Menahem Nassi

Iterative convolution backprojection algorithms for image reconstruction from limited data

Image-reconstruction algorithms implemented on existing computerized tomography (CT) scanners require the collection of line integrals that are evenly spaced over 360 deg. In many practical situations, some of the line integrals are inaccurately measured or are not measured at all. In these limited-data situations, conventional algorithms produce images with severe streak artifacts. Recently, several other image-reconstruction algorithms were suggested, each tailored to a specific type of limited-data problem. These algorithms make minimal use of a priori knowledge about the image; only one has been demonstrated with real x-ray data. We present a new operator framework that treats all types of limited-data image-reconstruction problems in a unified way. From this framework we derive iterative convolution backprojection algorithms that make no restrictions on the location of missing line integrals. All available a priori information is incorporated by constraint operators. The algorithm has been implemented on a commercial CT scanner. We present examples of images reconstructed from real x-ray data in two limited-data situations and demonstrate the use of additional a priori information to reduce streak artifacts further.

Iterative Reconstruction-Reprojection: An Algorithm for Limited Data Cardiac-Computed Tomography

Cardiac X-ray computed tomography (CT) has been limited due to scanning times which are considerably longer (1 s) than required to resolve the beating heart (0.1 s). The otherwise attractive convolution-backprojection algorithm is not suited for CT image reconstruction from measurements comprising an incomplete set of projection data. In this paper, an iterative reconstruction-reprojection (IRR) algorithm is proposed for limited projection data CT image reconstruction. At each iteration, the missing views are estimated based on reprojection, which is a software substitute for the scanning process. The standard fan-beam convolution-backprojection algorithm is then used for image reconstruction. The proposed IRR algorithm enables the use of convolution-backprojection in limited angle of view and in limited field of view CT cases. The potential of this method for cardiac CT reconstruction is demonstrated using computer simulated data.

A Method for Stop-Action Imaging of the Heart Using Gated Computed Tomography

A new method for the reconstruction of limited angle projection data in rotary fan-beam X-ray computed tomography (CT) is presented. Missing views resulting from ECG-gated cardiac CT are estimated, and the standard fan-beam reconstruction algorithm is used to convolve and backproject both measured and estimated views. The estimation of the missing views takes place in three stages: first, the projection data is augmented by incorporating into each missing view the line integrals that do not pass through the heart, and which otherwise would be considered missing due to ECG-gating; second, line integrals corresponding to source positions in the range 180°±fan angle away from missing view angles are reflected; third, those line integrals that remain missing are estimated by interpolation. This method has been applied to ECG-gated cardiac imaging in dogs without requiring extensive interpolation; end-systolic and end-diastolic images were generated with short-interval gating (¿cycle) and total scan time (breath holding period) of 12 s. An important advantage of this method over other proposed limited angle reconstruction techniques is that it uses the existing fan-beam convolution-backprojection algorithm for image reconstruction.

Quantitative evaluation of left ventricular function using computed tomography.

Computed tomography (CT) provides a noninvasive technique with high resolution cross-sectional tomographic images which allow volume measurements of an object, independent of its geometric configuration. A phantom of known volume with controllable periodic motion was used to validate the CT method of volume determination. A good correlation (P less than 0.05) was achieved. Missing angle reconstruction algorithms for gating were applied to estimate left ventricular volumes and ejection fraction in an experimental animal, and the results compared with a standard angiographic method. Left ventricular volumes correlated poorly, whereas the ejection fraction obtained correlated well (r = 0.9). The discrepancies may be attributed in part to the CT method in which difficulties were recognized in defining the left ventricular borders at the base of the heart and partial volume effect, and in part to inaccuracies in the standard angiographic method. Once validated, this method has been applied to the animal model in the form of a pilot study.

