Digital mammography image simulation using Monte Carlopeplowde/p015.pdfvarious kVp settings and has...

Digital mammography image simulation using Monte CarloDouglas E. Peplowa) and Kuruvilla VergheseDepartment of Nuclear Engineering, North Carolina State University, Box 7909, Raleigh,North Carolina 27695

~Received 21 December 1998; accepted for publication 8 December 1999!

Monte Carlo simulations of digital images of the contrast detail phantom and the ACR phantom arepresented for two different x-ray digital mammography modalities: a synchrotron mammographysystem and a next-generation scanning slot clinical system. A combination of variance reductionmethods made it possible to simulate accurate images using real pixel dimensions within reasonablecomputation times. The complete method of image simulation, including a simple detector responsemodel, a simple noise model, and the incorporation of system effects~MTF!, is presented. Thesimulated images of the phantoms show good agreement with images measured on the two systems.© 2000 American Association of Physicists in Medicine.@S0094-2405~00!00603-9#

Key words: digital mammography, image simulation, Monte Carlo

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I. INTRODUCTION

A rapidly expanding area in medical applications of x rafrom synchrotrons1,2 is synchrotron mammography. Severgroups worldwide@for example, in Italy3,4 and the NationalSynchrotron Light Source~NSLS! at Brookhaven NationaLaboratory~BNL! in the U.S.5# have been generating exciing results in synchrotron mammography using monoengetic, parallel, plane-polarized x rays, with a high degreecollimation, long air gaps to reduce x-ray scatter contribtion, and even crystal analyzers to virtually eliminate imadegradation due to scatter. Diffraction of the transmitbeam from the object using a Bragg or Laue analyzerbeen shown to produce images that are unparalleled in cland contrast.6 A group in Russia has been doing similar ivestigations using x-ray tubes instead of synchrotron beand generating high quality images.7 Chapmanet al.6 haveshown that the transmitted and diffracted images cancoupled to obtain a pure absorption image with imagingtails smaller than ever seen before. Simultaneously withdevelopment of synchrotron mammography, next-generaclinical mammography systems with slot geometry and dtal detectors8 have been undergoing clinical trials. Scattcontribution is reduced through the use of a narrow collimtor slot and detector array scanned across the objectquantify the amount of scatter in these two types of modties, a Monte Carlo study was proposed. In this paperpresent the results of a code designed to create accsimulated images for the study of scatter contributions.

Most of the previous Monte Carlo studies9–11 have at-tempted to evaluate mammography systems based on sistudies that quantify the scattered radiation striking theage plane from a slab of material, usually water or LucThese studies may show trends with energy or slab thickncorrectly, but they do not include the full three-dimensioneffects, such as air scatter or edge effects. Recently, JHuda, and Walker12 studied scanning slot systems usingthree-dimensional~3-D! model. However, they only focuseon the average scatter-to-primary ratio~S/P! observed in a

568 Med. Phys. 27 „3…, March 2000 0094-2405 Õ2000Õ27„

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strip located at the center of the image. Spyrouet al.13 hasrecently performed some Monte Carlo image simulationsusing an analog code that required 18 days to run,14 even fora very simple phantom and system. What is really needea way to determine whether or not objects of certain siand densities can be seen in the image produced by the mmography system in question. To answer this, a full 3model and an entire accurately simulated image are requ

Full-field image simulation for realistic pixel sizes~50 or100 mm! using standard Monte Carlo techniques wouldquire prohibitively long computing times. Larger pixel sizecould be used for the purpose of modeling to reducetimes, but the clinical relevancy would be lost. Small objecsuch as fibrils or calcifications, would not be discernibwhen using large pixel sizes. In order to simulate imagwith accurate pixel sizes in reasonable times, a combinaof three variance reduction techniques are implemented.

In Sec. III of the paper we describe the methods usedthe Monte Carlo simulation code written to generate imafrom the synchrotron-based system and from the Fischernoscan™, a new digital scanning-slot system that is repsentative of the next generation of clinical mammograpmachines. The code is verified by comparison to a largeof published computational results and also to images msured on both systems. The concepts presented in this pshould be applicable also to image simulations using genpurpose codes such asMCNP™. In fact, Los Alamos NationalLaboratory15,16 is currently investigating the incorporation oimage simulation capability within a future version oMCNP™.

By comparing real digital images taken by the synchtron and the Senoscan™, in this paper we will demonstthat image simulation by Monte Carlo is possible within resonable computing times. Hopefully this modeling abiliwill prove as valuable to mammography and other imagproblems in medical physics as it has proven in many otfields. Our focus in this paper is to show that with the rigcombination of variance reduction methods, Monte Cacan be used to simulate accurate images within a reason

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569 D. E. Peplow and K. Verghese: Digital mammography image simulation 569

computing time, which has not been done previously. Tdetector response and noise models we have used in destrating the image simulation capability are simple nowcould be improved later.

