Self-Calibration of Central Aperture Spherical Transducer for Accurate Acoustic Power Measurement in HIFU Treatment

In clinical practice, monitoring with ultrasound imaging is often necessary during High Intensity Focused Ultrasound (HIFU) treatment. The central aperture spherical transducer, also known as the spherical annular transducer, is a key component in ultrasound ablation therapy and is used for imaging. The radiation acoustic power of the transducer is a critical parameter that affects treatment efficacy and patient safety, and therefore, requires strict control.

The Radiation Force Balance (RFB) method is the preferred method for measuring acoustic power according to the International Electrotechnical Commission (IEC) guidelines. However, it has only been applicable for measuring flat acoustic power until the study by Beissner in 1987, which established the relationship between focused sound field acoustic power and radiation force. Shouwend, based on Beissner's work, derived the formula for calculating the acoustic power of the central aperture spherical transducer in 1998. This method has since been adopted by several national and international standards. While the RFB method is simple and easy to use, it only measures the average acoustic power over a period of time and is not sensitive enough to detect sudden bursts of sound signals that may occur during HIFU treatment. Additionally, the RFB method is susceptible to measurement inaccuracies due to the absorption of high-intensity sound energy by the target, which can cause permanent thermal and mechanical damage in prolonged high-power measurements.

The Hydrophone method can provide comprehensive information on the sound field distribution, including sound intensity and pressure, while scanning the sound field during the HIFU treatment. However, the high energy in the focal area of the HIFU sound field can easily damage the hydrophone, making it less applicable in the measurement of HIFU acoustic power. Moreover, both the RFB and Hydrophone methods require expensive specialized equipment and specific measurement environments.

To achieve a more precise and simple measurement device with minimal measurement error, it is necessary to study the electro-acoustic characteristics of the transducer. The Self-Calibration method was first proposed by Cartensen in 1947 and has been widely used for transducer calibration in marine acoustics. With the advancement of sound field theory, the Self-Calibration technique has been applied to both flat and spherical transducers, and can be used to measure electro-acoustic parameters such as sound power. Based on this, an international standard for the Self-Calibration of the spherical transducer was established (IEC TS 62903:2018), which has since been further applied to the measurement of electro-acoustic parameters of cylindrical focusing transducers.

This paper systematically studies the electro-acoustic characteristics of the central aperture spherical transducer based on the reciprocity principle in the spherical wave sound field. We provide a calculation method and data charts for the diffraction correction coefficient and average reflection coefficient, thereby expanding the Self-Calibration theory of the transducer. Based on this, we establish a Self-Calibration method for the central aperture spherical transducer using a flat reflector. The results show that the Self-Calibration method is more stable than the RFB method and less susceptible to environmental interference, making it more suitable for measuring acoustic power at the mW level. Our method can measure five electro-acoustic parameters, including output sound power, radiation conductance, electro-acoustic conversion efficiency, free-field current response, and free-field voltage sensitivity. The feasibility and effectiveness of our method are verified through experiments using * transducers.