Gregory J. Klein

List-mode maximum-likelihood reconstruction applied to positron emission mammography (PEM) with irregular sampling

Presents a preliminary study of list-mode likelihood reconstruction of images for a rectangular positron emission tomograph (PET) specifically designed to image the human breast. The prospective device consists of small arrays of scintillation crystals for which depth of interaction is estimated. Except in very rare instances, the number of annihilation events detected is expected to be far less than the number of distinguishable events. If one were to histogram the acquired data, most histogram bins would remain vacant. Therefore, it seems natural to investigate the efficacy of processing events one at a time rather than processing the data in histogram format. From a reconstruction perspective, the new tomograph presents a challenge in that the rectangular geometry leads to irregular radial and angular sampling, and the field of view extends completely to the detector faces. Simulations are presented that indicate that the proposed tomograph can detect 8-mm-diameter spherical tumors with a tumor-to-background tracer density ratio of 3:1 using realistic image acquisition parameters. Spherical tumors of 4-mm diameter are near the limit of detectability with the image acquisition parameters used. Expressions are presented to estimate the loss of image contrast due to Compton scattering.

Real-time system for respiratory-cardiac gating in positron tomography

A Macintosh-based signal processing system has been developed to support simultaneous respiratory and cardiac gating on the ECAT EXACT HR PET scanner. Using the Lab-View real-time software environment, the system reads analog inputs from a pneumatic respiratory bellows and an ECG monitor to compute an appropriate histogram memory location for the PET data. Respiratory state is determined by the bellows signal amplitude; cardiac state is based on the time since the last R-wave. These two states are used in a 2D lookup table to determine a combined respiratory-cardiac state. A 4-bit address encoding the selected histogram is directed from the system to the ECAT scanner, which dynamically switches the destination of tomograph events as respiratory-cardiac state changes. To test the switching efficiency of the combined Macintosh/ECAT system, a rotating emission phantom was built. Acquisitions with 25 msec states while the phantom was rotating at 240 rpm demonstrate the system could effectively stop motion at this rate, with approximately 5 msec switching time between states.

Non-rigid summing of gated PET via optical flow

A method for summing together datasets from gated cardiac PET acquisitions is described. Optical flow techniques are used to accurately model non-rigid motion present during the cardiac cycle so that a one-to-one mapping is found between each voxel of two gated volumes. Using this mapping, image summing can take place, producing a composite dataset with improved statistics and reduced motion-induced blur. Results using a data from a gated cardiac study on a dog are presented.

Four-dimensional affine registration models for respiratory-gated PET

The heart position shifts considerably due to motion associated with the respiratory cycle, and this motion can degrade the image quality of cardiac-gated positron emission tomography (PET) studies. One method to combat this motion-induced blur is a respiratory-gated acquisition followed by recombination of registered image volumes using a rigid-body motion assumption; however, nonrigid deformation of the heart from respiratory motion may reduce the effectiveness of this procedure. We have investigated a 12-parameter global affine motion model for registration of different respiratory gates in an end-diastolic cardiac PET sequence. To obtain robust estimates of motion, a four-dimensional registration model was devised that encouraged smoothly varying motion between adjacent respiratory time frames. Registration parameters were iteratively calculated using a cost function that combined a least squares voxel difference measure with a penalty obtained from a prediction prior. The prior was calculated from adjacent time frames assuming constant velocity and an affine model. After registration, the principal extension ratios were calculated to measure the degree of nonrigid motion. In data from ten subjects, extension ratios of over 5% were common, indicating that an affine model may provide better registrations and in turn, better motion-corrected composite volumes than could a technique restricted to the six-parameter rigid body assumption.

Automated 3-D segmentation of respiratory-gated PET transmission images

As a preliminary step toward performing respiration compensated attenuation correction of respiratory-gated cardiac PET data, we acquired and automatically segmented respiratory-gated transmission data for a dog breathing on its own under gas anesthesia. Transmission data were acquired for 20 min on a CTI/Siemens ECAT EXACT HR (47-slice) scanner. Two respiratory gates were obtained using data from a pneumatic bellows placed around the dogs chest. For each respiratory gate, torso and lung surfaces were segmented automatically using a differential 3-D image edge detection algorithm. Three-dimensional visualizations showed that during inspiration the heart translated about 4 mm transversely and the diaphragm translated about 9 mm inferiorly. The observed respiratory motion of the canine heart and diaphragm suggests that respiration compensated attenuation correction may be necessary for accurate quantitation of high-resolution respiratory-gated human cardiac PET data. Our automated image segmentation results suggest that respiration compensated segmented attenuation correction may be possible using respiratory-gated transmission data obtained with as little as 3 min of acquisition time per gate.

