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Area of Science:

  • Biomedical Engineering
  • Nonlinear Dynamics
  • Control Theory

Background:

  • Encapsulated microbubbles (EMBs) are crucial for biomedical applications like ultrasound imaging and drug delivery.
  • Controlling the nonlinear dynamics of EMBs is challenging but essential for precise applications.
  • Existing control methods struggle with the complex behavior of EMBs in biological environments.

Purpose of the Study:

  • To develop a data-driven method for controlling encapsulated microbubbles (EMBs) using acoustic fields.
  • To apply Koopman operator theory and Koopman linear quadratic regulator (KLQR) for precise EMB manipulation.
  • To investigate and overcome the unique dynamic challenges posed by EMBs, including their slow manifold.

Main Methods:

  • Utilized Koopman operator theory to linearize the nonlinear dynamics of EMBs.
  • Designed acoustic control signals using a Koopman linear quadratic regulator (KLQR) based on the Marmottant model.
  • Analyzed the impact of EMB encapsulation and slow manifold dynamics on control performance.

Main Results:

  • Demonstrated effective control of EMBs to achieve specific behaviors like subharmonic resonance amplification and quasiperiodic oscillations.
  • Identified that the slow manifold in EMB dynamics presents unique control challenges.
  • Showcased the necessity of carefully constructed Koopman eigenfunctions to capture relevant dynamics for robust control.

Conclusions:

  • Koopman operator theory provides a powerful framework for controlling nonlinear systems like EMBs.
  • The KLQR controller is effective in driving EMBs to target behaviors, despite dynamic complexities.
  • Addressing the slow manifold dynamics is critical for successful acoustic control of encapsulated microbubbles in biomedical applications.