Enhancements are described for an approach that unifies edge preserving smoothing with segmentation of time sequences of volumetric images, based on differential edge detection at multiple spatial and temporal scales. Potential applications of these 4-D methods include segmentation of respiratory gated positron emission tomography (PET) transmission images to improve accuracy of attenuation correction for imaging heart and lung lesions, and segmentation of dynamic cardiac single photon emission computed tomography (SPECT) images to facilitate unbiased estimation of time-activity curves and kinetic parameters for left ventricular volumes of interest. Improved segmentation of lung surfaces in simulated respiratory gated cardiac PET transmission images is achieved with a 4-D edge detection operator composed of edge preserving 1-D operators applied in various spatial and temporal directions. Smoothing along the axis of a 1-D operator is driven by structure separation seen in the scale-space fingerprint, rather than by image contrast. Spurious noise structures are reduced with use of small-scale isotropic smoothing in directions transverse to the 1-D operator axis. Analytic expressions are obtained for directional derivatives of the smoothed, edge preserved image, and the expressions are used to compose a 4-D operator that detects edges as zero-crossings in the second derivative in the direction of the image intensity gradient. Additional improvement in segmentation is anticipated with use of multiscale transversely isotropic smoothing and a novel interpolation method that improves the behavior of the directional derivatives. The interpolation method is demonstrated on a simulated 1-D edge and incorporation of the method into the 4-D algorithm is described.
KEYWORDS: Data modeling, Heart, Blood, Matrices, Spectral resolution, Tissues, Data acquisition, Monte Carlo methods, Biological research, Systems modeling
Physiologic systems can be represented by compartmental models which describe the uptake of radio-labeled tracers from blood to tissue and their subsequent washout. Arterial and venous time-activity curves from isolated heart experiments are analyzed using spectral analysis, in which the impulse response function is represented by a sum of decaying exponentials. Resolution and uniqueness tests are conducted by synthesizing isolated heart data with predefined compartmental models, adding noise, and applying the spectral analysis technique. Venous time-activity curves are generated by convolving a typical arterial input function with the predefined spectrum. The coefficients of a set of decaying exponential basis functions are determined using a non- negative least squares algorithm, and results are compared with the predefined spectrum. The uniqueness of spectral method solutions is investigated by computing model covariance matrices, using error propagation and prior knowledge of noise distributions. Coupling between model parameters is illustrated with correlation matrices.
KEYWORDS: 3D modeling, Positron emission tomography, Data modeling, Visualization, Tomography, 3D image processing, Magnetic resonance imaging, Data acquisition, Software development, 3D acquisition
In the physiologic modeling of dynamic positron emission tomography (PET) data, one is typically interested in the average reconstructed activity for voxels within the boundaries of some volume of interest (VOI), the uncertainty of this value, and possibly correlations with other VOIs. These calculations have been partially carried out in the past by drawing appropriate 2D regions on a number of reconstructed images in a PET volume, and then summing the voxel values within these regions. Summing voxel values in this fashion provides a value for activity within a volume, but does not allow calculation of the statistical uncertainty. To perform the latter task, calculations must be performed on the raw tomographic data, and thus the 2D regions must be specified on the originally acquired tomographic slices. We have developed software enabling clinicians to specify regions along any preferred viewing axis, and yet perform calculations on these regions to obtain the complete VOI covariance matrix. In this process, 2D regions are first drawn on slices of arbitrary orientation. Stacks of these regions are then tiled together to form a closed 3D surface model for each VOI. Cross sections of these VOIs in the originally acquired orientation are obtained by intersecting the 3D surface models with a series of appropriately transformed slicing planes. The resliced regions are then projected into tomographic sinogram space and the activity and uncertainty is calculated for each region. Knowledge of the complete covariance matrix allows combination of these 2D region activity values into 3D volume activity values and uncertainties.
The purpose of this research was to compare a physiological model of 82Rb in the myocardium with two reduced order models with regard to their ability to assess physiological parameters of diagnostic significance. A three compartment physiological model of 82Rb uptake in the myocardium was used to simulate kinetic region of interest data from a positron emission tomograph (PET). Simulations were generated for eight different blood flow rates reflecting the physiological range of interest. Two reduced order models which are commonly used with myocardial PET studies were fit to the simulated data and the parameters of the reduced order models were compared with the physiological parameters. Then all three models were fit to the simulated data with noise added. Monte carlo simulations were used to evaluate and compare the diagnostic utility of the reduced order models.
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