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# Whole-Body Imaging Using Low Frequency Transmission Ultrasound

Open AccessPublished:February 23, 2023

### Rationale and Objectives

To indicate that 3D low-frequency ultrasound tomography with 3D data acquisition (volography) is a safe, low-cost, high-resolution, whole-body meso-scale medical imaging modality that gives high-resolution quantitatively accurate clinically relevant images.

### Materials and Methods

We compare the speed of sound accuracy in various organs in situ. We validate our 3D ultrasound tomography images using MRI and gross section anatomy as ground truth in 10-day old piglets. Data acquisition is accomplished with the QT Scanner at ∼1 MHz center frequency, and array transceivers for reflection data @3.6 MHz. Images are generated with unique model-based 3D ultrasound tomography algorithms. In reflection, we use 3D refraction-corrected ray tracing to allow 360° compounding with sub-mm resolution. Four 10–12 day old pigs were anesthetized and whole-body images were acquired via low-frequency transmitted ultrasound and 3T MRI.

### Results

Tissue values were within an average of 1.07% (0.5%) of the literature values. We also show the detailed correlation of our images with MRI images in axial, coronal, and sagittal views. Volography images of a piglet show high resolution and quantitative accuracy, showing more contrast &resolution than 3T MRI, including the kidney showing medulla, cortex and fibrous cover, and small intestines with ileal lumen detail visible.

### Conclusion

We establish that 3D ultrasound tomography (volography), yields high-resolution quantitatively accurate images whole-body images in presence of bone and air which are potentially clinically useful but have not appeared in the literature.

## Key Words

#### Abbreviations:

LRE (Low Resource Environments), DMD (Duchenne Muscular Dystrophy), SOS (speed of sound), MRI (magnetic resonance imaging)

## INTRODUCTION

### Low-Frequency 3D Transmission Ultrasound Tomography: Volography

We show for the first time quantitatively accurate, high-resolution ultrasound tomographic images in the presence of bone and air. Bone and air have been viewed as barriers to more extensive deployment of medical ultrasound in comparison to more standard modalities such as CT and MRI. Furthermore, although there are recent improvements in ultrasound imaging, such as automated breast ultrasound, and improvements in digital X-ray tomography, such as digital breast tomosynthesis—neither of these improvements are isotropic. By contrast, ultrasound tomography with 3D inversion algorithms (which we term, for reasons explained in the methods section below, volography) is model-based and consistently nearly isotropic in 3D. There is also a great clinical need for a new body imaging modality that can be used for screening healthy individuals, children, and infants at high-risk for disease because of genetic, environmental, or familial factors and for those ill patients who are at risk from complications of radiation, high magnetic fields, heavy metal-based contrast injections or anesthesia if imaged with other modalities. We are particularly thinking of the few available options for infants, small children, and screening of otherwise healthy, at-risk individuals. Finally, there is a great need for a low-cost, comprehensive medical imaging modality that can be deployed in low-resource environments (LRE). There are billions of people in the world who have no access to comprehensive medical imaging—a key diagnostic tool that could dramatically improve medical care.
This modality of 3D transmission ultrasound tomography/volography (USV) has already shown promise even in the presence of bone (

Guasch L, Calderón Agudo O, Tang M-X, et al. Full-waveform inversion imaging of the human brain. npj Digital Med 2020;3:28. https://doi.org/10.1038/s41746-020-0240-8.

,
• Wiskin J.
• Malik B.
• Borup D.
• et al.
Full wave 3D inverse scattering transmission ultrasound tomography in the presence of high contrast.
,
• Simon B.
• Dimitri K.
• et al.
Ultrasonic computed tomography based on full-waveform inversion for bone quantitative imaging.
). Also, presently an understanding of the physics of ultrasound in a complex anatomical setting and skill are necessary to obtain medically useful high-quality images with ultrasound (
• Heldt T.
). We believe that transmission ultrasound-based operator independent quantitatively accurate whole-body volography is a solution providing high-quality whole-body medical images.

