PHYSICAL PRINCIPLES OF MAMMOGRAPHY
European School of Medical Physics, Archamps, November 2005
Dr David Dance
Joint Department of Physics,
Institute of Cancer Research and Royal Marsden Hospital, London SW3 6JJ, United Kingdom
1 Properties of the female breast
Compressed breast thickness
Compressed breast area
2 -11 cm
35 cm2 - large enough to require several exposures
Composition -
mixture of adipose and glandular tissues.
glandular tissue is most sensitive to carcinogenesis
Atomic compositions. Data from Hammerstein et al. Radiology 130 (1979) 485-491
PERCENTAGE COMPOSITION BY WEIGHT
DENSITY
H
C
N
O
Gm/cc
Fat
11.2
49.1-69.1
-
18.9-35.7
0.93
Gland
10.2
10.8-30.5
3.2
55.2-75.9
1.04
calcium hydroxyapatite or phosphate, size 0 - several mm2
important to see 200 micron calcifications
Calcifications -
Breast glandularity varies with breast size and age,
though there is a large variability. Figure shows glandularity of typical breasts for women aged 50-64 from two
regions in UK (Dance et al. PMB 45 (2000) 3225-40.
Glandularity (%)
100
80
60
40
20
0
0
2
4
6
8
10
Breast thickness (cm)
2 Photon interactions
Variation of attenuation with type of tissue :
Fibro-glandular tissue has a much higher attenuation coefficient than fatty tissue.
The difference in attenuation between fibro-glandular tissue and carcinoma can be small.
Carcinomas more likely to be seen as a change in breast
architecture.
Data from Johns and Yaffe, PMB 32 (1987) 675-695
1
The photoelectric cross section dominates below 22
keV.
Only a small energy transfer for scatter processes.
Large attenuation coefficient at low energies means
low transmission through the breast.
Scattering Processes
At low energies it is not sufficient to assume that all scattering processes are from free electrons. Allowance
must be made for electron binding. For most purposes it is sufficient to assume atomic binding. Two scattering
processes must be considered: coherent and incoherent scattering. In coherent scattering all the electrons scatter
in phase and there is no energy transfer, but only a change in photon direction. This is dominant in the forward
direction and decreases with increasing momentum transfer. Away from the forward direction, incoherent scattering becomes important. This is scattering with energy transfer to a recoil electron and approaches the standard Klein-Nishina cross section for large momentum transfers.
Comparison of scattering processes for breast tissue at
20keV.
The Klein-Nishina formula is a poor approximation in
the forward direction but is a good approximation in
the backward direction where the contribution of coherent scattering is smaller.
.
3 Important physical parameters
Requirements for mammography



high contrast
good resolution (unsharpness)
low dose


low noise
large dynamic range
2
Contrast
Factors, which affect contrast:
object
background
transmitted spectrum
receptor
scatter
Variation of contrast with photon energy. Contrast
calculated ignoring degradation due to unsharpness
and scatter.
Contrast decreases rapidly with increasing photon
energy.
Low energy is necessary to achieve adequate contrast, but this is in conflict with the requirements of
low dose.
Unsharpness
Unsharpness contributions :
geometric unsharpness
receptor unsharpness
movement unsharpness
Dose
Factors, which affect dose :
breast thickness
breast composition
photon spectrum
receptor sensitivity
Various dose specifications have been suggested : incident or surface dose, mid-breast dose, mean breast dose
and the mean dose to the glandular tissues within the breast, which are the tissues at risk of radiation induced
carcinogenesis. The latter quantity is the quantity of choice and has been recommended by the ICRP and generally adopted in national dosimetry protocols.
There is a dose penalty for using low energy photons to image the breast. Low energy photons are strongly absorbed and contribute only to dose and not to the image.
3
Transmission of photons through breast tissue.
Dose varies rapidly with depth. Surface dose is not a good
indicator of risk.
Dose depends upon tissue type.
There is a large advantage in reducing the breast thickness
by compression.
Dependence of mean glandular dose on breast composition
and thickness.
Noise
Factors, which affect noise :
quantum mottle
light photons
screen structure
film granularity
Signal-to-Noise Ratio for a 100 micron calcification.
Calculated for a Min-R/OM screen/film combination,
ignoring unsharpness and only including contribution
of quantum mottle.
There is a threshold energy above which the calcification will not be seen.
4 X-ray Tube
4
X-ray spectra
The choice of photon energy for mammography is a compromise between contrast and dose. To find the optimum energy, it is necessary to introduce further constraints in terms of the contrast needed or the signal-to-noise
ratio (SNR). One approach is to calculate the SNR for fixed dose to the breast.
Dependence of SNR for fixed breast dose on photon energy
and breast thickness. SNR calculated for imaging a 100 micron calcification and ignores unsharpness. Noise due to
quantum mottle only.
Each curve is for fixed breast thickness and the position of the
maximum gives an optimum energy in terms of SNR. This is
probably most relevant to digital imaging.
Optimal energies bands for mammography based on SNR for fixed dose :
2cm breast 14-18 keV
6cm breast 19-23 keV
4cm breast 17-21 keV
8cm breast 20.5-23.5 keV
1.25
Relative number of photons
A
1.00
Mammographic X-ray spectrum from a Mo target at 28kV filtered by
30 micron Mo.
The Mo characteristic X-ray lines are well suited to imaging all but the
largest breasts where a higher energy spectrum might have some advantages.
0.75
0.50
The X-ray spectrum is chopped at 20keV because of the Mo filter.
0.25
0.00
10
15
20
25
30
Photon energy (keV)
Transmission through a 30 micron Mo filter
The Mo K-edge is at 20keV and there is a step in the photoelectric
cross section at this energy. The result is decreased transmission
above the K-edge.
5
Possible K-edge filter materials for mammography:



