Rayleigh imaging in spectral mammography
This is the submitted manuscript of:
Berggren, K., Danielsson, M. and Fredenberg, E. , “
Rayleigh imaging in spectral mammography ,” Proc. SPIE 9783, Medical Imaging 2016: Physics of Medical Imaging, 97830A (2016).
The published version of the manuscript is available at: https://doi.org/10.1117/12.2217048 All publications by Erik Fredenberg: https://scholar.google.com/citations?hl=en&user=5tUe2P0AAAAJ ayleigh imaging in spectral mammography
Karl Berggren *ab , Mats Danielsson a and Erik Fredenberg ba Department of Physics, Royal Institute of Technology (KTH), 10691 Stockholm, Sweden b Philips Healthcare, Smidesv¨agen 5, 17141 Solna, Sweden
ABSTRACT
Spectral imaging is the acquisition of multiple images of an object at different energy spectra. In mammography,dual-energy imaging (spectral imaging with two energy levels) has been investigated for several applications, inparticular material decomposition, which allows for quantitative analysis of breast composition and quantitativecontrast-enhanced imaging. Material decomposition with dual-energy imaging is based on the assumption thatthere are two dominant photon interaction effects that determine linear attenuation: the photoelectric effect andCompton scattering. This assumption limits the number of basis materials, i.e. the number of materials thatare possible to differentiate between, to two. However, Rayleigh scattering may account for more than 10% ofthe linear attenuation in the mammography energy range. In this work, we show that a modified version of ascanning multi-slit spectral photon-counting mammography system is able to acquire three images at differentspectra and can be used for triple-energy imaging. We further show that triple-energy imaging in combinationwith the efficient scatter rejection of the system enables measurement of Rayleigh scattering, which adds anadditional energy dependency to the linear attenuation and enables material decomposition with three basismaterials. Three available basis materials have the potential to improve virtually all applications of spectralimaging.
Keywords:
Mammography, Photon counting, Spectral imaging, Material decomposition, Rayleigh scattering
1. INTRODUCTION
Material decomposition with spectral x-ray imaging was introduced for medical imaging about four decades ago
1, 2 and specifically applied to mammography about ten years later. Since then, the most common implementationof spectral mammography has been dual-energy imaging, i.e. spectral imaging with two images at two differentenergy spectra. Dual-energy imaging has been applied for contrast-enhanced K-edge imaging, to measure theamount of contrast material and energy-weighting to improve the image signal-to-noise ratio.
6, 7
It has also beenused in unenhanced material decomposition with two basis materials, for example, to improve lesion visibility
3, 8 to differentiate between lesion types
9, 10 and to measure the volumetric breast density. Unenhanced material decomposition in dual-energy imaging is done under the assumption that x-ray attenua-tion is determined by only two independent interaction effects, the photoelectric effect and Compton scattering,
1, 2 and adding additional energy levels would therefore not add independent energy information. This assumptionis practical because the complexity of an imaging system generally increases with the number of energy levels,and the mentioned interaction effects do contribute the largest cross sections in the mammography energy range.Nevertheless, many current mammography applications of spectral imaging are restricted by only having accessto two basis materials. The third most probable interaction effect for breast tissue in the mammography en-ergy range is Rayleigh scattering (coherent scattering). Even though the cross section for Rayleigh scatteringis substantially lower than for the photoelectric effect and Compton scattering, the effect might still be usedas an independent energy dependency in material decomposition if the imaging system has 1) efficient-enoughscatter rejection to treat scattering as attenuation, 2) capability to measure at three different energy spectra,i.e. triple-energy imaging, and 3) high enough signal-to-noise ratio to allow for the effect to be detected despitethe relatively low cross section. Adding Rayleigh scattering as an independent energy dependency would enablematerial decomposition with three basis materials, which has the potential to improve virtually all applications ofunenhanced spectral imaging. For instance, skin thickness could be measured and accounted for more accurately *E-mail: [email protected]) breast x-ray beam Si-strip detector lines pre- collimator compression plate breast support _ + HV rejection high low detector line ASIC 1010101 1010101 AC (b) (cid:1) (cid:2) xyw zh min h max Scatter pointR (c)
Figure 1: (a) The Philips Microdose SI system. (b) Schematic of the collimator structure and the photon-counting detector with two energy thresholds. (c) Schematic of a scattering event and the geometry used in Eq.2, where x and y are the axes on the post-collimator plane, w is the width of a post-collimator slit, θ and φ are spherical angles and the object is placed along the z -axis between h min and h max above the post-collimatorplane.in measurements of volumetric breast density, characterization of lesions as benign or malignant could be donemore accurately, and the effect of breast thickness variations, which has hampered previous attempts to improvethe visibility of malignant lesions, could be accounted for.The purpose of this study is to investigate whether the use of Rayleigh scattering as a third independent inter-action effect is feasible on a modified version of a commercially available spectral photon-counting mammographysystem.
