A mathematical approach enabling the calculation of the total endolymph flow in the semicircular ducts.
1. A mathematical treatment of the flow inside the vertebrate labyrinth is given. The main difference to former theories (e.g. the "torsion pendulum" theory) is that the entire system formed by the three semicircular ducts, interconnected by the crus commune and the utriculus, is considered, instead of a single duct circuit. 2. The theory consists of a geometrical description of a labyrinth rotating in space, the solution of the continuity equation, determination of the initial velocities in all the ducts in a "cupulometry" experiment and derivation of the equation of motion (e.o.m.). 3. Equations for a system consisting of two ducts and for the classical single-duct system are special cases of the three-duct system. 4. Three different methods for the solution of the e.o.m. are described: an analytical one, a Runge-Kutta simulation and an "asymptotic" method. The last method includes approximations of the solution of the e.o.m. on a long and a short time scale. Its advantage is that it gives an insight based on rather manageable formulae. 5. The physiological basis of the presented theory, biological applications and verification are given in a separate paper (Muller & Verhagen, 1988).
Muller
M
M
Department of Experimental Animal Morphology and Cell Biology, Agricultural University, Wageningen, The Netherlands.
Verhagen
J H
JH
D000818:Animals; D004710:Endolymph / Q000502:physiology*; D007761:Labyrinthine Fluids / Q000502:physiology*; D008433:Mathematics; D008954:Models, Biological; D012665:Semicircular Canals / Q000502:physiology*; D014714:Vertebrates / Q000502:physiology*