Inherently 3-dimensional method for measurement of computed tomographic resolution anisotropy.

Inherently 3-Dimensional Method for Measurement of
Computed Tomographic Resolution Anisotropy
Stephen E. Jones, PhD, MD,* Michael Grasruck, PhD,Þ Bernhard Schmidt, PhD,Þ Ijad Madisch, MD,*
Ryan Egeland, MD, PhD,þ Tom Brady, MD,* and Rajiv Gupta, PhD, MD*
Objective: Current techniques to measure computed tomography (CT)
spatial resolution use separate methods for in-plane and out-of-plane
directions. The growing use of near-isotropic voxel size necessitates a
new single method that inherently measures resolution in any direction.
Method: We introduce a method using a set of numerous glass
microspheres suspended in a small volume from which a mean sphere
image is constructed. Projecting asymptotes after imaging different
microsphere sets with decreasing diameters provides an inherently 3-
dimensional measure of spatial resolution and anisotropy. We apply
the method to both a flat-panel and multidetector CT scanner.
Results: The full-width at half-maximum from line profiles through
mean sphere in transverse directions corresponds to known micro-
sphere diameters. Increased longitudinal full-width at half-maximum
corresponds to known anisotropy, which is larger for a multidetector
CT scanner than for a flat-panel CT scanner.
Conclusions: A new single method to measure CT resolution is
inherently isotropic.
Key Words: CT, anisotropy, resolution, calibration, flat-panel CT
(J Comput Assist Tomogr 2006;30:962Y971)
Continuous improvements in multidetector computedtomography (MDCT) technology now permit imaging
with near-isotropic voxels. The recent introduction of flat-
panel detector-based volume CT (fpVCT) scanners has
eliminated the discrepancy between in-plane and z resolution.
With fpVCT, isotropic resolution of the order of 150 Km is
possible at the center of the scanner. For MDCT scanners,
although the in-plane resolution is slowly increasing, the push
toward isotropy is primarily due to ever-smaller detector rows
along the z axis.
Although the distinction between in-plane (x-y plane)
and out-of-plane (z axis) resolution is blurring, the current
methods used to measure or calibrate spatial resolution
remain unique. The standard method to measure x-y reso-
lution uses a line-pair phantom, with increasing line-pair
density aligned in the x-y plane. As the line-pair density
increases, the ability of the scanner to discern them as
separate lines declines. The limit of this process describes the
spatial resolution of the scanner. Figure 1 shows the highY
spatial resolution Siemens ConeBeam phantom (QRM
GmbH, Moehrendorf, Germany) and the Catphan CTP528
(CAT) high-resolution module (The Phantom Laboratory,
Salem, NY) in an fpVCT scanner. The CAT phantom pro-
vides line-pair inserts in steps of 1 line-pair per centimeter
(lp/cm) from 16 to 21 lp/cm, and the Siemens ConeBeam
phantom provides line-pair inserts in steps of 2 lp/cm from 18
to 24 lp/cm. From these images, one can deduce that the
resolution of the fpVCT scanner used is somewhere between
22 and 24 lp/cm.
An alternative method for measuring x-y resolution is
by determining the modulation transfer function (MTF) of the
scanner. The x axis of an MTF curve denotes the spatial
frequency. The y axis is the percentage of contrast that is
transferred to the image (ie, the ratio of contrast in the CT
image to the actual contrast of the object). The MTF, there-
fore, describes the spatial resolution of the scanner as a
function of the spatial frequency.
To determine the MTF, a thin tungsten wire (typically
100 Km in diameter) is scanned. The image of the wire
denotes the point-spread function (PSF) of the scanner. One
can think of the PSF as the response of the imaging system to
an impulse input (ie, the impulse response of the system). The
Fourier transfer of the impulse response is the MTF.
Traditionally, the spatial frequency that results in 10%
modulation transfer is cited as the spatial resolution of the
scanner. Figure 2 shows the MTF curve for an fpVCT scanner
obtained using a 100-Km tungsten wire. As can be seen, 24 lp/
cm yields 10% modulation transfer, matching the spatial
resolution predicted by the line-pair phantom (Fig. 1).