II. DIGITAL MAMMOGRAPHY SYSTEMS

A. Synchrotron imaging

The new synchrotron-based digital mammography sysis still in its early experimental phase of development. Tconcept is being developed in the United States at the N~BNL! and at the Advanced Photon Source at Argonnetional Lab. The basic system consists of a plane-polarizparallel, monoenergetic source of radiation collimated intrectangular beam. Since the beam is fixed in position bymonochromator, the object and the imaging platescanned through the beam. Since the beam is parallel, tis no geometric magnification and large air gaps are useaddition to various collimators to reduce the amount of scter. A schematic diagram is shown in Fig. 1.

The system used to take images for this project was onX15A beamline of the NSLS. The energy of the beam canselected to be between 18 and 42 keV and the beam si1330.1 cm. The air gap between the target and the implate is 26 cm. Currently, the image is recorded by a FHR-III image plate and developed by a Fuji BAS2000 imaplate reader.

B. Fischer Senoscan™

The Fischer Senoscan™ system, shown schematicalFig. 2, is a scanning slot system that uses a linear CsI/Cdetector array. The tungsten anode is well collimatedrotates at the same rate as the detector, scanning the bwith a fan beam of x rays in five seconds. Like conventiosystems, the x-ray source spectrum consists of bremsslung and it is polyenergetic. The machine can be operatevarious kVp settings and has a choice of three filter matals, which greatly reduce the L lines from tungsten.

The machine used for this study was at the UniversityNorth Carolina Hospitals as part of the clinical trials fFDA approval, which are currently ongoing at several si

FIG. 1. Imaging with a monoenergetic beam from the synchrotron. Twhite radiation from the synchrotron~W! passes through the double monchromator~M! to select a single energy of photons. The fan beam is comated by horizontal slits~C! and the dose is measured by ionization chabers ~IC!. An absorber~A! is used to attenuate the beam. The stage~S!holding the target object~T! and the image plate~P! are scanned through thfixed beam. Exposure to the plate is regulated by the speed of the swhich is controlled by the current from the second ionization chamb~Figure not to scale.!

Medical Physics, Vol. 27, No. 3, March 2000

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in the U.S. This machine and other digital mammograpunits are expected to replace the film/screen systems useclinics today.

C. Mammography phantoms

To compare the two systems, digital images were takentwo very common mammography phantoms—the contrdetail ~CD! phantom and the American College of Radiolgists ~ACR! phantom. The CD phantom is a 1.5 cm thicslab of Lucite with embedded disks of Lucite of varyinthicknesses and diameters. Thicknesses range from 0.1down to 0.0063 cm, representing density changes ofdown to 0.45%. Radii vary from 0.35 to 0.016 cm. Mammography systems are graded on how many objects caseen in the image. The ACR phantom is a 4.9 cm thick bloof Lucite containing a rectangular wax insert with embeddnylon fibers ~fibril simulations!, aluminum oxide spheres~calcification simulations!, and the top portions of plasticballs ~tumor simulations!. Information pertaining to theplacement and composition of the materials of the objewas obtained from the manufacturer, Gammex RMI. Scmatics of the two phantoms are shown in Fig. 3.

III. DESCRIPTION OF THE CODE

MCMIS ~Monte Carlo Mammography Image Simulation! isa detailed code specifically for the simulation of digitmammography systems, including scanning-slot systeThis code was written so that three variance reduction teniques can be used together. These are source rasteseparation of the scattered and unscattered image, andpoint–detector scheme. The code uses four input decksscribing the problem, various cross section tables and outseveral image files, image files describing stochastic untainty, and tables describing dose and exposure. The ccontains four source models, three detector geometriesthree detector types. These models and all of their parameare listed in one of the input decks. The geometry ofobject being imaged and a list of materials are listed in ot

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input decks. The last input deck contains information forMonte Carlo run—number of histories, variance reductmethods to use, etc. In addition to the image, this codecalculates for each region the energy deposited, the totalthe exposure, and the dose.

A. Source models

Four types of monoenergetic sources can be modeledMCMIS. Polyenergetic sources can be simulated by addtogether a set of monoenergetic images weighted bypolyenergetic spectrum, which allows the user to usesame monoenergetic runs to simulate different polyenergsource spectra. The code is designed in a manner suchsources are at a highz location, pointed down at some targplane. The detector lies on a lowerz plane and the image iviewed as a picture withx andy coordinates.

The four source models are the following.

~1! A polarized parallel beam, from a rectangular source r

FIG. 3. Schematics of the two common mammography phantoms used ireal and simulated images. The upper drawing is the contrast detail pha(10.8314.931.5 cm thick! and the lower drawing is the American Collegof Radiologists phantom (10.16310.1634.88 cm thick!.


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tered over a rectangular target, with a scanning slotented in thex direction moving in they direction.~syn-chrotron system!.

~2! An isotropic point source rastered over a target thacurved in thex direction, with a scanning slot oriented ithe y direction moving in thex direction ~Fischer sys-tem!.

~3! A polarized pencil beam, for comparing to other MonCarlo studies.

~4! An isotropic point source rastered over a flat rectangutarget, with a scanning slot oriented in they directionmoving in thex direction. This is also for comparing toother work in the literature.

‘‘Rastering’’ refers to the use of a stratified sampling rotine used to evenly sample the source over the target aThis is a common variance reduction technique and heeliminate quantum mottle in the image.