2. METHOD2.1 Spectral photon-counting mammography system
The Philips Microdose SI (Philips Healthcare, Solna, Sweden) is a scanning multi-slit mammography system(Fig. 1a and 1b). The image receptor consists of 21 photon-counting line detectors with a pixel pitch of 50 µ m. A low-energy threshold in the electronics rejects virtually all electronic noise. Even though the commerciallyavailable system features only one high-energy threshold that enables dual-energy imaging, one can simulate aone-shot triple-energy system by performing two image acquisitions with the same exposure settings but withthe high threshold at different levels. The main difference between this method and a triple-energy system isthe increased exposure with a factor two which is mainly a benefit in a phantom study since it improves imagestatistics. The main drawback of this implementation in clinical setting is the large risk of vibration and motionblur from the patient which is why in a clinical system one would use a detector system with three or moreenergy thresholds and acquire one-shot triple-energy images.The system processes the images from the 21 lines into one image for each energy bin, all detector channelsare individually calibrated against PMMA so the output images are equivalent PMMA thicknesses with inter-channel variations calibrated away. The three thresholds used produces three different images, the low threshold,that is set just above the electronic noise level, generates a conventional photon-counting image of the wholespectrum referred to as the sum image. The middle threshold generates a medium image of approximately theupper two-thirds of the spectrum and the high threshold generates a high image of the upper one-third of thespectrum. −3 −2 −1 Energy [keV] µ [ mm − ] PhotoelectricRayleighComptonTotal
Figure 2: The energy dependencies of the three major interaction effects at mammographic x-ray energies. Theplot is logarithmic on both axes to visualize the exponents in the approximation Eq. 1 (the exponent correspondsto the slope of the curve).
For most natural body constituents at mammographic x-ray energies, it is fair to ignore absorption edges. X-rayattenuation is then made up of three independent interaction effects, namely the photoelectric effect, Comptonscattering, and Rayleigh scattering. The contributions of these effects on the linear attenuation, µ , as a functionof photon energy, E , are approximately µ ( E ) = a P E E − + a R E − . + a C , (1)where a P E , a R and a C are material dependent constants for the respective interaction effects. Equation 1is an approximation and the actual dependencies are plotted in Fig 2. The photoelectric effect follows anexponential energy dependency quite accurately, but Rayleigh and Compton scattering have somewhat morecomplex energy dependencies. Nevertheless, the energy dependencies of the three effects differ substantially andany complex behavior can therefore be handled by more advanced calibration models and algorithms.
