Krivovichev Gerasim V, Tregoubov Vladimir P
Department of Modelling of the Electromechanical and Computer Systems, Saint-Petersburg State University, Russian Federation.
Acta Bioeng Biomech. 2011;13(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.
本文的主要目的是提出一种纤毛运动数学建模的新方法。这种方法基于动力学反问题的求解，该反问题由相继铰接的刚性杆系统的拉格朗日方程描述。在这种情况下，众所周知，广义力可以作为时间函数来确定。建议用广义坐标、速度以及模型参数的函数来表示这些函数，模型参数的值通过参数优化问题的解来确定。此外，还阐述了一种特殊的纤毛运动控制算法。该算法基于纤毛在一个摆动周期内平衡位置变化的假设。数值结果与在多核草履虫中观察到的纤毛运动非常吻合。
