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(Radiology. 1999;212:270-275.)
© RSNA, 1999

Technical Developments

Volumetric Imaging with Ultrasonic Spiral CT1

Haim Azhari, DSc and Didi Sazbon, MSc

1 From the Department of Biomedical Engineering, Technion, Israel Institute of Technology, Haifa 32000, Israel. Received September 15, 1997; revision requested November 24; final revision received November 20, 1998; accepted January 15, 1999. Supported in part by the Israel Science Foundation (grant Z-953/93), the Technion Vice Provost for Research Fund (J. Tal Equipment and Research Fund 130-304), the Irving and Adele Rosenberg Foundation, and the Israel Cancer Association (grants 960023-B and 972025-B). Address reprint requests to H.A. (e-mail: haim@biomed.technion.ac.il).


   Abstract
TOP
 Abstract
Introduction
 Materials and Methods
 Results
 Discussion
 Appendix
 References
 
To examine the feasibility of implementing spiral computed tomography (CT) in ultrasonic imaging as a potential method for breast screening, an algorithm for x-ray spiral CT was applied to ultrasonic waves on a specially built ultrasonic tomographic system. Three-dimensional reconstructions of various phantoms were obtained. Spiral ultrasonic CT is feasible, and it may have clinical merit as a breast imaging method.

Index terms: Breast, US, 00.12989 • Computed tomography (CT), ultrasound (US) • Ultrasound, experimental studies, 00.12989 • Ultrasound computed tomography (US/CT), 00.12989


   Introduction
TOP
 Abstract
 Introduction
Materials and Methods
 Results
 Discussion
 Appendix
 References
 
Breast cancer is a major cause of mortality in women. Current statistics indicate that one in eight women (12.5%) may be affected by breast cancer in their lifetimes (1). Mammography is currently the accepted screening tool for breast imaging. However, mammography has some major disadvantages. It has been proved ineffective as an imaging modality for women with dense breasts and undesirable in young women (ultrasonography is the preferred modality in these cases [2,3]), has limited tissue characterization capability, and provides only two-dimensional projections of the breast. Furthermore, mammography involves hazardous ionizing radiation, which renders this method undesirable for mass screening and frequent follow-up.

Ultrasonic imaging, in comparison, is considered safe; is suitable for women in any age group; enables tissue characterization on the basis of a variety of parameters such as backscatter, attenuation, and speed of sound (3–6); depicts tissue morphology; and is a relatively cost-effective modality. Currently, pulse-echo imaging (B scan) is the most widely applied ultrasonic technique, but its ability to discriminate between solid masses is limited (7). Ultrasonic computed tomography (CT) has been suggested as an alternative imaging technique that provides better tissue characterization (8,9), but the large number of projections required to obtain a high-spatial-resolution image requires use of large (and costly) transducer arrays or results in a long acquisition time.

Spiral CT is a relatively new approach implemented in modern x-ray imaging (10–12). With spiral CT, a continuous scan is obtained of a volume of interest, which provides the data for a three-dimensional (3D) reconstruction of the studied object. Spiral CT provides information for a much more detailed 3D reconstruction of the object and is more efficient than is conventional CT performed with the same scanning parameters. On the basis of its 3D nature, spiral CT can provide longitudinal and arbitrarily oriented cross sections in addition to the axial images commonly obtained with conventional CT.

The objective of this study was to examine the feasibility of implementing spiral CT in ultrasonic imaging as a potential method for 3D breast imaging.


   Materials and Methods
TOP
 Abstract
 Introduction
 Materials and Methods
Results
 Discussion
 Appendix
 References
 
Ultrasonic CT
Ultrasonic CT images are commonly reconstructed from the detected acoustic waves passing through an insonified object (forming its acoustic projections) by means of a backprojection process. Projections of the object are acquired from various directions around it to constitute its Radon transform. By using the relation between the Fourier transform of the projection and the two-dimensional Fourier transform of the object (by means of the slice theorem [13]), the measured projections are used to obtain the Fourier domain of the object. The image of the object can be reconstructed by using the inverse Fourier transform of these data. With ultrasonic CT, tomograms can be obtained that depict the acoustic attenuation coefficients or the local refraction index, defined as 1/wave velocity. By ignoring diffraction effects, a relatively simple model is implied for ultrasonic CT. The ultrasonic wave propagation paths in soft tissues are assumed to be approximately along straight lines (8,14). Hence, images can be reconstructed in a manner similar to that with x-ray CT by applying the filtered backprojection algorithm (14). (A more accurate model that accounts for diffraction effects would require a computationally more intensive algorithm [15]). Consequently, the following relations can be implemented.

