Three-dimensional ultrasound imaging

Ultrasound is an inexpensive and widely used imaging modality for the diagnosis and staging of a number of diseases. In the past two decades, it has benefited from major advances in technology and has become an indispensable imaging modality, due to its flexibility and non-invasive character. In the last decade, research investigators and commercial companies have further advanced ultrasound imaging with the development of 3D ultrasound. This new imaging approach is rapidly achieving widespread use with numerous applications. The major reason for the increase in the use of 3D ultrasound is related to the limitations of 2D viewing of 3D anatomy, using conventional ultrasound. This occurs because: (a) Conventional ultrasound images are 2D, yet the anatomy is 3D, hence the diagnostician must integrate multiple images in his mind. This practice is inefficient, and may lead to variability and incorrect diagnoses. (b) The 2D ultrasound image represents a thin plane at some arbitrary angle in the body. It is difficult to localize the image plane and reproduce it at a later time for follow-up studies. In this review article we describe how 3D ultrasound imaging overcomes these limitations. Specifically, we describe the developments of a number of 3D ultrasound imaging systems using mechanical, free-hand and 2D array scanning techniques. Reconstruction and viewing methods of the 3D images are described with specific examples. Since 3D ultrasound is used to quantify the volume of organs and pathology, the sources of errors in the reconstruction techniques as well as formulae relating design specification to geometric errors are provided. Finally, methods to measure organ volume from the 3D ultrasound images and sources of errors are described.

Three-dimensional ultrasound imaging

Ultrasound is an inexpensive and widely used imaging modality for the diagnosis and staging of a number of diseases. In the past two decades, it has benefited from major advances in technology and has become an indispensable imaging modality, due to its flexibility and non-invasive character. In the last decade, research investigators and commercial companies have further advanced ultrasound imaging with the development of 3D ultrasound. This new imaging approach is rapidly achieving widespread use with numerous applications. The major reason for the increase in the use of 3D ultrasound is related to the limitations of 2D viewing of 3D anatomy, using conventional ultrasound. This occurs because: (a) Conventional ultrasound images are 2D, yet the anatomy is 3D, hence the diagnostician must integrate multiple images in his mind. This practice is inefficient, and may lead to variability and incorrect diagnoses. (b) The 2D ultrasound image represents a thin plane at some arbitrary angle in the body. It is difficult to localize the image plane and reproduce it at a later time for follow-up studies. In this review article we describe how 3D ultrasound imaging overcomes these limitations. Specifically, we describe the developments of a number of 3D ultrasound imaging systems using mechanical, free-hand and 2D array scanning techniques. Reconstruction and viewing methods of the 3D images are described with specific examples. Since 3D ultrasound is used to quantify the volume of organs and pathology, the sources of errors in the reconstruction techniques as well as formulae relating design specification to geometric errors are provided. Finally, methods to measure organ volume from the 3D ultrasound images and sources of errors are described.

A real vessel phantom for flow imaging: 3-D Doppler ultrasound of steady flow

Vascular phantoms are used to assess the capabilities of various imaging techniques, such as x-ray CT and angiography, and B-mode, power Doppler, and colour Doppler ultrasound (US). They should, therefore, accurately mimic the vasculature, blood, and surrounding tissue, in regard to both imaging properties and vessel geometry. In the past, a variety of walled and wall-less vessel models have been used. However, these models only approximate the true vessel geometry, and generally lack pathologic features such as plaques or calcifications. To amend these deficiencies, we have developed a real vessel phantom for US and x-ray studies, which comprises a fixed human vessel specimen, cannulated onto two acrylic tubes, and embedded in agar in an acrylic box. Earlier, we demonstrated a good overall correlation between x-ray angiography, CT, and 3-D B-mode US images of this phantom. Here, we extend its use to flow imaging with 3-D power and 3-D colour Doppler US.

Analysis of geometrical distortion and statistical variance in length, area, and volume in a linearly scanned 3-D ultrasound image

A linearly scanned three-dimensional (3-D) ultrasound imaging system is considered. The transducer array is initially oriented along the x axis and aimed in the y direction. After being tilted by an angle theta about the x axis, and then swiveled by an angle phi about the y axis, it is translated in the z direction, in steps of size d, to acquire a series of parallel two-dimendional (2-D) images. From these, the 3-D image is reconstructed, using the nominal values of the parameters (phi, theta, d). Thus, any systematic or random errors in these, relative to their actual values (phi0, theta0, d0), will respectively cause distortions or variances in length, area, and volume in the reconstructed 3-D image, relative to the 3-D object. Here, we analyze these effects. Compact linear approximations are derived for the relative distortions as functions of the parameter errors, and hence, for the relative variances as functions of the parameter variances. Also, exact matrix formulas for the relative distortions are derived for arbitrary values of (phi, theta, d) and (phi0, theta0, d0). These were numerically compared to the linear approximations and to measurements from simulated 3-D images of a cubical object and real 3-D images of a wire phantom. In every case tested, the theory was confirmed within experimental error (0.5%).

