Analytical solution of a microrobot-blood vessel interaction model.

This study develops a dynamics model of a microrobot vibrating in a blood vessel aiming to detect potential cancer metastasis. We derive an analytical solution for microrobot's motion, considering interactions with the vessel walls modelled by a linear spring-dashpot and a constant damping value for blood viscosity. The model facilitates instantaneous state transitions of the microrobot, such as contact with the vessel wall and free motion within the fluid. Amplitudes and phase angles from the transient solutions of dynamics model of the microrobot are solved at arbitrary moments, providing insights into its transient dynamics. The analytical solution of the proposed system is validated by experimental data, serving as a benchmark to examine the influence of pertinent parameters on microrobot's dynamic response. It is found that the contact force transmitted to the vessel wall, assessed by system's transmissibility function dependent on damping and frequency ratios, decreases with increasing damping ratio and intensifies when the frequency ratio is below $\sqrt{2}$ . At the frequency ratio is equal to 1, resonance phenomenon is dominated by the magnification factor linked to the damping ratio, increasing the amplitude of resonance as damping decreases. Finally, different sets of system parameters, including excitation frequency and magnitude, fluid damping, vessel wall's stiffness and damping, reveal multi-periodic motions and fake collision of the microrobot with the vessel wall. Simulation results imply that these phenomena are minimally affected by vessel wall's stiffness but are significantly influenced by other parameters, such as fluid damping coefficient and damping coefficient of the blood vessel wall. This research provides a robust theoretical foundation for developing control strategies for microrobots aimed at detecting cancer metastasis.