Left ventricular finite element model bounded by a systemic circulation model.

A series of models were developed in which a circulatory system model was coupled to an existing series of finite element (FE) models of the left ventricle (LV). The circulatory models were used to provide realistic boundary conditions for the LV models. This was developed for the JSim analysis package and was composed of a systemic arterial, capillary, and venous system in a closed loop with a varying elastance LV and left atria to provide the driving pressures and flows matching those of the FE model. Three coupled models were developed, a normal LV under normotensive aortic loading (116/80 mm Hg), a mild hypertension (137/89 mm Hg) model, and a moderate hypertension model (165/100 mm Hg). The initial step in the modeling analysis was that the circulation was optimized to the end-diastolic pressure and volume values of the LV model. The cardiac FE models were then optimized to the systolic pressure/volume characteristics of the steady-state JSim circulatory model solution. Comparison of the stress predictions for the three models indicated that the mild hypertensive case produced a 21% increase in the average fiber stress levels, and the moderate hypertension case had a 36% increase in average stress. The circulatory work increased by 18% and 43% over that of the control for the mild and moderate hypertensive cases, respectively.

An FDK-like cone-beam SPECT reconstruction algorithm for non-uniform attenuated projections acquired using a circular trajectory.

In this paper, Novikov's inversion formula of the attenuated two-dimensional (2D) Radon transform is applied to the reconstruction of attenuated fan-beam projections acquired with equal detector spacing and of attenuated cone-beam projections acquired with a flat planar detector and circular trajectory. The derivation of the fan-beam algorithm is obtained by transformation from parallel-beam coordinates to fan-beam coordinates. The cone-beam reconstruction algorithm is an extension of the fan-beam reconstruction algorithm using Feldkamp-Davis-Kress's (FDK) method. Computer simulations indicate that the algorithm is efficient and is accurate in reconstructing slices close to the central slice of the cone-beam orbit plane. When the attenuation map is set to zero the implementation is equivalent to the FDK method. Reconstructed images are also shown for noise corrupted projections.

Reconstruction of dynamic renal tomographic data acquired by slow rotation.

UNLABELLED: Nuclear medicine renal studies can be performed using slow-rotation SPECT, but reconstruction of such data is largely underdetermined. METHODS: A new method of reconstruction of data acquired using slow camera rotations was developed. In this method we used a factor model of the data in which the factors and factor coefficients were determined by modeling their relationship directly with the projection measurements. This was done by solving a least-squares problem that fits the projections of factors and factor coefficients to the projection data with nonnegativity constraints imposed on the solution. The method was tested on computer simulations and applied to experimental renal (99m)Tc-mercaptoacetyltriglycine canine and patient studies. RESULTS: Computer simulations showed that the extracted time-activity curves of kidneys agreed well with the simulated curves for data with noise levels similar to those in the experimental studies. In the canine study, the method showed that >2 factors were necessary to adequately reproduce the kinetics of the kidney. In the patient study, the method was able to extract separate factors that correspond to the kidney cortex and the kidney pelvis. CONCLUSION: The computer simulation, the canine study, and the patient study all show that reconstructions of the data obtained with 1 detector displayed artifacts, whereas reconstructions of the data obtained with 2 and 3 detectors were free of artifacts. Computer simulations showed that the method gives accurate results that allow quantitation.

Effect of truncated projections on defect detection in attenuation-compensated fanbeam cardiac SPECT.

UNLABELLED: For some camera systems used in cardiac SPECT, the limited field of view of fanbeam-collimated detectors produces truncation in the projection data. This truncation may generate artifacts and distortions in the transmission CT images and in the attenuation-corrected myocardial SPECT images (that use the transmission CT images as attenuation maps), thus affecting clinical diagnosis. Concern over this problem stimulated us to evaluate the effect of truncation with human observer performance studies. METHODS: A three-dimensional mathematical cardiac-torso phantom that realistically models the attenuation and 201Tl uptake distributions in different organs of the upper torso was used for the investigation. Five degrees of truncation (from 0% to 40% truncation) in the projection data were simulated by the use of five different detector sizes collimated by fanbeam collimators. The attenuation maps were obtained by reconstructing the truncated transmission data generated from these fanbeam geometries. The emission data obtained with the same fanbeam geometries were reconstructed by using the maximum likelihood-expectation maximization algorithm and were corrected for attenuation using the reconstructed attenuation maps. Two observer performance studies were performed. In Study 1, the images were reconstructed without using the body contour as support, whereas in Study 2, the exact body contour was used in reconstructing both the attenuation maps and the attenuation-corrected SPECT images. RESULTS: The results of the receiver operating characteristics analysis indicate that there is very little difference between detection for the various degrees of truncation, and this difference only becomes noticeable for severe truncation of greater than 40%. CONCLUSION: Using the acquisition and processing methods, we found the use of the body contour as support in reconstructing truncated transmission CT and SPECT data reduces the loss of defect detectability in attenuation-compensated myocardial SPECT images due to truncated data.