Intra- and inter-observer variability and reliability of prostate volume measurement via two-dimensional and three-dimensional ultrasound imaging

We describe the results of a study to evaluate the intra- and inter-observer variability and reliability of prostate volume measurements made from transrectal ultrasound (TRUS) images, using either the (optimal) height-width-length (HWL) method (V = pi/6 HWL) with two-dimensional (2D) TRUS images (obtained as cross-sections of three-dimensional [3D] TRUS images) or manual planimetry of 3D TRUS images (the 3D US method). In this study, eight observers measured 15 prostate images, twice via each method, and an analysis of variance (ANOVA) was performed. This analysis shows that, with the 3D US method, intra-observer prostate volume estimates have 5.1% variability and 99% reliability, and inter-observer estimates have 11.4% variability and 96% reliability. With the HWL method, intra-observer estimates have 15.5% variability and 93% reliability, and inter-observer estimates have 21.9% variability and 87% reliability. Thus, in vivo prostate volume estimates from manual planimetry of 3D TRUS images have much lower variability and higher reliability than HWL estimates from 2D TRUS images.

Analysis of linear, area and volume distortion in 3D ultrasound imaging

We have developed a three-dimensional (3D) ultrasound imaging system that uses a side-firing probe, axially rotated under computer control, to acquire a series of 2D images, from which the 3D image is reconstructed. For an undistorted reconstruction, the inner radius R0 of the 2D images and the total scanning angle theta must be known accurately. Here, we describe (a) a theoretical analysis of the relative distortion in image shape, length, area, and volume due to an error delta R in R0 or delta theta in theta; (b) measurements of these in simulated and real 3D images; and (c) a method to calibrate R0, theta, and image scale accurately. Theoretically, all four relative distortions vary as P delta R/R + Q delta theta/theta, where magnitude of P < or = 1, magnitude of Q < or = 1, and R is the average distance of the object from the axis. In every case, the simple theoretical formulas for P and Q agree with image measurements to within the measurement uncertainty.

A three-dimensional ultrasound prostate imaging system

We have developed a three-dimensional (3D) transrectal ultrasound imaging system, based on using a motorized 5 MHz transducer assembly, rotated under microcomputer control, to collect a series of 100 two-dimensional (2D) images, digitized by a video frame-grabber. These are then reconstructed into a 3D image on a computer workstation, permitting the prostate anatomy to be visualized in three dimensions, and distance and volume measurements to be performed. The accuracy of the distance measurements was assessed with a string test phantom, and that of the volume measurements with balloons of known sizes. Also, the resolution degradation engendered by the reconstruction algorithm was assessed by comparing the full-width at half-maximum (FWHM) of string cross-sectional images in the 3D image to their 2D counterparts. The results show that distance and volume measurements are both accurate to about +/- 1%, and that the reconstruction algorithm increases the mean FWHM by 8 +/- 3% axially and 3 +/- 3% laterally.

Experimental and theoretical x-ray imaging performance comparison of iodine and lanthanide contrast agents

Contrast agents based on the lanthanide elements gadolinium and holmium have recently been developed for magnetic resonance imaging (MRI). Because of the increased atomic number of these elements relative to iodine, these new compounds, used as x-ray contrast agents, may yield higher radiographic contrast, and hence improved x-ray image quality, relative to conventional iodinated compounds, for clinically useful x-ray spectra. This possibility has been investigated, in independent experimental and theoretical studies, for two x-ray imaging systems: a digital radiographic system, using an x-ray image intensifier (XRII) and charge-coupled device (CCD) detector; and a conventional screen/film system, using a Lanex Regular screen. Iodine, gadolinium, and holmium contrast agents were investigated over a wide range of concentration-thickness products (0.1-0.6 M cm) and diagnostic x-ray spectra (60-120 kVp). A simple theoretical model of x-ray detector response predicts the experimental radiographic contrast measurements with a mean absolute error of 8.0% for the XRII/CCD system and 5.9% for the screen/film system, and shows that the radiographic contrast for these two systems is representative of all XRII and screen/film systems. An index of image quality is defined, and its dependence on radiographic contrast, x-ray fluence per unit dose, and detective quantum efficiency (DQE) is shown. Theoretical values of the index, predicted by our model, are then used to compare the performance of the three contrast agents for the two systems investigated. In general, iodine performance decreases steadily with increasing kVp, gadolinium performance has a broad maximum near 85 kVp, and gadolinium outperforms holmium. Gadolinium outperforms iodine for spectra above (and vice versa below) about 72 kVp, depending slightly on spectrum filtration, object thickness, and detector type. Thus, raising the kVp to shorten exposure times or reduce x-ray tube heat loading results in a loss of image quality with iodine, but not with gadolinium. Similarly, beam-hardening artifacts in performing video densitometry with iodine would be reduced with gadolinium. Gadolinium-based contrast agents are thus shown to offer several practical advantages over conventional iodinated contrast agents.