### Comparisons With Conventional Imaging Modalities

Certain disorders, such as Duchenne muscular dystrophy (DMD), sports injuries, and muscle deterioration due to diabetes or neuropathy require close monitoring of muscle or other tissue during recovery or treatment. Arthropathies require a monitoring of cartilage tissue for correct diagnosis. In the case of trauma, the location of large-scale, expensive modalities may be distant, and the time taken to transport a patient to these may be detrimental to their recovery, especially in LRE. Magnetic resonance imaging (MRI) is a popular option at present for body region imaging (
• Ab Mumin N.
• Ramli Hamid M.T.
• Wong J.H.D.
• et al.
Magnetic resonance imaging phenotypes of breast cancer molecular subtypes: a systematic review.
). However, MRI:
• 1.
Does not always quantitatively image certain tissues (cartilage, periosteum, and ligaments—see Wiskin et al (
• Wiskin J.
• Malik B.
• Borup D.
• et al.
Full wave 3D inverse scattering transmission ultrasound tomography in the presence of high contrast.
) where these structures do not produce a signal),
• 2.
requires a strong magnetic field, which is difficult to get in certain situations (e.g., LRE),
• 3.
requires specialized training,
• 4.
may require a contrast agent injection,
• 5.
may be contra-indicated for some patients,
• 6.
requires expensive and large machinery not appropriate for LRE,
• 7.
Is not easily adapted for use with intervention or biopsy.
Another option is computed tomography (CT). However, this involves potentially harmful ionizing radiation, does not provide high soft tissue contrast, and requires large and expensive machinery.
On the other hand, ultrasound-based modalities are inexpensive, safe at the low energies, used very efficiently, and fast compared with the long times required for MRI images (
• Zhi H.
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• Yang H.
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• Kim W.H.
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• Li Y.
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,
• Van Zelst J.C.M.
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,
• Iuanow E.
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Accuracy of cyst versus solid diagnosis in the breast using quantitative transmission (QT) ultrasound.
,
• Wang H.
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). It is easily adapted to point-of-care devices for trauma and sports injury and is adaptable to a partial-angle imaging data acquisition protocol (
• Rothberg J.M.
• Ralston T.
• Rothberg A.
• et al.
Ultrasound-on-chip platform for medical imaging, analysis, and collective intelligence.
). This latter creates an “open” scanner design that is particularly attractive for claustrophobic patients and infants. Further, an open design creates a platform useful for intervention or biopsy. Finally, the low-cost and lack of special hardware (such as super-cooling and radiation shielding) make this ideal for LRE's (
• Malik B.
• Iuanow E.
• Klock J.
An Exploratory multi-reader, multi-case study comparing transmission ultrasound to mammography on recall rates and detection rates for breast cancer lesions.
). The difficulty with the present standard ultrasound is that it does not work well in the presence of bone and air due to the high contrast in the speed of sound (SOS) and impedance.
Indeed there is a long history of ultrasound tomography involving a large number of research groups (

Johnson SA, Stenger F, Wilcox C, et al. In Acoustical Imaging (ed John P. Powers) 409-424 (Springer US, 1982).

,

Jirik R, Peterlik I, Ruiter N, et al, Sound-speed image reconstruction in sparse-aperture 3-D ultrasound transmission tomography, EEE Trans Ultrason Ferroelectr Freq Control 2012;59:254–264.

,

Ruiter NV, Zapf M, Hopp T, et al, 3D ultrasound computer tomography of the breast: a new era?, Eur J Radiol 2012;81:S133–S134. https://doi.org/10.1016/S0720-048X(12)70055-4.

,
• Ozmen N.
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Comparing different ultrasound imaging methods for breast cancer detection.
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• Ramirez A.B.
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,
• Andre M.
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• et al.
High speed data acquisition in a diffraction tomography system employing large-scale toroidal arrays.

Leach, J.R. S. Azavedo, J. Berryman, et al., In Medical Imaging 2002: Ultrasonic Imaging, Tomography and Therapy: Comparison of ultrasound tomography methods in circular geometry, 2002, 362-377.

,

Duric, N. P. Littrup, E. Holsapple, et al. in Medical imaging 2003: ultrasonic imaging and signal processing. (SPIE Medical Imaging Conference): Ultrasound tomography of breast tissue, 2003, 24-32.

,
• Duric N.
• Littrup P.
• Babkin A.
• et al.
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,
• Li C.
• Duric N.
• Littrup P.
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,

Duric ND, Li C, Littrup P, et al. Medical Imaging 2009: Ultrasonic Imaging, Tomography and Therapy. SPIE 72651G: Detection and characterization of breast masses with ultrasound tomography:clinical results 2023:1:8.

,
• Huthwaite P.
• Simonetti F.
• Duric N.
Combining time of flight and diffraction tomography for high resolution breast imaging: initial invivo results (l).
,
• Ranger B.
• Littrup P.
• Duric N.
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,
• Carson P.L.
• Scherzinger A.
• Meyer C.
• et al.
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) beginning with Greenleaf and Johnson (

Greenleaf JF, Johnson SA, Lee SL, et al. In acoustical holography: volume 5 (ed Philip S. Green) 591-603 (Springer US, 1974).

,

Greenleaf JF, Johnson SA, Samayoa WF, et al. In acoustical holography: volume 6 (ed Newell Booth) 71-90 (Springer US, 1975).