molybdenum
rhodium
palladium
20 keV
23.3 keV
24.3 keV
X-ray tubes are available with a dual anode and a selection of filters. The anode, filter and tube potential are
selected automatically after a brief pre-exposure to establish the transmission through the breast.
1.25
The figure shows the spectrum obtained using a rhodium target and a rhodium filter at 28 kV.
Relative number of photons
E
1.00
This higher energy spectrum is better suited to imaging larger breasts.
0.75
0.50
0.25
0.00
10
15
20
25
30
Photon energy (keV)
Figure shows relationship between contrast (of a calcification) and mean glandular dose for different target/filter
combinations. Each curve shows the variation as the tube
voltage is changed from 25- 32 kV. None of the new
spectra can match the Mo/Mo contrast at 26 kV and only
one spectrum can match Mo/Mo at 28 kV (Mo/Rh) and
some dose saving is then possible. If the contrast requirement is relaxed (say to match Mo/Mo at 30 kV), a
larger dose saving is possible and other target/filter combinations can be used.)
8.0
Mean glandular dose (mGy)
25 kV
Mo/Mo
Mo/R h
6.0
26 kV
R h/Al
28 kV
R h/R h
W /R h
30 kV
4.0
32 kV
2.0
0.0
0.20
0.25
0.30
0.35
Contrast
Figure shows the relationship between the mean
glandular dose and the choice of X-ray spectrum in
digital mammography for the task of imaging a
particular detail at a signal-to-noise ratio of 5. Results are for an 8cm thick breast of 10% glandularity. The W/Rh spectrum is the best of those illustrated. It is important to note that the choice of optimum spectrum is dependent on breast thickness.
The following reference discusses the choice of
spectra for screen-film and digital mammography: Influence of anode filter material and tube potential on contrast, signal-to-noise ratio and average absorbed dose in mammography: a Monte Carlo study, Dance et al BJR
73 (2000) 1056-67)
6
Focal spot size and imaging geometry
If we ignore movement unsharpness, then an estimate U of the overall unsharpness can be obtained by combining the geometric and receptor unsharpness in quadrature.
U
1
 m  1 2 f 2  F 2
m
Here m is the magnification, f the focal spot size and F the receptor unsharpness. The first squared term is the
geometric unsharpness and is zero for magnification 1. The unsharpness has been normalised to correspond to
sizes in the object plane
Variation of unsharpness with (actual) focal spot size
and image magnification. Receptor unsharpness of 100
micron assumed.
Curves shown for focal spot sizes of 0, 100, 600, 1000
micron.
An actual focal spot size of 0.6mm or less and an FFD
of at least 60cm are recommended. For moderate focal
spot sizes, the overall unsharpness increases with magnification and contact mammography only should be
used.
Increasing the FFD or decreasing the OFD will decrease magnification and improve the unsharpness.
For a small focal spot size, magnification decreases
unsharpness but will increase dose. Because of the air gap, there will be a decrease in scatter (no grid is normally used for magnification), and a larger image on the same receptor means the effect of noise is reduced.
5 Breast Compression
Reasons for compression :







reduced dose
reduced scatter - improved contrast
softer spectrum - improved contrast
reduced geometric unsharpness
reduced movement unsharpness
reduced dynamic range of image
reduced tissue overlap - better visualisation
6 Anti-scatter grids
The contrast in the image is degraded by the scattered radiation recorded by the image receptor. The amount of
degradation varies with photon energy, breast size and image receptor. It can be quantified using the contrast
degradation factor CDF which is the ratio of the image contrast with and without the effects of scatter.
CDF 
1
1 S P
where S and P are the energies absorbed in the receptor from secondary and primary radiation respectively.
Grid parameters for a typical mammographic grid:
7




