The need for cross section data for medical x-ray - Carleton University

THE NEED FOR CROSS SECTION DATA
FOR MEDICAL X-RAY SCATTER IMAGING
PAUL C. JOHNS 1,2 , MATTHEW P. WISMAYER 1 , & ROBERT J. LECLAIR 3
1
Dept. of Physics, Carleton University, Ottawa, Ontario
2
Dept. of Radiology, University of Ottawa
3
Dept. of Physics & Astronomy, Laurentian University, Sudbury, Ontario
Email: johns@physics.carleton.ca Web pages: http://www.physics.carleton.ca/~johns
leclair@laurentian.ca
http://laurentian.ca/physics/facstaff/leclair.html
Presented at the
5th Annual Canadian Light Source Users’ Meeting, Saskatoon, Saskatchewan, Canada,
16 November 2002.

P.C. Johns, M.P. Wismayer, R.J Leclair - Poster # 14 at the 5th Annual Canadian Light Source Users’ Meeting, Saskatoon, Canada, 16 November 2002.
2.
ABSTRACT
Several labs throughout the world are working on a novel x-ray imaging technique, for medical diagnosis,
which uses the scattered radiation rather than the transmitted primary. In medical x-ray imaging, up to
90% of the photons approaching the image receptor have been coherently or incoherently scattered.
Coherent scatter is particularly interesting because the x-ray diffraction cross sections of various tissues
can be quite different for specific angles and photon energies. Our numerical modelling predicts that for
several examinations, such as in neuroradiology and in breast imaging, utilizing the forward-scattered x
rays will provide more information than using the primary x rays, for the same patient radiation dose. In
order to optimize the design of these new imaging systems, there is a need to catalogue the differential
scatter cross sections or form factors over as wide a range of x = λ -1 sin θ/2 as is possible. Current work
on measuring the cross sections or form factors will be summarized. The potential of synchrotron radiation
to provide more accurate measurements will be discussed.

P.C. Johns, M.P. Wismayer, R.J Leclair - Poster # 14 at the 5th Annual Canadian Light Source Users’ Meeting, Saskatoon, Canada, 16 November 2002.
3.
1. INTRODUCTION
The basis of diagnostic radiology conventionally has been to form projection images using x-ray photons, using
the geometry of Figure 1. The spatial distribution of energy absorbed by the receptor forms the image. The
radiation from a diagnostic x-ray tube spans a range of energy per photon from E . 16 keV up to that corresponding
to the potential, usually # 150 kV.
X-Ray Tube
Primary
Photon
Patient
Scattered
Photon
Anti Scatter
Grid
FIGURE 1. Standard projection
x-ray geometry.
X-Ray
Intensity
}
Scatter
Image
Receptor
Position

P.C. Johns, M.P. Wismayer, R.J Leclair - Poster # 14 at the 5th Annual Canadian Light Source Users’ Meeting, Saskatoon, Canada, 16 November 2002.
4.
Attenuation in the patient is via three processes: photoelectric absorption, inelastic or incoherent (often called
Compton) scattering, and elastic or coherent scattering. For E > 25 keV, over 50% of the interactions in tissues are
scatterings. 1 Figure 2 shows the cross sections for these 3 processes in water versus photon energy.
H 2
O
Interaction Cross Section ( cm 2 / e − )
0.6
0.4
0.2
0.8 x 10 −24 ↑
incoherent
← photoelectric
Photon Energy (keV)
0.3337 x 10 24 electrons / cm 3
FIGURE 2. X-ray interaction cross sections for
water in the photon energy range of diagnostic
radiology. (Data from Ref. 2).
0
↑
coherent
10 50 100 150