The MTF and line-pair phantom measure the in-plane
resolution of the scanner. A different metric, viz, the slice
sensitivity profile (SSP), is used to characterize the spatial
resolution in the z direction. The SSP is measured using a
phantom containing a thin gold foil oriented in the slice
direction. The number of CT slices that contain the gold foil
provides a measure of the spatial resolution in the z dimen-
sion. To estimate this number, the density of the CT slice is
plotted against the slice position and the full-width at half-
maximum (FWHM) of this curve is determined. The SSP of
fpVCT is shown in Figure 3. As can be seen, the FWHM of
the SSP curve for the fpVCT is $300 Km. Clearly, the z
resolution of fpVCT is different from the in-plane resolution
of the scanner.
From the *Department of Radiology, Massachusetts General, Hospital, Boston,
MA; †Siemens Medical Solutions, Siemens, Forchheim, Germany; and
‡Harvard Medical School, Boston, MA.
Received for publication March 19, 2006; accepted May 12, 2006.
Reprints: Stephen Jones, PhD, MD, Department of Radiology, FND 216,
Massachusetts General Hospital, 55 Fruit St, Boston, MA 02114-2698
(e-mail: sejones@partners.org).
Sources of funding: Dr Grasruck and Dr Schmidt are employees of Siemens
Medical Solution. Dr Gupta’s research was supported by CIMIT (DoD),
RSNA, and Siemens Medical Solutions.
Copyright * 2006 by Lippincott Williams & Wilkins
ORIGINAL ARTICLE
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Spatial resolution is clinically relevant in reducing
partial volume averaging that contaminates the edges of high-
contrast objects. Clinical interest is the ability to visualize
small flecks of calcium, as might occur with pathologies such
as atherosclerosis, possibly providing further assessment of
the risk of plaque to rupture.1,2 Clearly, this capability re-
quires near-isotropic voxels. Inasmuch as the question of the
smallest possible calcification visible is related to the
question of resolution, an inherently 3-dimensional method
of measuring resolution is clinically useful to establish the
lower limit of visible calcifications.
This article introduces a method to measure resolution
that is manifestly 3-dimensional by imaging sets of numerous
microspheres of different sizes, in which the diameters are
comparable with, and span, the detector pixel size. From each
set, the image of an average microsphere is easily computed.
As the sphere diameter becomes much smaller than the pixel
size, the image will asymptote to the PSF, whose FWHM is a
measure of inherent resolution. By comparing the FWHM of
the average sphere along the 3 cardinal directions, a measure
of anisotropy is obtained. By this method, in-plane and out-
of-plane resolutions are measured using the same method.
Meinel et al3 used metal spheres of a single size (790Km
in diameter) to measure spatial variation of resolution within a
CT scanner, but required mathematical deconvolution to
extract the resolution. Fahrig and Holdsworth,4 Jaffray et al,5
and Cho et al6 also describe methods using steel balls of a
single diameter. Our proposed method computes the PSF by
FIGURE 2. Modulation transfer function of MGH-Siemens
fpVCT obtained using a 100-Km tungsten wire, 120 kV, and
H95a reconstruction filter. A 10% modulation occurs with a
line-pair spacing of 24 lp/cm.
FIGURE 3. Slice sensitivity profile of MGH-Siemens fpVCT
measured using a 100-Kmgold foil in a polymethylmethacrylate
cylinder. The FWHM is 0.31 mm.
FIGURE 1. Selected CT images
through a highYspatial resolution CAT
phantom with line-pair inserts from 16
to 21 lp/cm in steps of 1 lp/cm (right).
The left image is a zoomed-in view of
Siemens ConeBeam phantom with
line-pair inserts from 18 to 24 lp/cm
(left). The images were acquired
using the Massachusetts General
Hospital (MGH)YSiemens fpVCT
scanner at 120 kV, 10 mA, and
reconstructed using a sharp H95a
kernel.
J Comput Assist Tomogr & Volume 30, Number 6, November/December 2006
Method for Measurement of
CT Resolution Anisotropy
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using a series of microspheres and the ensemble properties of
the set to overcome discrepancies in their size.
