Influence of temperature-dependent thermal parameters on temperature elevation of tissue exposed to high-intensity focused ultrasound: numerical simulation

Parameter estimation in high-intensity focused ultrasound therapy

Hyperthermia using High-Intensity Focused Ultrasound (HIFU) is an acoustic therapy for cancer treatment. This technique consists of an increase in the temperature field of the tumor to achieve coagulative necrosis and immediate cell death. Therefore, for having a successful treatment, the physical problem requires to know several properties due to the high variability from individual to individual, or even for the same individual under different physiological conditions. This article presents a numerical simulation of hyperthermia therapy for cancer treatment using HIFU, as well as the estimation of parameters that influence the physical problem. Two mathematical models were considered to solve the forward problem. The acoustic model based on acoustic pressure performs a frequency-domain study, and the bioheat transfer model a time-dependent study. These models were solved using Comsol Multiphysics® software in a 2D-axisymmetric rectangular domain to determine the temperature field. Parameter estimation was coded in Matlab Mathworks® environment using a Bayesian approach. The Markov Chain Monte Carlo method by the Metropolis-Hastings algorithm was implemented, and the simulated temperature measurements were considered. Results suggest that specific HIFU therapy can be performed for each patient by estimating appropriate parameters for cancer treatment and provides the possibility to define procedures before and during the treatment.

Influence of temperature-dependent acoustic and thermal parameters and nonlinear harmonics on the prediction of thermal lesion under HIFU ablation

According to the traditional method of high intensity focused ultrasound (HIFU) treatment, the acoustic and thermal characteristic parameters of constant temperature (room temperature or body temperature) are used to predict thermal lesion. Based on the nonlinear spherical beam equation (SBE) and Pennes bio-heat transfer equation, and a new acoustic-thermal coupled model is proposed. The constant and temperature-dependent acoustic and thermal characteristic parameters are used to predict thermal lesion, and the predicted lesion area are compared with each other. Moreover, the relationship between harmonic amplitude ratio (P₂/P₁) and thermal lesion is studied. Combined with the known experimental data of acoustic and thermal characteristic parameters of biological tissue and data fitting method, the relationship between acoustic and thermal characteristic parameters and temperature is obtained; and the thermal lesion simulation calculation is carried out by using the acoustic and thermal characteristic parameters under constant temperature and temperature- dependent acoustic and thermal characteristic parameters, respectively. The simulation results show that under the same irradiation condition, the thermal lesion predicted by temperature-dependent acoustic and thermal characteristic parameters is larger than that predicted by traditional method, and the thermal lesion increases with the decrease of harmonic amplitude ratio.

Experimental validation of acoustic and thermal modeling in heterogeneous phantoms using the hybrid angular spectrum method

PURPOSE

The aim was to quantitatively validate the hybrid angular spectrum (HAS) algorithm, a rapid wave propagation technique for heterogeneous media, with both pressure and temperature measurements.

METHODS

Heterogeneous tissue-mimicking phantoms were used to evaluate the accuracy of the HAS acoustic modeling algorithm in predicting pressure and thermal patterns. Acoustic properties of the phantom components were measured by a through-transmission technique while thermal properties were measured with a commercial probe. Numerical models of each heterogeneous phantom were segmented from 3D MR images. Cylindrical phantoms 30-mm thick were placed in the pre-focal field of a focused ultrasound beam and 2D pressure measurements obtained with a scanning hydrophone. Peak pressure, full width at half maximum, and normalized root mean squared difference (RMSDn) between the measured and simulated patterns were compared. MR-guided sonications were performed on 150-mm phantoms to obtain MR temperature measurements. Using HAS-predicted power density patterns, temperature simulations were performed. Experimental and simulated temperature patterns were directly compared using peak and mean temperature plots, RMSDn metrics, and accuracy of heating localization.

RESULTS

The average difference between simulated and hydrophone-measured peak pressures was 9.0% with an RMSDn of 11.4%. Comparison of the experimental MRI-derived and simulated temperature patterns showed RMSDn values of 10.2% and 11.1% and distance differences between the centers of thermal mass of 2.0 and 2.2 mm.

CONCLUSIONS

These results show that the computationally rapid hybrid angular spectrum method can predict pressure and temperature patterns in heterogeneous models, including uncertainties in property values and other parameters, to within approximately 10%.

