Key words
C-arm flat-panel detector computed tomography - flat-panel detector - patient alignment
- heel effect - image quality
Introduction
C-arm flat-panel detector computed tomography (CACT) allows acquisition and reconstruction
of CT-like images in a flat-panel angiography system providing cross-sectional information
during an interventional procedure. In addition to the diagnostic value, CACT images
can be fused with real-time fluoroscopy, thus considerably expanding the diagnostic
and therapeutic options of an angiographic system [1]. Therefore, the use of CACT is on the rise in many radiologic and neuroradiologic
interventions [2]
[3]. Although the low-contrast performance of CACT is inferior compared to multi-detector
CT (MDCT) systems, comparative studies using the same radiation exposure for both
techniques confirm higher spatial resolution for CACT compared to MDCT [4]
[5]. Furthermore, it has been shown that quantitative measurements in the same region
are sufficiently reliable [6]. However, due to the conical beam geometry used in CACT as well as in cone-beam
CT (CBCT) with wide aperture angles, it is to be expected that the homogeneity of
the radiation field and thus the image quality of CACT and CBCT is significantly influenced
by the heel effect of the X-ray tube anode.
Compared to MDCT, the maximum X-ray tube power of CACT is lower. Furthermore, the
flat-panel detector installed in CACT reaches its maximum quantum efficiency at an
X-ray high voltage of around 80 to 90 kVp [7]
[8]. Therefore, the pre-filtration of CACT is normally restricted to the inherent X-ray
tube filtration of 2.5 mmAl and the use of bow-tie filters which can increase image
quality is omitted. The lower beam hardening of CACT compared to conventional CT combined
with the use of lower tube potential results in a softer X-ray spectrum of CACT. These
technical limitations particularly favor beam hardening and photon starvation artifacts
[9].
If the angular distribution of an X-ray tube spectrum or the heel effect is aligned
along the patient table in CACT, the image quality might be affected by the patient
alignment and could have an impact on the reliability of quantitative measurements.
Previous investigations demonstrated the artifacts, for example, intensity inhomogeneities
or errors induced in quantitative densitometry, caused by the heel effect and its
influence on the image quality in CBCT [11]
[12].
To the best of our knowledge, the impact of patient alignment on CACT image quality
has never been studied.
The purpose of this study was to investigate the impact of patient alignment on the
image quality represented by physical image parameters.
Materials and Methods
Phantom
In order to assess image quality in terms of high and low contrast resolution in this
study, an ACR phantom (American College of Radiology CT accreditation phantom, Model
464, Gammex-RMI, Middleton, Wisconsin) was used in this study. This phantom consists
of a water-equivalent material and contains four modules [13]. Each module has a diameter of 20 cm with a length of 4 cm. A sketch and an AP projection
of an ACR phantom are shown in [Fig. 1a, b]. The modules are designed to determine image quality parameters, such as CT number
and low- and high-contrast resolution. Since the influence of patient alignment can
be greatest at the end of the phantom, only the first and the last modules of the
phantom were utilized in this study. These modules are described as follows:
Fig. 1 a Sketch of an ACR phantom. b ACR phantom imaged by CACT. The solid (blue) arrow indicates the range of selected
images for noise determination along the z-axis (see the Results section). c Module 1: The numbers in square present the count of line pairs per cm (lp/cm). d Module 4: The numbers indicate different materials: ① Air, ② Bone, ③ Polyethylene,
④ Water-equivalent material, ⑤ Acrylic. The black, dashed ring indicates the water-equivalent
cylinder.
Abb. 1 (a) Skizze eines ACR-Phantoms. (b) CACT-Aufnahme eines ACR-Phantoms. Zur Bestimmung des Rauschens entlang der z-Achse
wurde der mit dem blauen Pfeil markierte Bereich ausgewählt. (c) Modul 1. Die Zahlen präsentieren die Anzahl der Linienpaare pro cm (lp/cm). (d) Modul 4. Die Zahlen geben verschiedene Materialien an: ① Luft, ② Knochen, ③ Polyethylen,
④ Wasseräquivalentes Material, ⑤ Acryl. Der schwarze, gestrichelte Kreis zeigt den
Wasser-äquivalenten Zylinder.
Using the first module, module 1, the spatial resolution or high contrast can be determined.