MATERIALS AND METHODS
Flat-panel Volume Computed Tomography
An fpVCT scanner combines the advances in CT with
digital flat-panel detector technology. In effect, an fpVCT is a
conventional MDCT in which the rows of detector elements
(typically 4, 16, or 64 rows) have been replaced by an area
detector, for example, with up to 2048 � 1536 elements. It is
therefore capable of producing 1536 slices, spanning $18 cm,
in one rotation. The z coverage afforded by these scanners is
large enough to image an entire organ such as brain, heart, liver,
or kidneys in one axial scan. Unlike micro-CT, VCT is suitable
for in vivo imaging of large animals or for human studies. By
virtue of their ultra-high, isotropic spatial resolution, which can
potentially reach 150 � 150 � 150 Km3 at the isocenter, these
innovative systems bring into focus anatomy that heretofore has
been in the domain of microscopy. The CT gantry integrated
with modified x-ray tube, filters and beam-formers, collimator,
and a 2-dimensional digital flat-panel detector system forms the
basis of the fpVCT scanner.
The MGH fpVCT (Siemens Medical Solutions, Er-
langen, Germany) uses a modified Sensation-16 gantry inte-
grated with a digital flat-panel detector and a modified x-ray
tube (Fig. 4). In this prototype, the x-ray source-to-detector and
source-to-isocenter distances were 930 mm and 573 mm,
respectively. A single flat-panel detector with an active area of
40 � 30 cm was used. A wide anode angle was used to allow
true cone-beam geometry with a cone angle of $16 degrees.
With a source-to-detector distance of $90 cm, this translates
into a z coverage of $18 cm. In the current prototype, the tube
is Bon^ only during the acquisition of a projection. A duty
cycle of 50% was used. Pulsed operation of the tube
reduced motion blurring and the overall x-ray dose during a
scan. To minimize the penumbra effect, a focal spot size of
0.5 mm was used.
The MGH-Siemens fpVCT uses a PaxScan 4030CB
(Varian Medical Systems, Palo Alto, Calif) CsIYamorphous
silicon flat-panel detector. This detector provides a field of
view of 25 � 25 � 18 cm3 when geometric magnification is
taken into account. The detector consists of a 2048 � 1536
matrix of elements, each with a dimension of 194 Km2. The
readout speed can be varied up to a maximum of 120 frames
per second. As the gantry rotates, projection images are
acquired and 2-dimensional projections are reconstructed into
a volumetric stack of slices using a 3-dimensional recon-
struction algorithm.
The reconstruction algorithm solves the inversion
problem; that is, it finds the volumetric stack that, when
forward projected, will yield the given projection data as the
ray-sum at each pixel. The system geometry for each projection
is first computed with the help of a calibration phantom.
Projection data from 360 degrees, geometric parameters for
each projection, and a kernel that describes what to emphasize
in the resulting image (ie, bone, soft tissue, etc) serve as inputs
to the reconstruction algorithm. An adaptation of direct 3-
dimensional Feldkamp algorithm, a simple and robust recon-
struction algorithm, is used in the current VCT prototype
system. This algorithm is a generalization of the standard
filtered back projection. Essentially, each voxel in the final
image is a weighted sum of corrected filtered projection values.
For this article, microsphere samples were scanned in
fpVCT at 100 kV, 30 mA, and an x-ray tube duty cycle of 50%. A
rotation time of 20 seconds was used for acquiring the 600
projections. Images were reconstructed with a nominal isometric
voxel size of 0.2 mm. The microsphere samples were also
scanned in a Siemens Sensation-64 (S-64) MDCT scanner at
120 kV, 50 mA, and a rotation time of 0.33 seconds. A sharp
reconstruction kernel was used in the ultra-high-resolution mode.
Microsphere Phantom
Microspheres were obtained from commercial vendors,
made from soda lime glass (Whitehouse Scientific, Chester,
UK; Polysciences, Warrington, Pa) with nominal diameters of
FIGURE 4. A schematic (left) and photograph (right) of the MGH-Siemens fpVCT at the MGH.
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75,180, 275, 625, 1000, and 1700 Km, and tungsten carbide
(Industrial Tectonics Inc, Dexter, Mich) with nominal
diameters of 500 and 600 Km. The distribution of the smallest
3 sets of glass beads was narrowed by further sieving the beads
with mesh sizes just above and below the desired diameter.
