created for two objectives. The first one was to calculate the input signal which defines the relationship between the thoracic signal and the cranial fluid pressure. The second was to analytically prove from the output signal, the relationship between the variations of the cochlear response with the movement of the cerebrospinal fluid (CSF).

The input signal is represented by

At the same time, it is known that

Because the respiratory and cardiac movements are transported by the blood to the cerebrospinal fluid [

The blood pressure variation

This differential equation can be considered as a definite integral with

Equation (

The resulting amplitude

The intralabyrinthine pressure ILP in the inner ear is considered as the output signal (Figures

We can deduce the relationship between the intracranial and the intralabyrinthine pressure by substituting (

By replacing

To estimate the variation of the time constant

vibrating very differently which we called the transition signal part; this turbulent transition process was observed each time after a variation of the respiration frequency (

when they are both on the same phase.

Thereafter, using (

We show here the partition of one sequence of sinusoidal curve; this sequence can be a wavelength of intralabyrinthine pressure

Each peak is divided into an up-going edge and a down-going edge. The resulting solution was found to contain two time constants variables

The vertical axis of (a) and (b) is the time constant values, and the horizontal axis is the sinusoidal modulation (

The mean values of time constant variation

The mean

Intralabyrinthine pressure monitoring in humans is potentially interesting in two situations [

Very long time constants were observed by Densert et al. [

Knowing that

We can quantify the characteristic of

Comparisons were made between our curves (Figures

Studies in guinea pigs have shown a relation between acute inner ear pressure changes and cochlear function at low-level DPOAE. The inner ear pressure was represented by the variation of the time constant [

The modeling process is the only way to understand the hydrodynamical interactions between the intracranial and intralabyrinthine fluids in the inner ear, because it provides a noninvasive measurement. Using the fact that intralabyrinthine pressure changes induce characteristic phase shifts of DPOEAs around 1 kHz. The results are consistent with previous estimations of the time constant of the inner ear derived from invasive animal experiments. Noninvasive measurements of the time constant at low-frequency pressure waves may turn out to be applicable to monitoring the normal physiology and pathophysiology of the inner ear. This modeling was applied to healthy subjects, changes in the mathematical equations of this model will be necessary, if we want to estimate the time constant for different pathological conditions.

The authors would like to acknowledge the support of Eric Le Page, Director of OAEricle Laboratory (Australia). They would like to thank the professors of ESITPA for their encouragement for the finalization of this work.