11, 15
Forefficient spectral imaging it is necessary to be able to treat scattering processes as attenuation, i.e. scatteredphotons need to be rejected by the detection system. It has previously been established that the multi-slitgeometry of the Philips Microdose SI rejects virtually all Compton scattered radiation but Rayleigh scattedphotons have a substantially narrower angular distribution, and the rejection efficiency for these might be lower.The fraction of Rayleigh scattered photons incident on the detector from a line of material with atomic number Z , linear attenuation µ ( E ), attenuation from Rayleigh scattering µ R ( E ), and located between h min and h max is p R = R h max h min dz R slit sin θdθdφ θR | F ( Ehc sin θ , Z ) | q ( E ) e − µ ( E )( h max − z ) µ R ( E ) R h max h min dz R total sin θdθdφ θR | F ( Ehc sin θ , Z ) | q ( E ) e − µ ( E )( h max − z ) µ R ( E ) (2)where E is the x-ray energies spanning from 0 to E max , x , y , z and R , θ , φ are the coordinate systems depictedin Fig. 1c, slit indicates the area covered by a slit, F ( v, Z ) is the atomic form factor, h is Planck’s constant, c is the speed of light and q ( E ) is the incident spectrum. We have modified a Philips Microdose SI mammography system to perform triple-energy imaging by performingtwo image acquisitions with different high-energy thresholds. This generates in total four images: two sum imageshich should be identical, except for quantum noise, and that images the total spectrum above the electronicnoise level, one medium energy image with a threshold set to capture approximately the top 66% of the spectrumand one high energy image to capture approximately the top 33% of the spectrum. All exposure settings werecalibrated against a PMMA step-wedge so that the images were represented as equivalent PMMA thicknesses.This calibration also removes non-linear detector response and inter-channel variations. One sum image wasdiscarded and the other three were calibrated against a three material phantom consisting of CIRS (CIRS Inc.,Norfolk, VA) glandular and adipose tissue equivalent material and aluminium.For each pixel the system output is three PMMA thicknesses, ( t , t , t ), that are mapped against the refer-ence materials glandular tissue, adipose tissue and aluminium, ( t g , t a , t al ). The three-material calibration wasperformed by calculating calibration functions for each reference material using linear interpolation on each in-dividual channel. The reference points were determined from the median over a region-of-interest (ROI) for eachcombination of material. For all images, a background of 5 mm PMMA and 20 mm of 30% glandular CIRSbreast-tissue equivalent material was used to get the total material attenuation in the average mammographyrange. The calibration points used were the 27 possible combinations of t g = 0 , ,
20 mm, t a = 0 , ,
20 mm and t al = 100 , , µ m. Verification measurements were done on a separate image set on the mid-points of eachcalibration region, i.e. the 8 combinations of t g = 5 and 15 mm, t a = 5 and 15 mm, and t al = 200 and 400 µ m.Pixels with values outside of the calibration range were flagged and not included in the remaining calculations.
3. RESULTS3.1 Theoretical analysis
Figure 3a shows a 38-kVp tungsten mammography spectrum along with the fraction each interaction effectmakes up of the linear attenuation for a 55 mm thick compressed breast consisting of 5 mm of skin, 15 mm ofglandular tissue and 35 mm of adipose tissue. The contribution by Rayleigh scattering is relatively constant inthe relevant energy range and accounts for 11% of the total linear attenuation when weighted with the spectrum.The contributions by the photoelectric effect and Compton scattering are 56% and 33%, respectively.Figure 4 shows the intensity of Rayleigh scattering over an area of 100 ×
100 mm for an object consisting of40 mm of carbon (an elemental material was used rather than breast tissue in order to simplify calculation of theform factor). The area of a collimator slit is shown as a black line. The fraction of scattered radiation that hitsthe detector calculated according to Eq. 2 was 1%, i.e. the scatter rejection was found to be 99%. The amountof scattered radiation hitting adjacent detector lines was not included in this number and the actual efficiencywill be slightly lower. Still, we expect the scatter rejection efficiency to be sufficiently high for treating Rayleighscattering as absorption. The results from the measurements are presented in Table 1 and Fig. 5. All measurement points except point8 are within the measurement error from the corresponding true points and even though the errors are quitelarge, there is no clear overlap between the different measured points. I.e. one can differentiate the materialdifferences in the order of the difference selected for the measurements points: 10 mm glandular or adipose tissueor 200 µ m aluminium. The error bars in Fig. 5 show the estimated error of the measurement points (one standarddeviation). The relatively large errors suggest that improved statistics would be desirable to reduce uncertaintyof the results. However, the measurement points do also show signs of systematic deviations which may be causedby noise in the calibration data, variations between image acquisition, or a sub-optimal implementation of thecalibration, for example in the selection of ROIs for determining the calibration values and the measurementvalues.For some of the measurement ROIs, a high fraction of pixels were discarded because of having out-of-rangevalues. Noteworthy were the points with the highest total attenuation, points 5, 6 and 7, which had 12%, 22%and 10% of the pixels outside of the calibration range.
