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IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 19, NO. 9, SEPTEMBER 2000
ECG-Correlated Imaging of the Heart with Subsecond
Multislice Spiral CT
Marc Kachelrieß*, Stefan Ulzheimer, and Willi A. Kalender
Abstract—The new spiral multislice computed tomography
(CT) scanners and the significant increase in rotation speed offer
great potential for cardiac imaging with X-ray CT.
We have therefore developed the dedicated cardiac reconstruction algorithms 180 multislice cardio interpolation (MCI) and
180 multislice cardio delta (MCD) and here offer further details
and validation. The algorithm 180 MCI is an electrocardiogram
(ECG)-correlated filtering (or weighting) algorithm in both the
cardiac phase and in the -position. Effective scan times (absolute
temporal resolution) of as low as e
ms are possible,
assuming
simultaneously measured slices at a rotation
time of rot
s and
for the table feed
per rotation, where denotes the collimated slice thickness. The
relative temporal resolution (fraction of the heart cycle depicted
in the image), which is the more important parameter in cardiac
imaging, will then be as low as
% of the heart cycle.
The second approach, 180 MCD, is an ECG-correlated partial
scan reconstruction of
data with
(fan-angle).
Its absolute temporal resolution lies in the order of 250 ms (for
the central ray, i.e., for the center of rotation), and the relative
temporal resolution
increases with increasing heart rate, e.g.,
from typically
% at H
min 1 to
% at
1
min , assuming again rot
s. For validation
H
purposes, we have done simulations of a virtual cardiac motion
phantom, measurements of a dedicated cardiac calibration and
motion phantom, and we have reconstructed patient data with
simultaneously acquired ECG.
Both algorithms significantly improve the image quality compared with the standard reconstruction algorithms 180 multislice
linear interpolation (MLI) and 180 multislice filtered interpolation (MFI). However, 180 MCI is clearly superior to 180 MCD for
all heart rates. This is best illustrated by multiplanar reformations
(MPR) or other three-dimensional (3-D) displays of the volume.
180 MCI, due to its higher temporal resolution, is best for spatial
and temporal four-dimensional (4-D) tracking of the anatomy. A
tunable scanner rotation time to avoid resonance behavior of the
heart rate and the scanner’s rotation and shorter rotation times
would be of further benefit.
= 56
3
=4
= 05
180 +
= 120
= 25
= 12 5
= 60
= 05
8
= 50
Index Terms—Computed tomography (CT), four-dimensional
(4-D) reconstruction, heart, multirow detector systems, multislice
spiral CT (MSCT).
NOMENCLATURE
Indicator function: 1 if odd, otherwise 0.
Rectangle function with support
and area 1.
Manuscript received January 25, 2000; revised May 30, 2000. This work was
supported by Bayerische Forschungsstiftung, under Grant AZ262/98. The Associate Editor responsible for coordinating the review of this paper and recommending its publication was G. Wang. Asterisk indicates corresponding author.
The authors are with the Institute of Medical Physics, University of
Erlangen-Nürnberg, 91054 Erlangen, Germany (e-mail: [email protected]).
Publisher Item Identifier S 0278-0062(00)08084-8.
0278–0062/00$10.00 © 2000 IEEE
Triangle function of characteristic width
.
( half width) 1,
Maximum function,
.
Minimum function,
.
Projection angle,
for a sequence (360 ) scan or -interpolated data,
for a spiral scan.
Angle associated with reconstruction posi.
tion
Angle of rotation during one heart cycle.
Angles suitable for interpolation at
with
.
Angle within fan,
.
Cardiac phase (with respect to R–R) as a
.
function of the view angle,
Cardiac phase about which to center the
reconstruction.
Characteristic width of the phase weighting
.
function
Notation used for the window setting, is
its width in
the window’s center in HU,
HU.
Table feed per 360 rotation.
Relative error in calcium scoring,
.
Fan-angle, in our case,
.
Abbreviation
denoting
the fraction of a full rotation needed for
reconstruction.
Patient’s heart rate.
Number of heart beats per rotation.
Slice index and number of simultaneously
.
measured slices,
Pitch,
.
Projection data for systems with
simul.
taneously measured slices,
-interpolated spiral raw data at position
and
for algorithm .
Notation for the calcification score. The
true value is to be achieved and the measured value has been achieved.
Nominal slice thickness.
Threshold used for calcium scoring.
Absolute temporal resolution
effective
.
scan time,
Time for a 360 rotation.
Relative temporal resolution
relative
width (with respect to R–R) of the succes-
KACHELRIEß et al.: ECG-CORRELATED IMAGING OF THE HEART
-axis
sive intervals in the cardiac R–R cycle. For
measured data, is given as the FWTM of
.
the phase sensitivity profile.
Relative temporal resolution assuming that
we have to wait -rotations until new data
are available.
