Objective. Mapping of dose delivery in proton beam therapy can potentially be performed by analyzing thermoacoustic emissions measured by ultrasound arrays. Here, a method is derived and demonstrated for spatial mapping of thermoacoustic sources using numerical time reversal, simulating re-transmission of measured emissions into the medium. Approach. Spatial distributions of thermoacoustic emission sources are shown to be approximated by the analytic-signal form of the time-reversed acoustic field, evaluated at the time of the initial proton pulse. Given calibration of the array sensitivity and knowledge of tissue properties, this approach approximately reconstructs the acoustic source amplitude, equal to the product of the time derivative of the radiation dose rate, mass density, and Grüneisen parameter. This approach was implemented using two models for acoustic fields of the array elements, one modeling elements as line sources and the other as rectangular radiators. Thermoacoustic source reconstructions employed previously reported measurements of emissions from proton energy deposition in tissue-mimicking phantoms. For a phantom incorporating a bone layer, reconstructions accounted for the higher sound speed in bone. Dependence of reconstruction quality on array aperture size and signal-to-noise ratio was consistent with previous acoustic simulation studies. Main results. Thermoacoustic source distributions were successfully reconstructed from acoustic emissions measured by a linear ultrasound array. Spatial resolution of reconstructions was significantly improved in the azimuthal (array) direction by incorporation of array element diffraction. Source localization agreed well with Monte Carlo simulations of energy deposition, and was improved by incorporating effects of inhomogeneous sound speed. Significance. The presented numerical time reversal approach reconstructs thermoacoustic sources from proton beam radiation, based on straightforward processing of acoustic emissions measured by ultrasound arrays. This approach may be useful for ranging and dosimetry of clinical proton beams, if acoustic emissions of sufficient amplitude and bandwidth can be generated by therapeutic proton sources.

Previously we obtained range estimates with -0.2 ± 0.7 mm accuracy relative to Monte Carlo simulations for high dose spots (∼40 cGy) delivered to a gelatin phantom during delivery of a 6 Gy fraction. This improved device provides greater ease of use, positioning flexibility and receive sensitivity, which could enable range verification during pulsed delivery of a 2 Gy fraction.

Purpose: The purpose of this phantom study is to demonstrate that thermoacoustic range verification could be performed clinically. Thermoacoustic emissions generated in an anatomical multimodality imaging phantom during delivery of a clinical plan are compared to simulated emissions to estimate range shifts compared to the treatment plan. Methods: A single-field 12-layer proton pencil beam scanning (PBS) treatment plan created in Pinnacle prescribing 6 Gy/fraction was delivered by a superconducting synchrocyclotron to a triple modality (CT, MRI, and US) abdominal imaging phantom. Data was acquired by four acoustic receivers rigidly affixed to a linear ultrasound array. Receivers 1-2 were located distal to the treatment volume, whereas 3-4 were lateral. Receivers-room coordinates were computed relative to the ultrasound image plane after co-registration to the planning CT volume. For each prescribed beamlet, a set of thermoacoustic emissions corresponding to varied beam energies were computed. Simulated emissions were compared to measured emissions to estimate shifts of the Bragg peak. Results: Shifts were small for high-dose beamlets that stopped in soft tissue. Signals acquired by channels 1-2 yielded shifts of -0.2 +/- 0.7 mm relative to Monte Carlo simulations for high dose spots (similar to 40 cGy) in the second layer. Additionally, for beam energy >125 MeV, thermoacoustic emissions qualitatively tracked lateral motion of pristine beams in a layered gelatin phantom, and time shifts induced by changing phantom layers were self-consistent within nanoseconds. Conclusions: Acoustic receivers tuned to spectra of thermoacoustic emissions may enable range verification during proton therapy. (C) 2021 Elsevier B.V. All rights reserved.