Glass was chosen as a mimic of calcification, whose imaged
density should be in the range of 3000 to 4000 Hounsfield units
(HU). Tungsten carbide was chosen to investigate artifactual
changes in the FWMH due to the finite density of glass. The
atomic composition of soda lime glass was SiO2 (71%Y74%),
Na2O (12.0%Y15.0%), CaO (8.0%Y10.0%), with the remaining
small amount composed of oxides of Mg, Al, K, and Fe. The
density of soda lime glass was 2.42 to 2.50 g/cm3.
The rough size and character of the beads were also
examined using photomicrographs that also imaged a millimeter
scale, permitting measurement of bead diameters. By measuring
many beads, both a mean and distribution of diameters could be
compared with the manufacturer’s specifications.
The beads were mounted on thin flexible foam sheets
0.8-mm thick, laid out in strips 90 cm long and 4.5 cm wide.
Foam was chosen because for CT purposes, its density closely
matches air, thereby providing maximal contrast to the bead.
After a spray adhesive was administered to the foam surface,
numerous beads of a single size were randomly sprinkled onto
the foam from a height of $60 cm. The beads would imme-
diately attach to the foam by the adhesive. The number of beads
attached was not measured at that time, but the number dropped
was limited to reduce the number of bead pairs seen in close
proximity. The strip of foam was then rolled into a tight spiral,
with a resulting cylinder diameter of$3 and 4.5 cm long. The 6
glass bead rolls were then simultaneously imaged in the
isocenter of the MGH-Siemens fpVCT.
FIGURE 5. Photomicrographs of
glass microspheres used in a new
method to measure inherently
3-dimensional anisotropy of a CT
scanner. Six different sizes are used,
with ascending diameters as noted.
Superimposed with each image is a
scale with millimeter tick marks. The
apparent oblong circumference of
most beads is illusory because of
illumination; however, there is a
small fraction of defective beads
representing less than 5%. Slight
variations of diameter are visible.
FIGURE 6. Thin-section collapsed images
of glass microspheres using 6 different
diameters (as indicated) obtained on
MGH-Siemens fpVCT. Microspheres with
diameters down to 180 Km can be resolved,
with the 75-Km microspheres indiscernible
from the image noise. One sample bead for
each of the 180- and 275-Km sizes is
enclosed by a white box.
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Method for Measurement of
CT Resolution Anisotropy
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Image Analysis
Image analysis was conducted off-line using custom
algorithms written in Interactive Data Language (Research
Systems Inc, Boulder, Colo). The set of all images was
concatenated as a 3-dimensional data volume. Inasmuch as
all 6 bead suspensions were imaged together, the region
around the beads of a single size was separately segmented
to produce 6 volumes, each containing only beads of a single
size. The location of beads was obtained by searching for all
local maxima of HU greater than a specified threshold, from
which beads were excluded if they were too close to another.
The threshold was set just above the highest possible back-
ground level as determined from a histogram of all voxels. A
subvolume around each remaining bead was extracted,
whose size was greater than the imaged bead so as to provide
a margin of at least 2 voxels of background around the bead.
This set of subvolumes was then added together to produce
an average bead image. From this image, linear profiles
along the 3 cardinal axes were extracted, from which the
FWHM was obtained. In addition, 2-dimensional images
were extracted along the 3 cardinal planes that intersected
the center.
A plot of the FWHM versus known bead diameter
revealed an asymptote at the lowest diameter and could be
interpolated to a bead diameter of zero, in effect providing a
PSF. Comparing these results along the 3 cardinal directions
allows evaluation for anisotropy. All bead samples were
imaged and analyzed the same way on both the MGH-
Siemens fpVCT and a clinical S-64.
Although we use the FWHM as a measure of resolution,
other definitions exist3 and the current analysis can be easily
extended to incorporate them.
RESULTS
Figure 5 shows photomicrographs of the 6 different glass
microspheres. The apparent oval shape seen in many beads is
an illumination artifact. Random measurements of various
beads returned diameters in accordance with the manufac-
turer’s label. The variation of bead diameters, even after sieving,
FIGURE 7. The distribution of HU from all voxels within each microsphere phantom is obtained by computing the histogram
of all voxels within the scan volume. The y axis is logarithmic, and the parabolic profile at low HU represents image noise.
The tail of the distribution extending from the noise parabola toward high HU represents those voxels containing glass,
either partially or completely.
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remained around 10%. Although some instances of abnormally
shaped beads were seen, these formed a minority.