Refraction index projections can be estimated by measuring the time of flight of the ultrasonic wave through the object by using the following line integral (along each ray) (8):

where Nr is the refraction index, Ttrans is the transmission time, and Trec is the receiving time.

Attenuation coefficient projections can be estimated by measuring the amplitude of the through transmitted ultrasonic wave. In this case, the following line integral is used (8):

where µ0 is the equivalent attenuation coefficient (ie, ignoring dependency on the frequency), Atrans is the transmitted wave amplitude, and Arec is the received wave amplitude. In this study, we chose to focus on attenuation imaging alone. Tomograms, obtained with ultrasonic CT based on Equation (1), have been published previously (14,16).

Spiral CT
Spiral CT provides volumetric information from the object. Unlike conventional CT, which scans the object section by section (Fig 1a), spiral CT scans the entire object along a spiral path (Fig 1b). Accordingly, if the helical pitch (defined as the axial displacement of the detectors per revolution) is properly selected, spiral CT contains information from all regions of the object. Consequently, small abnormal regions located between two consecutive planes, which may disappear in the 3D reconstruction obtained with conventional CT, are likely to be detected with spiral CT. Naturally, this also depends on other scanning parameters (ie, section thickness [which is fixed by the collimator], the number of sampled rays, the number of projections acquired, and the quality of the reconstruction algorithm used).



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  		Figure 1. Schematic illustrates A, conventional 3D reconstruction versus B, volumetric spiral reconstruction. A set of parallel cross sections is provided in A, whereas a single data set (volumetric) is obtained in B. Note that small objects located between two consecutive scanned planes may disappear in A.

 
Spiral CT is also more efficient than conventional CT in the sense that it can provide a much larger number of sections within a given scanning time. Scanning time is determined by the time required to acquire a single projection ({Delta}t) multiplied by the number of projections (NP) required to reconstruct the object. Given a total scanning time (T) as a constraint, the number of available projections is determined by NP = T/({Delta}t). If the number of projections used to reconstruct a single section is N1, conventional CT can yield only NP/N1 sections, whereas spiral CT can yield NP - (2 · N1) sections. For example, if the total number of projections acquired is 640 and N1 = 64, conventional CT can produce only 10 sections whereas spiral CT can produce as many as 512 sections.

With ultrasonic CT, no hazardous radiation is involved. Therefore, total acquisition time is not limited by dose factors but merely by the patient's comfort. The time required to acquire a single ultrasonic projection ({Delta}t) is determined mainly by engineering factors (data storage and mechanical movements). The physical limitation here is almost negligible (ultrasonic travel time through 200-mm-thick tissue is about 0.13 msec). Thus, a projection of 128 rays, for example, will require about 17 msec plus the time required for the hardware to sample and store the data. (With modern hardware and array transducers, an acquisition rate of more than 10 projections per second can be achieved.)

Object reconstruction from spiral CT data can be achieved by using alternative approaches. In this study, linear interpolation of the projection data into a set of parallel planes (17,18) was used. The interpolation method is described in detail in the Appendix. Basically with this method, the spiral CT data set is first resampled into a set of many planar Radon transforms by using the interpolation algorithm. Then, by applying a conventional backprojection algorithm to each Radon transform, a set of parallel cross sections is generated. Consequently, the number of planes reconstructed is substantially larger than the number obtained by conventional CT with the same scanning parameters. This leads to a much more detailed 3D reconstruction of the object. However, the penalty for that procedure is an increase in the section sensitivity profile (ie, the effective section width is increased [19–22]). It should be noted that the section sensitivity profile depends strongly on the helical pitch used (ie, a smaller pitch will provide a narrower effective section width and vice versa). Nevertheless, with a smaller pitch, a larger number of windings will be required to cover the object, which leads to an increase in the total scanning time.