) in the 70, see Klock et al (

Klock JLM, Wiskin J, Malik B, and Natesan R, In emerging trends in ultrasound imaging, 43, 2018, Openaccessbooks, 1–18, Ch. 1 http://openaccessebooks.com/emerging-trends-ultrasound-imaging/transmission-ultrasound-imaging-using-3D-inverse-scattering.pdf, 2018

). QT Imaging has developed a high-resolution quantitatively accurate method for breast imaging, Wiskin et al (
• Wiskin J.W.
• Borup D.T.
• Iuanow E.
• et al.
3-D Nonlinear acoustic inverse scattering: algorithm and quantitative results.
) This scanner is useful for early detection, monitoring, and diagnosis of disease in the breast (
• Iuanow E.
• Smith K.
• Obuchowski N.A.
• et al.
Accuracy of cyst versus solid diagnosis in the breast using quantitative transmission (QT) ultrasound.
,
• Malik B.
• Iuanow E.
• Klock J.
An exploratory multi-reader, multi-case study comparing transmission ultrasound to mammography on recall rates and detection rates for breast cancer lesions.
) due to its stable quantitative images (

Malik B, Klock J, Wiskin J, et al. Objective breast tissue image classification using quantitative transmission ultrasound tomography Sci Rep 2016;6:38857. http://www.nature.com/articles/srep38857#supplementary-information.

). The breast scanner is FDA-cleared for generating transmission ultrasound images of the breast and has shown promise as a primary cancer screening modality with improved performance over X-ray mammography (
• Malik B.
• Iuanow E.
• Klock J.
An exploratory multi-reader, multi-case study comparing transmission ultrasound to mammography on recall rates and detection rates for breast cancer lesions.
). This technique has also been adapted to orthopedic imaging successfully (
• Wiskin J.
• Malik B.
• Borup D.
• et al.
Full wave 3D inverse scattering transmission ultrasound tomography in the presence of high contrast.
). The scanner shown in Figure 1—below, collects highly redundant ultrasound data that is used to create 3D reconstructions of tissue characteristics SOS, attenuation (not shown), and reflectivity).

### Low-Frequency 3D Transmission Volography

A key feature of the volography reconstruction is that it is not constructed “slice” by “slice” as in standard tomography. Rather all of the data levels contribute to all of the image volume levels due to the height and 3D nature of the acoustic field. Ultrasound, unlike, for example, X-rays, cannot be constrained to a single plane (
• Wiskin J.W.
• Borup D.T.
• Iuanow E.
• et al.
3-D Nonlinear acoustic inverse scattering: algorithm and quantitative results.
). Conversely, all image levels contribute to all data levels in the forward problem (see 3D vs 2D algorithm in the methods section below). The term “volography” distinguishes this 3D method from standard 2D tomography. We have also developed a high-resolution nonquantitative reflection mode image that is refraction-corrected (RCRefl) image (
• Wiskin J.
• Borup D.
• Johnson S.
• et al.
Three-dimensional nonlinear inverse scattering: quantitative transmission algorithms, refraction corrected reflection, scanner design and clinical results.
) and the images obtained from each view can be compounded over an entire 360°. In the case of a partial angle data collection process, the addition can take place over the sector that is collected. The reason this compounding can be done is due to the refraction correction process that involves a priori knowledge of the SOS map of the 3D volume of the whole-body being imaged. Normally compounding different reflection images separated by more than 10–15° results in substantial artifacts and doubling phenomena. This is because the “back-projection” utilized in standard B-mode imaging does not consider refraction effects brought about by SOS heterogeneity within the tissue. Furthermore, if the ray modeled in the back-projection process used to create the reflection image were a straight line (i.e. no refraction), the image of a reflector (a cartilage, muscle, ligament, kidney, etc.) is back-projected to the incorrect spatial position due to SOS differences. Consequently, when the images from different angles are added together there is a substantial blurring and doubling of images (
• Wiskin J.
• Borup D.
• Johnson S.
• et al.
Three-dimensional nonlinear inverse scattering: quantitative transmission algorithms, refraction corrected reflection, scanner design and clinical results.
). The refraction-correction process is discussed in more detail in the methods section and results in a high-resolution (sub-mm) (
• Malik B.
• Terry R.
• Wiskin J.
• et al.
Quantitative transmission ultrasound tomography: imaging and performance characteristics.
) reflection image that is complementary to the SOS map, in that it emphasizes connective tissue and interfaces, whereas the SOS map gives the correct tissue properties of the piglet, even when near air (as shown here for the first time) and bone. This data is also valuable for the quantitative assessment of tissue characteristics (
• Oelze M.L.
• O'Brien W.D
Application of three scattering models to characterization of solid tumors in mice.
).

### Unique Advantages of 3D Volography Reconstruction

Note that full wave inversion methods as opposed to ray-tracing-based inversion can be carried out in 2D for ultrasound imaging. However, we have presented evidence that 3D acquisition and reconstruction are required for the quantitative accuracy, lack of artifact, and high-resolution required for clinical applications (

Guasch L, Calderón Agudo O, Tang M-X, et al. Full-waveform inversion imaging of the human brain. npj Digital Med 2020;3:28. https://doi.org/10.1038/s41746-020-0240-8.