The ability of extremely and very low frequency (ELF/VLF, 0-30 kHz) radio waves to penetrate conductive media is well established. Magnetic field penetration into a thin but highly conductive box using an ELF/VLF loop antenna transmitter is investigated. The work is relevant for electromagnetic shielding of ELF/VLF sensors, defect detection, inductive power transfer, and through container imaging. Analytical solutions are reviewed for related shielding problems, however, determining the penetration through a realistic shield geometry and finite sized near-field source requires a numerical approach. Surface integral equation (SIE) methods are well suited for shield modeling due to the low surface area to volume ratio of the shield. Method of moment techniques have been successfully applied to solving SIEs in the past, however, enforcing algorithm stability at low frequencies is known to require considerable effort. To alleviate the low-frequency concerns, a high-order locally corrected Nyström (LCN) scheme is utilized to solve an SIE based on an augmented Müller formulation of Maxwell's equations. To validate the LCN simulations, an experiment is conducted using a loop antenna inside a 1.2 m aluminum cube of 2.7 mm thickness with an external ELF/VLF loop transmitter. Experimental results are shown to match within 3 dB of the LCN code predictions.

This conference paper provides a cursory overview of thermoacoustic phenomena and attempts to highlight aspects that may be unfamiliar to the mathematical community or could benefit from more rigorous mathematical analysis. A new clinical application, thermoacoustic range verification during particle therapy, is presented. The goal is to ground expectations and generate further interest in thermoacoustics within the mathematical community.

The problem of magnetic field penetration into a conductive enclosure due to a low frequency loop transmitter is considered using simulations and experiment. The problem is relevant for electromagnetic shielding, through bunker communications, through conductor imaging, and several related problems. The primary difficulty lies in the multiple spatial scales due to the large wavelengths in the exterior and interior air regions in contrast to the short wavelengths in the highly conductive shell region. Although analytical solutions are possible for spherical shields and other specific geometries, determining the penetration through realistic conductive shields requires a numerical approach. Typical finite element methods can be employed to the shielding problem, however, appropriately meshing the enclosure and the air regions can be difficult when the skin-depth and wavelength in the shell are much smaller than the dimensions of the enclosure. To alleviate the multi-scale and near-field nature of the problem, a high-order locally corrected Nyström scheme is utilized to solve a surface integral equation based on an Augmented Müller formulation. The Nyström-SIE method is ideally suited for shield modeling due to the low surface area to volume ratio of the shield and the exponential convergence properties of the code. To validate the theoretical predictions from the model an experiment using two loop antennas inside and outside a 1.2 m aluminum cube of 3 mm thickness is conducted. It is shown that the experimental results agree with numerical predictions.

Radio frequencies at or below the VLF range (3-30 kHz) are uniquely capable of penetrating highly conductive materials. This can be exploited to detect objects hidden within metal containers. In this paper, we present observations of VLF scattering in such a situation, using VLF transmitters as signals of opportunity. Scattering is detected in the near field from an object inside an aluminum enclosure, and a gradiometric method is presented to differentiate the scattered signal from the plane wave that is incident onto the system.

Most scatterers of very low frequency electromagnetic waves can be treated as equivalent dipoles. When the incident field is a plane wave, polarization of the scattered field can be exploited. In this preliminary report we assume multiple receivers lie in a plane orthogonal to the incident electric field. Receivers are positioned around the circumference of a five-meter radius circle enclosing the region of interest (ROI). Receivers are in the near field and phase of the measurements varies slowly with position, particularly for highly conductive scatterers. From noise-free (simulated) data, coordinates of a single scatterer can be recovered from nulls of the measured data. Accuracy is limited by the density of the receiver positions around the ROI. When multiple scatterers are present, some coordinates can be approximated from amplitude measurements. Additive white noise reduces accuracy of single-scatterer localization by as much as 10% when SNR=10 dB.