Weighting function of characteristic width
for 180 MCI that weights the distance
of a measured point to the reconstruction
.
plane,
Weighting function of characteristic width
for 180 MCI that weights the cardiac
phase deviation of a measured point to the
%.
desired reconstruction phase,
Weight used for -interpolation for the th
available projection value at slice .
Axis of rotation.
Arbitrary selectable reconstruction posi.
tion,
Characteristic width of the distance
.
weighting function
-position of detector array center,
.
-position of the center of the th measured slice,
.
I. INTRODUCTION
T
HE latest great step in computed tomography (CT) development was the introduction of multislice CT scanners in
1998. The number of simultaneously acquired detector slices
. This new technology allows us
nowadays is typically
to increase the -resolution or the volume coverage by about
[1]. In addition, overlapping data acquisition,
a factor of
, with being
which means spiral pitch
the collimated slice thickness, allows us to drastically increase
the temporal resolution without decreasing the spatial resolution by using data from successive rotations for reconstruction.
Of course, the motion must be periodic in some sense as it is the
case with cardiac motion. Potential distortions from this periodicity, as they might result from patient breathing or from contrast injection, are of low speed compared with the cardiac motion and do not take a significant influence. Moreover, because
the transit time of the detector array and a given reconstruction
has increased, multislice technology allows us to
position
become phase-selective: for a retrospectively selected cardiac
and reconstruction position
, simply
phase
(in spatial domain) and to
the detector row(s) closest to both
(in temporal domain) has to be chosen for reconstruction.
Although similar ideas have been proposed for single slice
CT, a few years ago [2], [3], their generalization to multislice
CT turned out to be very effective and to overcome the known
problems of cardiac imaging from single slice CT [4], [5]. Unlike other manual approaches that retrospectively select the best
images for diagnosis [6], [7] or retrospectively determine the optimal “timing shift” about which to center a partial scan reconstruction [8], the algorithms developed by our group are dedi-
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cated cardiac reconstruction algorithms that automatically allow
us to reconstruct complete volumes at any cardiac phase. They
require the simultaneously recorded electrocardiogram (ECG)
of the patient for synchronization purposes. Synchronization is
done with respect to the R-peaks, the most pronounced peaks
of the ECG signal. Cardiac cycles are defined as the R–R intervals of the ECG, and the cardiac phase runs from 0% to 100%
within each cardiac cycle.
This paper will briefly state the definitions of the two algorithms 180 multislice cardio interpolation (MCI) and 180
multislice cardio delta (MCD) and then evaluate their performance in comparison to the standard -interpolaton algorithms
180 multislice linear interpolation (MLI) and 180 multislice
filtered interpolation (MFI). Simulated raw data of a virtual cardiac motion phantom, measurements of a dedicated physical
cardiac calibration and motion phantom, as well as measured
patient data are used to evaluate our approaches. Theoretical
evaluations of both algorithms, 180 MCI and 180 MCD, including image noise, -resolution, and temporal resolution, are
given elsewhere [5].
II. MATERIALS AND METHODS
For our patient examinations, we have used the four-slice
scanner SOMATOM Volume Zoom (Siemens Medical Systems,
s. The
Erlangen, Germany) with a rotation time
. Per rotation, 1160 projections, each
fan-angle is
with 4 672 channels, are collected. The scan parameters were
mm table feed
chosen as 4 1 mm collimation and
per rotation. This ensures the complete coverage of the heart
during a single breath-hold and achieves high -resolution. The
patient’s ECG signal was recorded simultaneously during the
scan to correlate the cardiac phase to the projection angle .
It is well known that quantitative cardiac imaging, such as
coronory calcification measurements, suffer from intrascanner
and interscanner variability [9]. To reduce these variations and
to improve calcium scoring, a semiantropomorphic cardiac
phantom (QRM GmbH, Möhrendorf, Germany) has been
designed that not only allows for stationary calibration inserts,
but is also able to move arbitrary objects along arbitrary, freely
progammable three-dimensional (3-D) paths [Fig. 1(a)], as
described in [10] and [11]. We used this phantom equipped with
the motion insert — this insert consists of an open water tank
that contains the object to be moved by an external robot — to
evaluate the cardiac reconstruction algorithms. Measurement
of the dedicated cardiac motion and calibration phantom was
performed using the same scan parameters as for our patient
measurements. The motion phantom generates a realistic ECG
signal, which is processed by the same ECG monitor as has
been used for the patient scans. Thus, phantom scans and
patient scans are directly comparable.
In addition, we have simulated raw data for the virtual cardiac phantom [4], [5], [10] to be reconstructed with the various
approaches. The phantom consists of a lattice of calcifications;
some of them are subjected to motion, and some of them are stationary, to be used as a reference standard. Fig. 1(b) shows the
three rows of calcifications of varying diameter: 3 mm, 2 mm,
and 1 mm. The five columns consist of stationary cylinders
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(a)
(b)
Fig. 1. Two phantoms are used to evaluate our algorithms. Both (a) the physical heart phantom and (b) the virtual heart phantom are semiantropomorphic
phantoms to mimic the patient anatomy, including cardiac motion. The motion insert (here, a water equivalent rod with a calcium cylinder) of the physical phantom
can move arbitrary objects along one arbitrary, freely programmable 3-D path at a time. The virtual phantom can move arbitrary objects along many arbitrary,
freely programmable 3-D paths at a time. Here, it moves six objects horizontally and three objects along z ; thus, two paths at a time are simulated.