P.C. Johns, M.P. Wismayer, R.J Leclair - Poster # 14 at the 5th Annual Canadian Light Source Users’ Meeting, Saskatoon, Canada, 16 November 2002.
Figure 3 shows for the two scattering processes, for H 2 O, the differential cross sections per unit angle versus
scattering angle θ. The incoherent cross section is reduced for θ . 0 because of the atomic binding of electrons.
The coherent cross section is strongly peaked at a small θ and at 25 keVexceeds that for incoherent for θ < 24.6 o .
For lower E this angle is larger. Hence, radiation which reaches the image receptor after one scattering has a large
coherent-scattered component. 5-7
5.
H 2
O 25 keV
FIGURE 3. Cross sections at 25 keV for x-ray
scattering in H 2 O at angle θ into a ring of
infinitesimal width dθ. The integrals of these
curves are the total scatter cross sections.
[Sources of form factors used: coherent -
Ref. 3 (25 o C), incoherent - Ref. 4].
dσ/dθ ( cm 2 / e − / radian )
0.5 x 10 −24 0.4
total
0.3
↓
0.2
coherent
0.1
↓
↑
incoherent
0
0 30 60 90 120 150 180
θ, Scattering Angle (degrees)

P.C. Johns, M.P. Wismayer, R.J Leclair - Poster # 14 at the 5th Annual Canadian Light Source Users’ Meeting, Saskatoon, Canada, 16 November 2002.
In conventional projection imaging, most of the photons approaching the image receptor have been scattered in the
patient; the scatter-to-primary ratio can be as high as 10 (Ref. 8). Scatter can significantly degrade projection image
quality [contrast (C) and signal-to-noise ratio (SNR)]. The usual fix is geometric rejection using an antiscatter grid
of miniature Pb septa arranged like a venetian blind.
An alternate approach is to use the scattered x rays. Previous investigators have demonstrated imaging for medicine
using the forward scatter 9-11 and backscatter, 12,13 and the use of forward scatter for non-destructive testing. 14,15 In
principle, simultaneous measurements of forward scatter, backscatter, and transmitted primary x rays could be
made, as in Fig. 4.
X-ray tube
focal spot
Target object
6.
Concentric
annular detectors
for forward scatter
∗
hν o
FIGURE 4. Concept for simultaneous
measurement of primary plus
two types of scatter leaving the
patient.
Annular detector
for backscatter
Background
object
L
d
Detector for
transmitted
radiation

P.C. Johns, M.P. Wismayer, R.J Leclair - Poster # 14 at the 5th Annual Canadian Light Source Users’ Meeting, Saskatoon, Canada, 16 November 2002.
7.
2. SCATTERING FORM FACTORS
The differential cross section per unit solid angle for Thomson scattering from a free electron at angle θ is
2
d
eσ
Thomson
re
2
= + θ , (1)
dΩ
2 ( 1 cos )
where r e is the classical electron radius. For multielectron systems, the scattered waves interfere. The coherent
scattering cross section per electron per steradian is
d σ
dΩ
e coh e
2
2
r
2
F x Z
= + θ
2 ( 1 cos ) ( , )
Z
, (2)
where Z is the atomic number, and F(x,Z) is the coherent scatter form factor for element Z. Note 0 # F(x,Z) # Z.
The parameter x arises from considerations similar to Bragg’s law for crystalline specimens, and is
x
1 θ E θ
= sin = sin
λ 2 hc 2
Contours of x are shown in Figure 5.
. (3)
For compounds or mixtures, the simplest model is the Independent Atom Model (IAM),
2 2
FIAM
( x) = ∑ niF ( x, Zi
)
i
, (4)
where n i is the number fraction of element i. In fact, the scattered waves from different atoms interfere, and the
IAM is valid only at large x, which corresponds to intra-atomic interference. Except for materials with very simple
structure, F(x) is difficult or impossible to calculate and must be measured.

P.C. Johns, M.P. Wismayer, R.J Leclair - Poster # 14 at the 5th Annual Canadian Light Source Users’ Meeting, Saskatoon, Canada, 16 November 2002.
For incoherent scattering,
8.
d
σ
dΩ
e incoh e
2
r
F
SxZ
2
= + θ
KN
2 ( 1 cos ) ( , )
Z
, (5)
where F KN is the Klein-Nishina factor and S(x) is the incoherent scattering function. For this type of scattering it
is legitimate to sum the contributions from each atom independently.
FIGURE 5. Shown are lines of equal x value, as per
Eq.(3), in terms of x-ray photon energy E and scattering
angle θ. The shaded region is that which is practical to
access in radiology.