PURPOSE:To demonstrate robustness of thermooacoustic range verification to acoustic heterogeneity and discrepancies between assumed and true propagation speed, i.e., soundspeed errors.METHODS:A beam sweeper was used to deliver 250 ns pulses that deposited 0.26 Gy of 16 MeV protons and 2.3 Gy of 60 MeV helium ions into water and oil targets, respectively. Thermoacoustic signals were detected by a 96-channel ultrasound array with a 1-4 MHz sensitivity band (-6 dB), bandpass filtered and backprojected to create thermoacoustic images in the plane of the ultrasound array. The same soundspeed and transducer array were used to estimate range and generate the ultrasound images onto which Bragg peak locations were overlaid. An air-gap phantom that displaced the Bragg peak by 6.5 mm demonstrated accuracy. Robustness to soundspeed errors was demonstrated in a waterbath as the assumed propagation speed scanner setting was altered by ± 5 % . Tissue-mimicking gelatin and a bone sample were introduced to demonstrate robustness to acoustic heterogeneity relative to ultrasound images of the underlying morphology.RESULTS:Single ion pulse measurements sufficed during the helium run, but signal averaging was required for protons. Range and entry point into the target were estimated from data collected by transducers placed at least 6 cm distal to the Bragg peak. When ultrasound images depicted the air-target interface where the beam enters, estimates of the entry point agreed with ultrasound images and range estimates agreed with Monte Carlo simulations to within 300 μm, even when thermoacoustic emissions traveled through a strongly scattering bone sample. Estimated Bragg peak locations were translated 6.5 mm by the air-gap phantom and correctly identified scenarios when the beam stopped inside the bone.CONCLUSIONS:Soundspeed errors dilate and acoustic heterogeneities deform ultrasound images. When thermoacoustic receivers are co-located with the ultrasound imaging array, the same transformations shift thermoacoustic range estimates. Therefore, thermoacoustic range verification is robust relative to ultrasound images of underlying anatomy. When the treatment target is visible in ultrasound, e.g., prostate, online thermoacoustic range estimates could verify that the treatment spot is inside the target.

PurposeRange errors constrain treatment planning by limiting choice of ion beam angles and requiring large margins. Ionoacoustic range verification requires recovering the location of an acoustic source from low frequency signals. A priori information is applied to stably overcome resolution limits of inverse acoustic source imaging in this simulation study. In particular, the accuracy and robustness of ionoacoustic range verification for lateral and oblique delivery of high‐energy protons to the prostate is examined.MethodsDose maps were computed using GEANT4 Monte Carlo simulations via the TOPAS user interface. Thermoacoustic pulses were propagated using k‐Wave software, with initial pressures corresponding to instantaneous dose deposition and piecewise constant maps of tissue properties derived from the planning CT. A database of dose maps with corresponding thermoacoustic emissions and Bragg peak locations, referred to as “control points,” were precomputed. Corresponding thermoacoustic emissions were also precomputed. Pulses were recorded at four coplanar locations corresponding to the outer surface of a virtual transrectal array. To model experimental beam delivery, k‐Wave results were convolved in time with a Gaussian envelope to account for noninstantaneous proton delivery by a synchrocyclotron. Thermoacoustic pulses were bandlimited below 150 kHz, and amplitudes were directly proportional to charge delivered. To test robustness of our method, white noise was added. Range was estimated in a two‐step process. The first step obtained a preliminary range estimate by one‐way beamforming. The second step was taken using data corresponding to the “control point” nearest to the preliminary range estimate. For each receiver, the time of flight difference, ∆t, between the measured and control thermoacoustic signals were accurately estimated by applying the Fourier shift theorem. Receiver‐Bragg peak distance was then estimated by adding vs∆t to the known distance of the control point, where vs is soundspeed. A linear system of equations based upon all receiver locations and distances was solved to recover the Bragg peak location. All simulations were performed relative to the planning CT. Because ultrasound (US) images were not available, results were overlaid onto the planning CT.ResultsBeamformed estimates from noise‐free data tracked all beam locations within 1 cm. Final estimates for oblique and lateral beams were accurate to within 1.0 and 1.6 mm respectively. Average errors of final range estimates for oblique beams from data with SNR = 0 dB were no greater than 2.0 mm.ConclusionsIonoacoustic range verification may improve current practice. Ionoacoustic range estimates can be inherently co‐registered to ultrasound images of underlying anatomy. To ensure estimates are robust in clinical practice, dose maps based upon the planning CT should be overlaid onto ultrasound volumes acquired at time of treatment and acoustic simulations re‐computed to provide a database of control points and corresponding thermoacoustic emissions. Computation times for beamformed estimates are already fast enough for online range verification, but are not accurate enough for a measurement aperture limited to the surface of a transrectal ultrasound probe. Accelerated acoustic simulations will be required to enable online two‐stage correction, but offline calculation is already suitable for adaptive planning.

