Positron Emission Tomography » Dynamic

Dynamic PET imaging usually involves a sequence of contiguous acquisitions each of which can range in duration from 10 seconds to over 20 minutes. Data from each of the frames is independently reconstructed to form a set of images which can be visualized and used to estimate physiological parameters. This approach involves selection of the set of acquisition times, where one must choose between collecting longer scans with good counting statistics but poor temporal resolution, or shorter scans that are noisy but preserve temporal resolution.

List-mode data acquisitions provide extremely high temporal resolution with full spatial resolution. List-mode data can be binned into sinograms, allowing frame durations to be determined after acquisition. Alternatively, the problem of temporal binning can be avoided entirely by directly using the arrival times in the list-mode data to estimate a dynamic image. This is the approach that we have taken in our dynamic work..

Our approach is similar in spirit to that of Synder who developed a list-mode EM method for estimation of dynamic PET images using inhomogeneous Poisson processes. Each voxel has an associated time-varying tracer density that is modeled using basis functions that are based on assumptions about the physiological processes generating the data, e.g. blood activity curves convolved with a basis of exponentials. The observed list-mode PET data are then inhomogeneous Poisson processes whose rate functions are linear combinations of the dynamic voxel tracer densities. We follow a similar approach but instead work with rate functions formed as a linear combination of B-spline basis functions estimated with a conjugate gradient penalized ML approach. Not only do the linearity of the model and compact support of the basis functions lend themselves to efficient computation of the estimates, but also we can better represent the dynamic activity seen in experimental data that is not well modeled by the more restrictive physiological models.

An advantage of using list-mode data arises in cases where the number of detected photon pairs is far less than the total number of detector pairs. This is often the case in modern 3D PET systems which can have in excess of 10^8 sinogram elements in a single frame. To reduce this number to manageable proportions, the data are often rebinned by adding adjacent elements together. Alternatively, the raw list-mode data case be stored and the need for rebinning is avoided. Parra and Barrett describe a list-mode maximum likelihood method for estimation of a temporally stationary image. While this method will often reduce storage costs and avoid the need for rebinning, the random spatial ordering of the detected events in the list-mode data does not lend itself to fast forward or backprojection or exploitation of the many symmetries in 3D projection matrices. To avoid this problem we use a hybrid combination of the standard sinogram and list-mode formats that allow the reconstruction algorithm to exploit the same matrix symmetries used in our static imaging work. All events in a dynamic study are collected into a single standard sinogram which is augmented by a ``timogram'' that contains the arrival times of each event stored so that they are indexed using the values in the associated sinogram.

Our preliminary results on direct dynamic imaging are based on reconstruction of volumetric data as a set of continguous 2D slices in which we estimate a continuous time-activity curve for each voxel. We have applied this approach to both simulated and experimental PET data. Experimental data include a brain activation study using O-15-labelled water collected on the EXACT HR+ (courtesy of Dave Towsend and colleagues, University of Pittsburgh) and a C-11-labelled raclopride study collected on the EXACT HR++ (courtesy of Peter Blookmefied and colleagues at the Hammersmith Hospital, London). In each of these studies, we used single-slice rebinning of the 3D data into equivalent sets of 2D sinograms (and their related timograms) and then reconstructed the volumes slice by slice. The result is a 4D function that may be best viewed as a 2D or 3D movie showing the changes in tracer density. we show sample transaxial images from the raclopride study and time activity curves for various regions of interest. These results are preliminary but appear consistent with the dynamics one would expect with raclopride.

Figure: Sample transaxial images from a raclopride study and time activity curves for various regions of interest. These results are preliminary but appear consistent with the dynamics one would expect with raclopride C-11 Raclopride study (top-left) a 2D transaxial section through striatum showing activity integrated over the full 5,700 second acquisition; (top-right) and (bottom-right) sample images of the continuous time reconstructions obtained by sampling the B-spline curves at each voxel at times t=150sec and t=1200sec; we also show decay-corrected time activity curves averaged over 25-voxel ROIs for scalp (lower curve), cortex (middle curve) and striatum (upper curve). [Raclopride data courtesy of P. Bloomfield.

Video: This mpeg movie shows an animation of the activity in a 2D transverse section through the striatum. A total of 90 frames are included with an inter-frame interval of 30 seconds. [Caution: don't try this at home! size: 4.8MB]

Figure: This mpeg movie shows a 3D animation of O-15 labelled water as it passes through the carotid arteries and then quickly perfuses throuhout the brain. A total of 50 frames are used with an interval of 1 second between frames. [size: only 137K]

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