P.C. Johns, M.P. Wismayer, R.J Leclair - Poster # 14 at the 5th Annual Canadian Light Source Users’ Meeting, Saskatoon, Canada, 16 November 2002.
9.
3. MODEL OF X-RAY SCATTER IMAGING
To date, it has been difficult to compare quantitatively the performance of scatter imaging to primary imaging, and
to compare different scatter imaging approaches to each other. For primary imaging the standard analysis tool is
the model of Motz and Danos. 16 We have formulated analogous models for scatter imaging 17 and used them to
quantify the ultimate performance of scatter imaging based on the fundamental input parameters, namely dσ/dΩ,
independent of the engineering of a particular apparatus. The models are semi-analytic and intentionally simple.
For a given photon fluence entering the patient, the models calculate C and SNR, where the "signal" in the SNR
calculation is the difference in measurement between two objects that are to be distinguished. We analysed both
forward scatter (2 o -12 o ) and backscatter (158 o -178 o ) imaging. We also calculated C and SNR assuming hypothetical
capture of all scatter over 4π steradians. Our forward-scatter model is illustrated in Figure 6 and was verified
experimentally using polyenergetic beams and plastic targets. 18
Figure 7 shows numerical predictions for distinguishing white from gray brain matter in neuroradiology.
Conventional CT scanners can just barely do this, as the primary contrast is only . 0.5 %. Two small targets of
white and gray matter are modelled to be inside a sphere of water, radius R = 7.5 cm. Shown are maximum
achievable values of SNR, where the maximum is obtained by optimizing E. Using forward scatter gives a better
SNR than using primary for all target sizes d < 40 mm. Also, using only the forward scatter gives a better SNR than
using all the scatter. Although there are less photons available in the former case, so that the fractional Poisson
counting noise is greater, the difference in total scatter cross section is larger, and therefore so is the SNR of the
white/gray matter difference. These results are for monoenergetic beams. Calculations using typical medical
polyenergetic spectra show that the SNR reduction due to spectral blurring is modest. 20

P.C. Johns, M.P. Wismayer, R.J Leclair - Poster # 14 at the 5th Annual Canadian Light Source Users’ Meeting, Saskatoon, Canada, 16 November 2002.
10.
SNR max
10 2
10 1
10 0
10 -1
Total Scatter
Forward Scatter
Backscatter
10 -2
10 -3
Primary
White/Gray Matter
0.01 0.1 1 10 40
d, Thickness (mm)
FIGURE 6. Geometry for modelling forward-scatter
imaging. 17 Two materials of thickness d at the centre
of a spherical water phantom of radius R are to be
distinguished by their scatter signals.
FIGURE 7. The maximum SNR over all energies for
distinguishing white matter from gray matter, of
thickness d, cross sectional area 1.0 mm 2 , inside a 15
cm diameter spherical H 2 O phantom. Incident energy
fluence fixed at 1.88 x 10 11 keV cm -2 . (For details see
Leclair & Johns 19 ).

P.C. Johns, M.P. Wismayer, R.J Leclair - Poster # 14 at the 5th Annual Canadian Light Source Users’ Meeting, Saskatoon, Canada, 16 November 2002.
11.
Figure 8(a) shows SNR as a function of d for the optimum x
range of x min = 0.8 nm -1 to x max = 1.28 nm -1 for finding breast
tumours in normal fibroglandular tissue. Figure 8(b) shows
values of SNR for several polyenergetic beams. The angular
ranges were chosen such that the average momentum transfer
argument was from 0.8 to 1.28 nm -1 . Figures 8(a) and (b) both
predict an advantage of using scatter for breast cancer
detection.
SNR
Low-angle
scatter model
35 keV
Primary
model
19 keV
(a)
FIGURE 8. Predicted SNR values 21 as a function of d for
imaging of carcinoma versus fibroglandular structures
each of cross sectional area 0.196 mm 2 using (a)
monoenergetic beams and (b) polyenergetic beams. The
glandular dose is held constant at 2 mGy and a photon
counting detector is assumed.
SNR
Primary
Top: 30 kV Mo
Bottom: 30 kV W
Scatter
Top: 60 kV W
Middle: 30 kV W
Bottom: 80 kV W
Scatter
(30 kV Mo)
(b)
d, thickness (mm)