(left), horizontally moving cylinders (second left), stationary
spheres (middle), horizontally moving spheres (second right),
and spheres moving along (right), respectively. The simulated motion consists of a sinusoidal covering 80% of the cardiac cycle and a stationary part of 20% of R–R. Depicting the
phantom artifact-free indicates that the respective algorithm al% of one heart
lows us to freeze cardiac motion within
beat. The motion amplitude was simulated as 5 mm because
the typical linear dimension of cardiac motion lies in the order
of 10 mm [12], [13].
As a standard algorithm for comparison, we use 180 MLI [1],
which is a linear -interpolation between the two nearest data
points on each side of the reconstruction plane at . 180 MLI
was modified to take a slice number as an additional parameter to use only this slice for reconstruction. In this sense, it is
equivalent to the single slice algorithm 180 LI. This modification will have no significant impact on the achievable -resolu-
tion because all scans are performed overlapping, at pitch values
, and thus, no data gaps will be introduced by using one of
the -measured slices only. Moreover, the effective scan time
will remain the same as well:
of data contribute
to each image.
The second standard algorithm investigated is 180 MFI [1],
which is a standard -filtering approach that is typically used
in commercial multislice scanners. For overlapping data acquisition, as is the case in this paper, more than one gantry rotation will contribute to the image. To be more precise, roughly
rotations — this is the number of rotations necessary to advance the table by -collimated slice thicknesses
— will play a role for each interpolation. Although the exact
value depends on the width of the -filter, it can be expected that
the temporal resolution of 180 MFI is much worse compared
with 180 MLI, which only uses one gantry rotation [the exact
-rotations] for reconstruction. Thus,
value is
KACHELRIEß et al.: ECG-CORRELATED IMAGING OF THE HEART
some of the cardiac motion artifacts will be averaged away by
180 MFI because the contributing data might cover one complete or more than one heart cycle. However, this averaging will
evidently result in a significant loss of in-plane and -resolutions.
All reconstruction algorithms were implemented on a standard PC with the dedicated image evaluation and reconstruction
software package ImpactIR (VAMP GmbH, Möhrendorf, Germany). Reconstruction time lies below 2 s per 512 512 image
on a 700-MHz dual Pentium processor with 512 MB of memory.
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the fact that the corresponding slices used for interpolation
change too abruptly and too often during the interpolation of
one planar data set.
Therefore, a filtering (or weighting) approach appears to be
the most promising choice. These filtering algorithms are already known from standard multislice spiral CT [1]. For the
spatial direction ( -direction), 180 MCI simply uses this wellknown -filtering approach. In the temporal direction (cardiac
phase ), a -filtering approach is used
III. RECONSTRUCTION
We will denote the measured attenuation values (projections)
, where
stands for the
by
describes the gantry’s rotation
angle within the fan,
is the slice number. Because for
angle, and
a spiral scan there is a one-to-one correspondence between the
projection angle and the -position of the focus, the -position is not stated explicitly but can be derived from
The -position of slice
The reconstruction position will be denoted by , and because we are dealing with a phase-selective reconstruction, we
need to define the cardiac phase at which the reconstruction is
,
performed: . The ECG information will be denoted as
i.e., as the cardiac phase as a function of the rotation angle .
. Arithmetics using the cardiac phase
We have
are meant to be modulo 1.
and , assuming
For the interpolated data at position
-interpolation algorithm , the general interpolation equation
can be stated as
are real-valued and
where
defines the rebinning to access data points
from opposite views (180 algorithms). The denominator of the
-interpolation equation properly normalizes the procedure.
A.
with the weight
(1b)
chosen as the product of the distance and the phase weight. The
denotes the retrospectively selectable reconstrucparameter
tion position, and , the reconstruction phase, can be selected
retrospectively as well. The weight functions were chosen to be
triangular
simply is
where the weights
(1a)
-Interpolation 180 MCI
The algorithm 180 MCI uses data from successive heart
beats and successive gantry rotations to collect a complete data
set and to yield the optimal temporal resolution for a given heart
and rotation time
. Due to the complex -sampling
rate
pattern of multislice spiral CT and due to the potentially
arhythmic heart motion, a true linear interpolation algorithm
yields streaking artifacts in the resulting images that arise from
where
denotes the width of the filter in -direction and
% denotes the filter width for the cardiac phase.
is a
triangle function of base width 2 and area 1. The base width of
the cardiac weight function is , and we find that the fraction
. The relaof the cardiac cycle depicted in the image is
tive temporal resolution as given in the results section will be
slightly lower than because it is calculated as the full-width
at tenth maximum (FWTM) of the phase sensitivity profile because this represents the contributions of the cardiac phases to
the final image more adequately.
