Mechanics of the cupula: effects of its thickness

Mechanical aspects of the ampullar diaphragm, that is the crista ampullaris and the cupula, related to its thickness, are studied by a numerical method. Numerical methods are able to go beyond the limits of analytical approaches and are the only methods able to take into account this thickness. A finite elements method is applied to the median plane slice of the ampullar diaphragm. One assumes that the cupula sticks firmly without slipping, to the ampullar wall and to the crista ampullaris. The computation takes into account the pressures on the liquid interfaces and the deformations of the ampulla. So the volume swept over by the cupula during quasi-static deformations can be evaluated and the global elasticity coefficient of the human cupula can be calculated. The related value of the long time constant of the semicircular canal is close to the value obtained when measuring, in vivo, the activity on the vestibular nerve in animals. The thick cupula model clearly shows two different spatial distributions of strain on the hairs of the sensory cells, leading to a discrimination between the vestibular inflating pressure and the transcupular pressure difference. This result matches recent neurophysiological data and brings a new insight in the mechanics of the vestibular angular accelerometer and its regulation.