,
• Wiskin J.W.
• Borup D.T.
• Iuanow E.
• et al.
3-D Nonlinear acoustic inverse scattering: algorithm and quantitative results.
,

Wiskin J, Klock J, Iuanow E, et al. Quantitative 3D high resolution transmission ultrasound tomography: creating clinically relevant images, proc. SPIE Medical Imaging 2017 vol. 101390Y-101390Y-101391. https://doi.org/10.1117/12.2254639.

). Furthermore, it is known that the high contrast of the bone and air makes the imaging problem with traditional ultrasound difficult, so data redundancy is an attractive advantage. There have been some notable results using ray tracing and B-mode ultrasound (

Ruiter NV, Zapf M, Hopp T, et al, 3D ultrasound computer tomography of the breast: a new era?, Eur J Radiol 2012;81:S133–S134. https://doi.org/10.1016/S0720-048X(12)70055-4.

) and for imaging through the skull using a related FWI method (

Guasch L, Calderón Agudo O, Tang M-X, et al. Full-waveform inversion imaging of the human brain. npj Digital Med 2020;3:28. https://doi.org/10.1038/s41746-020-0240-8.

) in simulation, where specific mention is made of the importance of the 3D model. However, here we show high-resolution transmission ultrasound images resulting from clinical data (i.e., not simulation) using an inverse scattering algorithm. We show high-resolution quantitative results for a whole-body in the presence of both bone and air, thus showing clinical potential for high-resolution transmission ultrasound volography in the whole-body context. We verified quantitative and morphological accuracy by correlating our images with 3T MRI and gross anatomy whole-body slices of the same animal. We reconstruct the 3D images ∼64 times faster than previous reports (

Guasch L, Calderón Agudo O, Tang M-X, et al. Full-waveform inversion imaging of the human brain. npj Digital Med 2020;3:28. https://doi.org/10.1038/s41746-020-0240-8.

) while using 64 times fewer compute nodes thus providing clinically useful images.
This work expands this success of transmission ultrasound volography to the presence of air as well as bone, that is, to whole-body imaging. This is relevant since soft tissue in juxtaposition to bone and air represents two major high-impedance contrast scenarios in whole-body imaging. We also emphasize the importance of using 3D algorithms, especially in imaging of small to medium-sized animals, extremities, and infants. The acoustic field in transmission ultrasound is not constrained to a plane as it is in CT, so a 3D model is required which contributes to data redundancy and fidelity.
We compare the images obtained by our data collection system and method with physical anatomical slices and MR images of the same piglet and discuss the importance of data redundancy, the speed of the imaging process, and the clinical implications of the images and improvements over previous work.

## MATERIALS AND METHODS

### Data Acquisition

The data are collected on a 2D array consisting of 8 rows and 256 columns of elements at 0.5 mm pitch horizontally. The array is 20 mm tall and 128 mm wide. The sonification is via a pseudo-plane wave beam in the horizontal direction but not in the vertical as noted in (
• Wiskin J.
• Malik B.
• Borup D.
• et al.
Full wave 3D inverse scattering transmission ultrasound tomography in the presence of high contrast.
,
• Wiskin J.W.
• Borup D.T.
• Iuanow E.
• et al.
3-D Nonlinear acoustic inverse scattering: algorithm and quantitative results.
,
• Wiskin J.
• Malik B.
• Natesan R.
• et al.
). Note that even with a vertical focus at 6 cm the field diffracts and expands to a large vertical height after passing through it. The data are collected at 2° intervals for 180 views for both the transmission and the reflection arrays. The center frequency for the transmission transmitter and receiver array is 0.8 MHz. The transmitted signal is a chirp of 1536 samples, sampled at 33 MHz. The DA is carried out through custom-built DA boards and Fourier transformed to approximately 82 frequencies ranging from 3 = 0.3 MHz to 2.0 MHz inclusive. The data are collected for all views then the entire assembly moves vertically up, and the 360° rotation is repeated. The data are stored in the vectors $dωjθl∈CNR$. The reflection arrays are linear, with 192 elements and 0.375 mm pitch. The center frequency for the reflection arrays is ∼3.6 MHz.

### Reconstruction Algorithm: 3D vs 2D Algorithm

We introduce an important difference between standard tomography which reconstructs the image volume one slice at a time and what we tentatively term “volography” which reconstructs a volume using all levels of data simultaneously. One slice of data is used to reconstruct one slice of the image in tomography, whereas in “volography” a given level of data contributes to several levels of the image. Conversely, in tomography a given slice of the image contributes to (affects) one level of the data, whereas in “volography” a given slice of the image contributes to multiple levels of the data. This term is introduced only to impart the qualitative (and quantitative) difference between the two concepts, which appears to have not been fully appreciated.
This distinction is important for at least three reasons: (1) the reconstruction must take into account the true 3D nature of the acoustic energy field (2) without accounting for the 3D nature of the field and capturing the scattered field in the vertical direction important information is lost, and (3) there is an extra level of data redundancy with this approach.