The purpose of this work was to demonstrate that a clinical ultrasound transducer array can practically detect theimoacoustic pulses induced by irradiation by very high frequency (VHF) electromagnetic energy. This is an important step because theimoacoustic signal strength is directly proportional to the specific absorption rate (SAR), which is lower in the VHF regime than in microwave or optical regimes. A 96-channel transducer array (P4-1) providing 3 cm coverage was incorporated into a benchtop theimoacoustic imaging system for imaging fresh surgical specimens. Theimoacoustic signal was generated by 700 ns irradiation pulses with 11 kV/m electric field strength and 108 MHz carrier frequency. To improve SNR 1024 pulses were averaged at a 250 Hz repetition rate. Two sets of sinograms were acquired, separated by a 2 cm translation along the tomographic axis and reconstructed over a 6 x 6 x 5 cm(3) volume. Contrast and in-plane resolution were measured by imaging a homogeneous cylindrical phantom and an 80 micron wire designed to highlight E-field polarization effects. FWHM of the in-plane point spread function varied from 250 microns to 1.1 mm, depending upon transducer used and phantom orientation relative to the electric field. Several fresh human prostates were imaged immediately after surgery. Rudimentary comparison to histology was performed and volumetric reconstruction of the multi-channel P4-1 data visualizes anatomic features that are rarely seen in ultrasound, CT, or MRI. The single element transducer provided superior image contrast, but with inferior resolution.

The potential of particle therapy due to focused dose deposition in the Bragg peak has not yet been fully realized due to inaccuracies in range verification. The purpose of this work was to correlate the Bragg peak location with target structure, by overlaying the location of the Bragg peak onto a standard ultrasound image. Pulsed delivery of 50 MeV protons was accomplished by a fast chopper installed between the ion source and the cyclotron inflector. The chopper limited the train of bunches so that 2 Gy were delivered in 2 μs. The ion pulse generated thermoacoustic pulses that were detected by a cardiac ultrasound array, which also produced a grayscale ultrasound image. A filtered backprojection algorithm focused the received signal to the Bragg peak location with perfect co-registration to the ultrasound images. Data was collected in a room temperature water bath and gelatin phantom with a cavity designed to mimic the intestine, in which gas pockets can displace the Bragg peak. Phantom experiments performed with the cavity both empty and filled with olive oil confirmed that displacement of the Bragg peak due to anatomical change could be detected. Thermoacoustic range measurements in the waterbath agreed with Monte Carlo simulation within 1.2 mm. In the phantom, thermoacoustic range estimates and first-order range estimates from CT images agreed to within 1.5 mm.

Thermoacoustics has the potential to provide quantitative images of intrinsic tissue properties, most notably electrical conductivity in Siemens/meter, much as shear wave elastography provides tissue stiffness in kilopascal. Although thermoacoustic imaging with optical excitation has been commercialized for small animals, it has not yet made the transition to clinic for whole organ imaging in humans. The purpose of this work was to develop and validate specifications for a clinical ultrasound array for quantitative whole organ thermoacoustic imaging. Imaging a large organ requires exciting thermoacoustic pulses throughout the volume and broadband detection of those pulses because tomographic image reconstruction preserves frequency content. Applying the half-wavelength limit to a 200-μm inclusion inside a 7.5-cm diameter organ requires measurement sensitivity to frequencies ranging from 4 MHz to 10 kHz, respectively. A dual-transducer system utilizing a P4-1 array connected to a Verasonics V1 system as well as a focused single-element transducer sensitive to lower frequencies was developed. Very high-frequency (VHF) irradiation generated thermoacoustic pulses throughout a 6 × 6 × 5 cm3 volume. In the VHF regime, electrical conductivity drives thermoacoustic signal production. Simultaneous acquisition of thermoacoustic pulses by both transducers enabled comparison of transducer performance. Data from the clinical array generated a stack of 96 images with a separation of 0.3 mm, whereas the single-element transducer imaged only in a single plane. In-plane resolution and quantitative accuracy were quantified at isocenter. The array provided volumetric imaging capability with superior resolution whereas the single-element transducer provided superior quantitative accuracy in axial images. Combining axial images from both transducers preserved resolution of the P4-1 array and improved image contrast. Neither transducer was sensitive to frequencies below 50 kHz, resulting in a dc offset and low-frequency shading over fields of view exceeding 15 mm. Fresh human prostates were imaged ex vivo and volumetric reconstructions reveal structures rarely seen in diagnostic images. In conclusion, quantitative whole-organ thermoacoustic tomography will be feasible by sparsely interspersing transducer elements sensitive to the low end of the ultrasonic range.