Temperature Dependence of Tissue Thermal Parameters Should Be Considered in the Thermal Lesion Prediction in High-Intensity Focused Ultrasound Surgery

This study considers the temperature-dependent thermal parameters (specific heat capacity, thermal diffusivity and thermal conductivity) used when predicting the temperature rise of tissue exposed to high-intensity focused ultrasound (HIFU). Numerical analysis was performed using the Khokhlov-Zabolotskaya-Kuznetsov equation coupled with a bioheat transfer function. The thermal parameters were set as the functions of temperature using experimental data. The results revealed that, for liver tissue exposed to HIFU with a focal intensity of 3000 W/cm² for 10 s, the predicted focal temperature rise was 23% lower and the thermal lesion area 41% smaller than those predicted without considering the temperature dependence. The prediction was validated by experimental observations on thermal lesions visualized in a tissue-mimicking phantom. The present results suggest that temperature-dependent thermal parameters should be considered in the prediction of HIFU-induced temperature rise to avoid lowering ultrasonic output settings for HIFU surgery. The aim of the present study was to investigate how significantly the temperature dependence of the thermal parameters affects the thermal dose imposed on the tissue by a typical clinical HIFU device. A numerical simulation was performed using a thermo-acoustic algorithm coupling the non-linear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation (Meaney et al. 1998; Filonenko and Khokhlova 2001) and a bio-heat transfer (BHT) equation (Pennes 1948). Thermal parameters of liver tissue were modeled in the present study as functions of temperature and were incorporated into the BHT equation to compensate for the variations in thermal parameters with temperature. Experimental validation was achieved by comparing the predictions with the thermal lesions formed in the tissue-mimicking phantoms.

A closer look at ultrasonic attenuation and heating in a tissue-mimicking material

A well-characterized ultrasound tissue-mimicking material (TMM) can be important in determining the acoustic output and temperature rise from high intensity therapeutic ultrasound (HITU) devices and also in validating computer simulation models. A HITU TMM previously developed and characterized in our laboratory has been used in our acoustic and temperature measurements as well as modeled in our HITU simulation program. A discrepancy between thermal measurement and simulation, though, led us to further investigate the TMM properties. We found that the 2-parameter analytic fit commonly used to represent the attenuation of the TMM in the computer modeling was not adequate over the entire frequency range of interest, 1 MHz to 8 MHz in this study, indicating that we and others may have not been characterizing TMMs, and possibly tissue, optimally. By comparing measurements and simulations, we found that a 3-parameter analytic fit for attenuation gave a more accurate value for attenuation at 1 MHz and 2 MHz, and using that fit the temperature rise measurements in the TMM that agreed more closely with the simulation results.

The Influence of Dynamic Tissue Properties on HIFU Hyperthermia: A Numerical Simulation Study

Accurate temperature and thermal dose prediction are crucial to high-intensity focused ultrasound (HIFU) hyperthermia, which has been used successfully for the non-invasive treatment of solid tumors. For the conventional method of prediction, the tissue properties are usually set as constants. However, the temperature rise induced by HIFU irradiation in tissues will cause changes in the tissue properties that in turn affect the acoustic and temperature field. Herein, an acoustic–thermal coupling model is presented to predict the temperature and thermal damage zone in tissue in terms of the Westervelt equation and Pennes bioheat transfer equation, and the individual influence of each dynamic tissue property and the joint effect of all of the dynamic tissue properties are studied. The simulation results show that the dynamic acoustic absorption coefficient has the greatest influence on the temperature and thermal damage zone among all of the individual dynamic tissue properties. In addition, compared with the conventional method, the dynamic acoustic absorption coefficient leads to a higher focal temperature and a larger thermal damage zone; on the contrary, the dynamic blood perfusion leads to a lower focal temperature and a smaller thermal damage zone. Moreover, the conventional method underestimates the focal temperature and the thermal damage zone, compared with the simulation that was performed using all of the dynamic tissue properties. The results of this study will be helpful to guide the doctors to develop more accurate clinical protocols for HIFU treatment planning.

Validation of hybrid angular spectrum acoustic and thermal modelling in phantoms

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.