Spiral Ultrasonic CT Experimental System
The experimental system used to implement spiral CT to ultrasonic waves comprises a water bath with a specially built computer-controlled mechanism that can produce spatial motion with 3 df [x, z, {theta}] for a pair of 5-MHz focused transducers (Panametrics; Waltham, Mass). Section thickness is determined on the basis of the diameter of the acoustic beam generated by the transducers. We estimated it to be about 5 mm in this case. The system can scan a cylindric volume defined by the user (up to 20 cm in diameter and 30 cm high) located in the center of the water bath. The system can currently acquire a 15-cm-long projection with 600 rays in 10 seconds. The helical pitch, defined as the axial displacement of the ultrasonic transducers per revolution, can be set arbitrarily by the user (0–300 mm per revolution).

A pulser receiver (model 5800; Panametrics) was used to transmit and receive the ultrasonic waves. A two-channel 20-MHz analog-to-digital converter (model R2000; Rapid Systems, Seattle, Wash) was used to digitally store the detected waves. For image reconstruction, the peak-to-peak amplitude of each wave was registered. The system was controlled with a 66-MHz computer (PC/486; Fox Computers, Taiwan). Codes for data acquisition, image reconstruction, and image display were written in our laboratory by using a C++ compiler (Borland International, Scotts Valley, Calif).

Objects Tested and Protocols Used
Three objects were used to evaluate spiral ultrasonic CT performance.

Plasticine spherical target.—A 7-mm-diameter plasticine sphere (Cope 4516; PanArt, Jerusalem, Palestine) was used to simulate a single tissue target and allow comparison of conventional ultrasonic CT with spiral ultrasonic CT. The sphere was positioned within the scanner water tank. It was positioned in the water tank by using a very thin wire (about 0.2-mm diameter), which was too thin to be detected by the system (the corresponding ultrasonic wavelength in water is about 0.3 mm). Scout acoustic attenuation projections based on Equation (2) were acquired for general orientation. With use of these scout projections, the coordinates of the desired imaging windows (ie, minimum and maximum spatial coordinates of the scanned volume) were set manually.

Tomographic images of the sphere were initially obtained by using reconstructions of four conventional ultrasonic CT sections with a resolution of 128 x 128 pixels. Each pixel was 1 x 1 mm. A 10-mm distance between sections was used. (This distance was used to ensure the sphere was detected in only one section of the conventional ultrasonic CT scan.) Next, the same sphere was reconstructed with use of a spiral ultrasonic CT scan with four spiral windings and a 10-mm pitch. The corresponding cross sections were also reconstructed with a resolution of 128 x 128 pixels. In-plane resolution was again 1 x 1 mm.

On the ultrasonic attenuation tomograms, brighter gray levels indicated higher attenuation. Thus, because the ultrasonic attenuation coefficient of plasticine is higher than that of the background (ie, water), the sphere appeared as a bright spot on a relatively dark background. The sphere was detected within the tomographic reconstructions by two observers (H.A., D.S.) on the basis of consensus. The sphere was easily detected (Fig 2). Because we merely compared the two methods for detection, no tests of reproducibility were performed.



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  		Figure 2a. Plasticine spherical target. (a) Conventional 3D scan depicts four sections (slice 1–4) 10 mm apart (schematically illustrated on the left). Only the second section (slice 2) depicts a cross-sectional image of the upper part of the sphere. Note that the sphere would have been undetected with a slight change in section position. (b) Spiral CT scan was obtained with four spirals and 10-mm pitch (schematically illustrated on the left). The four sections (slice 5–8) depict cross sections located between the two dashed lines in the schematic and passing through the sphere. In this case, the spiral reconstruction consists of 16 sections.

 


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  		Figure 2b. Plasticine spherical target. (a) Conventional 3D scan depicts four sections (slice 1–4) 10 mm apart (schematically illustrated on the left). Only the second section (slice 2) depicts a cross-sectional image of the upper part of the sphere. Note that the sphere would have been undetected with a slight change in section position. (b) Spiral CT scan was obtained with four spirals and 10-mm pitch (schematically illustrated on the left). The four sections (slice 5–8) depict cross sections located between the two dashed lines in the schematic and passing through the sphere. In this case, the spiral reconstruction consists of 16 sections.

