CT BASED RADIOGRAPHY SIMULATIONS FOR BOTH
INDUSTRIAL AND MEDICAL RADIOGRAPHY
Feyzi Inane
Iowa State University
Center for Nondestructive Evaluation
Ames, IA 50010 USA
ABSTRACT. One of the important issues in the simulation work is proper representation of
the simulated objects. The geometrical shapes of the simulated objects may range from very
simple to very complicated geometries. In addition, a lot of objects come with heterogeneous
material properties that need to be included into simulations. These two issues play important
roles in both industrial and medical radiography simulations. CT (computed tomography)
became widely available to the radiography community in the recent years. Since this
technology provides two-dimensional images, CT images can be used to build models toward
using in simulation work. In this work, we developed a CT image based algorithm to account
for object shape complexities and heterogeneities. The resulting algorithm and absorbed energy
doses in a human body part and ideal detector images obtained through the algorithm will be
presented.
INTRODUCTION
In this article, we present an algorithm that utilizes CT data for industrial/medical
radiography simulations. One of the challenging issues in the real world cases is
representation of the test objects that can have very complex shapes and material that are
quite heterogeneous. Although CAD drawings can handle complex geometries, the same
can not be said for continuously changing material properties. This is especially true for
the human body that poses a real challenge to the CAD representation. In addition to its
irregular geometrical shape, human body is as heterogeneous as it can get. Although some
tissue types such as bone, muscle, cartilage are quite distinct, some other tissue types have
properties that are very close to each other. The differences between those tissues are very
subtle but real. Another problem with the human body is that transition from one type of
tissue to another type is usually very smooth resulting in difficulties in determining the
boundary. One escape from this bottleneck is utilization of CT images for modeling
purposes. With the rapid proliferation of CT and MRI capabilities in medical world, it is
very easy to obtain CT data for individuals. Although industrial CT is not as common as
medical CT, it is not that unusual to come across in industrial applications either. The
major difference between industrial materials and human body is that interfaces between
two types of materials in industrial parts are likely to form a very distinct boundary in
contrast with the human body. Therefore, CT images of heterogeneous industrial parts
will be made up of multiple regions that are internally homogenous. One exception to this
case shows up when the image pixels that coincide with the external and internal
boundaries can not match the boundary exactly. Such pixels are likely to have gray scale
values that are between the gray scale values of two bordering regions. In this paper, an
algorithm to utilize CT data will be outlined and some examples will be provided.
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/S20.00
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TRANSPORT ALGORITHM
The simulation algorithm is based upon a deterministic approach where the
governing equation is integral transport equation that is given below. Since the algorithm
has been outlined in previous articles [1-3], we will not provide any details regarding the
computational algorithm.
Rr
-]Z,t(r-RR''Q,E)dRn
dK+I(rT9E9Q)e
^ '
In equation (1), I(r,E,Q) is angular photon flux (fluence rate), q(rJEJB) is angular scattered
photon source, ^(rJE) is space and energy dependent linear total attenuation coefficient
obtained from XCOM, Berger et al [4], r is spatial coordinates vector (x,y,z), rr is spatial
coordinates vector for object boundary, Eis photon energy, Q is direction vector, R is
photon pathlength along direction vector, RT is photon pathlength from object boundary.
Since this article uses examples from the medical radiography world and absorbed dose
distributions are computed, we introduced the kerma (kinetic energy deposited into the
medium) approach into our algorithms. In kerma approach, an electronic balance is
assumed and energy deposited in the unit mass of medium is computed through equation
(2) given below.
Absorbed Dose(r) = J E E"/ I(r9E)dE
o
(2)
' ^
where Z^jp is mass-energy absorption coefficient that were taken from Hubbell et. al. [5].
The outcome of our computational algorithm is photon flux distribution, I(rJE), inside
medium and it is converted into absorbed dose distribution through equation (2).
