“As far as we know, our com puter has never had an undetected error.”
Weisert
As m entioned in th e introduction, th e purpose of this study is to establish th e feasibility of an MSGC for m edical imaging, especially m am m ography. A combi nation of com puter sim ulation and experim ents was used. C om puter simulation is a powerful tool, which can be used to model th e experim ental results of m any different set-ups and at a very small cost. The com parison of specific simulation results with experim ental d a ta can show if th e predictions are correct or not. The m odel can th en be extended to predict th e perform ance of a system which is optim ized for a p articu lar application, such as m edical imaging.
4.1
E G S 4
Electron G am m a Shower 4 (EGS4) [32] is a M onte-Carlo program developed to sim ulate the interaction of electrons and photons w ith m a tte r. It is used exten sively b o th in particle physics and in medical physics and has very good docu m entation. It was found not to be ideal for this stu d y for th e following reasons:
• T he physical m odel used for th e tran sp o rt of electron assumes th a t all th e electrons in m a tte r are free. This assum ption works nicely when th e energy
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Chapter 4. Simulation
of th e incoming particles is m uch higher th a t th e binding energy of electrons in m a tte r, and it reduces com puting tim e, b u t it does not give accurate results when th e energy of th e particles th a t are being tracked is com parable w ith th e binding energy of electrons. The program was originally developed for High Energy Physics applications, so this approach is understandable. In recent years th e program has been extended to cater for m any lower energy problems w ith biomedical applications in mind. One of th e additions has been th e th e PR ESTA subroutine, which makes corrections in th e step sizes of th e particle tra n sp o rt, and allows electron tran sp o rt down to 10 keV. But th e present study was concerned w ith showers in itiated by prim ary X-rays w ith energies in th e range from 6 to 20 keV, so even th e modified version of EGS4 is not really applicable.Table
4.1:
Processes tre a tedby ITS
3.0 [34].- E le c tr o n /P o s itr o n In te r a c tio n • E n e r g y lo ss str a g g lin g • E la stic s c a tte r in g
• P r o d u c tio n o f k n o ck -o n e le c tr o n s (6-ray)
• Im p a c t io n iz a tio n follow ed by p r o d u c tio n o f flu o res c en ce p h o to n s a n d /o r A u g e r e le c tr o n s
• P r o d u c tio n o f a n n ih ila tio n ra d ia tio n - P h o to n In te r a c tio n
• P h o to e le c tr ic a b so r p tio n w ith th e p r o d u c tio n o f p h o to e le c tr o n s , A u g e r e le c tr o n s and flu o r e sc e n c e p h o to n s • In c o h e re n t s c a tte r in g w ith th e p r o d u c tio n o f sc a tte r e d
e le c tr o n s
• C o h eren t sc a tte r in g • P air p r o d u c tio n
4.2 ITS
65
• The photoelectric effect, th e dom inant process of photon interaction atlow energies, is sim ulated in EGS4, bu t th e photons in teract only with th e K shells of elem ents. A significant p a rt of this study, th e absorption of 20 keV photons in xenon, could not be sim ulated w ith EGS4 because th e binding energy of th e K shell in xenon is 34.5 keV. A program able to handle L shell interaction was necessary.
• From the relaxation processes after a photoelectric interaction only the fluorescence is sim ulated by EGS4. It generates no fluorescence photons from other shells and no Auger electrons. Auger electrons in th e case of L shell ionization in xenon have initial energy of 5 keV and depending on th e pressure of th e gas th eir range can be significant. Again a program able to handle Auger electrons was necessary.
4 .2
IT S
T he Integrated Tiger Series 3.0 code (ITS) has been developed in SANDIA Labs and is described in its docum entation as “a software package for th e M onte-Carlo solution of linear, tim e independent coupled electron/ photon radiation tran sp o rt problem s, w ith or w ithout th e presence of macroscopic electric and m agnetic fields” [33]. This am ounts to th e same goal as EGS4 b u t th ere are im portant differences in how it is achieved. T he physical m odel of ITS allows th e produc tion and tran sp o rt of th e electron/ photon cascade from 1 GeV down to 1 keV. Table 4.1 gives a brief list of th e processes sim ulated by th e program .
