Use of a 4-D cardiac phantom to quantify Karhunen-Loeve images applied to myocardial gated SPECT

Abstract

Myocardial gated single photon computed tomography (gSPECT) is widely used for quantification of myocardial perfusion and contractile function. Using a modified 4D NCAT phantom, the purpose of this study was to evaluate the diagnostic performance of the Karhunen-Loeve transform (KLT) applied to gSPECT. For this purpose, perfusion was quantified by an index proportional to the size and the intensity of the defect (Pi) and kinetics by an index (Ki) which was the mean endocardial and epicardial wall motion. KLT provides an uncorrelated image series in which only the first two (KL0, KL1) contain the main part of information. It was found that KL0 reflects perfusion and KL1 kinetics

Full text

Page 1

Use of a 4-D Cardiac Phantom to Quantify
Karhunen-Loeve Images Applied to Myocardial Gated SPECT

L Comas, P Berthout, R Sabbah, JP Daspet, O Blagosklonov,
M Baud, J Verdenet, JC Cardot

Department of nuclear cardiology, Jean Minjoz Hospital, Besancon, France
Abstract
Myocardial gated single photon computed tomography
(gSPECT) is widely used for quantification of myocardial
perfusion and contractile function. Using a modified 4D
NCAT phantom, the purpose of this study was to evaluate
the diagnostic performance of the Karhunen-Loeve
transform (KLT) applied to gSPECT. For this purpose,
perfusion was quantified by an index proportional to the
size and the intensity of the defect (Pi) and kinetics by an
index (Ki) which was the mean endocardial and
epicardial wall motion. KLT provides an uncorrelated
image series in which only the first two (KL0,KL1)
contain the main part of information. It was found that
KL0 reflects perfusion and KL1 kinetics.
1. Introduction
Cardiologists assume that analysis of the perfusion and
motion of the heart, especially the left ventricle (LV), can
give precise information about the health of the
myocardium. With nuclear myocardial scan, it is possible
to get sequences of images over the whole cardiac cycle;
such sequences are real 3D movies of the cardiac motion
[1]. Traditionally, assessment of regional function is
made by expert visual evaluation but quantifying the
degree and extent of the LV functional abnormalities
permits a systematic assessment of the disease process on
the myocardial performance.
The Karhunen-Loeve transform is well known for its
compression and signal decorrelation properties. We use
it routinely in planar gated blood pool studies. The goal of
this study was to investigate KL transform for its capacity
to quantify perfusion and wall motion in gSPECT.
Because of the difficulty in determining the true
values in clinical studies, the analysis was performed
using simulations with a phantom, so this approach
allowed us to control the data and also to know the
"truth". All simulated data for this study were generated
using the 4-dimensional (4D) NURBS cardiac torso
phantom (4D-NCAT) developed at the University of
North Carolina at Chapel Hill [2]. The 4D NCAT
phantom was developed to provide a realistic and flexible
model of the human anatomy and physiology to be used
in medical imaging research [3].
2. Methods
2.1. Simulations
The heart was generated by using a volume of 256
images of 256*256 pixels. The field of view was 40cm.
The cardiac cycle duration was 60 beats per minute and 8
volumes per cycle are obtained. Acquisition was
simulated in ventral position. The patient was a man
(without breast attenuation). The energy of the radio
nuclide was 140 KeV. The number of counts per pixel
was defined in the following way: LV=100, VD=40,
Other tissues=30.
The heart was isolated in a 64*64 pixels*64 slices
zone (without interpolation) for each image cycle.
The resulting transaxial image sets were reoriented
into short-axis, vertical and horizontal long-axis sets.
From these series, we chose 3 short-axis slices (apical,
mid and basal) and a mid-vertical long-axis slice to use a
standard 20-segment classification (figure1).

Figure 1. Segmentation in 20 sectors.
A lesion is defined in NCAT as an independent
volume which is subtracted from normal thoracic volume.
Three localizations of
corresponding to main coronary artery territories
(anterior, lateral, inferior).
Perfusion defect : From a NCAT heart lesion volume,
we determined a percentage of fixation in the lesion.
Thus, we defined a population including one normal and
7 intensity reductions (10-20-30-40-50-60-70%) applied
in each of 3 territories (22 explorations).
Kinetics defect : We wanted to simulate the human
lesion were proposed
0276−6547/05 $20.00 © 2005 IEEE
431
Computers in Cardiology 2005;32:431−434.