### Paraxial Approximation

The reconstruction algorithm is based on an approximate factorization of the Helmholtz frequency domain wave equation. This yields the approximate 2–3 orders of magnitude speed up we see over simulations carried out (

Guasch L, Calderón Agudo O, Tang M-X, et al. Full-waveform inversion imaging of the human brain. npj Digital Med 2020;3:28. https://doi.org/10.1038/s41746-020-0240-8.

). We use a model based large-scale minimization based on an L2 minimization. The data residual is defined as the difference between the predicted and measured data at a particular frequency $ωj$, which ranges from ∼300 kHz to 1300 kHz in a typical inversion: We minimize the L2 norm of this error representation. The forward problem is solved via the paraxial approximation to the full Helmholtz equation, which is approximately 500 times faster. We also utilize Nvidia CUDA for an additional speed-up factor of 3–4.
The large-scale minimization utilizes an efficient form of gradient minimization technique called the nonlinear conjugate gradient algorithm of the Polyak-Ribiere-Polak type. More detail is given in (
• Wiskin J.W.
• Borup D.T.
• Iuanow E.
• et al.
3-D Nonlinear acoustic inverse scattering: algorithm and quantitative results.
,
• Wiskin J.
• Borup D.
• Johnson S.
• et al.
Three-dimensional nonlinear inverse scattering: quantitative transmission algorithms, refraction corrected reflection, scanner design and clinical results.
,
• Wiskin J.
• Borup D.T.
• Johnson S.A.
• et al.
Non-linear inverse scattering: high resolution quantitative breast tissue tomography.
).
This last observation is critical to the deployment of the machine to a clinic. The problem of local minimum (referred to in the seismic literature as cycle skipping) is solved by starting at a low enough frequency that the phase has been correctly accounted for. The initial image is created from a straight ray-based time of flight reconstruction.
This algorithm is mathematically equivalent to training a gauge invariant fully connected convolutional neural network with complex weights, which explains the efficiency when implemented on GPUs.

### Refraction Corrected Reflection Image Formation

While the inverse scattering solution for quantitative transmission ultrasound volography is more sophisticated mathematically, the refraction corrected reflection image supplies important high-resolution images of the connective tissue. There are 192 elements in the linear arrays. The three arrays are of different heights so as to vertically focus at different depths. The raytracing is carried out in parallel on Nvidia cards. The resulting reflection images at each angle are added together in azimuth angle to yield a single 360° compounded image. The resolution is sub-mm, (
• Malik B.
• Terry R.
• Wiskin J.
• et al.
Quantitative transmission ultrasound tomography: imaging and performance characteristics.
) and the reflection image can be considered to yield complementary (high-frequency) image data, whereas the SOS image is formulated from the transmission data (pitch-catch mode) which gives the low spatial frequency part of the image.

### Animal Imaging

Animal procedures for the pig were approved by the Institutional Animal Care and Use Committee (IACUC) at Texas A&M University. All animals were cared for in accordance with National Institutes of Health Public Health Service Policy on humane care and use of laboratory animals. Two male and two female 10–12 day old pigs weighing 3.0–5.1 kg were anesthetized using telazol (5–10 mg/kg) and isoflurane. Heparin was administered intravenously (e.g. through medial saphenous vein), and the subjects were euthanized (80–120 mg/kg Beuthanasia solution IV). Whole-body images were acquired immediately following euthanisation using quantitative transmission ultrasound followed by MRI (axial, coronal, and sagittal plane T1-, T2-, and PD-weighted images) using a three tesla system (Siemens Magnetom Verio, Malvern, PA). Following freezing at -20°C, 1 cm thick transverse plane sections of each pig were acquired using a bandsaw. The sections were cleaned and photographed. Ultrasound images were compared to MRI images and gross sections to determine which anatomic structures could be identified.
The ovine liver and kidney were obtained from Thistle Meats, Petaluma, placed in 3% molten degassed agar and scanned with ultrasound volography and reflection mode scanner as in Figure 1.

### Segmentation

We used a segmentation algorithm based on region growing using a connected threshold criterion as implemented in ITK/VTK. The resulting volumes incorporated ∼3000 to over 200,000 voxels (0.4 by 0.4 by 1 mm in size). The Table 1 lists these volumes of interest and corresponding values. The SOS values from the literature were averaged. The relative error between the QT value vs literature average was calculated as (QT value – Lit. value)/(Lit. value).
Table 1Comparison of QT Ultrasound Values Compared With Literature Values
Tissue type#pixelsVolume of Interest (VOI) cm3QT Image Values (m/s)Literature Values avgRelative Error
Muscle (epaxial)26,7504.2815761592.51.04%
Fat2,01,87532.3144714152.26%
Skin54380.8715631578.50.98%
Kidney24,9383.991552.315630.68%
Liver 286,25013.81563.615801.04%
Liver 175,00012156415801.01%
Bone 1 (preossified)23130.371790.517601.73%
Bone 2 (pelvic region)30000.48177517600.85%
Bone 3 (preossified)43310.693175417600.34%
Note 1: the speed of sound for the bone is considered midway between cartilage and bone since endochondral ossification is incomplete in 10–12 day old pigs. The bone was segmented in 3 distinct regions and compared with an estimate based on literature values for bone (2570 m/s) and cartilage (1660 m/s). The relative error is also shown.

