Author: Ye Chen, Koki Kasamatsu, Taeko Matsuura, Taichi Murakami 👨🔬
Affiliation: Hokkaido University, National Institutes for Quantum Science and Technology (QST) 🌍
Purpose: In proton therapy, CT-based estimation of the stopping power ratio (SPR) is a significant source of range uncertainty. Protoacoustics have been developed to estimate the range in vivo, but few studies have been performed to derive the patient-specific SPR from the observed waveforms.
Methods: As a first step, we developed a sensitivity matrix method using simulations on an abdominal phantom, assuming a liver tumor. Five or seven sensors were placed around the phantom surface to detect the time-of-arrival (TOA) of protoacoustic waves emitted by proton beams with gantry angles of 0 and 270 degrees. In each organ, the SPR and sound velocity (v) were assumed to be constant. The pre-treatment assumptions of SPR and v of the liver region were set to (SPRref, vref) = (1.0, 1540 m/s), and based on this, the values of TOAs (TOAref's) at each sensor and their partial derivatives in terms of SPR's and v's (sensitivity matrix) were calculated using k-WAVE. On the other hand, the observed TOAs differ from TOAref's due to the errors of both SPR and v. From the linear equation expressing the TOA deviation as a product of the sensitivity matrix and the SPR and v errors, the actual SPR and v were estimated using the least-squares method and compared with their true values, which were set to +3.5% and +3% of the pre-treatment assumptions, respectively.
Results: The errors in SPR were reduced from 3.5% to 1.3% (5 sensors) and 0.4% (7 sensors), respectively, while the errors in v were reduced from 3% to 0.1% (5 sensors) and 0.0% (7 sensors), respectively. The remaining errors were mainly due to the nonlinear terms not included in the sensitivity matrix.
Conclusion: The proposed method may allow for the evaluation of the patient-specific SPR. Further studies are needed to address the nonlinear terms.