Page 2

heart as well as possible when it has kinetics defects. The
diagram (figure 2) represents the functioning of a
pathological heart in the inferior territory. It should be
noted that endocardic displacement is always higher than
epicardic displacement. The wall motion is generally
lowered to the level of the hypo perfusion and dyskinetic
zones. So, we transformed a heart lesion volume by
modifying its time activity curve in 3 different ways
before adding to the healthy heart.
Kinetics and perfusion defect : The two types of
defects were cumulated to obtain a population of 55
explorations (1 normal, 3 territories * 3 time-activity
curve modifications * 6 defect severities). We ignored the
10% defect severities because it did not appear on the
images.


Figure 2. Schematization of the movements of the cardiac
muscle
To be closer to the acquisitions carried out on the
patient, it was necessary to take account, on the one hand,
of the heart dimensions and, on the other hand, of the
statistical noise.
Wall thickness : By 4 successive dilations, the cardiac
wall was expanded. The intensity in each dilation zone
corresponded to a decreasing percentage of the
myocardium activity. The lesions, which underwent the
same processing, were added to the heart and adjusted
inside the cardiac wall in order to attenuate the abrupt
transition between the lesion edge and the healthy wall.
Noise : it was generated by addition of a random
gaussian type noise according to the following equation:
CA2ARES
××±=

Where A was the initial image and C a random matrix.
Finally, to maintain a continuity from one slice to
another a 3D Butterworth smoothing (cut off frequency
0.75, order 5) was applied to the whole rebuilt volume.
2.2. Karhunen-Loeve transform
The KLT is a change of space [4]; the new base
orthogonal, is uncorrelated and ranked by decreasing
order of information. Each pixel vector characterized by 8
components depending on time (very correlated in the
base time) will be characterized by 8 components which
are uncorrelated in the new base. The new axes are the
eigen vectors of the correlation matrix. They permit to
separate, as well as possible, the various temporal
behaviours. The projection of the series on these new
axes gives 8 principal images in this uncorrelated base.
An compression effect can be obtained with a known loss
because the new axes are ordered by decreasing value of
information in the statistical meaning [5]. In the case of a
synchronized cardiac exploration, 99% of information is
contained in the first 3 principal images (KL0, KL1,
KL2). KL0 represents the average image of the cardiac
cycle. KL1 gathers the pixels by family of temporal
evolution. At each end of the color scale, are the pixels
whose temporal evolution is opposite and the background
noise is around zero [6-7].
2.3. Contours detection
An automatic method of detection of contours [8],
which we developed and validated, was applied to KL0
image of the various models. KL0 contours were used for
KL1 image. For the segmentation in 20 angular sectors,
the center was the center of mass of the myocardium.
2.4. Perfusion and kinetics quantification
For the quantification, we defined two indexes.
Perfusion: We calculated a perfusion index (Pi)
characterizing the intensity and the extent of the lesion :
NbtPi
×=
Where Nbt was the total number of pixels of the
myocardium, 100 corresponded to the intensity in the
healthy myocardium and Al intensity was calculated
directly in lesion volume. An identical calculation was
carried out on each of the 20 sectors.
Kinetics: Motion index Ki was calculated in the
following way:
RpSRpD ((mean Ki
−=
Al
×
100

2/)) RnS RnD(
+
)
−

where RpD and RpS were epicardic diastolic and systolic
radii and RnD and RnS were endocardic ones.

These two parameters were compared to QGS software
where ejection fraction (EF), end-diastolique volume
(EDV), end-systole volume (ESV), end-diastolique and
end-systolique perfusion (ED and ES), motion and
thickening are calculated automatically [9-10].?