Figure 6 shows thin section projection images using the
MGH-Siemens fpVCT for each bead size. The largest 3 bead
sizes are clearly visible above background noise. To increase
conspicuity of the smallest beads, the projected slabs were
further thinned; and the 180- and 275-Km beads are still
visible, although close to the background level. Although
windowing the gray-scale level was optimized for visualiza-
tion in each case, the smallest beads can no longer be seen
against the background.
To determine threshold levels for image analysis, a
histogram of all nonzero voxels was computed to determine
the background noise level, as shown for all 6 bead samples in
Figure 7. A logarithmic vertical scale is used that shows the
characteristic parabolic profile of the background, suggesting
a quasi-Gaussian distribution. At higher HU, beyond the
noise parabola, the distribution forms a tail of high-HU vo-
xels, which represent the beads. The tail is most conspicuous
for the largest-sized beads, and barely visible for the smallest.
A threshold was selected to be roughly the projected inter-
section of the noise parabola with the x axis. The mean noise
was computed aroundj935 HU for all sizes, with a threshold
around j500 HU. The peak in the tail of the 1700 beads at
2800 HU is due to the cupping artifact from the reconstruction.
After computing the average image of all isolated beads
within a given sample, linear profiles along the 3 cardinal
axes were obtained as shown for each bead size in Figure 8.
The x and y axes are orthogonal axes in the plane perpen-
dicular to the scanner centerline, and the z axis lies along the
scanner centerline. The horizontal axis is the distance along
the x, y, or z axes from the bead center in micrometers, and the
vertical axis is image density (HU). Data points for the x, y,
and z directions are indicated by the triangle, diamond, and
star, respectively, and are connected by an interpolated line
computed with a cubic spline. The FWHM for each curve is
printed in the upper left. For comparison, the vertical dashed
lines represent the expected bead diameter as specified by the
FIGURE 8. Linear HU profiles taken along 3 cardinal axes of an average-microsphere. The average sphere was constructed by
adding all microsphere images together after centering. Profiles for the x, y, and z axes are shown using a triangle, diamond, and
star, respectively. The vertical dashed lines represent expected diameters as given by manufacturer’s specifications. The FWHM for
each profile is displayed. The total number of microspheres used to create average sphere is displayed above each graph.
J Comput Assist Tomogr & Volume 30, Number 6, November/December 2006
Method for Measurement of
CT Resolution Anisotropy
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manufacturer’s label. For the largest beads, the dashed lines
appear close to the expected location for the FWHM, whereas
for the smallest beads, the profile width remains stable while
the expected width narrows. As the bead diameter decreases,
so does the peak amplitude, which by necessity never de-
creases below the threshold of $500 HU. The 1700-Km pro-
file shows the previously mentioned cupping artifact at the peak.
Figure 9 displays image profiles along the 3 cardinal
planes that intersect the bead center, specifically the x-y, x-z,
and y-z planes. The images are color coded according to the
displayed color bar so that white has the highest HU, followed
by green, blue, and then red. Vertical and horizontal linear
measurement bars are also displayed. Best seen in the largest
beads is good in-plane (x-y) symmetry, with decreased
resolution along the z axis causing ovoid distortion in the x-z
and y-z images. This behavior is again visible for the smallest
beads that are pixelated. Interestingly, for the smallest beads,
there is a subtle x-y asymmetry of unknown origin.
The reconstruction method used an exact voxel size of
234 Km. To test the effect of reconstruction voxel size on
computed FWHM, a second acquisition and reconstruction
were obtained using a voxel size of 107 Km. The linear pro-
files along the y axis are compared in Figure 10 for each
microsphere diameter. Although different voxel sizes cause
different sampling along each profile, the cubic spline inter-
polation profiles show good overlap, indicating that the anal-
ysis is robust to this range of voxel size. Reconstructed voxels
much larger than the individual detector size would produce
inaccurate results.