Analytic approximation of the log-signal and log-variance functions of x-ray imaging systems, with application to dual-energy imaging

In the analysis of x-ray system performance, the log-signal function, or negative logarithm of the relative detector signal, and the analogously defined log-variance function, are of central importance. These are smooth, monotonic functions of object thickness, which are nonlinear for nonmonoenergetic x-ray source spectra. If we assume a dual-energy decomposition of the object into two basis materials, then they can be written as analytic functions f(x,y) and f*(x,y), respectively, of the component thicknesses (x,y) of the object. In this paper, we analytically develop the Taylor series of these functions, prove that they converge everywhere, and parametrize their coefficients via suitable central spectral moments of the basis-material attenuation coefficients. We then show how the lower-order moments can be used to construct, in closed form, smooth, monotonic, second-order (conic) surface functions which closely approximate f(x,y) and f*(x,y) over the entire feasible domain. A simplified construction, based on using appropriate asymptotic values of the basis-material attenuation coefficients to match the asymptotic behavior of these functions, is also given. The inclusion of image components with K-edge absorption spectra, such as iodine, is done without effort. Extension of the results to the construction of similar (virtually exact) third-order (cubic) surface approximations is straightforward. As an illustration of the broad applicability of this approach, we extend our analysis to the construction of similar approximations to the inverse (decomposition) functions for an arbitrary dual-energy system, and investigate their numerical accuracy for a model dual-kVp system. We conclude that this extended analysis provides an accurate description of the system behavior in terms of a small number of physically meaningful parameters. This parametrization permits greater physical insight into the system behavior, while at the same time simplifying its mathematical description, and similarly facilitates the analysis of various measures of imaging performance via either analytic or numerical methods.

An in-line optical image translator with applications in x-ray videography

Many applications in radiography require, or would benefit from, the ability to translate, i.e. move, an optical image in the detector plane. In this paper, we describe the design and characterization of a prism-based optical image translator for insertion into existing XRII-video imaging systems. A pair of prisms rotatable about the optical axis form a very compact in-line optical image translator for installation in the parallel light path between an x-ray image intensifier and its video camera. Rotation of the prisms translates the XRII optical image on the camera target. With the addition of x-ray and light collimators to limit the image to a single video line, x-ray streak images may be acquired. By rotating an object in the x-ray beam during a streak, a complete computed tomography (CT) data set may be acquired. This image translator can translate an image anywhere in the focal plane of a 50-mm-output lens within a 40-mm-diam circle. The prisms have an aperture of 50 mm, permitting an optical speed of F/2 with a 50-mm output lens. The design is insensitive to angular alignment errors. This image translator is achromatic, since the spectral width of the output phosphorus of image intensifiers is sufficient to introduce blurring in a nonacrhomatic design. A prism-based image translator introduces image distortion, since the prisms do not operate at minimum deviation. The distortion is less than 4% over all parts of a typical detector area, and less than 1% in the central region of the image.(ABSTRACT TRUNCATED AT 250 WORDS)

An accurate method for direct dual-energy calibration and decomposition

We propose the use of conic and cubic surface equations (surfaces of second and third order) to directly approximate the dual-energy equations (the integral equations for the dual-energy log-signal functions, i.e., the negative logarithms of the relative detector signals, considered as functions of the basis-material component thicknesses of the object) and especially their inverses. These types of surface equations require a minimum number of calibration points, and their solutions are smooth, monotonic functions with the correct linear asymptotic behavior. The accuracy of this method is investigated and compared to that of conventional polynomial approximations, both for simulated and real calibration data, taken from two split-detector systems. These systems provide a more stringent test of our method than comparable dual-kVp systems, due to the greater nonlinearity of their log-signal and inverse functions. For these systems, we show that direct approximation of the inverse dual-energy equations using the simple eight-term rational form of the conic surface equation provides an extremely fast decomposition algorithm, which is accurate, robust in the presence of noise, and which can be calibrated with as few as 9 calibration points, or robustly calibrated, with a built-in accuracy check, using only 16 calibration points. Also, we show that extreme accuracy of approximation (to within less than 10(-6) in log-signal and 1 micron in material thickness) is theoretically attainable using the eighteen-term form of the cubic surface equation, which has a closed-form analytic solution. Finally, we consider the effects of noise on calibration accuracy, and derive simple formulas which relate the true and apparent root-mean-square (rms) accuracies. These formulas then allow the comparison of the true rms calibration accuracies of various surface approximations, considered as functions of the total calibration heat loading of the x-ray tube.

Theoretical optimization of a split septaless xenon ionization detector for dual-energy chest radiography

It is proposed that digital scanned projection radiography of the chest be performed by using an energy-sensitive septaless xenon ionization detector (SXID) to obtain dual-energy images. The proposed detector is composed of a front region, sensitive to low-energy x rays, and a rear region, sensitive to high-energy x rays, separated by a suitable filter layer. We have developed a simple, precise theoretical formulation for dual-energy optimization, and applied it to the split SXID. We describe the variation of optimum detector performance with source kilovoltage and filtration (material and thickness), and hence heat loading, under conditions of constant exposure and constant dose. We estimate dose as the average absorbed dose to an equivalent water layer of suitable thickness, assuming slab geometry, so that the calculation is as simple as that for exposure.