A count-based algorithm for attenuation-corrected volume determination using data from an external flood source.

We discuss the basic features of a count-based algorithm for attenuation-corrected volume determination, for use with planar gamma camera images. The attenuation correction is arrived at by combining the results of two 180 degrees opposed images with a transmission image obtained with an external flood source. A sample of the imaged radioactive volume is used to convert the attenuation-corrected count to an absolute volume. The algorithm is best suited to the measurement of small to medium-sized volumes of uniform activity, such as are encountered in cardiac blood-pool imaging.

SPECT liver imaging using an iterative attenuation correction algorithm and an external flood source.

The results obtained from the inclusion of a new intrinsic attenuation correction algorithm into a protocol for SPECT liver imaging are presented in this study. A total of six patients were evaluated with this protocol. The new algorithm uses a transmission tomographic acquisition that is obtained before a standard emission tomograph, and requires the use of an external flood source. The transmission tomograph results in an attenuation image, or map, of the patient. The attenuation map then serves as input into the final intrinsic correction algorithm, that also uses data from a standard emission acquisition. The results of the six patients studied show that the algorithm can correct for attenuation effects without degrading image quality. In all the cases studied, the attenuation corrected images made the cases easier to interpret than did the images obtained without attenuation correction.

Kinetic modeling of teboroxime using dynamic SPECT imaging of a canine model.

UNLABELLED: The tomographic utility of 99mTc-labeled teboroxime has been limited because of its fast washout from the heart, which requires rapid data acquisitions that have not been feasible until the recent development of multidetector SPECT systems. METHODS: Using a three-detector SPECT system to acquire dynamic tomographic data every 10.2 sec, we investigated the potential of modeling the kinetics of teboroxime to develop a sensitive and quantitative measure of cardiac perfusion. Seven studies were performed on four dogs; in three of the studies the LAD artery was occluded. The three-dimensional activity distributions were reconstructed and were corrected for attenuation using a transmission scan. Time-activity curves from the blood and tissue were fit to a two-compartment model with two-way exchange. RESULTS: Performing attenuation correction during the reconstruction process affected the washin parameter k21 significantly (p < 0.0001). The washin parameter k21 also decreased significantly (p < 0.002) when the LAD was occluded. CONCLUSIONS: The results indicate that the washin of teboroxime in myocardial tissue (k21) measured using dynamic SPECT imaging and kinetic modeling is an indicator of myocardial blood flow.

Quantitative potentials of dynamic emission computed tomography.

Statistical uncertainties in emission computed tomography were simulated in 60 computer studies involving various numbers of events and distributions of activity. Previous studies have shown that for a uniform disc of activity of rms percentage of uncertainty per resolution cell is: 120 X (number of resolution cells)1/4 X (number of events per resolution cell)- 1/2. In this work we examined the more general situation where one or two regions of uniform activity are surrounded by a uniform background, and found that for an equal number of recorded events the uncertainties were reduced when the activity was concentrated in a portion of the field. The empirical relation rms % uncertainty in nt = 120(N)1/4(nt)-3/4, where nt is the number of events in an average target (organ) resolution cell and N is the total number of events recorded, satisfactorily described the relationships between uncertainties, contrast, total number of detected events, and number of resolution cells for all 60 computer studies. By means of this relation, we show the theoretical possibility of gated cardiac imaging with 20% uncertainty in 1 cm X 1 cm regions, and of 1-sec cerebral blood-flow images with 20% uncertainty in 2 cm X 2 cm regions.

Design and clinical utility of a fan beam collimator for SPECT imaging of the head.

A long bore fan beam collimator for imaging the head was designed and constructed for a SPECT system with a rotating scintillation camera. In order to avoid the patient's shoulder during rotation of the camera with a thick camera housing, the long bore design is necessary to allow the collimator to get close to the patient's head for improved spatial resolution. Operating at the minimum radius of rotation, the prototype fan beam collimator provides about the same spatial resolution as the high resolution collimator, while the geometric efficiency is equal to approximately 85% of that of the general purpose and approximately 55% higher than the high resolution collimator. Images from a phantom study demonstrate good image quality and are void of artifacts. Comparative clinical studies on temporomandibular joints (TMJ) between the LEGP and fan beam collimators also confirm the superior image quality obtained with the fan beam collimator.

