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*To*: "Hartley, Lyn" <Lyn.Hartley@health.wa.gov.au>, radsafe@romulus.ehs.uiuc.edu*Subject*: Re: Scattering cross sections*From*: David Scherer <scherer@uiuc.edu>*Date*: Tue, 14 Apr 1998 11:51:39 -0500

You asked a few questions about photon scattering and CT contrast: >For a start is it the mass attenuation or absorption coefficient? > >What exactly is a scattering cross section? > >How does all of this enable me to calculate the scatter factor? > >And finally (and prosaically), why does scattered radiation decrease >contrast? Let's start with the last question. As I'm sure you understand, the reason you can reconstruct an object with CT is because different structures within the object attenuate the radiation beam differently. Let's say you have a uniform water bath (CT no.= zero) with one highly attenuating object in it (CT no. = 1000). The scanner recognizes the different CT numbers for these regions because less radiation reaches the detector when the beam passes through the object compared with other projections. Let's say the detector sees 10 mR on a projection without the object and 7 mR on a projection including the object. The difference in transmission is 30 percent. Now we add scatter to the picture. Lets say there is an addition of 10 mR due to scatter to all projectins. Now we see 20 mR on projections without the object and 17 mR on objects with it, a difference of only 15 percent. The net result is a decreased contrast in the reconstructed image. If you have a gamma source this can be dealt with electronically. The scattered photons have a lower energy, so you can count only those photons that match the original gamma ray energy. If you use a polychromatic source, e.g. x-ray tube, you cannot use this trick. Instead most medical scanners solve this problem by another feature of scattered photons: after scattering photons travel in a different direction. The manufacturers mount collimators on the detectors so that only photons that have travelled along a straight path from the original point source will reach the detector. The simplest arrangement is a pencil ray beam and a linear collimator. (That's why the original RMI scanner used this geometry.) It is not much of a leap to guess the collimator design for a fan beam geometry. Let me address your specific questions: 1. The attenuation and absorption coefficients are different things. The attenuation coefficient tells you how much energy fluency is removed from the primary beam. The absorption coefficient corrects this by adding back the energy fluence that is not absorbed but scattered within the medium. If you use a collimated system, scatter is mitigated and the important quantity is the attenuation coeficient. 2. The scattering cross section is the probability that a photon will be scattered by an atom in the medium it passes through. The numerical value of the probability is given by the Kline-Nishina formula, which can be found in almost any nuclear physics or radiation physics text book. Another key word to look for is "Compton Scattering." 3. Predicting the contrast degredation in an uncollimated CT system with a broad spectrum, fan beam source is not a back-of-the-envelope calculation. The scattered photons now have new energies and they can, in turn, be absorbed or scattered in the medium. You can't do it with simple quantities like attenuation coefficient and absorption coefficient. This is a radiation transport problem (a three-dimensional integro-differential equation). Many of the techniques developed for neutron transport can be used with varying success in this case, but most people who perform these calculations use the Monte Carlo technique. It would be simpler to reject the scatter with collimation rather than model it, especially since the scatter does not give you any useful information (with the usual reconstruction algorithms). For more details on CT systems you can look in any number of books on medical imaging or industrial CT. There are books that range from the king of pedestrian-level version I have given to high-speed productions. Which one is best depends on how much detail you need. Hope this helps. Contact me directly if you have more questions. Dave Scherer mailto:scherer@uiuc.edu

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