 
Egg phantom.—A hard-boiled egg was positioned within a condom. An egg was chosen because its acoustic properties are close to that of tissue and its internal geometry is known. The hard-boiled egg was positioned approximately at the center of the water tank of the scanner (by using the condom for suspension). By acquiring scout projections, the coordinates of the desired imaging window were set manually. A 3D reconstruction of the egg at 128 x 128 x 128-voxel resolution was obtained from a spiral ultrasonic CT scan with eight spiral windings and a 10-mm pitch. Voxel size ({Delta}x{Delta}y{Delta}z) was 1.00 x 1.00 x 0.62 mm. Again the images were analyzed by consensus. The purpose of this study was merely to validate that the reconstructions produced with spiral ultrasonic CT matched the expected cross sections of the hard-boiled egg. Hence, no tests of reproducibility were performed.

Breast phantom.—The breast biopsy phantom (model BB-1; ATS Laboratories, Bridgeport, Conn) mimics the appearance, size, and acoustic properties of the human breast. The phantom contains eight target structures embedded randomly throughout. The target structures are similar to abnormal tissue and are 5–10 mm in diameter. The phantom was imaged with spiral ultrasonic CT with 16 spiral windings and 5-mm pitch. A 128 x 128 x 64-voxel reconstruction of the phantom was obtained. Voxel size ({Delta}x{Delta}y{Delta}z) was 1.40 x 1.40 x 1.25 mm.

Abnormal tissue–mimicking targets were characterized in the tomograms with relatively higher attenuation coefficients (ie, high gray level) and a dark corona (presumably a diffraction effect). The same two observers detected the targets by consensus. For validation, the phantom was also scanned manually by a third observer with a conventional ultrasonic scanner (Synergy-B; Diasonics, Israel) with a 3.5-MHz transducer in the B-scan mode.

Reproducibility of Data Acquisition
The reproducibility of the system in acquiring the data required for image reconstruction was also evaluated. The system was given a reset command and the transducers moved to their home position. Then the system was ordered to acquire a single acoustic projection of the breast phantom with coordinates arbitrarily set by the user. The acquired data were stored on the computer disk. The procedure (ie, a reset command followed by an acquisition command) was repeated several times. Finally, the correlation coefficients between 10 pairs of these acoustic projections (acquired from the same location of the breast phantom) were calculated by using a library function (MATLAB; Math Works, Natick, Mass). A high correlation coefficient indicates high reproducibility.


   Results
TOP
 Abstract
 Introduction
 Materials and Methods
 Results
Discussion
 Appendix
 References
 
Spiral Ultrasonic CT versus Conventional Ultrasonic CT
Plasticine spherical target.—The cross sections of the plasticine sphere obtained with conventional ultrasonic CT are displayed in Figure 2a. Note that the second section was deliberately positioned to obtain a cross-sectional image of the upper part of the sphere; clearly, the sphere would not have been detected if the section position were changed slightly. On the other hand, spiral ultrasonic CT scans the entire volume, which can produce a large number of cross sections. The number of cross sections reconstructed in this case was arbitrarily set at 16. Four reconstructed cross sections passing through the sphere (covering the slab marked by the dashed lines in the schematic) are depicted in Figure 2b. Note that the sphere is clearly depicted.

Hard-boiled egg phantom.—Axial, longitudinal, and oblique (35° relative to the axial plane) cross sections of the hard- boiled egg obtained from the reconstructed spiral ultrasonic CT data are depicted in Figure 3. As can be noted, the structure of the egg is clearly visible in all the cross-sectional images. However, the longitudinal cross section is blurred and inferior in quality relative to the axial cross section. This may be attributed to the large helical pitch chosen.



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  		Figure 3a. Hard-boiled egg phantom. Spiral reconstructions obtained with eight spiral windings and 10-mm pitch depict the following cross-sectional views: (a) axial, (b) longitudinal, and (c) oblique (tilted 35° relative to the axial plane).

 


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  		Figure 3b. Hard-boiled egg phantom. Spiral reconstructions obtained with eight spiral windings and 10-mm pitch depict the following cross-sectional views: (a) axial, (b) longitudinal, and (c) oblique (tilted 35° relative to the axial plane).

 


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  		Figure 3c. Hard-boiled egg phantom. Spiral reconstructions obtained with eight spiral windings and 10-mm pitch depict the following cross-sectional views: (a) axial, (b) longitudinal, and (c) oblique (tilted 35° relative to the axial plane).