Correction of nonuniform attenuation in cardiac SPECT imaging.

Correction for photon attenuation in cardiac SPECT imaging using a measured attenuation distribution with an iterative expectation maximization (EM) algorithm and an iterative Chang algorithm were compared with the conventional filtered backprojection and an iterative EM algorithm without attenuation correction. The attenuation distribution was determined from a transmission computed tomography study that was obtained using an external collimated sheet source. The attenuation of the emitting photons was modeled in the EM algorithm by an attenuated projector-backprojector that used the estimated attenuation distribution to calculate attenuation factors for each pixel along each projection and backprojection ray. Results from a heart-lung phantom study and a 201Tl patient study demonstrated that the iterative EM algorithm with attenuation correction provided improved image quality in terms of reduced streak artifacts and noise, and more accurate quantitative information in terms of improved radioactivity distribution uniformity where uniformity existed, and better anatomic object definition.

Regional distribution of myocardial blood flow measured by single-photon emission tomography: comparison with in vitro counting.

An emission computed tomography system (SPECT), which uses a single large-field-of-view gamma camera, was evaluated for its ability to measure the relative distribution of myocardial blood flow and to assess the effect of attenuation, scatter, and cardiac motion on the tomographic images. Normalized regional myocardial counts from the SPECT images of the living dogs correlated closely with those from the anatomic slices and the samples counted at necropsy except for an over-estimate of tracer in the perfusion defect (SPECT) 57.7 compared to tissue count 32.1; p less than 0.05. The differences were less for the other imaging conditions. Heart and thorax motion, attenuation, and scatter contributed less than 25% to the over-estimate of defect counts. We conclude that the SPECT system accurately reflects regional distribution of myocardial blood flow except for overestimation of flow in regions of perfusion defects. Small perfusion defects might therefore be missed, but no artifactual defects are created.

Iterative reconstruction of fluorine-18 SPECT using geometric point response correction.

UNLABELLED: This article demonstrates resolution recovery in 18F SPECT image reconstruction by using an iterative algorithm that corrects for the system geometric response. METHODS: Patient and phantom studies were performed using a Picker PRISM 3000 three-detector SPECT system (Picker International, Inc., Cleveland, OH) to image 18F with 511 keV collimators. A measured point response function of the imaging system was used in an iterative reconstruction algorithm in which the projector and backprojector modeled the system point response function by using an efficient layer-by-layer blurring technique. The blurring function was a five-element kernel in the shape of a cross. The iterative reconstruction algorithm was an ordered-subset maximum-likelihood expectation maximization algorithm. RESULTS: The iterative reconstruction algorithm with geometric response correction showed an improvement in resolution over the filtered backprojection reconstruction and the iterative reconstruction without correction. CONCLUSION: The proposed iterative reconstruction algorithm with geometric response correction is efficient and effective with significant resolution recovery.

Application of convergent-beam collimation and simultaneous transmission emission tomography to cardiac single-photon emission computed tomography.

Single-photon emission computed tomography (SPECT) is the most commonly performed imaging technique for perfusion studies of the heart and brain. However, these organs are much smaller than the crystal surface of gamma cameras. SPECT sensitivity and resolution can be improved by using fan- and cone-beam collimators to magnify the image of these organs over a larger portion of the crystal face. Special orbits and reconstruction algorithms must be used with convergent-beam acquisitions to prevent image distortion. Differential attenuation of source activity in the chest is one of the most vexing problems in cardiac SPECT, especially with Thallium-201. Multi-headed cameras equipped with convergent-beam collimators allow a transmission image to be obtained at the same time as emission images. Applying a transmission map of the chest attenuation values to the emission images produces a truer picture of source distribution in the heart. This article reviews the technical problems associated with convergent-beam geometry and simultaneous transmission emission tomography SPECT imaging of the heart.

Evaluation of cardiac cone-beam single photon emission computed tomography using observer performance experiments and receiver operating characteristic analysis.