B. Basic transport

The geometry package ofMCMIS handles six basic shapecommonly found in phantoms and imaging systems. Thare spheres, cylinders~in any orientation!, rectangular boxesboiler plates~curved detector systems!, spherical chords~thetop of a sphere cut by a plane!, and compressed breast shap~half of a right elliptical cylinder!. Geometry regions can bnested to any level. This arrangement makes a descriptiocomplex phantoms very simple.

Materials are described by a list of elements: the mfractions (wi) of those elements and the density (r) of thematerial. Cross sections are calculated for an energy rang1 to 300 keV for any material consisting of elements wZ51 – 20. Photoelectric cross sections are taken fromITS17 library and scattering cross sections are calculatedintegrating the form factors for the materials.MCMIS has theability to use either the free-gas atomic form factors18 ormeasured molecular form factors19 for coherent scatter. In-coherent scatter was modeled using atomic incoherent stering factors.18

Interactions modeled in this code include the photoeltric effect, coherent scatter, and incoherent scatter. Impcapture~forcing a scatter and reducing the weight to accofor the fraction that would have been absorbed! and the last-flight estimator variance reduction techniques are availaas options. Both of these are well known and will notdiscussed here. The code does model polarization effecthat option is selected by the user, in the scattering intetions. K x-ray fluorescence can be modeled byMCMIS, butthis option is not available when using implicit capture sinphotoelectric events are not simulated.

C. Detector models

In addition to a perfectly absorbing detector designeduse in testing and benchmark problems, two more realidetectors are modeled byMCMIS. The models for these arstill simple but do include some aspects of detector respo

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The Fischer Senoscan™ detector is modeled as a CsI p0.015 cm thick. The density and thickness are left to the uas variable inputs and the nominal values used for this rewere supplied by Fischer Imaging.20 The second detector isphotostimulable phosphor imaging plate by Fuji. It is maof BaFBr0.85I0.15. Fuji literature with the imaging plate reports values of density thickness of 0.033 g/cm2 for the HR~high resolution! plate and 0.048 g/cm2 for ST ~standard!plate. Fuji literature also reports a thickness of 0.0150 cmthe phosphor layer.

In order to account for energy deposition across neighbing pixels, energy is deposited along the photon path throthe detector layer, weighted by the probability of the phosurviving up to that point in the layer. This is a simple modbut more complex than most used in radiographic simutions, which do not consider the spatial distribution of eneat all. Instead of continuing the Monte Carlo game in tdetector model, a ray-trace approach is taken. The distatraveled through each pixel is calculated and the probabiliof interaction in those lengths are found. Energy is then dtributed according to those probabilities in the pixels the pcrosses. A total ofE(12e2mt) energy is deposited, wheremis the total linear attenuation andt is the total distancethrough the detector layer. This simplified model doestake into account x-ray fluorescence or electron motisince that would be contained in the system MTF. Theergy deposition of the first interaction of the photon in tdetector is included in this model and everything after thaassumed to be in the MTF.

Three types of detector grids are available: a flat plateplate curved in the one direction, and a detector madeconcentric rings. The synchrotron system uses the flat pthe Fischer Senoscan™ uses the curved detector and cotric ring model is used for some test problems. Each detegrid type has many parameters set by the user. Scoressplit into two images: one for scattered photons and oneunscattered~source! photons.

MCMIS has the unique feature of modeling scanning sdetector motion. Both the synchrotron system and thecher Senoscan™ move the source and detector relative tobject being imaged. This motion is modeled byMCMIS bydefining a detector slot width (w) and a beam size (b). Atthe production of each source photon, a line is marked ondetector and the center of the slot is placed randomly wit6b/2 about this line, in the scan direction. Photons tstrike the detector region outside the slot are not scored.scanning slot option may be easily turned off by definingslot to encompass the entire detector.

D. Variance reduction

For an image of 10 cm by 10 cm with 100mm pixels ~a100031000 array! using 107 histories, the number of photons striking any one pixel will be 106A10. This would beseen in the image as quantum mottle and this amount wcompletely mask any details in the imaged object. To redthis mottle to 1%, a total of 1010 histories would be neededInstead, simulating ten histories per pixel~weighted by the


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angular distribution probability for source emission! willgive an image with considerably reduced mottle. This strfied sampling scheme used in Monte Carlo is what we csource rastering.

The path of a photon through a material is picked stochtically from the basic scattering and transport models.each interaction of the photon there is a small chance ofphoton scattering toward a given pixel in the detector, sviving through the material in between the interaction sand that pixel, and then interacting in that pixel. The poindetector scheme calculates this probability for every pixethe scanning slot of the detector at each interaction thatphoton has along its stochastic path. This way, each pixethe image receives some score with every history insteajust one pixel, where the simulated particle actually strikThis helps to minimize mottle in the image from scatter. Tscheme can also be thought of as a splitting game wherephoton is split into many pieces: many that are forcedinteract in the pixels of the detector and one that is prevenfrom striking the detector~the fraction that continues on inthe simulation!. When the weight of the surviving photobecomes low enough, Russian Roulette is played. Keepthe number of histories per pixel constant, the time requifor a simulation is inversely proportional to pixel size raisto the fourth power. Using this scheme for 100mm pixels ina realistically sized image would result in a prohibitivelarge simulation time.

