Parameter estimation strategies for dynamic cardiac studies using emission computed tomography.

Abstract

The conventional method of estimating cardiac functional parameters using emission computed tomography (ECT) uses reconstructed ECT images to delineate regions of interest. The temporal behavior of the concentration of radio-labeled tracers within these regions is used to estimate compartmental model parameters specific to the defined regions. This method ignores region specification errors and is subject to greater uncertainty. In this thesis, based on a rigorous framework, we develop strategies for joint estimation of heart boundaries and functional parameters. In this framework, we use the Cramer-Rao lower bound to characterize the ultimate estimation accuracy. The lower bound is based on an integrated data acquisition protocol in which all measurements required for functional parameter estimation (including plasma tracer concentration) are estimated from ECT data. The bound is independent of any image reconstruction and parameter estimation methods. The joint estimation uses maximum likelihood (ML) criteria and is based on an observation model that employs boundary parameterization. The ML estimator uses Fisher scoring, positivity constraints, and Marquardt's method. To overcome difficulties in boundary estimation in low count rate and low contrast situations, we extend the joint estimation to include the use of boundary side information and boundary regularization. To fuse boundary side information into the joint estimation, we derive a joint log-likelihood to include ECT measurements as well as auxiliary boundary measurements. In addition, we introduce registration parameters to align auxiliary boundary measurements with ECT measurements and jointly estimate these parameters with other parameters of interest from both measurements. We formulate myocardial boundary regularization in various ways and experimentally examine each formulation. Throughout the thesis, the lower bound serves as a gauge against which estimation performance is evaluated. We demonstrate in simulated low contrast $\rm H\sb2\sp{15}O$ perfusion studies that the estimation strategies (including use of boundary side information and boundary regularization) are nearly optimal for the nominal parameter values tested because they nearly achieve the lower bound for perfusion estimation.