A graph of the extrapolated FWHM versus known bead
diameter is shown in Figure 11, for beads imaged in both the
MGH-Siemens fpVCT and the S-64. Data points for the x, y,
and z axes are indicated by the star, diamond, and triangle,
respectively, and are connected by linear lines for better
visualization. The dashed diagonal line represents the ideal line
where the extracted FWHM equals the manufacturer’s stated
diameter. For large bead diameters, the FWHM appears to
asymptote the ideal line, whereas for small diameters, the
FWHM deflects and appears to form a new horizontal asymp-
tote, whose projected intersection with the y axis is a measure of
the FWHM obtained from the ideal PSF of the scanner (ie,
FWHM of the impulse response of the system). For the MGH-
Siemens fpVCT, the z axis FWHM is mostly larger than the x
and y axes for the smallest beads, with a PSF FWHM of$480Km
compared with $350 Km for x and y. For the S-64, the z
axis resolution is markedly larger than the other axes for all
bead diameters, with a PSF FWHM of 800 Km compared
with 350 Km for x and y. Interestingly, the fpVCT and S-64
have very similar in-plane resolution, whereas the fpVCT
has superior, and nearly isotropic, out-of-plane resolution.
Comparison of the MGH-Siemens fpVCT to the S-64
reveals comparable in-plane resolution and superior out-of-
plane resolution, as would be expected from the S-64 pixel
size. Figure 12 demonstrates a more practical comparison of
this difference in spatial resolution by imaging a human knee.
Image A was acquired using the MGH-Siemens fpVCT with
an H95 filter, whereas image B was acquired using an S-64
with an H70 filter. In these 2 images, the horizontal axis is
along the scanner’s in-plane x axis and the vertical axis is
along the scanner’s z axis. As can be seen in Figure 12A,
details of the bone trabeculae are visible. In this image, there
is practically no difference in the image quality in the
FIGURE 9. Two-dimensional HU profiles taken along 3 cardinal planes of an average microsphere, which was constructed by
adding all microsphere images together after centering. The HU value is represented by a color intensity, as shown by the color
bar to the left of each image. The horizontal and vertical length scales are indicated by white lines with printed magnitude.
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horizontal and vertical directions. S-64 (image B), on the
other hand, shows a marked decline in the spatial resolution in
the z direction because of spatial resolution anisotropy.
DISCUSSION
The ideal object to directly measure inherently 3-
dimensional resolution would be a 3-dimensional realization
of Dirac delta function, which is a point source with infinite
density. Clearly, such an object does not exist, but the fun-
damental idea of this method is to approximate a point source
by asymptotically extrapolating from a series of microspheres
with progressively smaller (but nonzero) diameters to the
ideal zero-diameter sphere.
One limitation of this method involves the actual round-
ness of the beads. As several photomicrographs revealed,
many beads can be significantly distorted. However, this
fraction is smaller than a few percent; and this issue is ad-
dressed by averaging over a large ensemble of beads, num-
bering as many as 1000.
A second limitation is the effect of the exact bead center
with respect to the voxel isocenter. Inasmuch as a large
ensemble of microspheres is imaged, we can assume a uniform
distribution of microsphere centers with respect to voxel iso-
centers. This distribution can be expected to broaden the
FWHM of the average microsphere, but the amount cannot be
larger than the size of the voxel because the microsphere cen-
ters are always located somewhere within the middle voxel. A
centering algorithm was attempted, but a reliable subvoxel
interpolation routine causing minute translations was never
achieved. Applying this routine never significantly changed the
results. This result was surprising for the smallest beads, which
are smaller than the voxel size. However, this result can be
explained as an unexpected feature of the selection criteria for
detecting a bead: The smallest beads not only span the size of
$1 voxel, but also have low image intensity. If the bead center
is located near the boundary of 2 voxels, the image intensity is
roughly divided between them, such that the magnitude of
either voxel falls below the detection threshold. By judiciously
selecting the threshold for small beads, the only beads detected
are those already centered sufficiently within the voxel so they
do not divide their HU to adjacent voxels. One improvement
would be a detection algorithm that surveys the HU of adjacent
voxels, in addition to that of the center voxel. By correctly
FIGURE 10. Comparison of linear profiles along y axis using 2 different reconstruction voxel sizes: 234 Km (diamonds) and
107 Km (stars). Despite the difference in voxel size, the same HU profile is obtained, demonstrating that 107 Km is below the
resolution limit of the scanner and results in oversampling of the reconstructed image.
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Method for Measurement of
CT Resolution Anisotropy
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accounting for Bsplit^ HU, the detection threshold may be
greatly lowered without the overwhelming addition of false
beads due to background noise.
