Rapid full-wave phase aberration correction method for transcranial high-intensity focused ultrasound therapies
The phase correction method introduced here was able to rapidly calculate the phases required to correct for aberrations. In the case where the acoustic properties were fully known (for the 3D-printed phase aberrator model), the simulation-based correction was able to recover 95 % of the peak pressure achieved with hydrophone time reversal for targeting the geometric focus (as seen in Table 2). The relatively small difference between the simulation-based and hydrophone-based corrections for the aberrator model (95 % of the peak pressure was recovered) is most likely due primarily to registration errors. The simulations require close matching between the simulated and experimental placement of the aberrator with respect to the transducer elements. Misregistration will lead to poorer corrections. Figure 9 demonstrates this effect with translational errors in a single plane. Relatively small misregistrations can cause a significant decrease in the pressures seen. For example, simulations on the misregistration for the aberrator model show that a 1-mm translation of the model results in a 1.1–7.8 % loss in the peak pressure. Misregistration causes less of an effect for the skull model, which has smoother variations over the area through which the beam travels. Figure 10 further demonstrates this fact. When there is longer correlation distance for the phase lengths, one would expect misregistration in that direction to be less disruptive, a factor for phase correction. The correlation pattern for the skull flap shows longer correlation distances along the y-axis, which agrees with the data in Fig. 9 showing more tolerance to misregistration along that axis. Furthermore, the skull flap displays broader areas of correlation than the aberrator model, again agreeing with the results in Fig. 9 that show that the skull flap is more tolerant to misregistration overall. The 50 % contour in the results for the skull flap encompasses an area of 205 mm2 while the area for the aberrator model covers 24 mm2.
The hydrophone time-reversal method is performed experimentally with the aberrator in place and is not subject to the registration requirements. However, there may be slight errors in the location of the transducer element positions or the power output of each element. We estimate a misregistration error of less than 0.25 mm in each direction for these experiments. Data from the aberrator model, where the acoustic properties are homogeneous and known, agree with this: 95 % of the pressure is recovered, which also agrees with the simulated misregistration data presented in Fig. 9.
The 3D-printed aberrator model introduced here is a useful tool for assessing the ability of phase correction methods in the absence of acoustic parameter uncertainties. In the skull flap, where acoustic parameter uncertainties are present, simulation-based corrections were only able to recover 70 % of the pressure achieved using hydrophone time-reversal when targeting to the geometric focus (and 61 % when steering) compared to 95 % in the aberrator model. The aberrator model could be used to evaluate other possible methods of phase correction (ray tracing or FDTD time-reversal, for example) and to compare using different transducers or setups without needing to account for possible errors in acoustic modeling.
The difference between the percentage of pressure recovered using the simulation-based and hydrophone time-reversal methods of phase correction in the aberrator model (95 %) and the human skull flap (70 %) demonstrates the necessity for accurate acoustic parameter estimation of the skull. In transcranial HIFU, a large barrier to treatments is the necessary power required to achieve sufficient heating at the focal location without causing damage to unintended locations. Although the acoustic model of the skull flap used in this paper showed a 1.52-fold increase in peak power over uncorrected results, the hydrophone time-reversal phase correction demonstrated a 2.17-fold improvement. This suggests that there may be benefit in further research into acoustic parameter estimation of the skull. The aberrator model parameters were determined via a through-transmission test on a rectangular block of the same material used to 3D print the model, while the bone was modeled using the method presented in [27], which assigned values based on CT images. However, there is some evidence that the method presented in [27] may not be accurate in all cases as simulations using the method deviated in temperature by 24 % compared to the observed data, and the peak focal point distance between the simulations and experimental measurements was off by an average of 1.6 mm [28].
Other non-invasive methods have shown recovery of 14–58 % of peak intensity of hydrophone-based corrections using human skull flaps [29] compared to this method’s recovery of 49 % of the peak intensity (70 % of the peak pressure) at the geometric focus. However, caution must be used in directly comparing results for different transducer setups and skulls. Larger aperture size will usually cause the ultrasound to travel through a larger, more inhomogeneous region, yielding a greater need for phase correction. Additionally, a change in frequency of the transducer will change the precision required for phase correction. Unquantified variations in acoustic properties between human skulls also make direct comparisons difficult. Ideally, phase correction methods should be evaluated on the same system using an aberrator model similar to the one used here to evaluate effectiveness absent these disparities.
The method introduced here is more computationally efficient when compared to other methods presented in the literature. Simulations on a GPU for the skull flap modeled with clinically relevant resolution were performed in approximately 15 min. This computational time is for the full 3D volume for each individual element, allowing for corrections at multiple treatment locations. This computational time represents an eightfold improvement over a similar FDTD-based time-reversal simulation that was performed for only a single treatment location [19].
The method described has the benefit of simulating a full 3D volume. While we have used the phase information to demonstrate the possibility for multiple treatment locations, it would also be possible to use the amplitude information for predicting off-focus hot spots. For transcranial treatments, this could allow risk assessment of skin burns or heating in important brain structures. Combining the phase correction method with rapid simulations could allow for many clinically valuable insights, including determining which patients may not be suitable for transcranial HIFU treatments, treatment envelope evaluation, establishing limits for the maximum allowable power, or treatment planning.