Fig. 2 shows a schematic plot of 180 MCI. The plot is drawn
and a heart rate of
for a four-slice scanner at
min , assuming
s. The four temporal axes correspond to the four measured slices reaching the reconstruction
position . Thus, they are shifted with respect to each other
, which is the time needed to increment the table by
by
a distance of . Only those data points falling below both the
-filter and the -filter will contribute to the image.
Although 180 MCI allows for arbitrary pitch values, it should
be taken care that
i.e.,
This restriction follows from the demand that the detector array
slice thicknesses during
should not advance by more than
of one heart beat. Otherwise, the request for inthe length
and arbitrary
would deteriorate
terpolation at arbitrary
the slice sensitivity profile (SSP) or the phase sensitivity profile
(PSP) and, thus, reduce the algorithm’s -resolution or its temporal resolution significantly.
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Fig. 2. Schematic plot of 180 MCI for the central ray for arbitrary z and c . The solid lines depict the measured spirals, whereas the dashed lines depict
the rebinned data obtained from opposite views. The numbers m at the top count the simultaneously measured slices m
1; 1 1 1 ; M . The figure is drawn for
M = 4; p = 3=7 0:43, and f t
= 3=4. Tick marks at the z -axis are spaced by the table feed d, and tick marks at the four temporal axes are separated
by t . The heart symbols map the reconstruction phase c onto the temporal axes. These axes are shifted by a temporal offset corresponding to the time needed
to advance the table by the distance S with respect to each other. The width w in R–R was chosen as w = 25% for this plot. The roman numbers i, ii, iii, and iv
correspond to the number of rotations involved in the graph. Concentrating, for example, on the temporal axis ticks labeled with the roman number ii shows the
z -positions of the respective slices at time t , i.e., just when the second rotation contributing to this figure has started. Moreover, at the figure’s top, the z -positions
of all four measured slices are denoted by the arabic numbers 1, 2, 3, and 4 for times t ; t ; t , and t .
=
For all 180 MCI reconstructions shown in this paper, we have
and have chosen the minimal possible width
used
to yield complete, i.e., at least
contiguous, -interpolated data. It can be shown that this minimal required width
and, thus, the maximal relative temporal resolution strongly
during one gantry
depend on the number of heart beats
rotation [3], [5]. We will give here an alternative derivation of
-adthe respective results. A complete data set consists of
jacent data on either side of the reconstruction plane, with
giving the fraction of a full rotation. During one
.
heart cycle, the gantry rotates by the angle
, which is valid for all patients
We will now assume
and for rotation times below or in the order of 0.75 s. This assumption ensures that the heart will not beat twice during one
rotation. It can be the case, however, that the gantry rotates twice
or even more often
until one cardiac cycle has
been finished. To be able to collect new data after one, two, or
,
even more rotations, we must demand
denotes the length of the newly acquired data
where
inverval and gives the number of rotations to wait until new
data are available. The gantry rotates by an angle of
while covering a given -position, i.e., while advancing by a
. This corresponds to
heart beats
distance of
, assuming that
and to a contiguous data range of length
of data is collected.
during each heart beat, a fraction
The product of the number of heart beats and the acquired interval size per beat must at least make a complete data set of
.
follows and, consequently,
.
size
The optimum situation is given whenever equality occurs. Using
, we find that the optimal relative temcan only be achieved if
poral resolution
with
(2)
From (2), it becomes clear that a tunable rotation time is required
to achieve the optimal relative temporal resolution for any constant heart rate. This is graphically depicted in Fig. 3: for all
are given. For
typical heart rates, the required settings for
KACHELRIEß et al.: ECG-CORRELATED IMAGING OF THE HEART
893
) and for
are given in (b) and (c) for completeness.
However, for the scanners available today, the rotation time
cannot be chosen freely. Only a few discrete values are available,
and thus, the optimal can only be achieved for a few heart
and
, these
rates. Assuming 0.5-s rotation time,
optimal heart rates would be 35 min , 45 min , 52.5 min ,
67.5 min , 105 min , and 135 min , as can be seen from
Fig. 3(a). For all other heart rates, 180 MCI yields a lower relative temporal resolution. Nevertheless, it has been shown that
typically lies in the range from 15% to 35%, depending on
the patient’s heart rate [5]. Thus, 180 MCI will still have significant advantages over standard reconstruction algorithms.
It must be mentioned that regardless of the heart rate,
180 MCI always is a phase-selective reconstruction algorithm
and all images will correspond to the same cardiac phase
throughout the complete volume.
(a)
B.
