Table 3.3: Quantitative comparisons of CW-BOS pressure maps with the transducer rotated or the camera translated.
Rotations Translations
0◦ 15◦ 30◦ 0 cm -2.5 cm 2.5 cm RMS projected pressure amplitude
in the focus (Pa·m) 6036 6292 6266 4419 4587 4378
% error in the focus 4.2% 3.8% 3.8% 0.9%
FWHM1(xaxis, mm) 1.5 1.7 1.4 1.5 1.6 1.6
FWHM1(zaxis, mm) 11.5 12.1 11.2 12.2 12.7 14.0
difference in the peak projected pressure is 141 Pa·m (6.0% of the hydrophone-measured peak amplitude).
Figure 3.12c further shows the aberrator placed against the left half of the transducer to aberrate the pressure field in they-zplane, and Figure 3.12d shows measured beam maps with this configuration. The maps show similar features, with an RMSE of 380 Pa·m (19.3% of the hydrophone-measured peak amplitude at x = -0.1 mm, z = 5.1 mm). The difference in the peak RMS projected pressure is 236 Pa·m (11.7% of the hydrophone- measured peak amplitude).
important to note that the reconstruction network operates only on one spatial location at a time, and does not make assumptions about spatial smoothness or structure of the beam in the imaged 2D plane, yet it produced beam maps that closely matched optical hydrophone measurements. This way, the technique maintains gen- erality for important applications where beam structure would be difficult to predict, such as when mapping aberrated fields or when the beam rotates or moves, as were demonstrated here.
CW-BOS is an inexpensive (under $2000 USD) and rapid 2D FUS beam mapping tool based on a consumer-grade tablet and camera, with no moving parts or parts that can experience wear from the FUS beam. To make it portable, the tank could be sealed, the tablet and camera could be rigidly attached to it, and FUS could be coupled into it via a mylar membrane. The result would be a fully portable push-button beam mapping method, which could be set up and performed more easily and faster than QA tests such as MRI temperature measurements in a phantom, without requiring MRI scan time or an MRI-compatible FUS system.Bowl-shaped transducers could be coupled into the tank via a coupling bag. Our total CW-BOS scan times were 3-5 minutes, which was dominated by the time taken for data transfer from the camera to PC, and comprised less than 8 seconds of FUS-on time. We expect that with optimization, the total scan dura- tion could be reduced to less than 10 seconds; reconstruction in MATLAB and Python then took another 20 seconds which could be further optimized, and does not require a high-end computer. Overall, the method achieved an approximate 2000x speedup compared to the time required to obtain the same information (RMS projected pressure over a 3 x 1 cm2FOV with 0.425 x 0.425 mm2spatial resolution) using a 3D hydrophone scan. While linear hydrophone scans along the axial and focal plane dimensions may suffice for quality assurance, those scans are still slower and involve more delicate and less portable hardware than CW-BOS imaging, and require careful alignment with the ultrasound focus. Overall, the most likely applications for CW-BOS projected pressure mapping will be those that are not well-served by hydrophones and in which speed, simplicity, and low cost are of highest importance, such as measuring changes in overall transducer output and detecting beam aberrations.
There are several possible ways to improve or extend the proposed technique. One potential source of error is the assumed parallel ray geometry between the background pattern and the camera; it may be possible to generate more accurate training histograms using ray tracing and accounting for refraction at the air-glass and glass-water interfaces(Glassner, 1989; Barsky et al., 2003). The dominant noise source in our measurements is likely electronic noise in the camera’s detector, but this needs to be characterized and a propagation-of-error analysis should be done to understand noise in the final maps and how to best mitigate it. Another possible source of error would be a mismatch between the assumed and actual distance between the expected transducer focus and the background pattern. The reconstructions are trained using histograms calculated for a specific distance between the midpoint of the nonuniform index of refraction
field and the background pattern, which corresponded in our experimental setup to the distance between the expected focus and the background pattern. This is a parameter that could be optimized: Moving the beam closer to the background pattern would magnify the blurring patterns by a factor<1, which would enable a larger field-of-view at the cost of reduced sensitivity. Moving the beam farther from the background pattern would magnify the blurring patterns by a factor>1, which would increase sensitivity at the cost of reduced field-of-view. A larger convolutional neural network that operates on entire photos rather than individual segmented histograms may achieve improved accuracy by learning spatial relationships between blurring patterns and FUS beam features, and it could enable the use of a single, dense background pattern to reduce acquisition times. However, this would require a much larger training corpus to maintain generality, as well as more computation and memory, both for training and reconstruction. RMS projected pressure was used as the reconstructed quantity in this work since it is proportional to transducer output, but it may be possible to extend the method to also reconstruct peak positive and negative pressure, or even a full cycle of the projected pressure waveform at each spatial location, which would be needed to reconstruct 3D beam maps that contain the same information as 3D hydrophone scans. A 3D system would also require the optics and the transducer to be rotated with respect to each other. We have previously developed a qualitative backprojection-based 3D CW-BOS beam mapping system(Kremer et al., 2014, 2015), and will extend the proposed 2D quantitative method to 3D beam mapping in future work. Finally, in this work we trained the reconstruction network from acoustic simulations of transducers at the same frequencies as those used in the experiments, but with two different focal lengths and across a range of peak pressures. This approach resulted in RMS projected pressure reconstructions that closely matched hydrophone measurements, even when an aberrator was placed on the surface of the 1.16 MHz transducer. However, further research is needed to optimize the training data for different applications. For example, it may not be necessary to train for multiple focal lengths when the reconstruction network will be used with just one transducer, but care must be taken to maintain accuracy when the beam is disturbed by an aberration. For such an application it may be better to perform simulations of the same transducer, with different sub-elements on its surface virtually switched off to mimic aberrations. This process would ideally be informed by the types of aberrations (e.g., bones versus failed transducer elements, air bubbles in the beam path, or system calibration errors(McDannold and Hynynen, 2006)) that are most likely to be encountered for a given clinical or research application. If the reconstruction network will be used for just a small range of driving voltages, it may be possible to also reduce the range of simulated pressures. It may also not be necessary to train the network for each transducer frequency, or it may be possible to train a single network across a range of frequencies, without compromising reconstruction accuracy. At the same time, the storage required for each network was small (<1 MB), so many networks could be trained and stored, and the most appropriate one could be selected for each mapping
task. While the proposed CW-BOS hardware is not currently compatible with very large-aperture transcranial FUS transducers whose foci do not extend beyond their shell, it may be possible to map these systems by projecting background patterns onto the transducer surface. These and related questions will be addressed in future work.