Analytical estimation of ultrasound properties, thermal diffusivity, and perfusion using magnetic resonance-guided focused ultrasound temperature data

Magnetic resonance imaging of blood perfusion rate based on Helmholtz decomposition of heat flux

Objective.Thermal property (TP) maps of human tissues are useful for tumor treatment and diagnosis. In particular, the blood perfusion rate is significantly different for tumors and healthy tissues. Noninvasive techniques that reconstruct TPs from the temperature measured via magnetic resonance imaging (MRI) by solving an inverse bioheat transfer problem have been developed. A few conventional methods can reconstruct spatially varying TP distributions, but they have several limitations. First, most methods require the numerical Laplacian computation of the temperature, and hence they are sensitive to noise. In addition, some methods require the division of a region of interest (ROI) into sub-regions with homogeneous TPs using prior anatomical information, and they assume an unmeasurable initial temperature distribution. We propose a novel robust reconstruction method without the division of an ROI or the assumption of an initial temperature distribution.Approach.The proposed method estimates blood perfusion rate maps from relative temperature changes. This method avoids the computation of the Laplacian by using integral representations of the Helmholtz decomposition of the heat flux.Main Result.We compare the reconstruction results of the conventional and proposed methods using numerical simulations. The results indicate the robustness of the proposed method.Significance.This study suggests the feasibility of thermal property mapping with MRI using the robust proposed method.

Evaluation of acoustic-thermal simulations of in vivo magnetic resonance guided focused ultrasound ablative therapy

PURPOSE

To evaluate numerical simulations of focused ultrasound (FUS) with a rabbit model, comparing simulated heating characteristics with magnetic resonance temperature imaging (MRTI) data collected during in vivo treatment.

METHODS

A rabbit model was treated with FUS sonications in the biceps femoris with 3D MRTI collected. Acoustic and thermal properties of the rabbit muscle were determined experimentally. Numerical models of the rabbits were created, and tissue-type-specific properties were assigned. FUS simulations were performed using both the hybrid angular spectrum (HAS) method and k-Wave. Simulated power deposition patterns were converted to temperature maps using a Pennes' bioheat equation-based thermal solver. Agreement of pressure between the simulation techniques and temperature between the simulation and experimental heating was evaluated. Contributions of scattering and absorption attenuation were considered.

RESULTS

Simulated peak pressures derived using the HAS method exceeded the simulated peak pressures from k-Wave by 1.6 ± 2.7%. The location and FWHM of the peak pressure calculated from HAS and k-Wave showed good agreement. When muscle acoustic absorption value in the simulations was adjusted to approximately 54% of the measured attenuation, the average root-mean-squared error between simulated and experimental spatial-average temperature profiles was 0.046 ± 0.019 °C/W. Mean distance between simulated and experimental COTMs was 3.25 ± 1.37 mm. Transverse FWHMs of simulated sonications were smaller than in in vivo sonications. Longitudinal FWHMs were similar.

CONCLUSIONS

Presented results demonstrate agreement between HAS and k-Wave simulations and that FUS simulations can accurately predict focal position and heating for in vivo applications in soft tissue.

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%.

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.

3D-specific absorption rate estimation from high-intensity focused ultrasound sonications using the Green's function heat kernel

PURPOSE

To evaluate a numerical inverse Green's function method for deriving specific absorption rates (SARs) from high-intensity focused ultrasound (HIFU) sonications using tissue parameters (thermal conductivity, specific heat capacity, and mass density) and three-dimensional (3D) magnetic resonance imaging (MRI) temperature measurements.

METHODS

SAR estimates were evaluated using simulations and MR temperature measurements from HIFU sonications. For simulations, a "true" SAR was calculated using the hybrid angular spectrum method for ultrasound simulations. This "true" SAR was plugged into a Pennes bioheat transfer equation (PBTE) solver to provide simulated temperature maps, which were then used to calculate the SAR estimate using the presented method. Zero mean Gaussian noise, corresponding to temperature precisions between 0.1 and 2.0°C, was added to the temperature maps to simulate a variety of in vivo situations. Experimental MR temperature maps from HIFU sonications in a gelatin phantom monitored with a 3D segmented echo planar imaging MRI pulse sequence were also used. To determine the accuracy of the simulated and phantom data, we reconstructed temperature maps by plugging in the estimated SAR to the PBTE solver. In both simulations and phantom experiments, the presented method was compared to two previously published methods of determining SAR, a linear and an analytical method. The presented numerical method utilized the full 3D data simultaneously, while the two previously published methods work on a slice-by-slice basis.