## RESULTS

The images shown below are reconstructed in approximately 20–25 minutes depending on the number of data levels that are collected using 2 NVidia RTX 6000 cards. The data collection process is approximately 15–25 minutes, depending and the number of data levels.
Figure 2 compares the reflection image in reverse grayscale with an MR image. The anatomy observed in the two modalities is correlated. The kidneys as well as the vertebral body clearly show up in both images. Note the hairs on the surface of the skin are visible on the piglet torso, indicating the high-resolution.
In Figure 3 we see the SOS images. The bladder, liver, stomach, intestines, and lungs are all clearly shown and differ in their gray-scale values by their SOS values and boundaries. Note also that the SOS of the cartilaginous preossified bone in the postnatal piglet shows up as ∼1790 to 1755 m/s (see Table 1), which seems a reasonable value between cartilage and ossified bone. This is useful as it allows a clear delineation of the stomach and bones.
We also observe that the unconstrained segmentation of the bone yields a different value for the average SOS depending on where it is seeded. It is known that endochondral ossification is incomplete but ongoing, and so it is to be expected that various parts of the bone will have ossified before others. The largest segmentation includes both ossified and unossified sub-volumes of bone. Therefore, the average is somewhat lower (1755) than for the more targeted regions.

### Additional Validation of the QT Image Quality Can Be Seen by Performing Whole-Body Sectioning

Figure 4 shows the detailed correlation of the axial view of the pig with USV and a gross section of the same slice.
The parts of the kidney (cortex, medulla, and renal pelvis), body wall musculature, digestive tract, and vertebrae are visible. Figure 5 shows the same axial cross-section in Figure 4 of the refraction corrected reflection image (RCRefl) in standard grayscale. The renal medullae appear more clearly in this image.
Segmentation results in the muscle SOS values shown in Table 1. Segmentation based on SOS as also performed for fat, skin, kidney, two sites in the liver, and bone at three different sites. The skin is more difficult to accurately segment and is based on SOS as well as being constrained within an ellipsoidal volume to give an accurate estimate of the average skin SOS.
The bone is formed through endochondral ossification, so we used a value of 1760 (m/s) (between 1660 for cartilage and 2500 m/s for mature bone) for the literature value.
Figure 6 shows a comparison of the QTUS refraction corrected reflection image (inverted grayscale) and a transverse plane PD-weighted MRI image of the same slice. The kidneys, epaxial muscles, skin, other muscle groups, and intestines are all visible in this view. It is indicative of the highly resolved image (in 3D).
We also performed ex vivo imaging of whole organs from larger animals to show the ability of QTUS to delineate structures within organs. Figure 7 shows an expanded view of ovine kidney to show the medulla, pyramids, calyces, pelvis, and cortex in detail. This is a RCRefl image and thus does not contain quantitative information like SOS but does indicate the detail that is achievable in whole-body imaging. Figure 8 shows a montage of ex-vivo RCRefl image slices spaced 4 mm apart through the liver. The hepatic veins, the portal system, and biliary ducts are clearly shown. The next step is showing such resolution is possible in vivo.
The reflection and SOS are co-registered and can be fused to enhance clinical utility as in Figure 9 showing the increased anatomical detail that can be achieved by such a technique.