To use the point–detector scheme without excessivlong computing times, the scattered and unscattered imaare computed separately. For the unscattered image, a MCarlo simulation is hardly necessary. It can be calculasimply by the exponential attenuation of every material inline between the source and the target pixel. This is veryand can be done in a few minutes for a full-field image us100mm pixels, allowing the smallest details of the objectbe seen in the image. The scattered image does not ssmall scale structure and can be modeled using larger psizes, which drastically reduces the time required bypoint–detector scheme. Pixel sizes up to 0.5 cm were usethis study. The fine mesh unscattered image and the comesh scattered image can then be added together.

IV. TRANSPORT MECHANICS BENCHMARKS

A series of comparisons of the basic parts of our MoCarlo code package were made against previously publisworks. This was done to ensure that the fundamental traport, tracking, interaction, and scoring mechanisms incode worked properly. In this section we will briefly reviethe comparisons. Detailed graphs and tables of each cparison would require more space than alloted in a jourarticle and interested readers are referred to the first authdissertation.21

A. Transmission, backscatter, and absorption

For an infinite slab of water, Boone22 calculated the pri-mary transmission, the total absorption, forward scatter emsion, and backward scatter emission of a monoenergetic

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cil beam of photons. This was done for a variety of slthicknesses and primary photon energies.MCMIS was alsoused to calculate the same quantities and the results avery closely with Boone’s values.

Another check of the transport mechanics used inMCMIS

is Boone’s calculation of the mean number of scatterevents for photons that have escaped the slab. Thesebers calculated byMCMIS also compare very well with thosfrom Boone.

B. Scattering distributions

Chan and Doi10 computed the following for monoenergetic pencil beams of photons hitting a slab of water: angudistributions of scattered photons, as a function of incidphoton energy and slab thickness; mean exit angle of stered photons, as a function of incident photon energyslab thickness, spectral distributions of scattered photonsa function of incident photon energy, slab thickness andangle; mean energy of scattered photons, as a functioincident photon energy, slab thickness, and exit angle; stral distributions of scattered photons, as a function of indent photon energy and slab thickness for all exit angcombined; mean energy of photons emerging at any angla function of incident photon energy and slab thicknenumbers of transmitted primary and scattered photonsfunction of incident photon energy and slab thickness; aother quantities.MCMIS was used to calculate the same quatities listed above and they all agreed very closely withresults of Chan and Doi. Re-runningMCMIS using the mea-sured molecular coherent scattering form factor of waslightly changed the distributions at low angles and lowergies.

C. Dose

MCMIS calculates dose by taking the energy depositedgeometric region and dividing by the mass of the materiathat region. Exposure is calculated using a pathlength t~similar to a total flux tally! but weighted by the energy othe photon and the energy absorption coefficient for air. Tcode then reports dose or exposure in rads or roentgenspectively, per photon.

Liu, Goodsitt, and Chan23 have reported the dose per unskin entrance exposure for various combinations of kVp stings and spectral HVLs.~The half-value layer is the amounof material required to reduce the exposure in half. Thisused as a measure of beam hardness.! In their paper theyfocus on magnification mammography, but it still providesuseful check. The model used by Liuet al. included a diver-gent point source located 65 cm above the breast supThe breast phantom simulated was a semielliptical right cinder with a 0.4 cm thick skin made of the same materiathe breast. Liuet al. calculated the dose per unit entranexposure as a function of breast thickness for two casestandard mammogram and a magnification image. The mnification shot gives the patient a lower dose for the saskin exposure. The ratios computed withMCMIS are 5%–20% lower than those of Liuet al. Considering that differen


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cross sections, energy absorption coefficients for air, andferent tube spectra were employed, this difference is reasable. These cases were for 28 kVp without a compresspaddle for a 50/50 adipose/glandular tissue breast. Liuported that their spectrum had a HVL of 0.31 mm Al whithe spectrum used in the analysis of theMCMIS data had aHVL of 0.334 mm Al.

MCMIS was also used to calculate the dose per unittrance exposure for a magnification image on a 100% gdular tissue breast at 30 kVp. Two calculations were maone without a compression paddle, using a spectrum wiHVL of 0.33 mm Al, and one with a 5 mmLexan compres-sion paddle, after which the spectrum then had a HVL0.42 mm Al. Agreement with the calculation of Liuet al.was similar to the above cases.

D. Scanning slot systems S ÕP

Jing, Huda, and Walker12 reported in 1998 on the S/Pratio of scanning slot mammography systems. They usedEGS4 Monte Carlo code package to calculate the ratioenergy from scattered radiation absorbed in the detectoenergy from the unscattered~primary! radiation. Simulationswere for point sources above a Lucite slab (20320 cm2 area!and a planar detector~60 cm from the source!. Only thecenter slit was considered. They investigated four paraeters: source energy, slab thickness, air gap size betweeslab and the detector, and the width of the slot. The molelar coherent scattering form factor reported by Leliveld24 wasused for Lucite. Most simulations were done for a perfecabsorbing detector but a few were performed usingGd2O2S:Tb 36.7 mg/cm2 plate. They then calculated the S/ratio over the entire slot for many cases of the four paraeters, all to a reported 1% stochastic error. In their pavalues for polyenergetic spectra are also reported.