Regional myocardial flow estimation using computed tomography

A novel method is presented for estimating regional myocardial blood flow (RMBF) using x-ray computed tomography (CT). Two major setbacks are removed from the existing methods; namely, the requirement for intra-arterial bolus injection of tracer, and the inability to determine regional volumes of tracer distribution when the corresponding partition coefficients are unknown. The mathematical model developed for RMBF estimation combines both the tracer dispersion process and the CT measurement process. Intravenously administered contrast media (tracer) is assumed to be perfectly mixed by the myocardium. Tracer dynamics, as measured by CT (CT#s. vs time curves) in the myocardial regions and in the left ventricular chamber, can then be used to compute cardiac output, regional volumes of tracer distribution, and absolute RMBF. These computations use the zeroth and the first moments of the measured CT#s. vs time curves. Errors due to partial volume effects, and methods for their correction, are analysed. This formulation is readily adapted to existing computed tomographic systems having the capability to produce multiple sequential CT scans.

Flow determination using computed tomography: application to aortic dissection. Part II.

Dynamic CT is not only useful in imaging an aortic dissection but may provide additional information concerning the hemodynamic significance of differing flow patterns in the false channel compared with the true channel. Once validated, the computed tomographic (CT) method of flow determination (See Part I) was applied to an experimental animal model with a surgically created aortic dissection. Good correlation was obtained for the flow estimates of cardiac output derived for the true and false channel (r = .82). The shapes of the curves, however, were distinct, reflecting different flow patterns for the true and false channels. Curve parameters, such as peak CT number (P = .0001), variance (P = .006), and, in particular, the number of mixers (a parameter used to quantify the degree of mixing) (P = .0001), demonstrated significant differences between the two channels of the dissection. The curve parameters derived can therefore be used to differentiate the true and false channels and may then predict the long-term outcome of the false channel, and the aortic branches derived from it.

Estimation of Regional Myocardial Blood Flow Using Computed Tomography: A Stochastic Formulation

Previously, we have presented a deterministic formulation for estimation of regional myocardial blood flow (RMBF) using X-ray computed tomography (CT) [1]. Quantitation of RMBF with the deterministic theory requires computing the zeroth and first moments of extrapolated myocardial contrast enhancement (CT numbers versus time) curves. This extrapolation is a potential source of error in the presence of recirculation, especially in myocardial regions with reduced flows. In the present paper, a stochastic approach for parameter estimation is undertaken, which renders an optimal RMBF estimate based upon the least squares error criteria. Random measurement errors are minimized, curve extrapolation is avoided, and the accuracy of RMBF estimates is predicted. The advantages of the stochastic versus the deterministic approach are demonstrated in the results obtained from the in vivo estimation of RMBF in normal and acutely ischemic myocardium of dogs.

Variability of myocardial CT measurements in vivo.

Variability of myocardial CT measurements, as indicated by standard deviations of mean CT numbers from four myocardial regions, was compared in 12-second scans, 3-second scans, and gated end-diastolic and end-systolic images, all from the same 12 seconds of scan data, both without and with radiographic contrast enhancement in experimental animals. There were statistically significant differences (P less than 0.05) in standard deviations of myocardial CT measurements when comparing 3-second and 12-second scans without contrast (10.4 vs. 7.7 CT#s), and 12-second scans without and with contrast (7.7 vs. 11.2 CT#s). Standard deviations of mean myocardial CT measurements were significantly greater (P less than 0.01) in gated images (end-diastolic) when compared with 12-second scans, both without contrast (22.2 vs. 7.7 CT#s) and with contrast (20.2 vs. 11.2 CT#s). In this study variability of myocardial CT measurements increased as scan time decreased, with radiographic contrast enhancement and with gating cardiac images.

An Improved Correction of Distorted Indicator-Dilution Curves

Venoarterial indicator dilution curves are distorted by non-ideal injection and by the monitoring system. An improved method of correcting these curves is developed assuming that a linear model of perfect mixers in series can be fitted to the physiologic system response as well as to the subsystem responses.