Another criticism is that the density of glass is finite and
does not truly reflect the infinite density of a point source
function. Applying the same technique using glass beads to
the tungsten carbide beads with diameters of 500 and 600 Km
tested this effect. The resulting images were so dominated by
saturation artifact as to cause false images with markedly
broad FWHM, which are not presented. For these technical
reasons, it is best for the selected material of nonzero diameter
beads to not have such a high density so as to completely absorb
all x-rays, and the choice of glass is judicious.
This method can detect very subtle asymmetries that
provide clues to previously unsuspected artifacts. For ex-
ample, one would expect no in-plane, or x-y, asymmetry; yet a
subtle asymmetry was seen (Fig. 11A). Any asymmetry is
difficult to explain; and one possibility is related to the
method of scanning where the gantry typically starts from the
3-o’clock position, breaking the symmetry, and collects data
FIGURE 11. A, Summary plot of the FWHM obtained from
linear HU profile along each cardinal axis of an average
microsphere, for each diameter. The diagonal dashed line
represents the ideal curve, and deviations from it for small
diameters reveal resolution limit of MGH-Siemens fpVCT.
B, Identical to A except using a Siemens S-64 scanner. Note
that although the x-y resolutions are similar, there is
considerable difference in the z direction (curves marked
with asterisks). The fpVCT, therefore, is more isotropic than
the S-64 scanner. FIGURE 12. Images of a cadaveric knee using MGH-SiemensfpVCT (A) and S-64 (B). The long axis of the knee was
oriented along the z axis of the scanner. In image A, the
details of the bone trabeculae are nearly indistinguishable in
the horizontal and vertical directions, indicating near isotropy.
For comparison, the same knee is scanned using an MDCT,
whose detector arrangement is far from isotropic. This
anisotropy can be clearly appreciated in image B.
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during the subsequent angle of 360 degrees. This asymmetry
may also arise from asymmetrical sampling of 360-degree
angular span by the acquired projection data. For example, if
there are substantially more projections when the x-ray beam
is horizontal as compared with when it is vertical, there will
be an anisotropy in x and y resolutions. This x-y anisotropy
could suggest a mechanical vibration artifact or an unknown
subtle software error regarding x and y coordinates.
Future work will apply this method to measure spatial
variation of resolution and anisotropy throughout the CT scan
field of view, which was presented by Meinel et al3 using
metal spheres of a single size. An advantage of these phan-
toms is that small regions of the scan field of view can be
sampled and the method is insensitive to exact orientation.
This is in contradistinction to the spatial resolution phantoms
currently in use (eg, wires or gold foils) that have to be
appropriately oriented in the bore of the gantry.
CONCLUSIONS
This article introduces a new method to measure 3-
dimensional CT resolution with inherent isotropy. By using a
series of glass microspheres with decreasing diameters, the
FWHM of the PSF can be estimated along any direction. The
phantoms and analysis are straightforward to fabricate and
use, and can easily be placed anywhere within the volume of
the bore. This method eliminates the use of multiple phantoms
to separately measure in-plane and out-of-plane resolution.
Practical recommendations for implementation include
the following: (1) At least 2 sets of beads should be smaller
than the known detector size, with the smallest diameter
approximately one half the detector size. (2) At least 2 sets of
beads should be much larger than the detector size, with the
largest diameter $5 times the detector size. (3) About 1 or 2
sets of beads should have diameters comparable with the
detector size. This collection of 5 or 6 diameters will permit
estimation of the asymptotes at both small and large scales.
(4) The reconstructed voxel size should be comparable with
or smaller than the detector size. Note that computational
requirements increase significantly for small reconstructions.
(5) The upper limit for the number of detected beads is de-
termined by minimizing the number of bead pairs that ap-
proach within several bead diameters of each other. (6)
Although a minimum of $50 beads provides adequate repro-
ducibility, more beads will provide increasing accuracy. Note
that for small diameters, this may necessitate placement of
$1000 beads in the phantom because of nondetection of
beads located at voxel boundaries.
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J Comput Assist Tomogr & Volume 30, Number 6, November/December 2006
Method for Measurement of
CT Resolution Anisotropy
* 2006 Lippincott Williams & Wilkins 971
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