## DISCUSSION AND CONCLUSION

We refer the reader to Malik et al (
• Malik B.
• Terry R.
• Wiskin J.
• et al.
Quantitative transmission ultrasound tomography: imaging and performance characteristics.
) for discussion of the speed and reflection PSF in 3D, Contrast to noise ratio, (CNR) and other physical characteristics, Wiskin et al (
• Wiskin J.
• Malik B.
• Borup D.
• et al.
Full wave 3D inverse scattering transmission ultrasound tomography in the presence of high contrast.
) for reflection PSF measured in situ in the context of high contrast media (bone), and Klock et al (
• Iuanow E.
• Smith K.
• Obuchowski N.A.
• et al.
Accuracy of cyst versus solid diagnosis in the breast using quantitative transmission (QT) ultrasound.
,
• Malik B.
• Iuanow E.
• Klock J.
An exploratory multi-reader, multi-case study comparing transmission ultrasound to mammography on recall rates and detection rates for breast cancer lesions.
,
• Klock J.C.
• Iuanow E.
• Malik B.
• et al.
Anatomy-correlated breast imaging and visual grading analysis using quantitative transmission ultrasound.
) for studies carried out by radiologists and medical professionals to assess image quality in clinical settings. Careful discussions of the physical characteristics (measurement accuracy, Image uniformity, normalized absolute average deviation, CNR, spatial resolution (PSF) for both reflection and speed of sound) are given (
• Malik B.
• Terry R.
• Wiskin J.
• et al.
Quantitative transmission ultrasound tomography: imaging and performance characteristics.
) The results shown here extend earlier results (
• Wiskin J.
• Malik B.
• Borup D.
• et al.
Full wave 3D inverse scattering transmission ultrasound tomography in the presence of high contrast.
) showing that low-frequency transmitted ultrasound imaging can be extended beyond its FDA-cleared use for breast soft tissue imaging to the presence of air as well as bone. The application to larger whole-animal imaging is noteworthy by itself since neonatal pigs are similar in size to human infants and have similar anatomy and physiology and have been used as models for a variety of human neonatal diseases.
We refer to earlier publications where the sub-mm resolution (
• Wiskin J.
• Malik B.
• Borup D.
• et al.
Full wave 3D inverse scattering transmission ultrasound tomography in the presence of high contrast.
) in tissue and CNR (
• Malik B.
• Terry R.
• Wiskin J.
• et al.
Quantitative transmission ultrasound tomography: imaging and performance characteristics.
) are shown to be superior to MR. In particular, there are some tissues which give no signal in certain MR sequences (
• Wiskin J.
• Malik B.
• Borup D.
• et al.
Full wave 3D inverse scattering transmission ultrasound tomography in the presence of high contrast.
).
Notably, the presence of air and bone (high impedance contrast) has not resulted in artefacts that degrade the image. This is critical for clinical applicability. We envision these images being used to monitor and diagnose tumors in the whole-body context, even where historically ultrasound would be predicted to fail. The preservation of quantitative accuracy is documented here for ligaments, tendons, cartilage, muscle, skin, and fat. Remarkably even the cartilaginous bone appears to be quantitatively close to literature expected values (
• Wiskin J.W.
• Borup D.T.
• Iuanow E.
• et al.
3-D Nonlinear acoustic inverse scattering: algorithm and quantitative results.
).
Although there is more work to be done this extension to previous results (
• Wiskin J.
• Malik B.
• Borup D.
• et al.
Full wave 3D inverse scattering transmission ultrasound tomography in the presence of high contrast.
,
• Wiskin J.W.
• Borup D.T.
• Iuanow E.
• et al.
3-D Nonlinear acoustic inverse scattering: algorithm and quantitative results.
) opens the possibility of whole-body applications of 3D low frequency volography.
This work also describes important qualitative differences between 3D transmission ultrasound volography and more standard CT and MR reconstructions. In CT the field can be treated as essentially a 2D plane. This greatly simplifies the computational burden of reconstruction. In ultrasound however, the field cannot be constrained so the reconstruction must be based on 3D models of wave propagation and interaction with the tissue. In the case of MRI the field is 3D, but one slice at a time is relevant and one slice of the image is processed in sequence, until the slices are concatenated to form the final image. See Table 2 below for a summary of the differences between 2D and 3D algorithms.
Table 2Summary of Qualitative Difference Between Slice by Slice Reconstruction (Tomography) and What May Be Called Volography—That is, Volumetric Simultaneous Reconstruction Using All Data Levels at Once
2D–Tomography3D–Volography
DataA given level of data gives one slice of imageA given level of data contributes to all slices of the 3D image
ImageA given slice of the object contributes to one level of the data setA given slice of the object contributes to all levels of the data set
Note that once the SOS map has been introduced, the refraction-corrected reflection can be created in seconds. This allows a real-time update for purposes of monitoring a needle biopsy or other procedures. The liver and kidney images are RCRefl and ex-vivo, unlike the piglet images where the entire piglet is imaged in-situ. These images show the near histological resolution of anatomic details that is possible using the refraction-corrected algorithm.
We have compared the SOS values as measured on the quantitative SOS images obtained by QT transmission ultrasound volography based on full waveform inversion (or inverse scattering) in Table 1.

### Clinical Applications

The ability to collect data in a timely manner in conjunction with the speed of reconstruction (approximately 30 minutes with the in situ two NVIDIA RTX 6000 cards) is roughly 64 times faster than other published results (

Guasch L, Calderón Agudo O, Tang M-X, et al. Full-waveform inversion imaging of the human brain. npj Digital Med 2020;3:28. https://doi.org/10.1038/s41746-020-0240-8.

) requiring a multinode supercomputer. We have verified a 6X speed up with A100 cards, (
• Wiskin J.
• Klock J.
) which is important for clinical applications, and deployment in LRE. This is a proof of concept device in terms of data acquisition as well as processing. Simulations (

Guasch L, Calderón Agudo O, Tang M-X, et al. Full-waveform inversion imaging of the human brain. npj Digital Med 2020;3:28. https://doi.org/10.1038/s41746-020-0240-8.