4.2.1 D escrip tion o f th e Program
As th e nam e suggests, th e In teg rated Tiger Series is an incorporation of a num ber of different codes in a single library. The user has to ru n a program called th e
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Chapter 4. Simulation
UPDATE em ulator to extract th e modules needed. The same program can be used to modify th e FORTRAN code by inserting or deleting lines. There are th ree m ain options to be chosen according to th e geom etry of th e problem in hand: T I G E R A code for one-dimensional problem s m ade of layers of different m a te
rials.
C Y L T R A N A three-dim ensional description of particle trajectories w ithin an axi-sym m etric cylindrical geometry.
A C C E P T The option used in this work. It is a general three-dim ensional tra n s p o rt code th a t uses the com binatorial geom etry scheme in which th e vol umes of m aterial inserted in th e process are built up of prim itive bodies, like a sphere, a box or a cone. These bodies can then be combined, using th e union, th e difference or th e intersection between bodies, or com bination of bodies, to create com plicated geometries [35].
O ther options th a t can be combined w ith th e three m ain ones are th e M-codes option for macroscopic electric a n d /o r m agnetic fields, th e P-codes option for low energies and m achine com patibility options (VAX, IBM or CRAY).
T he P-codes give an improved modelling b o th of th e ionization process and th e subsequent relaxation processes and were always used in this study. W ith the P option, ITS is a more suitable program th a n EGS4 for simulation of th e absorp tion of low energy X-rays in MSGCs, because there is more detailed modelling of th e photoelectric effect, fluorescence and Auger electron emission. Photoelectric interactions are sim ulated for all K, L, M and N shells as long as th e binding en ergy of th e shell is above 1 keV. A fter th e photoelectric interaction, fluorescence and Auger emission are sim ulated, taking into account electron transitions from all th e above shells until the atom retu rn s to its ground state.
No published flow chart of th e program has been found in th e literatu re or in its m anuals, and th e comments th a t exist w ithin the code are very brief. The
4.2 ITS
67
authors of th e code (particularly R .P. Kensek of SANDIA labs) were very willing to reply to enquiries and give ad hoc explanations of p articu lar points. They suggested th a t one of th e best accounts on modelling of ITS is to be found in th e docum entation of a similar program called ETRAN [36]. Figure 4.1 shows a flow chart of th e operation of th e ITS code, as utilised in this p ro ject, in an a tte m p t to fiU this gap.The cross sections for all th e processes Hsted in Table 4.1 are generated by a program called XGEN before th e m ain ru n of th e M onte-Carlo. T he in p u t files used for XGEN and ITS are given in A ppendix A.
4.2.2
H ow ITS Works
All M onte-Carlo simulation program s m ake use of random num bers to sample various quantities—like energy deposition—from known distributions. These dis tributions depend on th e energy of th e particle and have to be re-calculated every tim e th e energy of the particle changes. ITS, which Kensek has classified as a “Class I” code, pre-calculates a table w ith electron tran sp o rt step sizes for a num ber of different energies. It also pre-calculates samphng distributions based on these step sizes. T h at saves a lot on com puting tim e, because for a given electron energy th e program looks up th e appropriate step size from th e table and th en samples th e pre-calculated distributions th a t correspond to th a t step size. The disadvantage of this m ethod is th a t th e step size cannot be changed if necessary, for instance when a boundary betw een zones is crossed. In this case ITS deposits energy in b o th zones proportionally to th e length of th e electron track in each one of them . “Class II” codes, like EGS4, sample a distance for each step and th en calculate th e necessary distributions based upon this distance. This is more tim e consuming, b u t m ore flexible.