This module has eight aluminum bar resolution patterns, i. e., 4, 5, 6, 7, 8, 9, 10,
and 12 lp/cm, which are illustrated in [Fig. 1c]. The depth of the patterns is 3.8 cm along the z-axis.
The CT numbers of different materials can be determined using module 4, which contains
five cylinders of materials with different densities. The materials and their densities
are as follows: air (0 g/cm3), bone (1.95 g/cm3), polyethylene (0.94 g/cm3), water-equivalent cylinder (1 g/cm3), and acrylic (1.18 g/cm3).
Each cylinder has a diameter of 25 mm and a length of 4 cm, except for the water-equivalent
cylinder with a diameter of 50 mm. [Fig. 1d] shows a CT image of module 4. The experimental setups A and B are shown in [Fig. 2a, b], respectively.
Fig. 2 a Setup A. b Setup B. An image of module 4 depicts the different orientations of the phantom on
the patient support.
Abb. 2 (a) Setup A. (b) Setup B. Ein Bild des Moduls 4 illustriert die unterschiedliche Ausrichtung des
Phantoms auf dem Patiententisch.
Image acquisition
The phantom was placed in 2 positions (setups A, B) on the patient table in the isocenter
of the CACT – as follows:
For setup A the phantom was placed with the high-contrast segment (module 1) feet
first. For setup B the phantom was placed head first.
CACT of the phantom was acquired using a monoplane, ceiling-mounted, angiographic
system (Artis Q; Siemens Healthineers, Forchheim, Germany) using a CACT preset (6S
DynaCTBody, Dyna CT; Siemens Healthineers, Forchheim, Germany) with a 6 s rotation
run from –100° to 100° without additional filtering. Along this 200° rotation, 397
projections with a constant detector dose were acquired. The chosen acquisition geometry
was a table-side trajectory with a C-arm rotation around the phantom that usually
performed for body scans.
CACT was equipped with a 3-foci Gigalix X-ray tube (Siemens Healthineers, Forchheim
Germany) and a 30 × 40 cm flat-panel detector system [14]. The source-to-detector distance was 119.8 cm. The phantom was placed at the isocenter
of the system.
The measurements were performed using three different image acquisition protocols
with X-ray tube voltages of 81, 102, and 125 kVp using the large focal spot (0.7 mm).
[Table 1] presents the image acquisition protocols of the measurements.
Table 1
Image acquisition protocols of the measurements.
Tab. 1 Akquisitionsparameter der Messungen.
X-ray tube voltage (kVp)
|
setup
|
X-ray tube current (mA)
|
dose area product (cGy*cm²)
|
81
|
A
|
253
|
1879.6
|
81
|
B
|
255
|
1892.0
|
102
|
A
|
91
|
1226.6
|
102
|
B
|
92
|
1232.7
|
125
|
A
|
39
|
1039.5
|
125
|
B
|
39
|
1045.1
|
Images were reconstructed with four different convolution kernels: normal, hard, soft,
and very soft with a reconstructed slice thickness of 0.49 mm.
Afterwards, the images were exported and analyzed using plug-ins and macros for the
software program ImageJ (open-source image analysis software, version 1.50d; https://www.imagej.nih.gov/ij/).
The 2D intensity profile of the X-ray tube was measured using 55 kVp irradiating the
detector free-in-air. 1D profiles were calculated by averaging the 2D profile along
two axes parallel and perpendicular to the patient support using 200 lines. The 1D
profile can be utilized to calculate the anode angle α of the X-ray tube. The analytical
model for heel effect described by Dixon et al. [15]
[16] was used. The heel effect function ρ(x) can be approximated with an accuracy of
better than 0.16 % as
where β represents the anode attenuation along the central ray of the X-ray beam.
Furthermore, β is a function of the weighted average of attenuation coefficients
over the X-ray spectrum (E) with a value of 0.28 at 120 kVp being determined empirically.
F denotes the distance of the focal spot to the detector. For the calculation of the
anode angle only, the slope is considered.
Image Quality Assessment
The high-contrast resolution of imaging systems was measured in terms of MTF using
the bar patterns in module 1 of the phantom. Droege and Morin [17] devised a practical method for the MTF determination. This method was based on the
standard deviation measurements of the pixel values within an image of bar patterns.
Therefore, 10 × 10 mm2 square-shaped regions of interest (ROIs) were placed within bar patterns and the
background.