P.C. Johns, M.P. Wismayer, R.J Leclair - Poster # 14 at the 5th Annual Canadian Light Source Users’ Meeting, Saskatoon, Canada, 16 November 2002.
Table 1. Summary of selected literature on x-ray diffraction signatures of tissues and phantom materials.
Reference Technology Measured† Comments
Narten 3 (1970) diffractometer, Mo anode with H 2 O at 4, 20, 25, 50, 75, 100, 150, 200 o C,
monochromator, 17.4 keV. Thermodynamic
plus D 2 O at 4 o C. Other work includes CCl 4 .
estimate for x 6
0.
Kosanetzky et al 22
(1987)
Evans et al 23 (1991)
diffractometer, Co anode with
monochromator, 6.935 keV
60 kVp Cu anode spectrum,
heavily filtered, 46 keV average,
with multi-wire prop. counter
70 kVp W spectrum, θ = 6 o ,
HPGe energy dispersion
diffractometer without
Royle & Speller 25 (1995)
[+ Ref.24 (1992)]
Tartari et al 26 (1997)
monochromator, corrected.
Peplow & Verghese 27 synchrotron (NSLS Brookhaven),
(1998)
monoenergetic 8 keV and 20
Kidane, Speller, Royle,
& Hanby 28 (1999)
keV, angular dispersion
80 kVp W spectrum, θ = 6 o ,
HPGe energy dispersion
Lewis et al 29 (2000) synchrotron (Daresbury),
monoenergetic 8.05 keV
Desouky et al 30 (2001) diffractometer, Cu anode with
monochromator, 8.047 keV
Poletti et al 31 (2002) diffractometer, Mo anode with
monochromator, 17.44 keV
H 2 O, C 5 H 8 O 2 , C 16 H 14 O 3 , C 8 H 8 , C 6 H 11 NO,
C 2 H 4 , blood, muscle, fat, liver, tendon, bone,
white matter, gray matter.
H 2 O, C 5 H 8 O 2 , olive oil, blood, breast tissues:
adipose, fibroglandular, benign tumour,
carcinoma, fibrocystic disease, fibroadenoma.
Provides the gold standard for H 2 O.
Tabulated F 2 for 0 # x # 12.7 nm -1 .
Groundbreaking study for biological
materials, plastics. Cross sections given
graphically for 0.25 # x # 4.3 nm -1 .
Results spectrally blurred. Only
tabulated peak position in θ, peak
FWHM, and peak-to-large-angle ratio.
bone: femoral heads.
Looked at bone-to-marrow peak ratio as
indicator of bone mineral density.
C 5 H 8 O 2 , fat. F tabulated out to x = 6.2 nm -1 .
Minimum x value on graphs . 0.17 nm -1 .
H 2 O, C 5 H 8 O 2 , C 16 H 14 O 3 , kapton, fat, muscle, F obtained out to x = 10 nm -1 .
kidney, liver, pig heart, blood, formalin (10% Minimum x value ranged from 0.42 to
formaldehyde in H 2 O), breast tissue in formalin 1.08 nm -1 , sample dependent.
100 breast tissue samples:
adipose, fibrosis, fibroglandular, benign,
fibrocystic, fibroadenoma, carcinoma.
Peak positions tabulated. Graphs of F
for most tissue types shown for
0.8 # x # 3.25 nm -1 .
breast tissues: core biopsy samples of tumour “small-angle” experiment re collagen
and normal (reduction mammoplasty). structure, very low x. F not obtained.
biological samples freeze-dried to remove H 2 O: Tabulated peak positions in 2, FWHM of
blood constituents, albumin, milk powder, other peaks. Only graphed counts vs. 2.
H 2 O, C 5 H 8 O 2 , C 6 H 11 NO, C 2 H 4 , breast phantom F tabulated out to x = 8.0 nm -1 .
materials (3 from CIRS, 1 from RMI), breast Minimum x value measured not stated.
tissues: adipose, glandular.
Fernández et al 32 (2002) synchrotron (ESRF Grenoble),
monoenergetic 12.5 keV
breast tissues: adipose, connective tissue,
cancer.
"small-angle" experiment re collagen
structure, x - 0.005 nm -1 . F not obtained.
HStoichiometric formulae: C 5 H 8 O 2 = PMMA (poly methyl methacrylate) C 16 H 14 O 3 = polycarbonate ("Lexan") C 8 H 8 = polystyrene
("Lucite", "Perspex") C 6 H 11 NO = nylon C 2 H 4 = polyethylene
12.

