Comparing the Influence of Different-Order HIFU Harmonic Superposition on Focal Temperature of Biological Tissue

Document Type : Original Paper

Authors

1 School of Information Science and Engineering, Changsha Normal University, Changsha 410100, China

2 School of Information Science and Engineering, Xinyu University, Xinyu, 338004, China

10.22038/ijmp.2025.86253.2514

Abstract

Introduction: While high-intensity focused ultrasound (HIFU) is widely used for non-invasive tumor ablation, current models fail to account for the cumulative energy contributions of nonlinear harmonics (up to the 256th order), significantly limiting treatment precision. This study quantifies the role of harmonic superposition (1st+2nd+…+256th order) in regulating HIFU-induced focal temperature and establishes an optimized harmonic combination to enhance clinical parameter design.   
Material and Methods: A coupled acousto-thermal model, validated against MRI thermometry, was developed by solving the Westervelt equation and Pennes bioheat equation to simulate nonlinear acoustic propagation and transient temperature fields in ex vivo porcine muscle under HIFU irradiation. 
Results: The 1st+2nd+...+128th harmonic superposition model achieved <2.2% error in focal temperature prediction across all tested power levels (80–200 W), with errors of 1.6% at 80 W (48.18 °C simulated vs. 47.96 °C measured), 1.1% at 140 W (66.0 °C vs. 65.31 °C), 1.8% at 160 W (77.78 °C vs. 76.38 °C), and 2.2% at 200 W (82.25 °C vs. 84.11 °C). Mid-order harmonics (2nd–64th) contributed 75–80% of energy deposition, while high-order harmonics (>128th, e.g., 256th at 276.48 MHz) exhibited severe attenuation (135× higher than the fundamental wave). The linear propagation model (fundamental frequency only) underestimated temperatures by 4.8-23.9%, highlighting the necessity of nonlinear harmonic inclusion. 
Conclusion: This work establishes a harmonically optimized framework for HIFU treatment planning, addressing a critical gap in nonlinear acoustic modeling and enabling safer, precision thermal therapy.

Keywords

Main Subjects

References

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Iranian Journal of Medical Physics
Volume 22, Issue 4 - Serial Number 4
July and August 2025
Pages 279-289

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History

  • Receive Date: 21 February 2025
  • Revise Date: 08 August 2025
  • Accept Date: 10 November 2025

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