Kinetic analysis of dynamic tracer data is performed with the goal of evaluating myocardial radiotracers for cardiac nuclear medicine imaging. Data from experiments utilizing the isolated rabbit heart model are acquired by sampling the venous blood after introduction of a tracer of interest and a reference tracer. We have taken the approach that the kinetics are properly characterized by an impulse response function which describes the difference between the reference molecule (which does not leave the vasculature) and the molecule of interest which is transported across the capillary boundary and is made available to the cell. Using this formalism we can model the appearance of the tracer of interest in the venous output of the heart as a convolution of the appearance of the reference tracer with the impulse response. In this work we parameterize the impulse response function as the sum of a large number of exponential functions whose predetermined decay constants form a spectrum, and each is required only to have a nonnegative coefficient. This approach, called spectral analysis, has the advantage that it allows conventional compartmental analysis without prior knowledge of the number of compartments which the physiology may require or which the data will support.

Nonlinear edge preserving smoothing often is performed prior to medical image segmentation. The goal of the nonlinear smoothing is to improve the accuracy of the segmentation by preserving changes in image intensity at the boundaries of structures of interest, while smoothing random variations due to noise in the interiors of the structures. Methods include median filtering and morphology operations such as gray scale erosion and dilation, as well as spatially varying smoothing driven by local contrast measures. Rather than irreversibly altering the image data prior to segmentation, the approach described here has the potential to unify nonlinear edge preserving smoothing with segmentation based on differential edge detection at multiple scales. The analysis of n-D image data is decomposed into independent 1-D problems that can be solved quickly. Smoothing in various directions along 1-D profiles through the n-D data is driven by a measure of local structure separation, rather than by a local contrast measure. Isolated edges are preserved independent of their contrast, given an adequate contrast to noise ratio.

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.