RESULTS

In the absence of noise, SAR distribution estimates obtained from the simulated heating profiles match closely (within 10%) to the initial true SAR distribution. The resulting temperature distributions also match closely to the corresponding initial temperature distributions (<0.2°C RMSE). In the presence of temperature measurement noise, the SAR distributions have noise amplified by the inverse convolution process, while the resulting temperature distributions still match closely to the initial "true" temperature distributions. In general, temperature RMSE was observed to be approximately 20-30% higher than the level of the added noise. By contrast, the previously published linear method is less sensitive to noise, but significantly underpredicts the SAR. The analytic method is also less sensitive to noise and matches SAR in the central plane, but greatly underpredicts in the longitudinal direction. Similar observations are made from the phantom studies. The described numerical inverse Green's function method is very fast - at least two orders of magnitude faster than the compared methods.

CONCLUSION

The presented numerical inverse Green's function method is computationally fast and generates temperature maps with high accuracy. This is true despite generally overestimating the true SAR and amplifying the input noise.

Development and validation of a MRgHIFU non-invasive tissue acoustic property estimation technique

MR-guided high-intensity focussed ultrasound (MRgHIFU) non-invasive ablative surgeries have advanced into clinical trials for treating many pathologies and cancers. A remaining challenge of these surgeries is accurately planning and monitoring tissue heating in the face of patient-specific and dynamic acoustic properties of tissues. Currently, non-invasive measurements of acoustic properties have not been implemented in MRgHIFU treatment planning and monitoring procedures. This methods-driven study presents a technique using MR temperature imaging (MRTI) during low-temperature HIFU sonications to non-invasively estimate sample-specific acoustic absorption and speed of sound values in tissue-mimicking phantoms. Using measured thermal properties, specific absorption rate (SAR) patterns are calculated from the MRTI data and compared to simulated SAR patterns iteratively generated via the Hybrid Angular Spectrum (HAS) method. Once the error between the simulated and measured patterns is minimised, the estimated acoustic property values are compared to the true phantom values obtained via an independent technique. The estimated values are then used to simulate temperature profiles in the phantoms, and compared to experimental temperature profiles. This study demonstrates that trends in acoustic absorption and speed of sound can be non-invasively estimated with average errors of 21% and 1%, respectively. Additionally, temperature predictions using the estimated properties on average match within 1.2 °C of the experimental peak temperature rises in the phantoms. The positive results achieved in tissue-mimicking phantoms presented in this study indicate that this technique may be extended to in vivo applications, improving HIFU sonication temperature rise predictions and treatment assessment.

Sensitivity of tissue properties derived from MRgFUS temperature data to input errors and data inclusion criteria: ex vivo study in porcine muscle

This study evaluates the sensitivity of two magnetic resonance-guided focused ultrasound (MRgFUS) thermal property estimation methods to errors in required inputs and different data inclusion criteria. Using ex vivo pork muscle MRgFUS data, sensitivities to required inputs are determined by introducing errors to ultrasound beam locations (r error  =  -2 to 2 mm) and time vectors (t error  =  -2.2 to 2.2 s). In addition, the sensitivity to user-defined data inclusion criteria is evaluated by choosing different spatial (r fit  =  1-10 mm) and temporal (t fit  =  8.8-61.6 s) regions for fitting. Beam location errors resulted in up to 50% change in property estimates with local minima occurring at r error  =  0 and estimate errors less than 10% when r error  <  0.5 mm. Errors in the time vector led to property estimate errors up to 40% and without local minimum, indicating the need to trigger ultrasound sonications with the MR image acquisition. Regarding the selection of data inclusion criteria, property estimates reached stable values (less than 5% change) when r fit  >  2.5  ×  FWHM, and were most accurate with the least variability for longer t fit. Guidelines provided by this study highlight the importance of identifying required inputs and choosing appropriate data inclusion criteria for robust and accurate thermal property estimation. Applying these guidelines will prevent the introduction of biases and avoidable errors when utilizing these property estimation techniques for MRgFUS thermal modeling applications.