Volume 22, Issue 1 (7-2025)
lmj 2025, 22(1): 37-43 |
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Darban Hagh S, Behnia S, Fathizadeh S. Stability Control of Lipid Microbubbles in Therapeutic Ultrasound: A Lyapunov Exponent Approach for Non-Newtonian Biological Media. lmj 2025; 22 (1) :37-43
URL: http://icml.ir/article-1-680-en.html
URL: http://icml.ir/article-1-680-en.html
Abstract: (29 Views)
Introduction: Lipid microbubbles are crucial in modern medicine, in modern medicine as ultrasound contrast agents and as carriers for drugs and genes. However, the dynamic stability of these bubbles under the influence of physical parameters such as acoustic pressure, ultrasound frequency, and ambient temperature remains a major challenge in clinical applications. This study investigates the dynamic stability of microbubbles in non-Newtonian environments using Lyapunov exponent analysis.
Methods: In this study, the Ferrara-Kane mathematical model was used to simulate the dynamics of lipid-coated microbubbles. The nonlinear differential equations governing the system were solved numerically, and the effects of key parameters—such as acoustic pressure (0.1 to 5.2 MPa), frequency (1 to 5 MHz) , and temperature (295 to 350 Kelvin)—on the system's chaotic behavior were analyzed. The Lyapunov exponent was used as a quantitative criterion to assess the system's stability.
Results: The results showed that increasing acoustic pressure and temperature leads to chaotic behavior (positive Lyapunov exponent), while higher frequencies (above 3 MHz) enhance system stability. Additionally, the critical bubble radius for the stability-to-chaos transition was found to be approximately 2 μm. These findings define optimal parameter ranges for controlled microbubble excitation in sonoporation applications.
Conclusion: This study demonstrates that dynamic stability analysis of lipid microbubbles using Lyapunov exponents provides a powerful tool for optimizing therapeutic parameters. These results can aid in designing more precise protocols for targeted drug delivery and improving the efficiency of ultrasound-based therapies.
Methods: In this study, the Ferrara-Kane mathematical model was used to simulate the dynamics of lipid-coated microbubbles. The nonlinear differential equations governing the system were solved numerically, and the effects of key parameters—such as acoustic pressure (0.1 to 5.2 MPa), frequency (1 to 5 MHz) , and temperature (295 to 350 Kelvin)—on the system's chaotic behavior were analyzed. The Lyapunov exponent was used as a quantitative criterion to assess the system's stability.
Results: The results showed that increasing acoustic pressure and temperature leads to chaotic behavior (positive Lyapunov exponent), while higher frequencies (above 3 MHz) enhance system stability. Additionally, the critical bubble radius for the stability-to-chaos transition was found to be approximately 2 μm. These findings define optimal parameter ranges for controlled microbubble excitation in sonoporation applications.
Conclusion: This study demonstrates that dynamic stability analysis of lipid microbubbles using Lyapunov exponents provides a powerful tool for optimizing therapeutic parameters. These results can aid in designing more precise protocols for targeted drug delivery and improving the efficiency of ultrasound-based therapies.
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Received: 2025/05/9 | Accepted: 2025/06/17 | Published: 2025/06/22
Received: 2025/05/9 | Accepted: 2025/06/17 | Published: 2025/06/22
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