An image set including 50 images was utilized for the MTF calculation. Using the CT
numbers in the ROIs and their standard deviations, MTF values for each spatial frequency
(lp/cm) were calculated.
A Gaussian fit was used to estimate the 50 %, 10 %, and 2 % MTF values for all reconstruction
kernels.
Furthermore, for quantifying the effect of the phantom alignment on the CT numbers,
the CT numbers of the inserts in both setups were determined.
The low contrast resolution was assessed using the image noise, signal-to-noise ratio
(SNR), and contrast-to-noise ratio (CNR).
The image noise is defined as the standard deviation of the voxel density. The noise
parallel to the patient support (z-axis) was determined using ROIs with an area of
about 300 mm2 at the center of images along the ACR phantom. The noise profile by selection of 250
slices for different X-ray tube peak voltages was calculated in the central part of
the phantom. To avoid the impact of cone-beam artifacts on the results, images at
the border regions of the phantom were deselected (see [Fig. 1], top right). Furthermore, using the uniform module (module 2), the image noise perpendicular
to the patient support (x-axis) was also calculated. Mean averages using 25 images
were calculated.
SNR is defined as the ratio between the mean CT number and its standard deviation,
i. e.,
CNR is defined as
where
is the mean CT number within a defined ROI.
and σbg denote the CT numbers of the background and the corresponding standard deviation
in an ROI with the same area.
Image noise, SNR, and CNR were assessed using the density inserts placed in module
4 of the ACR phantom. ROIs of about 250 mm2 were placed in the density inserts, in order to measure the absorption of each insert.
The corresponding standard deviations were calculated in ROIs with the same area placed
at the middle of module 4. Mean averages were calculated using 25 images.
The normal kernel was utilized to calculate noise, SNR, and CNR, while MTF was determined
using four kernels.
For the evaluation of statistical significance, paired two-sided t-tests were applied.
A p-value of < 0.05 was considered statistically significant.
Results
[Fig. 3] shows the intensity profiles of CACT. On the top of this figure, the 2D profile
is depicted, while the bottom plots present the profiles along (z-axis) and perpendicular
(x-axis) to the patient support, respectively. The intensity profile on the z-axis
is an average of 200 rows and shows an intensity variation of about 4 %. The slope
of the 1D profile along the x-axis by averaging 200 rows caused by the heel effect
to deliver an anode-angle of α = (8.84 ± 0.02) degrees. The real anode angle obtained
from the technical manual of the facility with a 3-foci Gigalix X-ray tube is 11.5
degrees. The main difference between the measured value and real value of the anode
angle is the neglecting of the focus size (“point source”) in the equation (1) [15].
Fig. 3 2D intensity profile of the detector (top). 1D profile along the patient support
(bottom, left) and perpendicular to the patient support (bottom, right). The profile
along the x-axis indicates that the heel effect is perpendicular to the patient support.
Using equation (1) and 1D profile along the x-axis, an anode angle of α = (8.84 ±
0.02) degrees was determined. We presume that the kink in the profile along the z-axis
is caused by the use of a grid between the X-ray tube anode and the patient support.
Abb. 3 2D-Intensitätsprofil (oben). 1-D-Profil entlang des Patiententischs (unten, links)
und senkrecht zum Patiententisch (unten, rechts). Das Profil entlang der x-Achse zeigt
an, dass der Heel-Effekt senkrecht zum Patiententisch ist. Unter Verwendung von Gleichung
(1) und 1-D-Profil entlang der x-Achse lässt sich ein Anodenwinkel von α = (8,84 ± 0,02)
Grad bestimmt. Der Knick im Profil entlang der z-Achse wird vermutlich durch die Verwendung
eines Gitters zwischen der Röntgenröhre und dem Patiententisch verursacht.
The difference is also based on the energy dependency of the factor β. The measurement
with another X-ray tube high voltage, e. g. 120 kVp, might deliver a different anode
angle. Furthermore, the measurement of the 2D intensity profile was performed with
the grid, which has an impact on the determined anode angle from the measurement.
MTF values determined for both setups are shown in [Fig. 4]. For both setups the MTF assessed using a sharp convolution kernel shows the highest
high-contrast resolution, while the MTF calculated by a very soft kernel denotes the
lowest high-contrast resolution. Furthermore, 50 %, 10 %, and 2 % MTF values for all
reconstruction kernels are listed in [Table 2].