 
Breast biopsy phantom.—The abnormal tissue–mimicking targets were clearly depicted on the spiral ultrasonic CT reconstruction of the breast phantom. Coronal, axial, and sagittal cross-sectional images of the volumetric reconstruction depicting the abnormal tissue targets are given in Figure 4. The general orientations of the targets depicted in Figure 4 were confirmed with an independent B-scan study. On the basis of its volumetric nature, spiral ultrasonic CT allowed production of a 3D object that can be displayed in various modes. To further demonstrate the volumetric nature of the reconstruction, the boundaries of the breast phantom were semiautomatically traced, and a 3D computer rendering (Fig 5) was obtained. The breast phantom was virtually cut about 10 mm from its base to enable a look inside at its lesions. Furthermore, it should be noted that with use of a dynamic computer display mode, it is also possible to move virtually through the imaged breast and study its internal structure more closely.



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  		Figure 4a. Breast biopsy phantom. Spiral reconstructions, obtained with 16 spirals and 5-mm pitch, consist of 128 x 128 x 64 voxels of 1.4 x 1.4 x 1.25 mm. Abnormal tissue targets (arrows) are clearly visible. (a) Coronal cross section 10 (of 64). (b) Axial cross section 56 (of 128). (c) Sagittal cross section 80 (of 128).

 


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  		Figure 4b. Breast biopsy phantom. Spiral reconstructions, obtained with 16 spirals and 5-mm pitch, consist of 128 x 128 x 64 voxels of 1.4 x 1.4 x 1.25 mm. Abnormal tissue targets (arrows) are clearly visible. (a) Coronal cross section 10 (of 64). (b) Axial cross section 56 (of 128). (c) Sagittal cross section 80 (of 128).

 


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  		Figure 4c. Breast biopsy phantom. Spiral reconstructions, obtained with 16 spirals and 5-mm pitch, consist of 128 x 128 x 64 voxels of 1.4 x 1.4 x 1.25 mm. Abnormal tissue targets (arrows) are clearly visible. (a) Coronal cross section 10 (of 64). (b) Axial cross section 56 (of 128). (c) Sagittal cross section 80 (of 128).

 


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  		Figure 5. Breast biopsy phantom. On the 3D computer rendering, the phantom was virtually cut about 10 mm from its base to enable a look inside at its lesions. This type of presentation may provide a better orientation to the physician and may help plan more effective surgical procedures.

 
Reproducibility of Data Acquisition
Correlation coefficients were calculated between 10 pairs of acoustic projections acquired in the same location of the breast phantom on different scans. The mean correlation coefficient was 0.9976 (range, 0.9972–0.9980), indicating high reproducibility for data acquisition.


   Discussion
TOP
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
Appendix
 References
 
The feasibility of imaging with spiral ultrasonic CT was verified in this study. The ability to obtain 3D reconstructions of selected objects by measuring the through transmitted acoustic waves with spiral ultrasonic CT was demonstrated experimentally. This method may provide an additional imaging tool to the practicing radiologist.

Spiral ultrasonic CT offers several advantages. The first stems from the inherent properties of the ultrasonic modality, which is considered hazardless and relatively cost-effective. This implies applicability to mass screening and potential use in clinics and hospitals.

The second advantage is derived from the information provided by the ultrasonic CT images. Although the commonly used pulse-echo techniques have been very useful in depicting breast cysts (1,2), their ability to differentiate solid masses is limited (2). On the other hand, analyses based on speed of sound (23,24) and acoustic attenuation have demonstrated clinical potential (eg, Scherzinger et al [25] achieved approximately 90% sensitivity and specificity in depicting breast cancer with ultrasonic CT).

In addition, spiral ultrasonic CT offers the main advantage provided by x-ray spiral CT, which is a volumetric coverage of the object with an efficient scan. Volumetric imaging also offers better diagnostic potential over conventional two-dimensional imaging. This property was demonstrated in our study for the spherical target and the egg and breast phantoms. As shown in Figure 2, spiral ultrasonic CT depicted the spherical target that conventional ultrasonic CT may have missed. Furthermore, the 3D reconstructions obtained for the egg and breast phantoms enabled the display of arbitrarily oriented cross sections, as depicted in Figures 3 and 4, respectively. In addition, by using a dynamic display, the diagnostic physician could virtually move through the object and locate the lesions. Finally, with the 3D display of the breast (Fig 5), the surgeon could obtain a more realistic orientation and possibly design a better surgical intervention.