-Interpolation 180 MCD
The algorithm 180 MCD is a partial scan approach to reduce
the effective scan time. Contiguous spiral data corresponding
to a half scan are taken and used for reconstruction. Assuming
that the table feed is low enough to have a given reconstruction
covered by the detector array (length
) longer
position
than the duration of one heart beat, i.e., demanding again
(b)
allows us to center the partial scan data range of
around any cardiac reconstruction phase
by selecting the
appropriate detector lines for reconstruction. In other words,
because the temporal coverage of the active detector area and
exceeds the length
of one heart
a given -position
cycle, the temporal reconstruction center can always be chosen
, whereas the
to coincide with any desired cardiac phase
spatial reconstruction center can be freely selected as . Thus,
the interpolated raw data and the corresponding image will be
and
and 180 MCD is phase-selective.
centered about
The interpolation equation is
(c)
Fig. 3. Optimal t for 180 MCI as a function of the heart rate f for three
different pitch values. This plot assumes 8 = 0 (central ray) and, thus, f =
1=2. The curves yield (a) w = pf = 12:5%, (b) w = pf = 18:75%,
and (c) w = pf = 25%. The numbers matching the expression n to the
right of the solid curves correspond to the n and to the of (2). The dashed
curves correspond to the rotation time needed assuming a partial scan (half-scan)
reconstruction (such as 180 MCD, as given in the next section) that also shall
yield the same relative temporal resolution of w = 12:5%; 18:75%, or 25%,
respectively. Obviously, for a given heart rate, 180 MCI always performs better
(solid curves are above the dashed line) than does the partial scan approach. The
horizontal grid lines are placed at rotation time values of typical scanners (the
0.3-s line corresponds to a hypothetical scanner in the future), and the vertical
grid lines depict the intersection of our 0.5-s mode with 180 MCI.
(3a)
6
, the parameter of (2) ranges from 1 to 3. For each
value of , there are two curves corresponding to the plus or
the minus sign of the equation above. Each heart rate, thus, requires one of six possible rotation times to achieve the optimal
[Fig. 3(a)]. Moreover, the optimal settings for
as
mm,
mm, and
used for our patient scans (i.e.,
with
(3b)
is the view angle about which the reconstrucThe parameter
. The function detion is centered. It must fulfill
notes a rectangle function of width 1, and from Fig. (3b), it can
and : The
be seen directly that the data are centered about
first rectangle function takes care that the necessary 180 data
range, which is required for data completeness, will be available
and the second rectangle function collects those contributions in
that are separated by not more than a distance of
from the
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IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 19, NO. 9, SEPTEMBER 2000
Fig. 4. Schematic plot of 180 MCD for the central ray. The axes and the labeling are equivalent to Fig. 2. However, because 180 MCD has no explicit phase
weights, the weight function is illustrated as gray rectangles. The dark rectangles represent the heart beat around which the reconstruction is centered; i.e., all
contributions to the final image are taken from this heart beat. The interpolated data at z are made of exactly 180 of data (central ray), which stems from the
measured slices 3 and 4 (shaded area in the upper part of the graph).
desired reconstruction position . An illustration of 180 MCD
is given in Fig. 4.
Because 180 MCD only uses a half scan of data, its ab, which gives
solute temporal resolution will be
regarding the central ray only. The relative
temporal resolution of 180 MCD can, thus, be easily calculated
and yields
which is much more simple than for 180 MCI. The main drawback, as can be concluded from this equation, is that the relative
temporal resolution is getting worse with increasing heart rate.
This prediction will be confirmed by the phantom and patient
images in the results section.
IV. RESULTS
A. Patient Studies
A very good impression of the behavior of the two standard
algorithms 180 MLI and 180 MFI and the two dedicated
cardiac algorithms 180 MCD and 180 MCI is given in Fig. 5,
which shows various reconstructions of a patient with the low
heart rate
min . The axial views show optimal image
quality for both cardiac algorithms and a surprisingly good
image quality for 180 MLI, which only suffers from some
motion artifacts around the high-contrast calcifications. The
low artifact content for the axial 180 MLI image is due to the
short rotation time of 0.5 s, which for this patient corresponds
to 46% of the cardiac cycle. Of course, the relative and the absolute temporal resolutions for the cardiac algorithms are much
better and no artifacts appear in the axial images. Regarding the
corresponding 180 MFI image, we find severely overlapping
structures at the edge of the ventricles. The image seems to be
blurred compared with the other three images, and some of
the calcifications, although depicted without apparent motion
artifacts, have lost contrast. As mentioned above, this behavior
results from the very low temporal resolution of 180 MFI.
The image depicts the average of significantly more than one
cardiac cycle, and the averaging results in image blurring and
overlapping structures.