P.C. Johns, M.P. Wismayer, R.J Leclair - Poster # 14 at the 5th Annual Canadian Light Source Users’ Meeting, Saskatoon, Canada, 16 November 2002.
13.
4. MEASUREMENT OF CROSS SECTIONS
4.1 MOTIVATION
Optimizing the design of x-ray scatter imaging systems requires knowledge of scatter cross sections. From Figure
5, taking 16 # E # 140 keV and 0.5 o # θ # 179 o as practical limits for scatter imaging in diagnostic radiology, there
is a need to have a library of F values for tissues and phantom materials from x - 0.1 nm -1 through to the IAM
region, x $10 nm -1 .
While a number of groups have measured d e σ/dΩ or F at some values of x for H 2 O, plastics and tissues (Table 1),
there is variation in the values reported. Furthermore, the literature is considerably short of spanning the range of
x needed. For example, we used the diffraction data measured by Kidane et al 28 for the breast imaging simulations
shown above. Due to the limited range of x measured our simulations could not go below 0.8 nm -1 . Based upon
the measurements done by Lewis et al 29 with synchrotron radiation it is anticipated that capturing scattered x rays
in the range of 0.02 nm -1 to 0.1 nm -1 will provide useful diagnostic information. Perhaps a signal comprising a large
range of x from 0.02 to 1.28 nm -1 could maximize the amount of diagnostic information. But the cross sections need
to be measured to know for sure. For these reasons we have commenced our own measurements. 33
4.2 ANGLE-DISPERSIVE APPROACH
We have used two diffractometers made available to us by the National Research Council of Canada: Rigaku (Co
radiation, 6.93 keV), and Scintag (Cu, 8.02 keV). Using two machines, at different energies, allows methodology
developed on one to be checked on the other. Results can be applied at all energies via Eq.(3), e.g. 32 o at 8 keV
] 5 o at 50 keV (x = 1.8 nm -1 ).

P.C. Johns, M.P. Wismayer, R.J Leclair - Poster # 14 at the 5th Annual Canadian Light Source Users’ Meeting, Saskatoon, Canada, 16 November 2002.
14.
2.5
Rigaku diffractometer
Scintag diffractometer
Narten
Kosanetzky et al
Peplow & Verghese
IAM
F(x) ( free e − / bound e − ) 0.5
2.0
1.5
1.0
FIGURE 9. Comparison of coherent
scatter form factor for H 2 O measured
by us (Rigaku and Scintag
machines), Narten, 3 Kosanetzky et
al, 22 and Peplow & Verghese 27 . The
IAM curve is theoretical, and
assumes no inter-atomic interference.
0.5
0
0 1 2 3 4 5 6 7
x ( nm −1 )