MCMIS was used to simulate 79 of the monoenergecases reported by Jinget al. The point–detector scheme waturned off and the detector was defined to have one picorresponding to the slot. Scanning motion of the detecand of the slot was not used. All the S/P ratios were callated to a stochastic error of 1% or less. The results frMCMIS match those of Jinget al. very well, typically within3% of each other, and for a few cases at low energiessmall slot widths to within 8%.

V. IMAGE PROCESSING

One run of MCMIS will produce five images—one unscattered image on a fine mesh and four images on a comesh, with both mesh sizes as specified by the user. Thecoarse mesh images are an unscattered image, a scaimage, and the stochastic uncertainties from these imaFrom these images, several steps must be taken to formfinal simulated image.

A. Simulation of synchrotron images

The images taken by the synchrotron are not from a trmonoenergetic source and this must be taken into accousimulating an image. Since Bragg reflection of a particu

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order through a crystal is used to select the energy ofsynchrotron beam, reflections of other orders are also prein the beam. For example, for a 26 keV beam selected uthe @3,3,3# reflection from a Si crystal, there is a componeat 34.67 keV~19% of the intensity of the 26 keV! and a43.33 keV component~1.6% of the primary intensity!. Thisis easily accounted for in the Monte Carlo calculationsrunning each component energy and then adding the reweighted by the intensities. The intensities were suppliedthe X15A beamline personnel25 and are shown in Table I.

For each synchrotron image, four monoenergetic comnents are simulated. The four unscattered images on themesh are added together and the four scattered images ocoarse mesh are added together. The total scattered imathen interpolated using the fine mesh and then added tototal unscattered image creating the total Monte Carlo imaThe stochastic uncertainties in the final image were calated by propagating the stochastic uncertainties in the imcomponents.

To simulate the quantum mottle produced by photon stistics, an appropriate amount of noise~see the next section!is added to the Monte Carlo image. The amount of relatnoise for each simulated image was determined by the tflux recorded by the ionization chamber for the correspoing experimental image. The values of relative noisetypically one percent or less.

The next step in the image simulation process is to smthe image with the system MTF. The MTF~modulationtransfer function! is the norm of the Fourier transform of thpoint spread function and describes the spatial resolutionsystem. Applying the MTF to an image smears it slighttaking energy from one pixel and depositing it in the neigboring pixels. This accounts for the smear of the laser lithat liberates small amounts of energy from neighboring pels. In reality, we did not have access to MTF data on tsystem but we did measure the square-wave response~SWR!with a standard line-pair phantom. Since the SWR andsystem MTF are so similar,26 the SWR was used in place othe MTF. This will not smear the image quite as much asMTF, but the difference is very slight.

The energy liberated by the laser is in the visible ranand there is a quantum mottle associated with it. So, mnoise is added to the smeared image making the final silated image. An example of each stage in this proces

TABLE I. Energies and intensities~without any filtration! from the mono-chromator on NSLS beamline X15A. It should be noted that the 1.5–mm of added aluminum used in the synchrotron images preferentiallyduced the low-energy components of the beam.

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18 18 1 54 0.000 65 72 1.7e-6 90 1.9e-26 8.67 0.008 26 1 34.67 0.19 43.33 0.01634 11.33 4.26 34 1 45.33 0.099 56.67 0.0042 14 92.80 42 1 56 0.058 70 0.001


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shown in Fig. 4. A note about the scattered image—amount of scatter across this portion of the image—is vconstant, not showing any detail. The figure is shown wthe contrast maximized, which highlights the statisticvariation of a few percent.

B. Synchrotron imaging noise model

For a good simulation process for the synchrotron,image noise also needs to be modeled. The simulationsnot very useful if one has to take a real image to determthe amount of noise to complete the simulation. By analing the noise observed in the 14 synchrotron images andionization chamber readings~related to photon flux! for each,a simple noise model was developed.

Noise coming from each step in the image formation pcess needs to be considered, but the exact amounts and fare unknown. These steps include the uncertainty assocwith the number of photons striking a pixel, the amountenergy deposited in the plate, the number of photons libated by the laser reading the plate, etc. From the ionizachamber readings before the target, the amount of ene

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FIG. 4. Image processing for simulating the synchrotron images:~a! theunscattered image and the~b! scattered image calculated by Monte Carlo aadded together~c!. Quantum mottle noise is then added~d!. The image issmeared using the measured system MTF~e! and image plate reader noiseadded creating the final image~f!. Each image is scaled to maximize visucontrast.


Medical Physics, Vo

TABLE II. Parameters of the real and simulated synchrotron images.

# PhantomEnergy~keV!

Slitwidth

Real imagerelative

Uncertainty~noise!

Monte Carlo simulations

S/Pmid S/P

Unscat.time

~hours!

