Analytical Model of Prompt Gamma Timing for Spatiotemporal Emission Reconstruction in Particle Therapy

TL;DR

An analytical system model is proposed to speed up recalculations for new beam positions and to avoid statistical noise in the model, and the model calculation time was reduced by 1500 times, enabling many new studies for PGT-based systems.

Abstract

Particle therapy relies on up-to-date knowledge of the stopping power of the patient tissues to deliver the prescribed dose distribution. The stopping power describes the average particle motion, which is encoded in the distribution of prompt-gamma photon emissions in time and space. We reconstruct the spatiotemporal emission distribution from multi-detector Prompt Gamma Timing (PGT) data. Solving this inverse problem relies on an accurate model of the prompt-gamma transport and detection including explicitly the dependencies on the time of emission and detection. Our previous work relied on Monte-Carlo (MC) based system models. The tradeoff between computational resources and statistical noise in the system model prohibits studies of new detector arrangements and beam scanning scenarios. Therefore, we propose here an analytical system model to speed up recalculations for new beam positions and to avoid statistical noise in the model. We evaluated the model for the MERLINO multi-detector-PGT prototype. Comparisons between the analytical model and a MC-based reference showed excellent agreement for single-detector setups. When several detectors were placed close together and partially obstructed each other, intercrystal scatter led to differences of up to 10 % between the analytical and MC-based model. Nevertheless, when evaluating the performance in reconstructing the spatiotemporal distribution and estimating the stopping power, no significant difference between the models was observed. Hence, the procedure proved robust against the small inaccuracies of the model for the tested scenarios. The model calculation time was reduced by 1500 times, now enabling many new studies for PGT-based systems.

Figures (7)

• Figure 1: The multi-detector *pgt measurement principle: a beam particle passes a reference plane (black line) at time 0.0. After time $t_\mathrm{P}$ the particle causes a pg emission at position $\mathrm{P}$. The photon takes time $t_\gamma$ to travel from $\mathrm{P}$ to a detector (green) outside the irradiated target (orange), where it is detected at time ${t_D=t_\mathrm{P}+t_\gamma}$.
• Figure 2: (a) 2D representation of a detector (box) and three emission directions (dashed lines) with detector entry points $\mathrm{Q}_\text{i}$, $\mathrm{Q}_\text{ii}$, and $\mathrm{Q}_\text{iii}$ and path lengths in the detector before ($L_1$, red) and within detection interval $[l_1, l_2]$ ($L_2$, blue). (b) Sections of attenuation within the detector before detection time interval $n$ ($L_1$, red) and detection ($L_2$, blue) for all relevant combinations of the start ($>$) and end (•) of the detection time interval relative to the detector volume (green).
• Figure 3: (a) Time-difference spectrum between last and first energy deposition of a 4.4MeV-photon in the *mc simulation. (b) Number of energy depositions over path length in LaBr$_3$ in a *mc-simulation. The path length is calculated either using an energy-weighted centroid (blue) or the time after entry and speed of light (red). The fit of the time-based calculation to an exponential function is shown in green.
• Figure 4: (a) Element-wise histogram of ${h_{d,n,j,p}^\text{\acs*{mcsm}}-h_{d,n,j,p}^\text{\acs*{asm}}}$ relative to $\max_{n,j,p}h_{d,n,j,p}^\text{\acs*{mcsm}}$ in detector $d$ with energy threshold 1MeV. (b) Maximum positive (red) and negative (blue) elementwise differences of ${h_{d,n,j,p}^\text{\acs*{mcsm}}-h_{d,n,j,p}^\text{\acs*{asm}}}$ for each detector in the xz-plane. Inset: Maximum difference depending on the emission positions for detector position 73.
• Figure 5: System matrix elements without time resolution for detector position 73 and emission positions (a) ${z=-20cm}$, and (b) ${z=0cm}$. Red: *asm with (solid line) and without (dash dot) attenuation of neighboring detectors; blue: *mcsm simulated with only detector 73 (dots) or all 110 detectors (dash dash dot), and green: *mcsm with 1MeV threshold on the detected energy).