Validation of hybrid angular spectrum acoustic and thermal modelling in phantoms

Abstract

In focused ultrasound (FUS) thermal ablation of diseased tissue, acoustic beam and thermal simulations enable treatment planning and optimization. In this study, a treatment-planning methodology that uses the hybrid angular spectrum (HAS) method and the Pennes' bioheat equation (PBHE) is experimentally validated in homogeneous tissue-mimicking phantoms. Simulated three-dimensional temperature profiles are compared to volumetric MR thermometry imaging (MRTI) of FUS sonications in the phantoms, whose acoustic and thermal properties are independently measured. Additionally, Monte Carlo (MC) uncertainty analysis is performed to quantify the effect of tissue property uncertainties on simulation results. The mean error between simulated and experimental spatiotemporal peak temperature rise was +0.33°C (+6.9%). Despite this error, the experimental temperature rise fell within the expected uncertainty of the simulation, as determined by the MC analysis. The average errors of the simulated transverse and longitudinal full width half maximum (FWHM) of the profiles were -1.9% and 7.5%, respectively. A linear regression and local sensitivity analysis revealed that simulated temperature amplitude is more sensitive to uncertainties in simulation inputs than in the profile width and shape. Acoustic power, acoustic attenuation and thermal conductivity had the greatest impact on peak temperature rise uncertainty; thermal conductivity and volumetric heat capacity had the greatest impact on FWHM uncertainty. This study validates that using the HAS and PBHE method can adequately predict temperature profiles from single sonications in homogeneous media. Further, it informs the need to accurately measure or predict patient-specific properties for improved treatment planning of ablative FUS surgeries.

Keywords: Treatment planning; high intensity focused ultrasound; modeling; thermal ablation; validation.

Figure 1.

Experimental set-up for FUS sonications in homogeneous gelatin phantoms with real-time volumetric MRTI as shown in an axial T1-weighted MR image. (A) 256-element phased-array transducer is positioned below the phantom cylinder, coupled with room-temperature degassed, deionised water. The geometric focus was placed 19.5 mm into the base of the phantom. The MRTI image slab was oriented perpendicular to the direction of FUS beam propagation, with slices centred at the geometric focus. The base of the MRTI volume was 7.5 mm above the bottom of the phantom.

Figure 2.

Average peak temperature rise achieved in the simulated (dashed, n 1) and experimental (solid, n = 3) temperature profiles, with experimental error bars representing one standard deviation. Results are plotted as a function of milk concentration of the gelatin phantoms for both FUS sonication powers: 6.3 W (blue, circles) and 7.9 W (red, triangles).

Figure 3.

Transverse (top) and longitudinal (bottom) profiles of mean experimental (circle, black) and simulated (square, blue) temperature data in 50% milk composition phantoms at 7.9 W. Depicted transverse profiles are along the short-axis of the transducer face. For longitudinal profiles, the transducer is located to the left of the profiles. Experimental and simulated profiles are compared at multiple times points during heating (t = 3.04 and t = 9.76 s), at the time of experimental peak temperature rise (t = 16.48 s), and during cooling (t = 23.20 s and t = 29.92 s). Simulated profile resolution is down-sampled to 0.5 mm isotropic to match experimental spatial resolution.

Figure 4.

Average percent error in spatio-temporal peak temperature rise (black), transverse (blue, dashed) FWHM, and longitudinal (red, dotted) FWHM for all phantoms and sonication powers is plotted throughout FUS heating and cooling (n = 8; error bars ± one standard deviation). The shaded regions represent time-points during which the average spatial SNR in the MRTI experimental data across all phantoms was ≤ 20.

Figure 5.

Temporal temperature curves of the peak temperature voxel from experimental (black, solid) and corresponding simulated (blue, dotted) temperatures for (a) 10%, (b) 30%, (c) 50%, and (d) 70% milk at 7.9 W sonication. Experimental error bars represent one standard deviation (n = 3). The shaded envelope represents one standard deviation of the MC analysis. The black dotted lines represent the high and low extremes of the MC analysis.

Figure 6.

Output uncertainty (U_j) and relative output uncertainty $\left(U_j{\text{σ}}_{{\text{X}}_{\mathrm{j}}}\right)$ for three different output metrics of the MC simulations. (a) U_j when each parameter is varied individually (as specified in the legend). (b) $U_j{\text{σ}}_{{\text{X}}_{\mathrm{j}}}$ comparing the relative impact of each parameter on U_j. Output uncertainties were averaged over all phantoms and power levels. Error bars represent one standard deviation.