However, spiral ultrasonic CT also has several disadvantages that should be noted. Owing to the facts that through transmission is required and ultrasonic waves can barely penetrate the bones and the lungs, spiral ultrasonic CT is limited almost exclusively to the breast. Moreover, axillary regions of the breast or regions very proximal to the ribs cannot be imaged with this technique. Hence, spiral ultrasonic CT must be coupled with the standard pulse-echo technique. In addition, the major disadvantage of x-ray spiral CT also applies here. As a result of the interpolation between data acquired at different heights (relative to the spiral axis), the effective section profile is substantially increased (twice the spiral pitch [19–21]). Consequently, if the spiral pitch is large, notable blurring may occur along the longitudinal direction. This was demonstrated on the longitudinal cross-sectional images obtained in the egg (Fig 3). Optimization between the desired section sensitivity profile and the width of the pitch might give better results for a given imaged object.

In addition, several limitations of the present study should be pointed out. For computational simplicity, we ignored diffraction effects. This assumption is not entirely valid. A more accurate model should also account for diffraction effects. An algorithm that accounts for diffraction effects, such as the filtered backpropagation algorithm suggested by Devaney (15), might produce more accurate reconstructions. However, this algorithm is computationally much more intensive. Furthermore, Schreiman et al (26) have already demonstrated that clinically valuable images of the breast can be obtained with ultrasonic CT by means of a straight line model. As the objective of this study was merely to demonstrate feasibility, we chose to implement the simpler model.

A second simplification was to ignore the dependency of the attenuation coefficient on the frequency. A more accurate approach would be to apply spectral analysis to the signals. Alternatively, one can assume a linear relation between the attenuation coefficients and the frequency and can implement one of the methods reviewed by Kak and Slaney (14).

Finally, it should be pointed out that although attenuation tomograms were obtained in this study, with a slight modification (ie, measuring time of flight instead of wave amplitude), tomograms depicting speed of sound distribution may be produced. This acoustic parameter (ie, speed of sound) has been shown to provide valuable clinical information (23,24).

In conclusion, findings in this study demonstrate that spiral ultrasonic CT is feasible. This imaging method may find clinical application as a breast screening tool.


   Appendix
TOP
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Appendix
References
 
The interpolation method applied in this study is based on the method presented by Bresler and Skrabacz (17) and Ruimi (18). With this approach, the spiral data set in the projection domain is first converted (resampled) by means of interpolation into a set of planar Radon transforms. Then, application of a conventional two-dimensional reconstruction algorithm to each plane yields a set of parallel cross sections.

In spiral CT, the position, z, along the spiral axis and the angle, {theta}P, at which the projection is acquired, are linearly related by

where D is the spiral pitch.

To resample the spiral projections into a set of parallel Radon planes, the z value of each desired plane is first set. By using this relation, three consecutive projections (previous [prev], current [cur], and next) are selected that were acquired at different heights (z values) but correspond to the same angle. Then, the weighted average of these projections is calculated by

The weights, w, for 0 <= {theta} <= {theta}P are given by

and for {theta}P <= {theta} <= 2{pi} are given by

The resultant vector P({theta}) is the new resampled projection at angle {theta}. The procedure is repeated to cover all {theta} values from 0 to {pi}, and the filtered backprojection is applied to reconstruct the corresponding section (at the desired height z).


   Footnotes
 
Abbreviation: 3D = three-dimensional

Author contributions: Guarantor of integrity of entire study, H.A.; study concepts and design, H.A.; definition of intellectual content, H.A.; literature research, D.S.; experimental studies, H.A., D.S.; data acquisition and analysis, D.S.; manuscript preparation and editing, H.A., D.S.; manuscript review, H.A.


   References
TOP
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Appendix
 References
 

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  5. Glover GH, Sharp JC. Reconstruction of ultrasound propagation speed distributions in soft tissue: time-of-flight tomography. IEEE Trans Sonics Ultrasonics 1977; 24:229-234.
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