The MPRs, in contrast, are much more conclusive. Here,
180 MFI seems to perform better than does 180 MLI. Evidently, neither 180 MLI nor 180 MFI are phase-selective and
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=
Fig. 5. Comparison of the standard algorithms and the dedicated cardiac algorithms for a patient with the relatively low heart rate f
55 min . The cardiac
reconstructions were centered about c = 75%. In-plane image quality of 180 MLI is superior to 180 MFI, which shows double contours and significant image
blurring. However, 180 MLIs sagittal and coronal MPRs clearly show that the standard algorithms are not phase correlated: the anatomy is depicted discontinuously,
and the calcifications appear to be torn apart. This is not the case for 180 MFI because it averages over more than one complete cardiac cycle. Its z -resolution
is greatly reduced due to the cardiac motion, and the blurring disturbs the overall image impression. The cardiac algorithms show no motion artifacts but high
in-plane and z -resolutions, and their image quality is better compared with the standard z -interpolation approaches in all respects (0/500).
cannot depict the heart in the same phase of motion throughout
the complete volume. 180 MLI’s MPRs, thus, show severe
discontinuities. These are not shown by 180 MFI because
its blurring does not only affect the in-plane resolution, but
also the -resolution, and the respective discontinuities are
simply averaged or smeared away. The cardiac algorithms
180 MCD and 180 MCI depict the complete volume nearly
artifact-free with high resolution for both the axial images and
the multiplanar reformations. In contrast to 180 MCD, which
shows a few negligible streak artifacts in the MPRs, the cardio
interpolation algorithm 180 MCI depicts the volume without
apparent artifacts.
Higher heart rates, however, can only be coped with by
180 MCI. This is clearly demonstrated in Fig. 6, which does
the same comparison as Fig. 5, but for a patient with a heart
rate of 90 min . 180 MLI shows unacceptable discontinuities in the MPRs and motion artifacts in the transversal
image, 180 MFI suffers extremely from image blurring, and
180 MCD shows stepping artifacts in the MPRs. The image
quality of 180 MCI, in contrast, is very good for this relatively
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=
Fig. 6. Same comparison as in Fig. 5, but for a patient with a higher heart rate of f
90 min . The main difference here is that 180 MCD shows severe
artifacts in the MPR. Obviously, the partial scan approach cannot handle heart rates as high as 90 min well. Only 180 MCI yields good image quality in-plane
as well as in the MPR (100/800).
high heart rate. Artifacts appear neither in the axial image nor
in the MPR displays.
B. Physical Cardiac Motion Phantom
To confirm our findings in a well-defined environment, we
have measured the dedicated cardiac calibration and motion
phantom using the same scan parameters as for our patient
measurements. Some results can be seen in Fig. 7. Performing
a realistic three-dimensional (3-D) left anterior descending
coronary artery (LAD) motion yields unacceptable image
quality for 180 MLI [Fig. 7(a)]. The object’s contrast is not
recovered correctly, and the MPR pretends the object (a small
cylinder) is disrupted. The algorithms 180 MCD and 180 MCI
depict the object much better than does the standard approach.
In addition, the respective images suggest advantages of
180 MCI over 180 MCD already at this low heart rate. The
results of comparing two different heart rates (low 60 min
and high 105 min ) given in Fig. 7(b) confirm what has been
observed in patient measurements: 180 MCI achieves good
image quality for all heart rates, and 180 MCD only for low
heart rates.
C. Virtual Cardiac Motion Phantom
The virtual cardiac phantom was used to study motion and
motion artifacts for in-plane as well as axial motion at various heart rates. Images (axial and MPR) are given in Fig. 8.
KACHELRIEß et al.: ECG-CORRELATED IMAGING OF THE HEART
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shown in Fig. 8 — was performed. The underlying heart was
taken into account by thresholding the object function
using the threshold , subtracting and integrating. The score,
thus, is given by
(a)
(b)
Fig. 7. The measurements of the physical cardiac phantom using a motion
robot equipped with a 5-mm (diameter and height) HA400 (hydroxy apatite,
400 mg/cm ) cylinder that is oriented parallel to the z -axis prove again that the
dedicated cardiac algorithms are to be preferred over the standard 180 MLI
approach in the case of cardiac motion. (a) The motion performed was a
realistic 3-D LAD motion corresponding to a heart rate of 55 min . The
cardiac algorithms yield significantly better images in-plane (upper row) and
in the MPRs (lower row) compared with 180 MLI. (b) The phantom performs
the sinusoidal motion equivalent to the virtual cardiac phantom in x-direction
at 60 min
(upper row) and 105 min
(lower row). Although better than
the standard approach, 180 MCD is not able to depict the cylinder correctly
for the high heart rate. Only 180 MCI displays the calcification correctly for
all cases (0/800).
180 MCDs results are satisfactory only for
min
(assuming
s), and 180 MCI depicts the phantom correctly for a wide range of heart rates. Obviously, there is no significant difference whether the object moves in-plane or along
. The images for the standard algorithms were omitted because,
as has become clear above, they severely suffer from motion artifacts for all heart rates. Because the moving objects are at rest
over 20% of R–R, Fig. 8 confirms that 180 MCI is able to do
%. Obviously, the statement
with less than 20%; i.e.,
% is valid for all motion phases, although 180 MCI
would tend to show slight motion artifacts for phases with motion within the depicted 20%.