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1 CD 18 3 mm 0.0096 0.0047 0.0037 0.095 2.82 CD 26 3 mm 0.0079 0.0036 0.0032 0.064 2.63 CD 34 3 mm 0.0070 0.0031 0.0030 0.069 2.74 CD 42 3 mm 0.0058 0.0030 0.0027 0.065 2.8

5 CD 18 5 mm 0.0083 0.0063 0.0057 0.060 3.26 CD 18 10 mm 0.0091 0.014 0.012 0.039 6.57 CD 18 None 0.0078 0.040 0.034 0.008 23.0

8 ACR 18 3 mm 0.0094 0.011 0.010 0.046 4.49 ACR 26 3 mm 0.0089 0.010 0.0094 0.044 4.0

10 ACR 34 3 mm 0.0073 0.0092 0.0085 0.038 4.111 ACR 42 3 mm 0.0092 0.0090 0.0080 0.037 4.9

12 ACR 18 5 mm 0.0118 0.019 0.018 0.046 6.013 ACR 18 10 mm 0.0096 0.040 0.035 0.027 10.514 ACR 18 None 0.0119 0.11 0.095 0.016 30.4

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striking the image plate,E, can be found. From this, thnumber of photons is found and then the expected noise fquantum mottle,sE , can also be found. When this noiseadded to the Monte Carlo image~scattered plus unscattered!,the MTF tends to smear it, reducing the relative amount bfactor k. The difference in the relative noise observed in timage andksE /E is due to the process of reading the plawhich converts the stored energy into visible photons thatthen converted to an electronic signal.

A simple model for the total relative noise~uncertainty!observed in the final image was constructed by proposthat the relative variance of the final image, (s I /I )2, couldbe described by the sum of three terms:

S s I

I D 2

5S ksE

E D 2

1S K1

E D 2

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where the first term represents the amount of quantum mas discussed above; the second term represents procwith an error related to the energy deposited in the platE~for example, the number of light photons generated!; andthird term represents processes with a constant relativeance.

The two constantsK1 and K2 were found by fitting themodel to the amounts of relative noise observed in thesynchrotron images listed in Table II. The results of thnoise model are shown in Fig. 5. This model also predicvery well the relative noise in eight other synchrotron imagof Lucite and wax phantoms that were not used in findingtwo model constants. The measured relative noise levethese images were between 1% and 1.5% and the mpredicted values that followed the trends well and were tycally within 10% of the measured values.

The above model for image noise is not intended to buniversal model—it is an empirical model used to fit tnoise of the images in our synchrotron imaging system oThis system had the unique ability to measure photon

l. 27, No. 3, March 2000

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through the ionization chambers that most imaging systedo not have. Since the focus of this paper is the Monte Camethods, items such as detailed modeling of the CCDaliasing were not included.

C. Simulation of Senoscan™ images

To simulate polyenergetic images from tube anode stems like the Senoscan™, many monoenergetic runsMCMIS are required. These runs, made from 5 to 40 keV ikeV intervals, are added together, weighted by the tube stra. For this project, tube spectra from Boone27 were used.

Quantum mottle noise is added to the image and thetem MTF is applied. The MTF accounts for the focal spsize, scanning motion wobble, and x-ray fluorescence indetector. The MTF was supplied by Fischer Imaging Corpration and checked by an edge-phantom measurementcourse, the MTF effects and the noise effects are not in

FIG. 5. Predicted relative uncertainty in each synchrotron image usingthree-term noise model compared to the observed relative uncertaineach real image. The 14 images are those listed in Table II.

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ality separate—the best we can do in our simple simulais to apply them in steps. The Fischer detector systemmore complex than what was used for the synchrotronages and the noise was considerably less~see Table III!. So,we did not attempt to model the noise for this system.stead, we used an amount of noise typically seen inSenoscan™ images of 0.5%. This value was calculatedlooking at an area of the image that ought to have hadform values and finding the variance. For the images tafor this experiment, the values were all between 0.38%0.64%, with approximate median values of 0.5%.

Real Fischer images are corrected for the flux falloffward the nipple by dividing the entire image by the whiteliprofile, which is the flux profile recorded at a standard kand extra-large filter thickness. This is also done forsimulated image, dividing by a profile generated by a serate Monte Carlo run matching the specifications of the Fcher whiteline image.

VI. METHODS OF COMPARISON


Seven images of each phantom were taken usingX15A synchrotron imaging system at the NSLS. Imagwere made at 18, 26, 34, and 42 keV. Several collimasizes were used at 18 keV in order to observe the effectincreased scattered radiation in the image. Noise in theages was typically very low, in the 1% range. The detailseach measurement are listed in Table II. The image plwere read by the Fuji BAS2000 using a 100mm pixel size.

Monte Carlo based simulations were performed wMCMIS for the same conditions as the experimental imafrom X15A. Pixel size in the fine mesh image was 100mmand in the coarse mesh image was 0.5 cm. The scatteprimary ratios for a 232 cm area in the middle of the imagas well as over the entire image are listed in Table II. Coputing times for the entire Monte Carlo simulations~up tofour monoenergetic calculations! are also listed for the SunUltra 60 ~300 MHz!.

TABLE III. Parameters of the real and simulated Senoscan™ images.

# Phantom kVp Filter

Real imagerelative

uncertainty~noise!