A methodology for specifying PET VOIs using multimodality techniques

Volume-of-interest (VOI) extraction for radionuclide and anatomical measurements requires correct identification and delineation of the anatomical feature being studied. The authors have developed a toolset for specifying three dimensional (3-D) VOIs on a multislice positron emission tomography (PET) dataset. The software is particularly suited for specifying cerebral cortex VOIs which represent a particular gyrus or deep brain structure. A registered 3-D magnetic resonance image (MRI) dataset is used to provide high-resolution anatomical information, both as oblique two-dimensional (2-D) sections and as volume renderings of a segmented cortical surface. VOIs are specified indirectly in two dimensions by drawing a stack of 2-D regions on the MRI data. The regions are tiled together to form closed triangular mesh surface models, which are subsequently transformed into the observation space of the PET scanner. Quantification by this method allows calculation of radionuclide activity in the VOIs, as well as their statistical uncertainties and correlations. The methodology for this type of analysis and validation results are presented.

Deformable registration of multi-modal data including rigid structures

Multimodality imaging studies are becoming more widely utilized in the analysis of medical data. Anatomical data from computed tomography (CT) and magnetic resonance imaging (MRI) are useful for analyzing or further processing functional data from techniques such as positron emission tomography and single photon emission computed tomography (SPECT). When data are not acquired simultaneously, even when these data are acquired on a dual-imaging device using the same bed, motion can occur that requires registration between the reconstructed image volumes. As the human torso can allow nonrigid motion, this type of motion should be estimated and corrected. The authors report a deformation registration technique that utilizes rigid registration for bony structures while allowing elastic transformation of soft tissue to more accurately register the entire image volume. The technique is applied to the registration of CT and MR images of the lumbar spine.

Deformable model of the heart with fiber structure

A kinematic model of the heart with incompressibility constraints was implemented. It accounts for the effects of the heart fiber structure, which plays a major role in defining the exact motion of the heart during the cardiac cycle. The volume of the heart was divided into small cubical elements, and in each element the fiber direction was specified. This allows implementation of nearly any fiber structure and any geometry. We performed preliminary testing of the model. The model was deformed from its initial state to a final configuration, assuming that fibers shorten or elongate to some known new value for each element. This can simulate a beating heart if the elongations are known. The model was also deformed using imaging data as a priori information. Simple geometries of the cylinder and ellipsoid were used. We see the model as a tool to help in understanding the movement of the myocardium during the heart cycle and the impact of infarctions on that movement. We will use the model imaging information from experimental gated SPECT and PET. The validation of the model will be done with the tagged MRI imaging.

Elastic material model mismatch effects in deformable motion estimation

Deformable motion models are useful for analysis of dynamic datasets exhibiting non-rigid motion, as in gated cardiac PET. The authors employ an algorithm that obtains a vector field to describe the relative motion of each voxel between two data sets. The estimation is based on a two-component cost function: an image matching component, and a motion field smoothness component. An important aspect of obtaining an accurate motion field estimate is properly balancing the weight between the two cost components. The authors show that by using a material elastic model inspired by continuum mechanics, an intuitive interpretation of the weighting factors for the smoothness constraint may be obtained. Further, they show that mismatches between actual material elastic parameters and those used by the estimation algorithm can lead to greater estimation error. Results are validated using an ellipsoidal phantom simulating compressible and incompressible deformations.

4D affine registration models for respiratory-gated PET

The heart position shifts considerably due to motion associated with the respiratory cycle, and this motion can degrade the image quality of cardiac-gated PET studies. One method to combat this motion-induced blur is a respiratory-gated acquisition followed by recombination of registered image volumes using a rigid-body motion assumption; however, deformation of the heart from respiratory motion may reduce the effectiveness of this procedure. We have investigated a 12-parameter global affine motion model for registration of different respiratory gates in an end-diastolic cardiac PET sequence. To obtain robust estimates of motion, a 4D registration model was devised that encouraged smoothly varying motion between adjacent respiratory time frames. Registration parameters were iteratively calculated using a cost function that combined a least squares voxel difference measure with a penalty obtained from a prediction prior. The prior was calculated from adjacent time frames assuming constant velocity and an affine model. After registration, the principal extension ratios were calculated to measure the degree of non-rigid motion. In data from 10 subjects, extension ratios of over 5% were common, indicating that an affine model may provide better registrations and in turn, better motion-corrected composite volumes than could a technique restricted to the 6-parameter rigid body assumption.