Fig. 4 MTF calculated for different convolution kernels for an X-ray tube voltage of 102
kVp. The fit model is the Gaussian function. a Setup A. b Setup B.
Abb. 4 Berechnete MTF und Gauß-Fitfunktionen für verschiedene Faltungskerne bei einer Röhrenspannung
von 102 kVp. (a) Setup A. (b) Setup B.
Table 2
50 %, 10 %, and 2 % MTF for all reconstructions.
Tab. 2 50 %, 10 %, und 2 % MTF für alle Rekonstruktionen.
convolution
Kernels
|
50 % MTF
|
10 % MTF
|
2 % MTF
|
setup A
|
setup B
|
p-value
|
setup A
|
setup B
|
p-value
|
setup A
|
setup B
|
p-value
|
normal
|
4.9 ± 0.1
|
5.4 ± 0.1
|
< 0.001
|
9.0 ± 0.2
|
9.8 ± 0.2
|
< 0.001
|
11.7 ± 0.2
|
12. 8 ± 0.2
|
< 0.001
|
sharp
|
6.4 ± 0.2
|
6.8 ± 0.2
|
< 0.001
|
11.6 ± 0.3
|
12.4 ± 0.3
|
< 0.001
|
15.1 ± 0.4
|
16.1 ± 0.4
|
< 0.001
|
soft
|
3.4 ± 0.1
|
3.6 ± 0.1
|
< 0.001
|
6.1 ± 0.1
|
6.5 ± 0.2
|
< 0.001
|
8.0 ± 0.2
|
8.5 ± 0.3
|
< 0.001
|
very soft
|
2.7 ± 0.1
|
2.8 ± 0.2
|
0.002
|
4.9 ± 0.2
|
5.1 ± 0.4
|
0.002
|
6.4 ± 0.3
|
6.6 ± 0.5
|
0.009
|
The differences in MTF values measured by setups A and B for all convolution kernels
and at all used X-ray tube voltages are statistically significant (p < 0.01).
The related CT numbers of inserts with different densities for all X-ray tube voltages
measured by setups A and B were calculated and presented in [Table 3]. As expected, the measured CT numbers behaved linearly relative to material density.
Due to the beam-hardening effect of the photon fluence spectra, the CT numbers decrease
with X-ray tube voltage and material density. Based on this effect, the largest difference
in the CT numbers at the X-ray tube voltages of 81, 102, and 125 kVp for bone insert
was observed.
Table 3
CT numbers of different materials measured by setup A (a) and setup B (b).
Tab. 3 CT-Zahlen für verschiedene Materialien in Setup A und Setup B.
inserts
|
81 kVp
|
102 kVp
|
125 kVp
|
setup A
|
setup B
|
p-value
|
setup A
|
setup B
|
p-value
|
setup A
|
setup B
|
p-value
|
air
|
–870 ± 4
|
–880 ± 4
|
< 0.001
|
–882 ± 5
|
–893 ± 5
|
< 0.001
|
–900 ± 5
|
–914 ± 5
|
< 0.001
|
polyethylene
|
–110 ± 4
|
–109 ± 4
|
0.38
|
–134 ± 5
|
–127 ± 5
|
< 0.001
|
–192 ± 5
|
–181 ± 5
|
< 0.001
|
water-equivalent
|
10 ± 5
|
4 ± 5
|
< 0.001
|
–37 ± 5
|
–32 ± 5
|
< 0.001
|
–112 ± 5
|
–99 ± 6
|
< 0.001
|
acrylic
|
88 ± 6
|
85 ± 5
|
0.06
|
57 ± 6
|
58 ± 6
|
0.56
|
–12 ± 6
|
–5 ± 6
|
< 0.001
|
bone
|
1127 ± 7
|
1163 ± 6
|
< 0.001
|
930 ± 7
|
948 ± 6
|
< 0.001
|
724 ± 7
|
743 ± 6
|
< 0.001
|
Except the polyethylene insert at the X-ray tube voltage of 81 kVp and the acrylic
insert at the X-ray tube voltages of 81 and 102 kVp, the difference between the CT
numbers measured by setup A and setup B at all X-ray tube voltages for the inserts
was considered statistically significant.