MC simulations

S/Pmid S/P

1 CD 25 Al 0.005 29 0.095 0.0922 CD 30 Al 0.003 82 0.092 0.0873 CD 35 Al 0.003 93 0.089 0.0844 CD 30 Rh 0.004 63 0.094 0.0905 CD 30 Mo 0.006 44 0.096 0.093

6 ACR 30 Al 0.006 51 0.22 0.207 ACR 35 Al 0.005 09 0.21 0.198 ACR 40 Al 0.004 54 0.19 0.18


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Eight images were taken on the Fischer Senoscan™—images of the contrast detail phantom at various kVp settiand filters and three images of the ACR phantom usingaluminum filter. Before comparisons to the Monte Carlo images, the Senoscan™ images were reduced in resolufrom 54 mm pixel size to 108mm pixel size. This was onlydue to the large size of the files and the extra time requirerun the Monte Carlo simulations for the smaller pixel sizThis did not affect the visibility of any of the items in thimages. The parameters of the Senoscan™ images arein Table III along with the measured noise level of the rduced images. These values were typically around 0.5%

Monte Carlo simulations were performed usingMCMIS forthe same conditions as the Senoscan™ images. Pixel sieach fine mesh image was 100mm and in the coarse mesimage was 0.5 cm. The scatter-to-primary ratios for a 232cm area in the middle of the image as well as over the en

FIG. 6. Images of the contrast detail phantom. Top—real image obtawith the synchrotron system at 18 keV with no collimators. Bottom—MonCarlo simulation.

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image are listed in Table III. Computer times are not listfor each image since the same monoenergetic imagesused in making the different simulations at different kVsettings and different filters. The total times for all 36 mnoenergetic contrast detail phantom images were 12 h forfine mesh unscattered and 72 h for the coarse mesh scatimages. For the ACR phantom, the total fine mesh unstered images took 6 h and the coarse mesh scattered imatook 99 h. These times are for the Sun Ultra 60.

C. Contrast in the CD phantom

Contrast of an object in the CD phantom is calculatedfinding the difference in levels inside and outside of a de

FIG. 7. Images of the ACR phantom. Top—real image obtained withsynchrotron system at 18 keV with 5 mm collimators. Bottom—MonCarlo simulation.


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divided by the average level. For example, if the averapixel value inside the detail isa and the average pixel valujust outside the detail isb, the contrastc is

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In a perfect imaging system, the contrast would only dcrease for thinner details, not for smaller diameter detailsreal systems, the decrease in contrast that is observedsmaller objects of the same thickness is due to the scacomponent, the MTF of the system, and noise.

VII. RESULTS AND DISCUSSION


Examples of the measured image and the simulated immatching the measurement for both the CD phantom andACR phantom are shown in Figs. 6 and 7. Although oimage may exhibit a greater degree of darkening thanother in each set, the discernibility of the objects in eaphantom is nearly the same in the measured and simulimages, implying that the contrast values of the two imagmatch. The Monte Carlo images are, of course, cleanercause they do not contain the experimental artifacts cauby defects in the monochromators and in the image plate

For images taken with different collimator sizes, thewas no significant change in the observed contrast. Thesults fromMCMIS show average S/P ratios for the centerthe CD phantom images of 0.5%, 0.6%, 1.4%, and 4%the four different collimator sizes of 3 mm, 5 mm, 10 mand infinite~no collimators! used in the X15A images. Evethe image where the S/P was 4%, scatter did not decreascalculated contrast in the Monte Carlo image. Synchrotimaging is essentially scatter free and it appears that thelytically calculated unscattered image, with MTF applied anoise, would be sufficient to model the images.

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FIG. 8. Contrast of the details in the CD phantom as a function of the deradius. Each series of points is from a column of details of the same thness. Data from the real synchrotron image appear as points and the covalues calculated from the simulated image appear as lines: solid linesthe raw Monte Carlo images and dashed lines after the MTF and noisebeen added.

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Figure 8 shows the contrast from the first four colum~the same thickness in each column! of the CD phantomshown in Fig. 6. Figure 8 also shows the contrast calculafrom the Monte Carlo image before the MTF and noise wapplied, and it does not decrease with decreasing detaidius, indicating that the scatter component is small in schrotron images and only the MTF of the system~imageplate and image plate reader! and noise degrades the contraThe spread in the contrast values for the measured imagmainly due to artifacts in the image. This is more evidentthe smaller details, where the averaging is done over fepixels.


The simulations compare very nicely to the real Sencan™ images. An example of each phantom image takenthe Senoscan™ and its Monte Carlo simulation are showFigs. 9 and 10. The simulated images appear very similathe Senoscan™ images in the level of detail that is visibOne difference between the images is that the amounttype of artifacts in the real Senoscan™ images do not apin the simulation. The vertical and horizontal stripes in t

FIG. 9. Images of the contrast detail phantom. Top—real image obtawith the Fischer Senoscan™ at 25 kVp with an aluminum filter. BottomMonte Carlo simulation.


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real image do not appear in the simulation. These stripesa large part of the calculated noise in the real imageswhen the same noise level is applied to the simulated imathe same visual appearance is not achieved. The simulimages then appear to have more of a mottled look, andis one aspect of the simulation that needs improvement. Tis also evident in close comparison of the fourth fibril in Fi10. This detail is masked by the texture of the noise arounmore in the simulated image than the real image.