CT DATA MANIPULATION
Our computational algorithm uses voxels for geometric modeling of the problem
domain. All independent and dependent quantities such as interaction coefficients, photon
fluxes and photon sources are assumed to be constant throughout the voxels. Therefore, if
material properties can be assigned to a specific voxel, the algorithm can compute the
entire set of unknowns. The current art in the dosimetry community is to segment the
images and then use the segmented information to construct homogenous organ models to
be used in the computations [6-14]. In our work, rather than setting up a relationship
between a gray scale and an organ, we set up relationships between the voxel gray scales
and attenuation coefficients specific to that voxel. This has been done by assuming that
there are only four radiologically distinct tissues in the human body, namely adipose,
skeletal muscle, spongiosa, cortical bone and attenuation coefficients for all others can be
written as a combination of the attenuation coefficients of these radiologically distinct
tissue types. For example, cortical bone is quite distinct due to its elemental composition
and relatively high density. Spongiosa and cartilage have physical densities much higher
than the average as well. Adipose and yellow marrow have physical densities below 1.0
g/cm3. The other tissue types have similar elemental compositions that have densities a
little above 1.0 g/cm3. Even under these conditions, some of the tissues are expected to
interact with photons at interaction rates very close to each other. This can easily be
inferred from the linear attenuation plots in figure 1 . Attenuation data in figure 1 have been
generated by XCOM using tissue compositions from ICRU-44 [15]. As it is seen figure 1,
cortical bone stands out alone.
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Photon Energy (keV)
FIGURE 1. Linear attenuation coefficients of four tissue types.
Although adipose and muscle have difference compositions and physical densities,
attenuation coefficients are surprisingly close to each other. Therefore, photon-tissue
interaction rates should be very close to each other as well. A simple survey of Visible
Human Project [16] frozen data set from the head section shows that adipose provides a
gray scale level around 965, skeletal muscle 1060, spongiosa 7475 and cortical 2450.
Body variations and CT equipment settings can affect these values. Therefore, this
approach is open to more sophisticated methods that can determine the individual specific
gray scale values of distinct tissue types. Irregularity of the tissue boundaries, tissue
heterogeneities, systematic noise and having a tissue border passing through the middle of
a pixel are among causes of the variations in the gray scale levels. Profiles in figure 3 that
were extracted from the image in figure 2 clearly show those fluctuations. The locations
of these profiles are shown in figure 2. Rather than trying to come up with a new set of
attenuation coefficients for a given tissue type, tissue variability has been accounted for by
mixing distinct tissue attenuation coefficients based on the gray scale values. For example,
skeletal muscle and adipose tissue attenuation coefficients vary about 14, 9, 9 and 9 % at
50, 100, 150 and 200 &eF respectively. In the light of such small variations, using mixing
coefficients and accounting for tissue variability should be more realistic compared to
homogenous organ assumption.
FIGURE 2. Visible Human frozen data set c_vml 100 with profile positions marked.
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0
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'
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Pixel Number
FIGURE 3. 12 bit gray scale profiles taken from c_vml 10 in figure 2.
In using CT images as a model, we have adopted a common approach and stacked the
images. Gray scale of the voxel has been determined by averaging the gray scales of the
pixels involved in the formation of the voxel. Visible Human data set images are made up
of 512x512 pixels and pixel resolution is 0.53 mm x 0.53 mm with a 1.0 mm distance
between images. In our case, we have used 1.06 mm x 1.06 mm x 2 mm voxels with 12
bit gray scale values. Although gray scale range for 12 bit images is 0-4095, the maximum
gray scale value in Visible Human CT images is around 2500. In 12 bit images, gray scale
value 0 corresponds to black and 4095 corresponds to white. As stated above, we
determined the interaction coefficients for a specific voxel by using mixing coefficients
matching to the gray scale value specific to that voxel. These coefficients are shown in
figure 4. For example, linear attenuation coefficients for a gray scale value of 1150 are
obtained by summing muscle and spongiosa coefficients after they were multiplied by
mixing coefficients 0.783 and 0.277 obtained from figure 4. Background gray scale
values in the CT images were usually less than 700. Therefore, we assumed that this gray
scale value should represent the air. Interaction coefficients in the 100-965 range are
obtained by using only adipose tissue coefficients with the corresponding mixing ratio
because air coefficients are assumed to be zero. If the gray scale is larger than 2450, that
voxel is assumed to represent 700% cortical bone.