RATIONALE AND OBJECTIVES: Single photon emission computed tomography (SPECT) with a cone-beam collimator improves the trade-off between detection efficiency and spatial resolution for cardiac imaging. However, acquisitions using orbits where the focus remains in a plane do not provide sufficient data for exact reconstruction. In the current study the authors evaluate the clinical utility of planar-orbit cone-beam SPECT in detecting a simple myocardial defect. METHODS: Observer performance experiments compared high-resolution cone-beam with same-resolution parallel-hole and fan-beam collimator designs in myocardial defect detection using a computer-simulated cardiac model. The uptake of Thallium-201 in the myocardium and other tissue organs was modeled by a mathematical three-dimensional upper torso phantom from which physically realistic projections were simulated. Eight observers viewed reconstructed transaxial images from the three collimator designs and indicated the certainty with which they detected a Gaussian-shaped defect at a specified location. RESULTS: The area under the receiver operating characteristic curve indicated that the cone-beam design, regardless of slice position, was superior to the fan-beam, which in turn was superior to the parallel-hole design for the specified detection task. CONCLUSIONS: The observer study demonstrated that reconstruction artifacts resulting from insufficient data sampling do not hinder obtaining improved diagnostic information from planar-orbit cone-beam cardiac SPECT images compared to conventional cardiac SPECT using parallel-hole and fan-beam collimators.

Cone beam tomography of the heart using single-photon emission-computed tomography.

The authors evaluated cone beam single-photon emission-computed tomography (SPECT) of the heart. A new cone beam reconstruction algorithm was used to reconstruct data collected from "short scan" acquisitions (of slightly more than 180 degrees) of a detector anteriorally traversing a noncircular orbit. The less than 360 degrees acquisition was used to minimize the attenuation artifacts that result from reconstructing posterior projections of 201T1 emissions from the heart. The algorithm includes a new method for reconstructing truncated projections of background tissue activity that eliminates reconstruction ring artifacts. Phantom and patient results are presented which compare a high-resolution cone beam collimator (50-cm focal length; 6.0-mm full width at half maximum [FWHM] at 10 cm) to a low-energy general purpose (LEGP) parallel hole collimator (8.2-mm FWHM at 10 cm) which is 1.33 times more sensitive. The cone beam tomographic results are free of reconstruction artifacts and show improved spatial and contrast resolution over that obtained with the LEGP parallel hole collimator. The limited angular sampling restrictions and truncation problems associated with cone beam tomography do not deter from obtaining diagnostic information. However, even though these preliminary results are encouraging, a thorough clinical study is still needed to investigate the specificity and sensitivity of cone beam tomography.

An analytical approach to quantify uniformity artifacts for circular and noncircular detector motion in single photon emission computed tomography imaging.

Uniformity artifacts in rotating gamma camera tomography will result if there are errors in the correction factors which are routinely calculated from a static uniformity flood image. The accuracy of the correction factors is a function of the statistics in the collected flood image. Since the factors are applied to each projection view, an error in a correction factor will propagate as a projection error at the same pixel location for each view. For circular detector motion, the error in each projection is reconstructed as a ring whose maximum amplitude varies approximately inversely proportional to the square root of the distance of the projection error from the center of rotation. For noncircular detector motion the artifacts are not rings but are more complicated geometric curves. Simulations show that statistical fluctuations in the reconstructed image will mask the uniformity artifacts provided the correction flood satisfies minimum count requirements. An analytical expression is derived for the percent root-mean-square (% rms) error in the reconstruction and is compared with the percent relative amplitude error (% RAE) of the reconstructed artifacts in order to obtain expressions for uniformity flood counting statistics. For an elliptical source distribution with total counts equal to CT, the uniformity statistics required to reconstruct elliptical disks is inversely proportional to the square root of the area: U greater than or equal to KCT/area 1/2. The constant K depends on the filter function and type of detector motion.

Signal-to-noise efficiency in magnetic resonance imaging.

The dependence of signal-to-noise ratio (SNR) on the analog filter, the sampling rate and the number and dimensions of voxels is derived for magnetic resonance imaging (MRI). It is shown that the object signal-to-noise ratio scales directly with the voxel volume and the square root of the number of voxels. Defining an efficiency figure of merit as the SNR divided by the square root of the imaging time, it is shown that efficiency is always improved when imaging with the lowest possible resolution (largest voxel dimensions) consistent with viewing the desired anatomical detail. The results directly imply the relative efficiency of 3-D (volume), 2-D (plane), 1-D (line) and 0-D (point) imaging techniques. It is shown that spatial averaging is an inefficient method of noise reduction in MRI. As long as voxel size is maintained constant, one can image as many pixels in the readout direction as desired with no loss in SNR; that is, the number of pixels in the readout direction has no effect on the image SNR. Further, multiple sampling of each phase encoding value (to improve SNR) has no advantage over increasing the number of pixels in the phase encoding direction while leaving the voxel size constant. Some experimental observations are given.

