Simulation of controlled motion of a spherical magnetically active object in an elastic channel

Purpose of reseach. Mathematical modeling of the dynamics of controlled motion of a spherical magnetically active object in a curved channel by means of an external magnetic field created by a movable permanent magnet Tasks. Development of a system of differential equations describing the controlled motion of a magnetically active object in a curved elastic channel. Development of algorithms for localization of a magnetically active object inside a channel, calculation of the normal and magnitude of deformation during contact interaction. Setting up computational experiments in order to determine the nature of the movement of a magnetically active object in a curved channel and obtain the maximum values of the system parameters that ensure the controllability of the microrobot due to the movement of a permanent magnet. Methods. When modeling the motion of a magnetically active microrobot inside a biologically inspired curved channel, a system of differential equations and equations for an external inhomogeneous magnetic field is used. The model takes into account magnetic forces, environmental resistance forces, inertia forces, and gravity. Numerical integration methods are used to solve the equations of system dynamics. In the framework of this study, the model was implemented using the MATLAB. Results. The paper presents a mathematical model of the motion of a controlled magnetically active spherical object in a curved elastic channel simulating a blood vessel. The developed model takes into account hydrodynamic resistance, interaction with deformable channel walls and external magnetic influence. The numerical experiments performed demonstrate the possibility of predicting the trajectory of an object and reveal the limiting values of the system parameters at which controllability by a magnetically active microrobot is maintained. Conclusions. The movement of the particle along the sinusoidal channel is effectively ensured by the action of a permanent magnet. The resulting normal reaction of the canal wall does not exceed the values allowed for vascular structures, amounting to 5 mN at the peak and about 1 mN with prolonged exposure. Taking into account key physical and geometric parameters, such as the channel shape, magnetically active object properties, viscosity of the medium, friction forces and ponderomotor action, ensures the versatility of the model. The proposed methodology can be used to optimize magnetic navigation algorithms for endovascular embolization, targeted drug delivery, and other promising medical techniques.