Moreover, we have performed coronary calcium measurements using our virtual phantom to determine the accuracy of
the various algorithms. The coronary calcification score to be
used here is a simple volume score. Integration of a volume of
interest (VOI) placed around one of the phantom’s calcifications
— the reconstructed volume under consideration is the volume
For , we have chosen 130 HU because this is used for the wellis defined here
known Agatston score [14]. The true score
by placing the VOI around one of the steady objects (cylinders
is obtained by
or spheres), whereas the measured score
integrating around the corresponding moving object (cylinder
moving along or sphere moving along or ). The relative
error introduced by the reconstruction algorithm, then, is
which is graphically depicted in Fig. 9 for the 3-mm sphere
moving along and the three algorithms 180 MLI, 180 MCD,
and 180 MCI. Again, 180 MCI performs superior to the other
algorithms. This applies also to the resonance cases
min and
min , where 180 MCI and 180 MCD
yield the same temporal resolution (see below and Fig. 10). Apparently, the - and -filtering approaches yield less image errors than does the partial scan reconstruction. The scoring errors
of 180 MCD and 180 MLI increase with increasing heart rate.
This is not the case for 180 MCI. However, only the general bias
to the calcium quantification error of the respective algorithms
(180 MCI is clearly the best performing algorithm) should be
derived from this experiment. The exact error values are likely
to depend on the respective motion function and on the scoring
algorithm (e.g., an error of precisely 0%, as it is the case for
180 MCI at 105 min , is unlikely to occur for other motion
functions).
D. Other Results
Our cardiac algorithm implementations internally perform a
spinoff calculation of the so-called PSP. This profile contains
the weighted contributions of the cardiac phase to the reconstructed image (similar to the slice sensitivity profile that contains the weighted contributions of the -positions to the reconstructed image). Although its exact shape is not of importance,
its FWTM serves as a conservative measure of the achieved relative temporal resolution . The results for some typical heart
rates are given in Fig. 10. The relative temporal resolution of
180 MLI, which is not a cardiac algorithm and, thus, has no
, can be calculated because its PSP is of
knowledge about
triangular shape. It is included in the figure as well. It can be
seen that the cardiac algorithm 180 MCI always has a better
temporal resolution than do the other algorithms. The only cases
in which 180 MCI and 180 MCD are equally good regarding
temporal resolution are those cases in which the heart rate and
the scanner’s rotation time are in resonance, e.g., the 2 : 3 resonance at 80 min . Then, 180 MCI cannot gain new information from one of the succeeding heart cycles. These situations
can principally be avoided by selecting a different rotation time
if available [3], [5].
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IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 19, NO. 9, SEPTEMBER 2000
Fig. 8. Views of the virtual heart phantom at the heart rates 70 min , 90 min , and 135 min
for the two cardiac algorithms 180 MCD and 180 MCI.
The simulated motion function is sinusoidal with an amplitude of 5 mm over 80% of R–R and constant over 20% of R–R. The reconstructions have been
centered about the slow motion phase (i.e., about the constant part of the motion function). The coronal view shows the 2-mm calcifications of the virtual heart
(see navigation lines). Obviously, 180 MCI’s image quality is always superior to the algorithm 180 MCD, and its image noise is apparently lower than for the
partial scan approach (0/250).
6
Image noise properties as well as the -resolution using SSPs
of the two new cardiac algorithms 180 MCI and 180 MCD
have already been investigated in [5]. We will simply state the
results for completeness. Analyzing the SSPs of 180 MCI has
shown no significant loss in -resolution compared with standard algorithms. The full-width at half maximum (FWHM) of
to
, independent of the
the SSPs lies in the order of
pitch value and the patient’s heart rate. The typical theoretical
value that can be achieved by standard -filtering algorithms
over a wide range of pitch values is given by the FWHM of a
threefold convolution of a rectangle function of width and thus
. Comparing this value to 180 MCI
yields
shows that the cardio interpolation algorithms does not significantly change the -resolution. Similar results are obtained for
180 MCD, although, in general, its FWHM is with roughly
slightly smaller than for 180 MCI.
KACHELRIEß et al.: ECG-CORRELATED IMAGING OF THE HEART
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V. DISCUSSION
1
Fig. 9. Relative error in calcium scoring achieved by the three algorithms
180 MLI, 180 MCD, and 180 MCI as a function of typical heart rates.
Obviously, 180 MCI performs best for all heart rates regarding the errors in
calcium scoring.
Fig. 10. Relative temporal resolution w achieved by the three algorithms
180 MLI, 180 MCD, and 180 MCI as a function of typical heart rates.
Obviously, 180 MCI performs best for all heart rates, regarding the temporal
resolution. This plot assumes d S; M
, and t
: s.
=
=4
=05
Image noise of 180 MCD is increased by approximately
22% compared with 180 MLI because only half a rotation
(partial scan) contributes to each image. The noise properties of
180 MCI are more complex. If a resonance case occurs, i.e., if
the heart rate and the scanner’s rotation time are in resonance,
180 MCI cannot gain new information from successive heart
beats and gantry rotations, as has been mentioned above. Thus,
180 MCI uses the redundant data for averaging because it is a
filtering approach. Image noise will be very low in those cases.