Prostate cancer is difficult to image because contrast mechanisms of current modalities fail to distinguish healthy from cancerous prostatic tissue. Prostate cancer decimates citrate production and therefore overall ionic content of prostatic fluids. Amplitude of thermoacoustic pulses induced by very high frequency (VHF) irradiation increases with ionic content. Superior depth penetration over photo- and microwaveinduced thermoacoustic imaging is achieved at the cost of signal strength precisely because VHF energy loss is low in soft tissue. VHF-induced thermoacoustic imaging must overcome several challenges, including development of ultrasound transducer arrays suitable for clinical use. Sensitive single element ultrasound transducers yield good SNR after low noise amplification (54 dB) and signal averaging. Clinical ultrasound transducer arrays are less sensitive, particularly at frequencies below 1 MHz, which dominate power spectra of VHF-induced thermoacoustic pulses. Volumetric reconstruction of a fresh human prostate specimen in a 4.5 x 5.5 x 5.5 cm3 volume is displayed. We demonstrate that a clinical ultrasound array is sufficiently sensitive to high frequencies, but not low frequencies, for quantitative VHF-induced thermoacoustic computerized tomography (TCT). Simultaneous acquisitions by a clinical array with 1-4 MHz bandwidth and a single element transducer sensitive to kHz frequencies are compared and contrasted in images of resolution phantoms and a fresh human prostate. Combining images from both single element and phased array transducers retains superior image resolution of the phased array and contrast from the single element transducer. This demonstrates the importance of acquiring kilohertz frequencies for accurate image reconstruction over a large field of view, and will be useful in designing arrays suitable for a clinical prototype.

Applying the thermoacoustic (TA) effect to diagnostic imaging was first proposed in the 1980s. The object under test is irradiated by high-power pulses of electromagnetic energy, which heat tissue and cause thermal expansion. Outgoing TA pressure pulses are detected by ultrasound transducers and reconstructed to provide images of the object. The TA contrast mechanism is strongly dependent upon the frequency of the irradiating electromagnetic pulse. When very high frequency (VHF) electromagnetic irradiation is utilized, TA signal production is driven by ionic content. Prostatic fluids contain high levels of ionic metabolites, including citrate, zinc, calcium, and magnesium. Healthy prostate glands produce more ionic metabolites than diseased glands. VHF pulses are therefore expected to generate stronger TA signal in healthy prostate glands than in diseased glands. A benchtop system for performing ex vivo TA computed tomography with VHF energy is described and images are presented. The system utilizes irradiation pulses of 700 ns duration exceeding 20 kW power. Reconstructions frequently visualize anatomic landmarks such as the urethra and verumontanum. TA reconstructions from three freshly excised human prostate glands with little, moderate, and severe cancerous involvement are compared with histology. TA signal strength is negatively correlated with percent cancerous involvement in this small sample size. For the 45 regions of interest analyzed, a reconstruction value of 0.4 mV provides 100% sensitivity but only 29% specificity. This sample size is far too small to draw sweeping conclusions, but the results warrant a larger volume study including comparison of TA images to the gold standard, histology.