P.C. Johns, M.P. Wismayer, R.J Leclair - Poster # 14 at the 5th Annual Canadian Light Source Users’ Meeting, Saskatoon, Canada, 16 November 2002.
We have found that accurately measuring diffraction from amorphous materials on such machines is difficult. The
machines are designed for accurate peak location but continuous background and θ-dependent efficiencies interfere
with amorphous sample data. For crystalline samples these are of less concern because the local background can
be subtracted from each peak. Figure 9 shows a comparison of our results for water 34 with that of others. The
variation can significantly alter predicted values of C and SNR for x-ray scatter images, and thus has impact on the
design of scatter imaging systems. This variation must be resolved.
15.
4.3 ENERGY-DISPERSIVE APPROACH
Instead of a pure angle-dispersive reflection measurement one can use a mixture of angle dispersion and energy
dispersion in transmission mode. This is an extension of the method utilized by R. Speller’s lab. 24,25,28 This
approach is demonstrated in Figure 10, which shows our preliminary results for κ, the ratio of the fraction of the
incident photons that is scattered towards the detector to that which is transmitted as primary. The plots show κ
as a function of energy, obtained at 80 kV for PMMA and nylon, at four angles. Energies from 30 to 70 keV were
used in the analysis. Quite reasonable agreement between experiment and prediction (using the data of Kosanetzky
et al 22 ) was obtained. Note that no scaling was performed on our experimental data before the comparison.
The parameter κ is linearly related to the cross sections per solid angle through some transmission factors, which
are calculable, and in the limit of small sample thickness approach unity. Once κ is obtained, the coherent cross
section d e σ coh /dΩ can be found by subtracting the calculated incoherent component, and the form factor F(x)
extracted as per Eq.(2).

P.C. Johns, M.P. Wismayer, R.J Leclair - Poster # 14 at the 5th Annual Canadian Light Source Users’ Meeting, Saskatoon, Canada, 16 November 2002.
16.
=8 o
=6 o
FIGURE 10. X-ray scatter signatures
of PMMA and nylon measured
at four different angles using an 80
kV x-ray spectrum. 21 The solid and
dashed lines are the predicted results
for PMMA and nylon, respectively.
The solid and open circles are the
corresponding experimental results.
=2 o =4 o
-1
x(nm )

P.C. Johns, M.P. Wismayer, R.J Leclair - Poster # 14 at the 5th Annual Canadian Light Source Users’ Meeting, Saskatoon, Canada, 16 November 2002.
17.
5. SYNCHROTRON RADIATION AS MEANS TO MEASURE
CROSS SECTIONS
The CLS offers the following potential advantages for the measurement of form factors of tissues and phantom
materials:
• high intensity Y faster measurement Y less sample drying during measurement
• a larger range of x can be investigated. Low-angle x-ray optics permit measurements at very small θ and hence
small x that are impossible on a diffractometer
• better control of sample background and θ-dependent effects
• immediate proximity of an academic medical centre
• furthermore, for Canadian researchers, there will be no need to take tissue specimens across a national border
Either the angular-dispersive or energy-dispersive approach can be implemented. Since a range in x of over a factor
of 100 is desired, probably a hybrid approach will be needed. Angle-dispersive measurements could be made at
a small number of specific energies, and the results tiled together versus x.

P.C. Johns, M.P. Wismayer, R.J Leclair - Poster # 14 at the 5th Annual Canadian Light Source Users’ Meeting, Saskatoon, Canada, 16 November 2002.
18.
6. CONCLUSIONS
By treating scattered radiation as an additional information source rather than as a nuisance to be suppressed, a new
dimension is added to x-ray imaging. Our calculations predict that in some cases, such as neuroradiology and
mammography, scatter images will have better C and SNR than projection images, for the same radiation dose.
Alternatively, the SNR of conventional imaging could be matched by scatter imaging at lower dose. Better data
for tissue scattering cross sections are needed. Synchrotron radiation appears to offer advantages for making these
measurements.
ACKNOWLEDGEMENTS
This work was funded by the Natural Sciences and Engineering Research Council of Canada. The third author
acknowledges the support of the Laurentian University Research Fund. We thank Jim Sliwka for technical support.
We are grateful to Dr. Gary Enright and his staff at the Steacie Institute of Molecular Science, National Research
Council of Canada, Ottawa, for making x-ray diffractometers available to us and for assistance in their use.

P.C. Johns, M.P. Wismayer, R.J Leclair - Poster # 14 at the 5th Annual Canadian Light Source Users’ Meeting, Saskatoon, Canada, 16 November 2002.
19.
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