An analysis of the origin of differences between measured and simulated fields produced by a 15-element ultrasound phased array

Measurement and simulation of steered acoustic fields generated by a multielement array for therapeutic ultrasound

Modelling of fields generated by therapeutic ultrasound arrays can be prone to errors arising from differences from nominal transducer parameters, and variations in relative outputs of array elements when driven under different conditions, especially when simulating steered fields. Here, the effect of element size, element positions, relative source pressure variations, and electrical crosstalk on the accuracy of modelling pressure fields generated by a 555 kHz 32-element ultrasonic array were investigated. For this transducer, errors in pressure amplitude and focal position were respectively reduced from 20% to 4% and 3.3 mm to 1.5 mm using crosstalk prediction, and experimentally determined positions.

Towards using a focussed phased array of millimetre length scale elements for ultrasound imaging

Sparse phased array ultrasound transducers with millimetre length scale elements have previously been proposed for generating hyperthermia but not for imaging. Numerical simulation with a pseudospectral solver was used to investigate: (a) how the position of the maximum pressure in the focal region changed with element diameter and frequency; (b) how the size and position of the focal region changed with focal distance under steering; and (c) the imaging performance of 15 element random arrays. These analyses were performed for both piston-like and non piston-like millimetre diameter elements since previous work has shown a shift in the distance to the maximum pressure in the focal region with the latter. The results for these elements were compared with elements where the diameter was  <λ/2. The distance from the array to the position of maximum pressure in the focal region diverged from the value with element diameter  <λ/2; values for piston-like elements increased positively whilst values for non piston-like elements increased negatively. With distances expressed in λ, no difference was found for arrays at 1 MHz and 2.5 MHz. For piston-like elements, but not for non piston-like elements, two peaks were found in the focal region which were in-line with the direction of propagation for a focus on the central axis but which rotated to become parallel with the direction of propagation when steering exceeded 20°. The size and position of the focal region under steering was similar for the non piston-like elements and elements with diameter  <λ/2. Little difference was found in image quality or the size of the point spread function (PSF) between images at 2.5 MHz with piston-like and non piston-like behaviour for steering angles less than 20° when compared with a linear array of similar size. These results suggest that imaging with random arrays of millimetre length scale elements is possible.

Model-based feasibility assessment and evaluation of prostate hyperthermia with a commercial MR-guided endorectal HIFU ablation array

PURPOSE

Feasibility of targeted and volumetric hyperthermia (40-45 °C) delivery to the prostate with a commercial MR-guided endorectal ultrasound phased array system, designed specifically for thermal ablation and approved for ablation trials (ExAblate 2100, Insightec Ltd.), was assessed through computer simulations and tissue-equivalent phantom experiments with the intention of fast clinical translation for targeted hyperthermia in conjunction with radiotherapy and chemotherapy.

METHODS

The simulations included a 3D finite element method based biothermal model, and acoustic field calculations for the ExAblate ERUS phased array (2.3 MHz, 2.3 × 4.0 cm(2), ∼1000 channels) using the rectangular radiator method. Array beamforming strategies were investigated to deliver protracted, continuous-wave hyperthermia to focal prostate cancer targets identified from representative patient cases. Constraints on power densities, sonication durations and switching speeds imposed by ExAblate hardware and software were incorporated in the models. Preliminary experiments included beamformed sonications in tissue mimicking phantoms under MR temperature monitoring at 3 T (GE Discovery MR750W).

RESULTS

Acoustic intensities considered during simulation were limited to ensure mild hyperthermia (Tmax < 45 °C) and fail-safe operation of the ExAblate array (spatial and time averaged acoustic intensity ISATA < 3.4 W/cm(2)). Tissue volumes with therapeutic temperature levels (T > 41 °C) were estimated. Numerical simulations indicated that T > 41 °C was calculated in 13-23 cm(3) volumes for sonications with planar or diverging beam patterns at 0.9-1.2 W/cm(2), in 4.5-5.8 cm(3) volumes for simultaneous multipoint focus beam patterns at ∼0.7 W/cm(2), and in ∼6.0 cm(3) for curvilinear (cylindrical) beam patterns at 0.75 W/cm(2). Focused heating patterns may be practical for treating focal disease in a single posterior quadrant of the prostate and diffused heating patterns may be useful for heating quadrants, hemigland volumes or even bilateral targets. Treatable volumes may be limited by pubic bone heating. Therapeutic temperatures were estimated for a range of physiological parameters, sonication duty cycles and rectal cooling. Hyperthermia specific phasing patterns were implemented on the ExAblate prostate array and continuous-wave sonications (∼0.88 W/cm(2), 15 min) were performed in tissue-mimicking material with real-time MR-based temperature imaging (PRFS imaging at 3.0 T). Shapes of heating patterns observed during experiments were consistent with simulations.