) are useful, but there are substantial issues that arise when comparing with actual data: how to adapt to varied Signal to Noise ratios (SNR), which frequencies to use, how to most effectively use these frequencies, proper calibration of collected data to in silico data, unknown effects of real bone and air presence. These last effects include such things as mode conversion to shear waves, guided wave effects, Biot type waves in trabecular bone, proper treatment of attenuation, high impedance contrast, etc.

### Physical Characteristics and Safety

The point-spread-function relates directly to perspicuity and the ability to see small details and is the same or better than Malik et al (
• Malik B.
• Terry R.
• Wiskin J.
• et al.
Quantitative transmission ultrasound tomography: imaging and performance characteristics.
). In particular in Wiskin et al (
• Wiskin J.
• Malik B.
• Borup D.
• et al.
Full wave 3D inverse scattering transmission ultrasound tomography in the presence of high contrast.
) a full width at half-max estimate gives a resolution cell of ∼0.62 mm. The clinically apparent perspicuity is higher (
• Klock J.C.
• Iuanow E.
• Malik B.
• et al.
Anatomy-correlated breast imaging and visual grading analysis using quantitative transmission ultrasound.
) Tissue volume monitoring is also possible as the segmentation is capable of measuring volumes to mm3 accuracy. This forms the basis for a recent FDA-clearance for the use of the technology to monitor breast tissue volumes. The safety of ultrasound means this device can be used for healthy subjects or on those at risk from the effects of conventional X-ray CT or MRI.

### Cost LRE and Safety

Perhaps as important, is the inexpensive nature of the ultrasound scanner. The total cost of the reconstruction engine (including NVIDIA cards), 3D arrays for transmission, and linear arrays for refraction corrected reflection imaging, water tank, concomitant control software, and hardware, total DA software and hardware is substantially below MR and CT scanners, making the technology attractive to LRE. There is no need for contrast agents or ionization radiation, yet the contrast and spatial resolution are better than MRI. The information content of the SOS image is also unique. The speed of sound $c=K/ρ$, where K is the bulk tissue modulus, and ρ is mass density. These parameters are related to molecular structure and cross-linking. They supply direct information about the molecular state of tissue. The ability to scan as often as desired with no deleterious effects and monitor disease or suspected disease is unique. The scanner will be especially attractive to, but not limited to low income presently underserved areas and populations. As health care costs continue to rise, the availability of a safe, high-resolution, information rich image producing scanning device will be a valuable adjunct on many levels for multiple diseases and populations of patients.

### Tumor Monitoring

Tumor monitoring is also possible as the segmentation is capable of measuring volumes to sub mm3 accuracy and any change in a suspicious tumor will be measured very accurately similar to how it is performed for RECIST using CT and MR images. This monitoring capability requires a stable and artifact-free reconstruction. We also note that vesicle delivery of cancer drugs and other agents is highly improved via the SOS map which allows the accurate focusing of a phased array to a small volume of tissue. This characteristic of USV is especially important in the presence of bone, air, and prosthetic materials, since an incorrect SOS map will yield an incorrect deposition of energy near bone or high contrast boundary resulting in discomfort or pain to patients.

### Conclusion

We show for the first time, 3D quantitative ultrasound tomography (volography) gives accurate tissue characteristics suitable for clinical diagnosis (in the presence of air and bone). We verify SOS accuracy in various organs in situ and validate our 3D volography images against MRI and gross section anatomy ground truth. Unique protocols analogous to sequences in MR Imaging give (SOS) for muscle, skin, liver, kidney, fat, and preossified bone. We use 3D refraction-corrected ray tracing to allow 360° compounding and sub-mm resolution. Our algorithm is optimized for NVIDIA GPUs leading to 64X speedup even with a 64X reduction in hardware over published 3D algorithms. We note a near isotropic point spread function and higher contrast-to-noise ratio than MR, with 3D tomography, without the use of ionizing radiation, potentially harmful contrast agents, strong magnetic fields, and expensive machinery. This is important for monitoring sarcopenia, Duchene muscular dystrophy and presport-injury muscle strain, liver fat content estimation, 3D pediatric hip-structure monitoring, meta-static cancer monitoring, etc. The high-resolution, high-contrast imaging characteristics of low-frequency transmission ultrasound, its safety, and low cost make it ideal for many clinical applications currently not served by CT & MRI.

### ARRIVE and IACUC

All animal procedures were approved by the Institutional Animal Care and Use Committee (IACUC). The animal use protocol was approved by Texas A&M's IACUC for this study. This study is in accordance with ARRIVE guidelines.

### Data availability

The raw binary image datasets analyzed during the current study are available from the corresponding author upon reasonable request.

### Acknowledgements

We gratefully acknowledge the help of Robin Terry and Roman Alyas in the data procurement at Texas A&M, and D. Borup for early code and discussions.

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