Ex vivo imaging of fresh prostate specimens was performed to test the hypothesis that the thermoacoustic (TA) contrast mechanism generated with very high frequency electromagnetic (EM) irradiation is sensitive to prostate cancer. Ex vivo imaging was performed immediately after radical prostatectomy, performed as part of normal care. Irradiation pulsewidth was 700 ns and duty cycle was extremely low. Typical specific absorption rate (SAR) throughout the prostate was 70-90 kW/kg during pulsing, but time-averaged SAR was below 2 W/kg. TA pressure pulses generated by rapid heating due to EM energy deposition were detected using single element transducers. 15g/L glycine powder mixed into DI water served as acoustic couplant, which was chilled to prevent autolysis. Spatial encoding was performed by scanning in tomographic “step-and-shoot” mode, with 3 mm translation between slices and 1.8-degree rotation between tomographic views. Histology slides for 3 cases scanned with 2.25 MHz transducers were marked for comparison to TA reconstructions. These three cases showed little, moderate, and severe involvement in the histology levels surrounding the verumontanum. TA signal strength decreased with percent cancerous involvement. When VHF is used for tissue heating, the TA contrast mechanism is driven by ionic content and we observed suppressed TA signal from diseased prostate tissue in the peripheral zone. For the 45 regions of interest analyzed, a reconstruction value of 0.4 mV provides 100% sensitivity but only 29% specificity.

The thermoacoustic (TA) contrast mechanism relies on rapid tissue heating and subsequent thermal expansion. TA computerized tomography (TCT) is therefore inverse source imaging. The TA contrast mechanism provides information complementary to that revealed by current diagnostic imaging techniques, but has been limited to just a few centimeters depth penetration. In this article, whole organ TCT is demonstrated on a large swine kidney. TA sinograms show that TA signal generated by high-power, very high frequency (VHF) electromagnetic pulses is detectable after travel through 6 cm of soft tissue. Reconstructed images provide resolution sufficient to track progression of calyces throughout the kidney. Because VHF electromagnetic energy can easily penetrate the abdomen of large adults, our results indicate that whole organ TA imaging is feasible in vivo, provided an ultrasound array can be placed near the region of interest. Pulses of 22 to 25 kW with carrier frequency 108 MHz and 900 ns pulse width were applied at a 100-Hz pulse repetition frequency to generate a 13-kV/m electric field and TA signal. Only 2 to 5 mJ was absorbed in the kidney per pulse, causing temperature and pressure jumps of only 5e-6°C and 4 Pa averaged throughout the 141-g specimen. TA pulses were detected by focused, single-element transducers (V306, Panametrics), amplified by 54 dB and averaged 64 times to reduce electronic noise. Data were measured over a cylindrical measurement aperture of radius 5 cm and length 6 cm, by rotating the specimen 1.8 degrees between tomographic views and translating 2 mm between slices. Reconstruction via filtered backprojection yields in-plane resolution better than 5 mm, but suffers significant blurring between planes. Both in-plane resolution and slice sensitivity profile could be improved by applying shorter irradiation pulsewidths and using less directional transducers. Both hardware changes would be recommended for a clinical prototype.

Thermoacoustic (TA) imaging provides a novel contrast mechanism that may enable visualization of cancerous lesions which are not robustly detected by current imaging modalities. Prostate cancer (PCa) is the most notorious example. Imaging entire prostate glands requires 6 cm depth penetration. We therefore excite TA signal using submicrosecond VHF pulses (100 MHz). We will present reconstructions of fresh prostates imaged in a well-controlled benchtop TA imaging system. Chilled glycine solution is used as acoustic couplant. The urethra is routinely visualized as signal dropout; surgical staples formed from 100-micron wide wire bent to 3 mm length generate strong positive signal.

Electromagnetic absorption and subsequent heating of nanoparticle solutions and simple NaCl ionic solutions is examined for biomedical applications in the radiofrequency range at 13.56 MHz. It is shown via both theory and experiment that for in vitro measurements the shape of the solution container plays a major role in absorption and heating.