CONCLUSIONS

The ExAblate 2100, designed specifically for thermal ablation, can be controlled for delivering continuous hyperthermia in prostate while working within operational constraints.

The possible use of combined electrical impedance and ultrasound velocity measurements for the non-invasive measurement of temperature during mild hyperthermia

This paper explores the possibility of using combined measurements of electrical impedance and changes in ultrasound time of flight for determining deep body temperature during mild hyperthermia. Simultaneous electrical impedance spectra (1 kHz-1024 kHz) and ultrasound time-of-flight measurements were made on layered sheep liver and fat tissue samples as the temperature was increased from 30-50 °C. The change in propagation velocity for 100% fat and 100% liver samples was found to vary linearly with temperature and the temperature coefficient of the time-of-flight was shown to vary linearly with the % fat in the sample (0.009% °C-1%-1). Tetrapolar impedance measurements normalized to 8 kHz were shown to have a small sensitivity to temperature for both liver (0.001% °C-1 ≤ 45 °C) and fat (0.002% °C-1 ≤ 512 kHz) and the best linear correlation between the normalized impedance and the % fat in the sample was found at 256 kHz (gradient 0.026%-1, r2 = 0.65). A bootstrap analysis on 15 layered tissue samples evaluated using the normalized impedance at 256 kHz to determine the % fat in the sample and the temperature coefficient of the time of flight to determine the temperature. The results showed differences (including some large differences) between the predicted and measured temperatures and an error evaluation identified the possible origins of these.

Rapid transient pressure field computations in the nearfield of circular transducers using frequency-domain time-space decomposition

The fast nearfield method, when combined with time-space decomposition, is a rapid and accurate approach for calculating transient nearfield pressures generated by ultrasound transducers. However, the standard time-space decomposition approach is only applicable to certain analytical representations of the temporal transducer surface velocity that, when applied to the fast nearfield method, are expressed as a finite sum of products of separate temporal and spatial terms. To extend time-space decomposition such that accelerated transient field simulations are enabled in the nearfield for an arbitrary transducer surface velocity, a new transient simulation method, frequency-domain time-space decomposition (FDTSD), is derived. With this method, the temporal transducer surface velocity is transformed into the frequency domain, and then each complex-valued term is processed separately. Further improvements are achieved by spectral clipping, which reduces the number of terms and the computation time. Trade-offs between speed and accuracy are established for FDTSD calculations, and pressure fields obtained with the FDTSD method for a circular transducer are compared with those obtained with Field II and the impulse response method. The FDTSD approach, when combined with the fast nearfield method and spectral clipping, consistently achieves smaller errors in less time and requires less memory than Field II or the impulse response method.

Ultrasound array transmitter architecture with high timing resolution using embedded phase-locked loops

Coarse time quantization of delay profiles within ultrasound array systems can produce undesirable side lobes in the radiated beam profile. The severity of these side lobes is dependent upon the magnitude of phase quantization error--the deviation from ideal delay profiles to the achievable quantized case. This paper describes a method to improve interchannel delay accuracy without increasing system clock frequency by utilizing embedded phase-locked loop (PLL) components within commercial field-programmable gate arrays (FPGAs). Precise delays are achieved by shifting the relative phases of embedded PLL output clocks in 208-ps steps. The described architecture can achieve the necessary interelement timing resolution required for driving ultrasound arrays up to 50 MHz. The applicability of the proposed method at higher frequencies is demonstrated by extrapolating experimental results obtained using a 5-MHz array transducer. Results indicate an increase in transmit dynamic range (TDR) when using accurate delay profiles generated by the embedded-PLL method described, as opposed to using delay profiles quantized to the system clock.