The image noise within the same ROIs for all materials is presented in [Fig. 5]. The image noise measured in setup A for the air and bone inserts was systematically
higher compared to that measured in setup B, on average about 3 % and 4 % for the
air and bone inserts (p > 0.05), respectively.
Fig. 5 Noise calculated in five inserts. Data are normalized to the maximum value of noise.
Abb. 5 Auf den Maximalwert normiertes Rauschen.
The opposite behavior has been observed for the polyethylene, water-equivalent, and
acrylic inserts. The corresponding image noises were on average about 4 %, 6 %, and
2 % lower in setup A compared to those measured in setup B. [Fig. 6] shows the SNR values (p > 0.05).
Fig. 6 SNR calculated in five inserts. Data are normalized to the maximum value of SNR.
Abb. 6 Auf den Maximalwert normiertes SNR.
As expected, the SNR for all inserts behaves inversely to the image noise. This can
be explained by equation (2) and the almost constant CT numbers of the inserts measured
in setups A and B, which are already presented in [Table 3].
The CNR values for five inserts are shown in [Fig. 7]. Except for the water-equivalent insert, the CNR values for all inserts calculated
in setup A are on average about 4 % higher than those calculated in setup B (p > 0.05).
CNR for water-equivalent insert is small with corresponding large uncertainties.
Fig. 7 CNR calculated in five inserts. Data are normalized to the maximum value of CNR.
Abb. 7 Auf den Maximalwert normiertes CNR.
The noise profiles parallel and perpendicular to the patient supports for both setups
are presented in [Fig. 8]. The staircase-shaped behavior of the noise plot measured along the z-axis is because
of the different attenuation properties of the phantom modules. The radiation intensity
in the case of the uniform module has been less attenuated than in the case of other
modules, which is reflected by the gap in the noise diagram ([Fig. 8] (left)). The image noise that increases at the middle of images along the x-axis
is based on the cupping effect.
Fig. 8 Noise profile along the z-axis (left) and x-axis (right). The noise determination
was performed by the setup A (top) and setup B (bottom). The red, blue, and green
lines indicate the noise values for the X-ray tube peak voltages of 81, 102, and 125
kVp, respectively. The image noise increasing at the middle of images along the x-axis
is based on the cupping effect.
Abb. 8 Profil des Rauschens entlang der z-Achse (links) und der x-Achse (rechts) in Setup
A (oben) und Setup B (unten). Die roten, blauen und grünen Linien zeigen das Rauschen
für die Röhrenspannungen von 81, 102 und 125 kVp. Die Erhöhung des Rauschens in der
Mitte der x-Achse ist auf den Cupping-Effekt zurückzuführen.
Discussion
The presented investigation demonstrated a minor impact of patient alignment on CACT
image quality.
The 2D profile measurement showed that the change in image quality parameters, such
as MTF, SNR, and CNR, along the patient support (z-axis) was not based on the heel
effect of the X-ray tube anode. The intensity profile of CACT measured by the detector
system free-in-air showed an intensity gradient perpendicular to the patient support
(x-axis). This finding indicates that the anode heel effect is not in the longitudinal
direction to the z-axis.
Due to small varying of the radiation dose, given by dose area product, ranging from
0.5 % to 0.7 % for all X-ray tube voltages, the difference in image quality parameters,
such as image noise, SNR, CNR, and MTF, measured by both setups cannot be attributed
to the radiation dose.
The observed differences in image quality, dependent on the phantom alignment, are
mainly caused by the incomplete rotation of CACT around the z-axis. This incomplete
rotation leads to inhomogeneous irradiation of the object as compared to conventional
CT. This inhomogeneous dose distribution in the object/phantom results in asymmetrical
beam hardening and scattering [10]
[18] which lead to the orientation-dependent image quality observed in this study. This
assertion was clearly noted by the measured image noises for the bone (+ 4 %) and
acrylic (–2 %) inserts as the noise values showed reversed variation for setups A
and B. The same but inverse effect could be observed for the air (+ 3 %) and polyethylene
(–6 %) inserts. In addition, we verified the influence of the incomplete rotation
of CACT on image quality by rotating the phantom 180 degrees about its central axis,
see [Fig. 9]. The noise values in the bone and polyethylene inserts in the left setup ([Fig. 9a]) were lower than those measured in the right setup ([Fig. 9b]) about 13 %. The inverse behavior has been observed for the air and acrylic inserts
in the both setups (–12 %). While the SNR was increased for the air and acrylic inserts
in the right setup, those values for the bone and polyethylene inserts were decreased.