A simulation of emission and transmission noise propagation in cardiac SPECT imaging with nonuniform attenuation correction.

Transmission computed tomography provides information needed for nonuniform attenuation correction of cardiac single photon emission computed tomography (SPECT). Nonuniform attenuation correction is accomplished using an iterative ML-EM algorithm and a projection-backprojection operation that incorporates attenuation factors measured from the reconstructed transmission map. The precision and accuracy of the attenuation corrected emission reconstruction is a function of emission and transmission statistics. This paper presents an error propagation analysis that uses a mathematical cardiac chest phantom to simulate various combinations of total emission counts C and transmission flux I0 under ideal imaging conditions (without geometric response distortion and without scatter). The spatial average, spatial variance, and accuracy measures for a 4 x 4 pixel region in the heart are tabulated after 30 iterations of the ML-EM algorithm. The confidence intervals for these measures were determined from 1000 realizations of reconstructions from projections randomly generated with the same transmission and emission statistics. It can be shown empirically from the simulation results that the spatial %rms uncertainty for the simulated cardiac region has a simple expression: %rms2 = K1/C+K2/I0(2)+B2 where K1 and K2 are least-square estimates based on the simulation results, and B is the measured spatial %rms uncertainty for the simulation at infinite statistics. For a transmission incident flux of 1500 events per projection bin of 0.712 cm and typical clinical emission events totaling 1 x 10(5), the spatial %rms uncertainty is approximately 14%. At clinical transmission and emission statistics, the statistical noise in the simulated attenuation-corrected reconstructions are dominated by the emission statistics.

The solution of Bloch equations for flowing spins during a selective pulse using a finite difference method.

The movement of spins during periods of selective pulses result in a modulation of the signal intensity and phase of the received magnetic resonance imaging (MRI) signal, and is a major cause of signal loss from vessels imaged with slice-selective pulses. Methods are well developed for compensation of phase perturbations for spins flowing at constant velocity during the time of applied gradients. However, for spins flowing during selective pulses, the magnitude of the amplitude and phase perturbations has not been understood nor to this time has any method of flow compensation been proposed. This is due in part to the difficulty in using the Bloch equations to quantify the amplitude and phase modulation during radiofrequency (rf) excitation since solutions cannot be obtained analytically. In this paper a finite difference method is used to solve Bloch equations for flowing spins during a 90 degrees selective pulse. Compared with stationary spins, the magnetization distribution for flowing spins exhibits a shift of the slice profile in the direction of the flow, an expansion of the profile, phase shifts, and changes in profile shape. The profiles show residual phase errors which become more severe with higher flow velocities, with flow compensation schemes which apply in the case of spins flowing during applied gradients, and in the absence of an rf pulse. The measurement and understanding of the magnetization distribution is important to designing pulse sequences that compensate for flow. Flow compensated pulse sequences are necessary to reduce image flow artifacts and to increase signal of vessels in MR angiographic images.

An investigation of the effect of finite system resolution and photon noise on the bias and precision of dynamic cardiac SPECT parameters.

The exchange of a radionuclide (and similarly of oxygen) between blood and the myocardium is a dynamic process. Dynamic SPECT offers the possibility of directly quantifying the kinetic parameters which describe this process. In this paper we investigate and quantify the effect of typical SPECT system resolution and photon counting statistics on the bias and precision of dynamic cardiac SPECT parameters. System resolution and photon noise are only two of the image degrading processes which occur in SPECT. Therefore, the bias and precision quoted should be viewed as a lower limit on those which could be expected with an experimental study. Dynamic SPECT projection data are simulated using a realistic human torso phantom. Data are simulated assuming both perfect system resolution and a system resolution typical of a clinical SPECT system. A triple detector SPECT system which acquires a full set of projection data in 10 s using continuous detector motion is modelled. Kinetic parameters are estimated using a number of myocardial regions of interest. The results show that the rate constant characterizing the washing of activity into the myocardium is more sensitive to region of interest position than is the washout rate constant. The bias and precision of the dynamic parameters are estimated from multiple realizations of projection data exhibiting various noise levels. The main effect of increased photon noise in the projection data is to decrease the precision of the estimated parameters. However, there is also some evidence that for high noise levels the bias of the parameters may also be affected.