Bragg Peak Localization with Piezoelectric Sensors for Proton Therapy Treatment

Abstract

A full chain simulation of the acoustic hadrontherapy monitoring for brain tumours is presented in this work. For the study, a proton beam of 100 MeV is considered. In the first stage, Geant4 is used to simulate the energy deposition and to study the behaviour of the Bragg peak. The energy deposition in the medium produces local heating that can be considered instantaneous with respect to the hydrodynamic time scale producing a sound pressure wave. The resulting thermoacoustic signal has been subsequently obtained by solving the thermoacoustic equation. The acoustic propagation has been simulated by FEM methods in the brain and the skull, where a set of piezoelectric sensors are placed. Last, the final received signals in the sensors have been processed in order to reconstruct the position of the thermal source and, thus, to determine the feasibility and accuracy of acoustic beam monitoring in hadrontherapy.

Keywords: FEM method; Monte Carlo simulations; hadrontherapy; monitoring Bragg peak; piezoelectric sensors.

Figure 1

(a) Position of the sensors in the skull where the acceleration produced by the propagation of the pressure pulse will be evaluated; (b) Simulated volume and pressure source.

Figure 2

(a) PIC 255 Ceramic disc measured; (b) Mesh geometry for the finite element method.

Figure 3

Optimization process diagram with input parameters for the thermoacoustic and piezoelectric parts. Time and energy for the first model and diameter and thickness for second one.

Figure 4

Energy deposition for a proton beam with Gauss profile ($\sigma$ = 1 mm) and 10⁶ protons. (a) layer bone interaction with different beam energies; (b) Interaction with the water phantom and with a 1 cm bone layer; (c) Deposition in a plane for 100 MeV, the upper figure shows the phantom water and the lower one shows the interaction with a layer of bone.

Figure 5

(a) Pressure received at 20 mm from the Bragg peak on the proton beam emission axis; (b) simulated pressure as a function of the distance.

Figure 6

(a) Propagation of a longitudinal wave to the point $P\left(r,t\right)$ where the speed of sound changes due to the change of medium; (b) general diagram of the incidence and transmission angle in the skull; (c) transmission angle for longitudinal and shear waves in terms of the incidence angle; (d) power transmission and reception coefficients of the cerebrospinal fluid-skull interface.

Figure 7

(a) Signal received on one of the sensors and pressure on the surface of the skull; (b) Propagation in a plane in the X, Y plane 53 μs after the energy deposition.

Figure 8

(a) Resonance and anti-resonance frequency for the first vibration mode in terms of the diameter and thickness simulated. The horizontal plane represents the central frequency of the pressure pulse of Figure 5a; (b) Ratio $k_1/k_2$ for the first two modes of vibration. The shaded zone represents the area with the best diameter and thickness ratio is optimizing in this region the sensitivity and frequency response of piezoelectric ceramics.

Figure 9

Pressure and terminal voltage for the optimized piezoelectric ceramic for a pressure signal in the emitted source as shown in Figure 5a. The propagated pressure on the sensor surface is 0.28 Pa as shown in Figure 7a.

Figure 10

Receiving Voltage Response (RVR) for the piezoelectric ceramic PIC255 with diameter 25 mm and thickness 2 mm measured in the laboratory (solid line) together with its simulation (dotted line), the green area represents the standard deviation in the measurements. The optimized geometry shows a significant increase in the low-frequency band around 110 kHz.