Crista egregia: a geometrical model of the crista ampullaris, a sensory surface that detects head rotations

Abstract

The crista ampullaris is the epithelium at the end of the semicircular canals in the inner ear of vertebrates, which contains the sensory cells involved in the transduction of the rotational head movements into neuronal activity. The crista surface has the form of a saddle, or a pair of saddles separated by a crux, depending on the species and the canal considered. In birds, it was described as a catenoid by Landolt et al. (J Comp Neurol 159(2):257-287, doi: 10.1002/cne.901590207 , 1972). In the present work, we establish that this particular form results from principles of invariance maximization and energy minimization. The formulation of the invariance principle was inspired by Takumida (Biol Sci Space 15(4):356-358, 2001). More precisely, we suppose that in functional conditions, the equations of linear elasticity are valid, and we assume that in a certain domain of the cupula, in proximity of the crista surface, (1) the stress tensor of the deformed cupula is invariant under the gradient of the pressure, (2) the dissipation of energy is minimum. Then, we deduce that in this domain the crista surface is a minimal surface and that it must be either a planar, or helicoidal Scherk surface, or a piece of catenoid, which is the unique minimal surface of revolution. If we add the hypothesis that the direction of invariance of the stress tensor is unique and that a bilateral symmetry of the crista exists, only the catenoid subsists. This finding has important consequences for further functional modeling of the role of the vestibular system in head motion detection and spatial orientation.

The spatial orientation of crista ampullaris: implications for BPPV diagnosis and treatment

“…The crista ampullaris is a saddle-like structure ( 16 ), and Takagi's use of straight lines constructed at both ends of the sensory epithelium as the long axis of the crista ampullaris cannot represent the plane of the crista ampullaris. Our measurement data shows that the plane of the crista ampullaris is nearly perpendicular to the plane of the semicircular canal where it is located.…”

“…Secondly, the three-dimensional geometry of the crista ampullaris, particularly its saddle-like shape ( 16 ), may influence the Zero-Point Plane angle. Even when the crista ampullaris plane is parallel to gravity, otoconia adhered to the crista of this structure may still exert a pulling effect, resulting in a larger Zero-Point Plane angle.…”