The computed contrast for the two CD phantom imagas well as the contrast from the Monte Carlo image befthe MTF was used~to show contrast degradation from scattalone! are shown in Fig. 11. Unlike the synchrotron imagethe contrast of the Senoscan™ images are slightly degra

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FIG. 10. Images of the ACR phantom. Top—real image obtained withFischer Senoscan™ at 30 kVp with an aluminum filter. The nonuniformof the background is actually very slight—it is enhanced here in the choof gray scales used to maximize contrast in the image. Bottom—MoCarlo simulation.

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by the scatter contribution (S/P;9%). Being a scanning slosystem, this degradation is still less than in today’s convtional mammography units. After applying the MTF to thMonte Carlo image, the calculated contrast matches thetrast measured in the Senoscan™ image fairly well. Sincescatter degrades the contrast, modeling the Senoscan™require a calculation of the scatter component.

C. Prospects for simulations

In this paper we have focused on the methods requireperform Monte Carlo calculations for medical images in resonable amounts of time. To show this, we employed sosimple models for including detector response: the MTFthe various simulated systems and system noise. Howeuse of these simple models does not change the significof the results, showing that Monte Carlo image simulatcan be done in reasonable times and become a very utool in the study of mammography systems.

One major difficulty that presents itself is the accurainclusion of the noise and MTF into the simulation. In relife, noise comes from many parts of the imaging procesfrom source quantum mottle to electronics. The differecontributions to the system MTF also come from many dferent parts. The difficulty is that these effects on the imaare all happening together, at the same time. Including athese effects at the appropriate time would require verytailed modeling of each photon emitted from the source, ainteracts in the subject, then in the detector, creating a sithat is ultimately segmented into an image. Presently,would be a very complex and prohibitively time consumitask. As computers expand in capabilities, improvementall aspects of simulated imaging could be included. For nour approach of calculating an image using Monte Catransport techniques and post-processing by applying

FIG. 11. Contrast of the details in the CD phantom as a function of deradius. Each series of points is from a column of details of the same thness. Data from the Fischer Senoscan™ appear as points and the covalues calculated from the simulated image appear as lines: solid linesthe raw Monte Carlo images and dashed lines after the MTF and noisebeen added.


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MTF and a simplified noise model seems to be a reasoncompromise, as seen by the good comparisons of realsimulated images.

Noise in the image, especially for the overall ’texture’the simulations is probably the area that needs the mostprovement. The problem for the simulation is that each stem will have to be analyzed separately since each hadifferent combination of physical, electronic, and processstages leading to noise.

VIII. SUMMARY

Accurate Monte Carlo simulation of complex imaginproblems is possible by using a combination of three vaance reduction techniques: rastering, point detectors, andseparation of the unscattered and scattered componSimulated images from two new mammography systems,Fischer Senoscan™ and the synchrotron based systempared well to real images, both in the level of detail visiblethe images and the calculated contrast of standard detFull 3-D simulation, generating a complete image, shouldable to provide more information to system designers copared to simple pencil-beam simulations.

Now that Monte Carlo has been shown to be able to simlate full mammographic images, the opportunity to study dferent aspects of the imaging system and how they affectfinal image is at hand. Monte Carlo gives the analystability to perform experiments not possible in the lab, fexample, being able to separate photons scattered fromsubject from those scattered in the compression paddlewhatever else is of interest. Researchers will also be abldetermine how material composition information affects timage, just by running different simulations.

One interesting thing that resulted from this study is ththe amount of scatter in synchrotron images is so small, ster can safely be left out of the simulation process. For scning slot systems like the Fischer Senoscan™, even thothe amount of scatter is small compared to conventiomammography systems, the scatter does play an imporole in the image formation process and needs to be mode

ACKNOWLEDGMENTS

Research was carried out in part at the National Synchtron Light Source, Brookhaven National Laboratory, whiis supported by the U.S. Department of Energy, DivisionMaterials Sciences and Division of Chemical SciencMany thanks to Dr. W. C. Thomlinson and Dr. Z. Zhong fallowing this work to be done on beamline X15A. Dr. REugene Johnston of the University of North Carolina, ChaHill, provided assistance in both the synchrotron imagiand Senoscan™ imaging aspects of this study. We thankfor all of his valuable help. Fischer Imaging Corporatiosupplied a great deal of technical information and helpmodeling the Senoscan™. Special thanks to Dr. M. M. Tefor his time and energy in helping us. Mr. Peplow, a doctostudent at the time this work was done, was supported byR. Eugene Johnston, UNC-Chapel Hill, through his UArmy Medical Research and Material Command Breast C

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cer Research Grant. He was also supported by a NucEngineering Education Research~NEER! Grant from the De-partment of Energy, Idaho Operations Office. Monte Cadevelopment and the analysis of the experimental data wperformed on a Sun Ultra 2/200 donated by Sun Microstems, through their Academic Equipment Grant. Mathanks to Sun Microsystems. Thanks also to the referwhose thorough and thoughtful reviews improved this pap

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