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