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Mathematical modelling of ciliary movement mechanism

Krivovichev G.V., Tregoubov V.P.

Acta of Bioengineering and Biomechanics

2011

Vol. 13, no. 2

73-81

The main purpose of the paper was to present a new approach to the mathematical modelling of ciliary movements. This approach is based on the solution of the inverse problem of the dynamics, which is described by Lagrange's equations for the system of successively hinged rigid rods. In this case, as is well known, the generalized forces may be found as the time functions. It is proposed to represent these functions by the functions of generalized coordinates and velocities and also of the model parameters, whose values are determined as a solution of the parametric optimization problem. Besides, a special algorithm of ciliary movement control was elaborated. This algorithm is based on the hypothesis of variation of the equilibrium positions for cilia during one cycle of beating. The numerical results are in a good agreement with the cilia movements observed in Paramecium multimicronucleatum.