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\begin{document}                                                        
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\postertitle{\sf ESTIMATION OF TISSUE AND DOSE DEPENDENT RBE VALUES}
{\sf FOR HEAVY CHARGED PARTICLE TUMOR THERAPY}
{\sf M. Scholz$^{1,2}$}
{\sf $^1$Gesellschaft f\"ur Schwerionenforschung (GSI), Biophysik,  D-64291 Darmstadt}
{\sf $^2$Radiologische Klinik der Universit\"at Heidelberg, D-69120 Heidelberg}
\sf \small 
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\sf{\bf INTRODUCTION} 
\begin{list}{$\bullet$}{\leftmargin1mm \itemsep3mm \parsep0mm \labelsep2mm}
\item Relative biological efficiency (RBE) of particle beams compared 
to photons is a complex function depending on the particle type, field 
geometry, dose level and the biological endpoint.
\item Optimal application of charged particles in tumor therapy requires to 
take into account tissue and dose dependent RBE values.
\item Due to the complex dependencies, estimation of RBE cannot be based on 
experiments alone, but requires a biophysical model.
\item Most conventional approaches cannot be applied in the case of charged 
particle fields, because the are based on {\bf interpolation} between data 
sets (i.e. known $\alpha$ and $\beta$ values for different radiation 
components).
\item Systematics of RBE as function of particle type and beam energy is 
known with sufficient accuracy only for {\em in-vitro} systems, but not for 
tissue endpoints.
\end{list}
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\epsfig{file=alphabeta1.ps,width=60mm,height=75mm}
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Fig. 1: Dependence of predicted RBE values on the $\alpha$ and $\beta$ 
values of the photon dose response curves. Calculations are performed for the 
mid peak of an extended Carbon Bragg peak from 6-10 cm penetration depth.
\normalsize
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\sf{\bf PROPOSED SOLUTION:}\\
\begin{list}{$\bullet$}{\leftmargin1mm \itemsep3mm \parsep0mm \labelsep2mm}
\item Biophysical model, based on track structure, photon dose response 
curves and target size
\item Model predictions can be checked against large sets of experimental 
{\em in-vitro} data
\item Essential feature of the model: RBE is expected to be mainly 
determined by the shoulder of the photon dose response curve, i.e. the 
$\alpha/\beta$-ratio; absolute values of $\alpha$ and $\beta$ are of minor 
importance (Fig. 1)
\item Dependence on $\alpha/\beta$-ratio allows predictions of RBE even in 
the case of normal tissue response, where absolute values of $\alpha$ and 
$\beta$ are generally not known. 
\item Consistency of the model calculations can be checked by comparison 
with animal data for neutron irradiation, if secondary charged particle 
recoil spectra of neutrons are known. 
\end{list}
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Fig. 2: Comparison of model predictions with experimental data for normal 
tissue reactions in animals. 
\normalsize
}
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{\bf RESULTS:}
\begin{list}{$\bullet$}{\leftmargin1mm \itemsep3mm \parsep0mm \labelsep2mm}
\item Comparison of model predictions with experimental data for normal 
tissue complications in animals shows reasonable agreement.
\item Model has been used to estimated effective dose profiles for different 
combinations of $\alpha/\beta$-ratios for tumor and normal tissue, 
respectively. (Fig. 3)
\item Calculations are based on doses isoeffective compared to 2 Gy photon 
irradiation in the tumor volume between 6 and 10 cm penetration depth
\item Estimated RBE values for the tumor: RBE=2 for 
$(\alpha/\beta)_{Tumor}=10Gy$ and RBE=4 for $(\alpha/\beta)_{Tumor}=3Gy$
\item Gain factors calculated on the basis of effective dose and RBE 
emphasize in particular benefit in the case of small 
$(\alpha/\beta)_{Tumor}$-ratios (see Table below). 
\end{list}
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Fig. 3: Calculated physical (top) and effective dose profiles (middle and 
bottom) (4cm extended carbon peak) for different $\alpha/\beta$-ratios 
for tumor and normal tissue.
}
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Fig. 4: Schematic view of the physical dose profile and its composition from 
individual Bragg peaks (top) and expected dose profiles for biological 
isoeffects in the tumor region for different $\alpha/\beta$-ratios of the 
tumor tissue.
}
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\[ TGF = \frac{(Phys. Dose * RBE)_{Tumor}}{(Phys. Dose * RBE)_{Normal~T.}} \]
\\
\begin{tabular}{|c||c|c|c|} \hline
~& \multicolumn{3}{|c|}{\rule[-2mm]{0mm}{6mm} $(\alpha/\beta)_{Tumor}$} \\ \hline 
\rule[-2mm]{0mm}{6mm} $(\alpha/\beta)_{Normal~T.}$ & 
\hspace{3mm} 3 \hspace{3mm} & \hspace{3mm} 6 \hspace{3mm} &
\hspace{3mm} 10 \hspace{3mm} 
\\ \hline \hline
\rule[-2mm]{0mm}{6mm} 3 & 2.51 & 1.65 & 1.31 \\ \hline
\rule[-2mm]{0mm}{6mm} 6 & 3.47 & 2.12 & 1.65 \\ \hline
\rule[-2mm]{0mm}{6mm} 10 & 4.13 & 2.57 & 1.98 \\ \hline
\end{tabular}
\end{center}
\begin{center}
\[ BGF = \frac{RBE_{Tumor}}{RBE_{Normal~T.}} \]
\\
\begin{tabular}{|c||c|c|c|} \hline
~& \multicolumn{3}{|c|}{\rule[-2mm]{0mm}{6mm} $(\alpha/\beta)_{Tumor}$} \\ \hline 
\rule[-2mm]{0mm}{6mm} $(\alpha/\beta)_{Normal~T.}$ & 
\hspace{3mm} 3 \hspace{3mm} & \hspace{3mm} 6 \hspace{3mm} &
\hspace{3mm} 10 \hspace{3mm} 
\\ \hline \hline
\rule[-2mm]{0mm}{6mm} 3 & 1.52 & 1.00 & 0.79 \\ \hline
\rule[-2mm]{0mm}{6mm} 6 & 2.10 & 1.32 & 1.00 \\ \hline
\rule[-2mm]{0mm}{6mm} 10 & 2.50 & 1.56 & 1.20 \\ \hline
\end{tabular}
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~\vspace{5mm} \\ 
CONCLUSION:\\
\sf
\begin{list}{$\bullet$}{\leftmargin5mm \itemsep1mm \parsep0mm \labelsep2mm}
\item The model is able to predict RBE values for biological endpoints {\em 
in vitro} and {\em in vivo}. It will thus be used for estimation of 
clinically applicable RBE values for the treatment planning.
\item According to the model, RBE is expected to be determined mainly by the 
$\alpha/\beta$-ratio of the endpoint under consideration. Experimental 
evidence supporting this hypotheses comes from investigations using repair 
deficient cell lines as well as from clinical experience, where late effects 
show higher RBE than acute effects.
\item As the estimation of RBE values demonstrates, 
significant variations of RBE are expected depending on the specific 
conditions (tissue type, position in the field etc.). Therefore it is not 
adequate to use a single RBE value for all conditions.
\end{list}
\end{minipage}
\end{document}                                                          

