A fast nonlinear method for parametric imaging of positron emission tomography data

The goal of this work was to develop a novel method for analyzing positron emission tomography data. Parametric imaging is the part of the PET data analysis process whereby images of physiologic and biochemical parameters are generated. Parametric images represent a stage beyond a typical PET image, and reflect physiologic function in a quantitative way. There are several known methods for parametric imaging, but all have some drawbacks. The proposed new method is a very fast nonlinear method. All other methods are fast or nonlinear but not both.; PET data analysis proceeds in two stages. Image reconstruction yields an estimate of radiation intensity as a function of space and time: a dynamic PET image. Each pixel in a dynamic image is a time series: a time-activity curve (TAC). Parametric imaging is accomplished by fitting a mathematical model to TAC data to estimate physiologic parameters: a tracer kinetic model. An example of parametric imaging is estimation of myocardial perfusion in units of ml/min/g from dynamic 13N ammonia PET data.; Weighted nonlinear regression (WNLR) is the gold standard method for parameter estimation and parametric imaging with tracer kinetic models. The WNLR method has a strong theory and is quite general. But it is iterative and expensive to compute. Further, the iteration will not converge in the presence of the high noise typical of human studies. A fast alternative to WNLR methods are linearizing methods, which speed solution by using some form of integration followed by linear regression. Linearizing methods can be fast and accurate, but still have some drawbacks. No linearizing method handles nonlinear tracer kinetic models. And such methods require model-specific nonlinear algebra to recover the parameters of the tracer kinetic model.; We propose a new nonlinear method based on sigmoidal networks. Sigmoidal networks are a general method for the estimation of nonlinear functions by simulation. A model of TAC data is developed from which simulated data are drawn. A sigmoidal network is then optimized to fit the data. Once fit, the network produces nonlinear parametric images in only seconds. Further, we preprocesses the network training data by an optimal WNLR method computable by simulation only. Therefore, the method is a hybrid nonlinear method that combines the accuracy of WNLR with the speed of sigmoidal networks.; We have compared sigmoidal network methods to WNLR methods and linearizing methods for estimation of model parameters from 13N ammonia and 18F fluorodeoxyglucose data. Simulation studies have validated the sigmoidal network approach relative to WNLR using ranges of models parameters very similar to experimental data. Parametric images of experimental data generated by sigmoidal networks compare favorably to WNLR in statistical performance, but can be computed in just seconds versus hours for WNLR. Though linearizing methods for parameter estimation can be quite good, under some circumstances sigmoidal networks are closer to WNLR and even cheaper to compute than linearizing methods.