10 20 30 40
Energy [keV] F r a c t i on o f t o t a l a tt enua t i on (a) Energy [keV] F r a c t i on o f t o t a l a tt enua t i on P h o t o e l e c t r i c Rayleigh C o m p t o n (b) Figure 3: (a) The fraction each photon interaction effect contributes to the linear attenuation. (b) The fractionsof attenuation of the total attenuation, similar to Fig. 3a, but with intervals for all measurement and calibrationpoints. The intervals for the measured points are marked out by solid lines and the intervals for the the calibrationpoints are marked out with dashed lines. A 38 kVp tungsten mammography spectrum is included for referencein both plots. x [mm] y [ mm ] −50 0 50−50050 I n t en s i t y [ a . u ] −7 Figure 4: The intensity of Rayleigh scattering onto a 100 ×
100 mm surface. The black line illustrates thewidth of a post-collimator slit.No. True Adip. True Gland. True Al Meas. Adip. Meas. Gland. Meas. Al1 5 5 200 4.25 ± ± ±
762 5 5 400 3.54 ± ± ±
613 15 5 400 12.7 ± ± ±
774 15 5 200 12.7 ± ± ±
915 15 15 200 13.5 ± ± ±
916 15 15 400 12.6 ± ± ±
947 5 15 400 5.38 ± ± ±
618 5 15 200 7.77 ± ± ± Adipose [mm] G l andu l a r [ mm ]
12 3 4567 8 (a) Adipose [mm] A l u m i n i u m [ mm ]
12 34 5678 (b) Glandular [mm] A l u m i n i u m [ mm ] (c) Figure 5: The measured values, marked with x and error bars, together with the true values, marked with circles.The exact values are listd in Table 1. These plots represent the three projections of the 3D volume span by theglandular, adipose and aluminium thicknesses.
4. DISCUSSION AND CONCLUSIONS
With this work we set out to show that material decomposition with three basis materials is feasible on acommercially available spectral photon-counting mammography system by testing the following points 1) thescatter rejection of the system is efficient enough that Rayleigh scattering can be treated as absorption, 2) it isconceivable to modify the system to measure at three different energy spectra, i.e. triple-energy imaging, and3) the signal-to-noise ratio of Rayleigh scattering is high enough to allow for the effect to be useful, at least forlarge targets.For point 1) we have theoretically shown that the scatter rejection is high enough to consider Rayleighscattering as attenuation and thereby introducing a third energy dependence in material attenuation. From theview of the experiment we see that we can decompose images into three materials, but the current experiment isnot sufficient to rule out insufficient scatter rejection as a limiting factor. This can however be tested by imagingthe same object at different heights above the patient support. This is based on Eq. 2, the scattered photons willhave a longer distance to travel before reaching the post-collimator and therefore spread out more and reducingthe flux that passes the post-collimator, similar to the inverse square law.We have succeeded in modifying a commercially available mammography system for triple-energy imagingas in point 2). However, the double exposure method is only suitable for phantom studies and for a clinicalimplementation a one-shot triple-energy acquisition should be used. Two possible ways of implementing such anacquisition is by alternating the threshold between the different line boards or by using a detector system withthree or more electronic thresholds. These methods are however part of ongoing research.The signal-to-noise ratio is a limiting factor in the current experimental setup and further research is required,both concerning the current implementation to find the limiting factors but also in optimizing other systemparameters for improved SNR from Rayleigh scattering. For example, reducing the post-collimator width orincreasing the patient support to detector distance would improve the signal from attenuation by Rayleighscattering.Improving the electronics and detector is another interesting point. Energy resolution is one possible lim-itation, photons counted in the wrong bin would increase the noise while the average signal remains correct.Improved handling of charge sharing, chance-coincidence and pile-up are also possible improvements. Thesequestions require further study.Material decomposition with three basis materials has the potential to improve spectral mammography sub-stantially, for instance, by removing the effects of skin in breast-density measurements and the effects of thicknessand density gradients that have so far hampered the development of spectral lesion characterization and detec-tion. The breakthrough work of this study is the implementation of triple-energy imaging on a mammographysystem and decomposition into three basis materials using attenuation from Rayleigh scattering.
CKNOWLEDGMENTS
This work was partly funded by the Swedish Research Council.
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