432

Page 3

3. Results
An example is shown in figure 3

Figure 3 : KL0 and KL1 images for a normal model and a
40% perfusion and kinetics defect in an inferior territory.
The studied population comprised three kinds of
models. For the perfusion analysis we had 22
explorations, for the kinetic defect analysis 10 and for the
kinetics and perfusion defect analysis 55 explorations.
For KL0 and KL1 images, the selected parameters were
the minimum, maximum, mean and standard deviation.
This analysis related to the whole image, the myocardial
region of interest (LV ROI) and each left ventricle sector.
3.1. Parameters validation
In order to ensure the accuracy of the anomalies
brought to the model and the suggested indices, method
QGS was chosen and applied to explorations with
perfusion and kinetics defect while taking for parameter
Ki and Pi their 20 sectors mean value. We noted
0.28<EF<0.42, 38<EDV<42 ml, 23<ESV<30 ml,
2.39<motion<3.71mm and 12.72<thickening<20.5 %, As
with a usual patient population, motion and thickening
were correlated with EF (0.96 and 0.97) and with ESV
(r=-0.84 and –0.89).
Perfusion: Pi was compared to the ED and ES parameters.
Pi was correlated with ED (r=0.87) and with ES (r=0.88).
Kinetics: Ki was compared to the EF, EDV and ESV and
motion parameters. In order to take in account the
different processing methods, we calculated the
correlation between Ki and QGS parameters on 3
populations. Firstly, the 10 kinetic defect models with a
not closed cavity apex slice were used. Ki was correlated
to EF (r=0.95) and to ESV (r=-0.89). Secondly the 55
perfusion and kinetics defect explorations (where
contours for the apex short-axis slice could have a closed
cavity) were studied. Parameters had a poor correlation.
Thirdly, only mid and basal short-axis slices were kept. In
this case, correlation between Ki and EF was increased
(r=0.59 to 0.79) and also between Ki and motion (r=0.61
to 0.81).
The modifications brought to the time-activity curve
on the lesion allowed the generation of various kinetics
for which the parameters evolved like a true population.
The defined parameters Pi and Ki were correlated with
those routinely used by QGS.
3.2. Perfusion defect
For this analysis we used 22 models.
Whole image analysis : Only the KL0 mean was
correlated with Pi (r=0.835) and even more so if we
considered each axis separately.
LV ROI analysis : KL0min and KL0mean were correlated
with Pi (r=0.82 and 0.95). It should be noted that there
was no correlation between the parameters of KL0 and
those of KL1 and no correlation between Pi and KL1.
Sectorial analysis : it was carried out on 440
observations (183 healthy and 257 pathological). All the
KL0 parameters were correlated with Pi whereas KL1
ones were independent (table 1).
Table 1. Correlation coefficients between KL0 and Pi
with 440 observations about perfusion defect.
KL0min
0.84
KL0max
0.86
KL0mean
0.98
KL0sd
0.84 Pi

Only KL0 image was sensitive to a perfusion defect.
3.3. Kinetics defect
For this analysis we used 10 models.
Whole image analysis : It should be noted that KL0mean
and KL0sd were constant. No KL0 parameter nor KL1
parameter was correlated with the parameters EF, EDV
and ESV.
LV ROI analysis : The KL0 parameters were constant,
whereas KL1min and KL1max varied but they were not
correlated with the EF, EDV and ESV references.
Sectorial analysis : it was carried out on 200 observations.
The KL0 parameters did not vary. Only the KL1
parameters were correlated with Ki (table 2). We
observed no correlation between KL0 and KL1.
Table 2. Correlation coefficients between KL1 and Ki
with 200 observations for kinetic defect
KL1min
-0.85
KL1max
0.82
KL1sd
0.90 Ki

Only image KL1 was sensitive to the anomalies of
kinetics expressed by the motion index.
3.4. Perfusion and kinetics defect
Perfusion
corresponds to the most current situation.
For this analysis, we had 55 explorations.
Whole image analysis : Only, KL0mean and KL0sd was
correlated with Pi (r=0.80 and 0.82). No parameter of
KL0 nor of KL1 was correlated with the EF, EDV and
ESV parameters, although KL1min and KL1max varied.
LV ROI analysis : KL0min and KL0mean were
correlated with Pi (r=0.80 and 0.91), we noted no
and kinetics simultaneous anomaly
433

Page 4

correlation between Ki and KL images.
Sectorial analysis : it concerned 1100 observations.
KL0 parameters were correlated with Pi, KL1
parameters were correlated with Ki (tables 3-4).
Table 3. Correlation coefficients between KL0 and Pi
with 1100 observations for perfusion and kinetics defect.
KL0max
0.88
KL0mean
0.90
KL0sd
0.92 Pi
Table 4. Correlation coefficients between KL1 and Ki
with 1100 observations for perfusion and kinetics defect.
KL1min
-0.63
KL1max
0.75
KL1sd
0.76 Ki