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1125
1500
1875
2250
2625
3000
Gray Scale Range
FIGURE 4. Mixing ratios for various tissue types.
Approach described above can be implemented for industrial CT data as well. Gray scale
values corresponding to homogenous components will be pretty much constant except for
the fluctuations due to system noise and reconstruction algorithm. Gray scale values will
deviate from the mean values significantly at the component interfaces and external
boundaries where the pixel does not fit the boundary exactly. Gray scale for such a pixel
will be computed based on data coming from two different material types. For an external
boundary case, gray scale will represent material and air but two different materials for an
internal boundary. If a mixing ratios database as in figure 4 is constructed for such an
assembly, interaction coefficients can easily be computed for borderline voxels.
RESULTS
We demonstrated the idea by using the head section of the frozen Visible Human data
set. CT data have been stacked into a 4x106 voxel 3D structure. An 24 cm x 24 cm ideal
detector was placed right next to the object. Computations provided 3D absorbed dose
distributions. 2D distributions were extracted the 3D data set for display purposes. One of
these 2D dose distributions is given in figure 5 for lateral irradiation geometry. The left
distribution represents the primary beam only and does not include photon scattering. The
right distribution includes both primary and scattered beam components. As it is very
obvious from a comparison of two distributions, scattered photon flux deposits a
significant amount of energy into the medium. One other point about the distribution is
the resolution. Due to the very small size of the voxels, it is quite easy to distinguish a lot
of features in the distributions. Figure 6 displays a 256x256 pixel image formed on the
ideal detector. The left images in these figures represent primary beam only cases where
the scattered flux component has not been included into calculations. The right images
include both primary and scattered flux components. These images have been formed by
logarithmic energy fluxes that were scaled to fit into 5-bit 0-255 gray scale range. The
third set of results shows flux profiles incident upon an ideal detector. Those profiles are
displayed in figure 7. The left graphic in figure 7 displays lateral case uncollided flux
profiles that are the center columns of the two-dimensional flux distributions on the
detectors. The profiles in the right graphic belong to the scattered photon fluxes for
various energy groups.
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0.1
0.2
0.3
0.0
0.1
0.2
0.3
0.4
0.5
Absorbed Dose (mGy)
Absorbed Dose (mGy)
FIGURE 5. Lateral case (left) primary flux and (right) total flux absorbed dose distributions.
CONCLUSIONS
We developed an algorithm that can utilize CT data for simulations in both industrial
and medical radiography. The algorithm is capable of handling all physics of the x-ray tube
energy range and it is based on the deterministic integral transport equation. Modeling has
been handled by forming three dimensional voxel structures by stacking up the CT slices.
Each voxel was handled separately rather than correlating each voxel to a specific
organ/material through a laborious segmentation and image-processing step.
This
eliminates the need to segment the human CT data to determine the organ or component
boundaries in a CT slice. As it has been shown this approach provides an alternative to
solid modeling/mesh generation procedure that can be done through CAD packages. It has
also been shown that a very complex problem domain can easily be introduced into a
simulation program through the algorithm described in this article.
FIGURE 6. Lateral case energy fluence images for (left) uncollided flux and (right) total flux.
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FIGURE 7. Various energy group photon flux profiles taken from detector flux distributions for (left)
uncollided flux and (right) scattered flux.
ACKNOWLEDGMENTS
This work was funded by The Roy J. Carver Charitable Trust.
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