, which is for example
Especially for
min at
s, noise reductions of down to 42% of
the original 180 MLI image noise values have been observed.
However, these resonance cases are not what 180 MCI has
been designed for. It is rather desirable to have a high temporal
resolution and to avoid resonances by properly selecting the
rotation time (cf. Fig. 3). For those optimal situations, image
noise is very close to 180 MLI. Typical values are 90% of the
original 180 MLI image noise; i.e., noise is reduced by 10%
for those cases.
The limitations of cardiac imaging using standard CT scanners have been greatly overcome by introducing the dedicated
reconstruction algorithms 180 MCI and 180 MCD. We have
shown that these new algorithms are clearly superior to the standard -interpolation algorithms. Effective scan time can be significantly reduced, and the motion artifacts are almost completely eliminated using the phase-correlated reconstruction algorithms. Phase selectivity and high temporal resolution have
been demonstrated clearly. However, 180 MCD is useful only
for relatively low heart rates, and even there, 180 MCI produces better images than does 180 MCD. For higher heart rates,
180 MCI is clearly superior. This is due to 180 MCI’s high
temporal resolution. Relative temporal resolution of down to
12.5%, corresponding to an absolute effective scan time of 56
, and
ms, can be achieved, assuming
s. It has been shown that the scan parameters must be restricted
to allow us to reconstruct at any retrospectively
to
and heart phase .
selectable reconstruction position
The advantage of the retrospective gating methods is that
they can cope with patient cases, such as severe arhythmic
heart motion and extremely varying heart rate, during one scan.
An impressive example is shown in Fig. 11. The patient’s heart
rate varies between 42 min and 97 min during the 30-s
scan. Nevertheless the images show that 180 MCI is able to
resolve the aortic valve throughout the complete cardiac cycle
with acceptable image quality [Fig. 11(c)]. It must be noted that
these images of the aortic valve are taken from the oblique slice
depicted in Fig. 11(b), and consequently, almost the complete
volume and the complete range of heart rates from 42 min
to 97 min
contribute to each oblique MPR! Considering
these facts clearly shows the great flexibility and potential of
180 MCI for cardiac imaging.
True 3-D displays such as the shaded surface display (SSD)
of the heart given in Fig. 12 demonstrate again the image
quality of 180 MCI. Although the segmentation of complete
volumes at different heart phases still requires high effort, it
results in very descriptive images. Of course, animations of
such 4-D data sets can be performed as well; examples are
provided at http://www.imp.uni-erlangen.de/e/research/cardio/.
The advantages of our cardio interpolation approaches
180 CI for single-slice and 180 MCI for multislice spiral CT
over the partial scan approaches 180 CD and 180 MCD are
also reflected by current investigations of other groups and
manufacturers: This year they started to switch from “half
scan” or partial scan to “multisector” or “pulse-rate adaptive”
reconstruction algorithms [15]–[16]. These algorithms, similar
to 180 MCI, use data of adjacent heart cycles to improve
the temporal resolution. However, due to the absence of a
true phase weighting approach, they seem to be less elegant
and tend to show new artifacts [17]. The advantages of the
new cardiac imaging algorithms can further be improved by
a rawdata-based motion detection (kymogram) to allow for a
phase-selective reconstruction of the heart without acquiring
the ECG [18].
It has been proven that the dedicated cardiac algorithms are
clearly superior to the standard -interpolation approaches.
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IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 19, NO. 9, SEPTEMBER 2000
(a)
(b)
(c)
=
Fig. 11. Patient with strongly varying heart rate. For each image reconstructed (z
1 mm, 2 mm, 1 1 1 ; 99 mm), the local mean heart rate, i.e., the mean heart
rate contributing to each reconstructed image, is given in (a). The patient’s global mean heart rate during the data acquisition was 79 min . The 180 MCI
reconstructions (b) and (c) show that the cardiointerpolation algorithm can handle this situation well. For example, the aortic valve can be depicted in its different
functional states with sufficient temporal and spatial resolution (100/700).
Fig. 12. SSD of the complete heart at three different reconstruction phases c . The fast-moving right coronary artery is only depicted well in the second image,
which has been centered at diastole. An animated video of the same patient is available at http://www.imp.uni-erlangen.de/e/research/cardio/.
Phase selectivity and a high temporal resolution have become
available. Especially, 180 MCI improves cardiac imaging by
subsecond multislice CT drastically. The potential for accurate
calcium scoring has been demonstrated. Cardiac CT imaging
could be improved further by freely selectable
and by
higher rotation speeds.
KACHELRIEß et al.: ECG-CORRELATED IMAGING OF THE HEART
ACKNOWLEDGMENT
The authors thank Dr. S. Achenbach, Dr. W. Moshage, and Dr.
U. Baum, who carried out the patient studies for a very efficient
and pleasant cooperation and Dr. C. Becker for the case with
varying heart rate presented in Fig. 11.
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