lines/cm
interspace
lead height
grid ratio
31
paper
1.5 mm
5.0
Variation of S/P ratio with breast thickness. Min-R screen, 28kV Mo/Mo.
Without a grid, the CDF for a 5cm breast
is 0.65.
S grid and M grid indicate values corresponding to the use of particular stationary and moving grids
Grid performance can be assessed in terms of the contrast improvement factor CIF and the Bucky factor BF.
The CIF is the ratio of the contrasts with and without the grid and is given by :
CIF 
1
1  Ts S Tp P
The BF is the ratio of the exposures with and without the grid and is given by :
BF 
CIF
Tp
Ts and Tp are the transmissions of secondary and primary photons through the grid respectively.
For medium to large breasts, the contrast improvement associated with the use of the grid is important. For a
2cm breast the CIF is only 1.2 whereas the BF for the M-grid is 1.7
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7 Screen/film receptor
Speed
Factors which affect speed :
K-edge
keV
CaWO4
Gd2O2S
La2O2S
Y2O2S
69.5
50.2
38.9
17.0
screen thickness
photon spectrum
Light
efficiency
%
3.5
15
12
18
light output
screen composition
film response
film processing
(Light efficiency data taken from Stevels, 1975)
Energy absorption efficiencies for various phosphors.
Each curve is for a screen 100 micron thick (i.e. all
screens have similar resolution) with a 50% phosphor packing density.
The Gd2O2S and CaWO4 phosphors have the best
energy absorption efficiency.
Taking into account the light efficiency of the
phosphor means that Gd2O2S is the phosphor of choice.
Energy absorption efficiency for Kodak Min-R screen
(33.9 mg/cm2 Gd2O2S)
Calculations of efficiency vs energy for both primary
and secondary photons for a 6cm thick breast.
The higher efficiency for the secondary photons is due
to the greater path length and lower energy. This effect
enhances the S/P ratio.
For Gd2O2S, a 20 keV X-ray will produce about 1200
light photons of typical energy 2.4 eV.
9
Resolution
Factors which affect resolution:




screen thickness
absorptive dyes
incident photon spectrum
crossover (double screen system only)
Spread of light fluorescent photons as they pass from
screen to emulsion.
The screen is placed behind the emulsion to bring the
X-ray photon interaction point as close as possible to
the emulsion
MTF measured by Kuhn and Knüpfer (Medical Physics 19
(1992) 449) for mammographic screens constructed to a
standard prescription and to achieve high detail or low dose.
Mammographic screen films
Important factors are
contrast
latitude
sensitivity
processing
granularity
reciprocity failure
Film characteristics and film gamma for two mammographic screen films. The region of high gamma or good
contrast is very limited and correct exposure is very important [Data from Meeson et al. BJR 74 (2001) 825-835].
10
Wiener spectra, DQE and NEQ
Noise power (Wiener) spectra for a mammographic
screen-film combination. Data taken from Nishikawa
and Yaffe (Medical Physics 12 (1985) 32). MinR screen
with Ortho M film. O.D. 1.0
At normal optical densities and moderate frequencies,
the quantum mottle is the largest noise contribution. At
low and high OD and at high frequencies, the film granularity dominates.
The detective quantum efficiency (DQE) and the noise equivalent quanta (NEQ) are useful measures of the imaging performance which take account of the noise. Bunch [e.g. SPIE 1090 (1989) 67 and SPIE 3659 (1999)
120] has measured DQE and NEQ for various mammographic screen-film combinations. For the MinR screen
used in conjunction with OrthoM film, the highest value of the DQE is 0.27, much lower than the efficiency
shown earlier. This is because of the additional noise introduced in converting absorbed X-ray energy into an
image.
Detective quantum efficiency
0.5
The figure shows the DQE for the MinR2000
screen-film combination. For this combination, the
highest DQE value is about 0.4. The highest values
of the DQE and NEQ occur at optical densities
higher than 1.0, and there is a significant loss of
performance at high and low optical densities and
at high frequencies.
2
0.4
4
6
0.3
0.2
10
0.1
15
20
0.0
4.9
5.1
5.3
5.5
5.7
5.9
Log10 (X-ray quantum f luence)
The desirability of using an optical density greater than 1.0 is consistent with work by Young et al. (table below
and Clin. Radiol. 49 (1994) 461). These authors found that that the cancer detection rate in the UK National
Breast Screening Programme was dependent upon the optical density on the film, with the higher detection rates
found at higher optical densities.
Table: Small cancer detection rates in the UK Breast Screening Programme.
Optical density range
Small cancer detection rate (%)
0.8 - 0.99
1.0 - 1.19
1.2 - 1.39
1.4 - 1.59
1.6 - 1.79
1.8 - 1.99
0.13  0.02
0.11  0.01
0.16  0.01
0.17  0.01
0.18  0.02
0.20  0.02
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9 General references
Säbel M and Aichinger H 1996 Recent developments in breast imaging Phys. Med. Biol. 41 315
Dance D R 2005 Physical principles of mammography in: Commissioning and routine testing of mammographic X-ray systems, A C Moore et al. IPEM Report 89, IPEM, York.
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