The Stopping Power of Frozen Water

In my last blog entry I commented on stopping powers of fast ions in medical physics, and announced the libdEdx library. (Stopping powers describe the energy loss of fast charged particles in material, thereby transferring energy to the target matter.) Stopping powers directly relate to the deposited dose, but there are plenty of more subtle effects where they may or may not have a profound influence:

• Range of ions in matter. Often the mean excitation energy (not to be confused with the ionization potential or w value...) in the Bethe-equation is used as a macroscopic fitting parameter for the range of ions. Effects such as an primary particle dependent I-value are reported, even this is unphysical. Discussion is going on what the I-value for water actually is covering the 75 to 85 eV interval. PSTAR claims 75 eV. More recent studies seem to agree on a value close to 80 eV.
  
• Ionization chambers rely on a solid assertion of stopping power ratios, since these detectors measure dose to air. In order to translate this to dose to water, you should know the particle spectrums and the stopping power ratio of water to air (see e.g. IAEA TRS-398 dosimetry protocol, so far one of the best out there, even though it has its flaws...) Or, you can use a parametrization, as Armin tries to show in our recent yet unpublished paper (pre-print).
  
• Detector and biology response models such as the Katz or LEM model rely on the stopping power of ions. How large these effects are, is still to be investigated, and is something we want to look at using libdEdx and libamtrack.

There may be many more applications, whereas the first two mentioned here are quite well researched. Frustrating enough, if you have to calculate e.g. the stopping power ratios for a given particle spectrum, you have to rely on the ICRU49 (PSTAR/ASTAR) table and the ICRU73, and they are not calculated consistently. Ok, the errors may be minor for practical dosimetry purposes, but thinking of primary standard laboratories such as PTB in Braunschweig or NPL in London who try to increase the precision at least one order of magnitude, you may get into difficulties.

How can this be, don't we have a large data base on experiments for various ions on various targets? Well, yes, for some ion/target combination, but not for all of them. Peter Sigmund from University of Southern Denmark, (now Professor Emeritus), once showed a very nice matrix of combinations at our 4th Danish Workshop, where all the experimental gaps are.
Even worse is the situation for compounds, here no or very little data are available.

So, we decided to take this up a the 5th Danish Workshop on Particle Therapy, in order to sort out the field, and give the research some direction.
This brings me back to the title of this blog entry: The workshop was scheduled to take place tomorrow (30th November) in Aarhus, but exactly due to the stopping power of frozen water, we had to cancel it. Several key persons were stuck in various airports and could not make it because of snowstorms.

Now... this massive amount of snow in Aarhus at this time of the year is not common, and frankly, I wonder if I am going to make it to work tomorrow. Instead, I would like to invite you - dear reader of this blog - to stop a few minutes with me and silently enjoy the scenery below, accompanied with a piece of J.S. Bach.

One Stopping Power Library to Rule Them All: libdEdx

Stopping powers describe the energy loss of charged particles traversing matter. In particle therapy, stopping powers are an essential ingredient for calculating the dose distribution of ion beams.

A direct way of calculating the stopping power is using the Bethe equation. However, this equation requires a good knowledge of the ionization potential (in particle therapy jargon: "the I-value") and for compounds this value is pretty ill researched. The I-value can be found experimentally, but there are only few experimental data available for compounds relevant for particle therapy, such as various tissue types and even for water. Our postdoc. Armin Lühr has recently submitted a paper where he takes a closer look on these issues which is available on the archive: http://arxiv.org/abs/1010.5356

Several programs provide stopping powers, either as analytic calculations or inter/extrapolated experimental data. The list below may be incomplete, but these are the codes I have been in touch with so far:

• ESTAR: for electrons. (Fortran77)
• PSTAR: for protons. (Fortran77)
• ASTAR: for alpha particles (Fortran77)
• MSTAR: for alpha particles and heavier ions up to Z=18. Basically MSTAR is scaling ASTAR data, where the scaling factors are fitted to experimental data. (Fortran77)
• ATIMA: code developed by GSI. (Java wrapping a Fortran core)
• TRIM/SRIM: Application which can simulate any ion on any compound.

And various tables provided by the ICRU:

• ICRU 49: proton data and alphas, equivalent with PSTAR/ASTAR.
• ICRU 73: ions heavier than helium, old version
• ICRU 73: new version after errata, quite similar to MSTAR, even if calculated differently.

and in summary they don't agree too well at lower energies (say below 10 MeV/u).

Nonetheless: from an application developer point of view this leaves you in a dilemma of choosing the proper code for your application, and most likely we will see more updates, since the issues are not solved yet with the erratum of the ICRU73.

In addition, from a technical point of view most stopping power codes are not written in convenient ways which allows a clean integration into your application. This is a common thing which happens when physicists develop code: the code will always be optimized to work nicely on the developers computer and fulfill their specific needs. Platform portability, an API, and install scripts following de-facto standards are mostly absent.

This is why we started the development of libdEdx.

libdEdx is meant to be a platform independent stopping power library which contains multiple tables to choose from, and can be extended with additional algorithms/tables. Currently libdEdx includes ESTAR,PSTAR,ASTAR,MSTAR and ICRU73 data as well as an implementation of the Bethe-equation akin to that found in SHIELD-HIT.
The material database is based on the extensive ICRU set found in the ESTAR table, and using Braggs additivity rule libdEdx can extend the MSTAR/ICRU73 data set to cover the ESTAR material list.

libdEdx comes along with an installer based on cmake, and the first official release should be able to run on Windoze just as well as Unix/Posix/Linux compliant platforms.

Surely, Geant4 also offers a range of stopping power tables to choose from, but you do not want to install entire Geant4 just to access the stopping power values.

Our bachelor student Jakob Toftegaard (who very conveniently has a background in physics and computer science) did most of the coding. A very early experimental pre-release is available on sourceforge, but if you want to experiment with it and even contribute you can also grab the most recent version from the SVN repository.

P.S.: Armin and David will present libdEdx on the MC2010 conference in Stockholm on the 9th to the 12th November. Posters can be found here.