We noted no correlation between KL0 and KL1.
KL0 image reflected the perfusion and KL1 image
reflected the wall motion.
4. Discussion and conclusions
The modifications model validation and the proposed
perfusion and kinetics parameters were evaluated with
QGS software which is commonly used in hospital
routine. The apparent differences between our method
and the QGS one came from various causes : The used
slices automatic choice was not always the same from one
method to another. It was more sensitive for the apical
short-axis slice. The contours detection methods were
different because of the intensity threshold (possible
closed cavity for apical short-axis slice) and because the
choice of the selected center of mass was not the same
(seen on mid vertical long axis slice). Indeed, if we
eliminated the apex short-axis and the long axis slices, we
found a better correlation between Ki and EF and ESV
(r=0.59 became 0.79 and -0.43 became -0.65). This study
showed that the modified NCAT model seemed well
adapted to the measurement of perfusion and kinetic
defects. However, it does not take account of the effect of
partial volume since the images of diastole and systole
have the same intensity and it is not possible to calculate
a thickening parameter.
For KL quantitative analysis, we never observed
correlation between KL0 and KL1 images. From the 3-
step analysis (whole image, LV ROI, sector), we noted
that it was not necessary to measure the parameters on the
whole image, more especially in clinical routine where
digestive artifact fixation often appears as important as
the cardiac one. When LV ROI was observed, since the
myocardium is never completely diseased, the healthy
zones involved limits of parameters close to the normal.
With the regional analysis, we showed that the KL0mean
and KL0sd parameters were correlated with Pi and could
be retained for a perfusion defect measurement; for the
analysis of kinetics, since KL1mean was always close to 0,
KL1min, KL1max and KL1sd were correlated with Ki and
could be indicative for graduating the anomaly level.
The Karhunen-Loeve transform applied to myocardial
gated SPECT was validated to the NCAT modified model
Its interest was to show how to quantify the perfusion and
kinetics anomalies with only two images, KL0 for
perfusion and KL1 for kinetics. We are using this method
on patients acquisitions which confirms these results.
References
[1] Paul AK and Nabi HA. Gated myocardial perfusion
SPECT: basic principles, technical aspects, and clinical
applications. J Nucl Med Technol, 2004;32(4):179-187.
[2] Segars WP. Development and Application of the new
dynamic nurbs-based cardiac-torso (NCAT) phantom
[dissertation]. Chapel Hill: North Carolina Univ.; 2001.
[3] Faber T, Modersitzki J, Folks RD and Garcia EV.
Detecting changes in serial myocardial perfusion spect: A
simulation study. J Nucl Cardiol, 2005;12:302–310.
[4] Fukunaga K. Introduction
Recognition. Boston: Academic Press; 1990.
[5] Narayanan MV, King MA, Wernick MN, Byrne CL,
Soares EJ and Pretorius PH. Improved image quality and
computation reduction in 4-D reconstruction of cardiac-
gated SPECT images. IEEE Trans Med Imaging,
2000;19(5):423–33.
[6] Blagosklonov O, Sabbah A, Verdenet J, and Cardot JC.
Application of karhunen-loeve transform in nuclear
cardiology: Spatio-temporal smoothing and quantitative
image analysis. Computer in Cardiology, 2000;27:299–
302.
[7] Blagosklonov O, Berthout P, Comas L, Sabbah R,
Verdenet J, Baud M, and al. Using of karhunen-loeve
transform for analysis of cardiac function in myocardial
gated SPECT. SPIE Medical Imaging, 2003;5032:1217–
1224,
[8] Comas L, Berthout P, Sabbah R, Blagosklonov O,
Verdenet J, Baud M, and al. Automatic contours detection
in myocardial gSPECT. Computer in Cardiology.
2003;30:621–624.
[9] Germano G, Kiat H, Kavanagh PB, Moriel M,. Mazzanti
M, Su HT, and al. Automatic quantification of ejection
fraction from gated myocardial perfusion SPECT. J Nucl
Med. 1995;36(11):2138–47.
[10] Germano G, Erel J, Lewin H, Kavanagh PB, and Berman
DS. Automatic quantification of regional myocardial wall
motion and thickening from gated technetium-99m
sestamibi myocardial perfusion single-photon emission
computed tomography.
1997;30(5):1360–7.



Address for correspondence
Laurent COMAS
Explorations cardiaques radio-isotopiques, Hôpital J. Minjoz
25030 Besancon Cedex, France
E-mail : lcomas@chu-besancon.fr
to Statistical Pattern
J Am Coll Cardiol.
434