Simulation studies of time reversal‐based protoacoustic reconstruction for range and dose verification in proton therapy

Abstract

Purpose In vivo range verification in proton therapy is a critical step to help minimize range and dose uncertainty. We propose to employ a time reversal (TR)‐based approach using proton‐induced acoustics (protoacoustics) to reconstruct pressure/dose distribution in heterogeneous tissues. Methods The dose distribution of mono‐energetic proton pencil beam in a CT‐based patient phantom was calculated by Monte Carlo simulation. K‐wave toolbox was used to investigate protoacoustic pressurization, propagation and reconstruction in 2D. To address the tissue heterogeneity effect, a number of physical parameters, including mass density (ρ), speed of sound (c), volumetric thermal expansion coefficient (αV), isobaric specific heat capacity (Cp) and attenuation power law prefactor (α0), were empirically converted from CT number. The performance was evaluated using two figures of merit: mean square error (MSE) of pressure profiles and Bragg peak localization error (ΔBP). The impact of six parameters of the TR inversion was examined, including number of sensors, sampling duration, sampling timestep, spill time, noise level and number of iterations. Results The quantitative accuracy of TR reconstruction and its dependency on the selected parameters is presented. Under optimum conditions, the positioning accuracy of the Bragg peak can be controlled below 1 mm. For instance, MSE is 0.0123 and ΔBP is 0.59 mm under the following conditions (32 sensors, sampling duration: 600 µs, sampling timestep: 40 ns, spill time: 1 µs, no noise). Conclusions The feasibility of TR‐based protoacoustic reconstruction in 2D for proton range verification was first demonstrated. The approach is not only applicable to pencil beam, but also has potential to be extended to passive scattering systems.

Feasibility study of 3D time‐reversal reconstruction of proton‐induced acoustic signals for dose verification in the head and the liver: A simulation study

“…For the head case, MSE decreases monotonically from 0.034 to 0.022 between 120 and 160 μs, while Δ BP drops rapidly from 31.9 mm at 120 μs to 3 mm at 130 μs. For the liver case, both MSE and Δ BP drop rapidly in the range between 50 and 100 μs, and a diminishing return is found beyond 100 μs, a pattern consistent with our previous finding in 2D 15 …”

“…The phantom consists of 150 × 90 × 590 voxels with a voxel size of 3 × 3 × 3 mm 3 . To take tissue heterogeneity into account, a number of physical parameters (i.e., mass density, speed of sound, isobaric specific heat capacity, attenuation power prefactor, and volumetric thermal expansion) in each voxel were converted based on the CT number through empirical fitting functions 15 …”

“…It can be mitigated by introducing different computational grids (i.e., changing the voxel size) in the forward and inverse steps 18,22 . The physical parameters at each voxel in both original volume size and larger volume size were derived from the corresponding CT number 15 . A timestep of 10 ns was selected to record acoustic signals, while a coarser temporal resolution was modeled through downsampling the recorded signals corresponding to various timesteps.…”

“…Motivated by these previous studies, our group attempted to address the challenge of protoacoustic reconstruction for range and dose verification in heterogeneous tissues using two alternative approaches. The first approach is time‐reversal (TR) reconstruction 15 . A TR reconstruction algorithm consists of two steps: (1) forward propagation, in which an external source excites the medium and the resulting acoustic waves are recorded, and (2) back propagation, in which the detected waveform signals are reversed in the time domain and back‐propagated in order to achieve one goal, that is, waveform signals focusing (i.e., constructive interference) at the original source location.…”

“…The results of two‐dimensional (2D) TR study have been reported in our previous work, 15 which comprehensively examined the impact of six parameters, including the number of sensors, sampling duration, sampling timestep, spill time, noise level, and number of iterations. To move a step closer towards practical applications, this paper extends the TR approach from 2D to 3D.…”