This is an indicator of the impact of phantom alignment on image quality.
Fig. 9 Rotating the phantom 180 degrees about its central axis to verify the influence of
incomplete rotation of the CACT on image quality.
Abb. 9 Um den Einfluss der unvollständigen Drehung des CACT auf die Bildqualität zu überprüfen,
wurde das Phantom um 180 Grad um seine Mittelachse gedreht.
Furthermore, the MTF was calculated using the method of Droege and Morin, which is
based on the standard deviation (noise) measurements of the pixel values within the
bar pattern. In both setups the high contrast inserts are irradiated differently.
This also caused different noise values in both setups that leads to variation of
the MTF.
The image noise increase at the middle along the x-axis is attributed to the cupping
effect [19]
[20]
[21]. We assume that the difference in the image quality parameters is also based on
the local dose that reaches the end of the phantom in both directions. Since the dose
measurement using the ACR phantom was not possible, we focused our analysis on the
noise determination along the z-axis, which reflects the local radiation dose. Both
the intensity and noise profile along the z-axis validated the different doses along
the patient support. The noise profile along the z-axis shows a reverse trend for
both setups.
Up to now, the low- and high-contrast performance of CACT compared to MDCTs has been
shown in previous studies. However, there is no study, to our knowledge, demonstrating
a relationship between patient alignment and CACT image quality.
Bai et al. [22] assessed the image quality of a CACT system (Axiom Artis dTA; Siemens Healthcare,
Forchheim, Germany) to that of two MDCT units (Lightspeed VCT; GE, Milwaukee, USA
and Sensation Cardiac 64; Siemens Healthcare, Erlangen, Germany). A male Anderson
Radiation Therapy 200 phantom was used and the radiation dose was measured with embedded
thermoluminescence dosimeters (TLDs). The result indicated that CACT applied fewer
doses to the phantom at a similar spatial resolution and low contrast detectability
to both MSCT units. In another phantom and cadaveric study, Werncke et al. [5] compared the effective radiation dose and image quality between a CACT unit (Artis
Zee Q; Siemens, Forchheim, Germany) with a standard 16-slice MDCT unit (GE Lightspeed
16; GE Healthcare, Waukesha, Wisconsin). The radiation dose was determined using 100
TLDs placed in an anthropomorphic whole-body phantom (adult male phantom with arms,
model 701 and model 701-10, CIRSinc, Norfolk, USA). The result of this study also
showed an improvement in the spatial resolution with CACT compared to MDCT at the
same radiation dose. However, recent studies indicate that, for the low range of the
X-ray tube high voltage, the related low- and high-contrast image quality of CACT
is similar to that of conventional CT [23]
[24].
Our study has a number of limitations: First, we used a cylinder-shaped phantom with
a radius of 20 cm which is only an approximation for a patient head. However, the
advantage of this simplifying approach is that well-known artifacts, which are current
limitations of C-arm CT, such as truncation artifacts and beam hardening, are avoided.
The impact of truncation artifacts might be reduced by using recently presented software-based
techniques, 3D camera systems [2], or extended-volume C-arm CT [3].
A more realistic phantom, for example with a spine, would introduce further artifacts
depending on the orientation of the phantom and was therefore not used in this study.
The results of this study can be used for investigations of the head. Second, for
obtaining the 2D and subsequent 1D intensity profiles and subsequently for calculating
the anode angle, we irradiated the detector system, which has an energy dependency.
Using another X-ray tube voltage, the anode angle would differ from 8.8 degrees. However,
the main limitation is that the angular radiation dose distribution was missing. In
order to obtain this information, a dose measurement using TLDs placed on the surface
of the phantom had to be performed. This is time-consuming and would in our opinion
not alter the obtained results.
Furthermore, it has to be mentioned that the standard C-arm calibration is conducted
using a copper filter. Therefore, the heel effect is considered. Furthermore, due
to the alignment of the X-ray tube, any possible effect should be low as demonstrated
in this study.
In conclusion, patient alignment has a minor influence on CACT image quality. This
effect is caused mainly by the incomplete rotation of CACT.