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IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL 13. NO. 2, JUNE 1994 217 Model-Based Estimation for Dynamic Cardiac Studies Using ECT Ping-Chun Chiao, W. Leslie Rogers, Neal H. Clinthorne, Jeffrey A. Fessler, and Alfred 0. Hero Abstract-In this paper, we develop a strategy for joint esti- mation of physiological parameters and myocardial boundaries using ECT (Emission Computed Tomography). We construct an observation model to relate parameters of interest to the projection data and to account for limited ECT system resolution and measurement noise. We then use a maximum likelihood (ML) estimator to jointly estimate all the parameters directly from the projection data without reconstruction of intermediate images. We also simulate myocardial perfusion studies based on a simplified heart model to evaluate the performance of the model- based joint ML estimator and compare this performance to the Cramer-Rao lower bound. Finally, we discuss model assumptions and potential uses of the joint estimation strategy. 1 .I t s ?/1J Yi j I. NOMENCLATURE detector position index time index emission position time observation of detected gamma rays at i-th detector position in ,j-th time interval mean observation at i-th detector position in j-th time interval j-th time interval system response function, i.e. the probability of detecting a gamma ray at i-th detector position given an emission at L boundary parameter vector emission space defined by left ventricular ROI emission space defined by myocardial ROI emission space defined by background region concentration function of left ventricular ROI concentration function of myocardial ROI concentration function of background region U, = JT, u(t)dt m(j) = JT, m(t)dt : 1-th time-integral concentration of b, = JT, b(t)dt : 3-th time-integral concentration of Y : vector concatenation of all yzJ Y : vector concatenation of all yzJ 0 : vector concatenation of compartmental H(@) : matrix kernel characterizing the kinetics U : vector Concatenation of all U, M : vector concatenation of all m3 B : vector concatenation of all b, A = [aT UT BTIT P = [AT STIT : 1-th time-integral concentration of left ventricular ROI myocardial ROI background region parameters of myocardial ROI 11. INTRODUCTION N ADDITION to providing morphological information I about imaged organs, a more powerful use of ECT (Emis- sion Computed Tomography) is to quantify physiological and biological processes through dynamic imaging. In dynamic tomographic studies, one images an organ of interest over time to observe the dynamic behavior of the employed radio- tracer. Ideally, the radiotracer is designed to measure specific physiological or biochemical processes. In steady state, the dynamic behavior of the radiotracer can usually be described by a linear compartmental model with constant compartmental parameters [ 11. Often, these parameters are directly related to the specific process [2]. By tomographically measuring the organ tracer concentration (output), one can determine the
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This note was uploaded on 01/10/2012 for the course EECS 551 taught by Professor Wakefield during the Spring '08 term at University of Michigan.

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