In this project, the content of an experimental database will be analysed and categorized in terms of radiation quality, tissue types and number of data points and dose levels in each experiment. In addition, the database is divided into seven sub-sets, each containing datapoints with (α/β)$$

1. Introduction

1.1 RBE

1.2 RBE Modelling from the Linear Quadratic Model

1.3 Linear Energy Transfer

1.4 The Rorvik Model

2. Methods

3. Results

4. Discussion and outlook

where D$$

where α and β are the LQ-model parameters. The first term in the exponential describes the initial slope of the cell survival curve, that is, the linear component caused by single track events. The second term describes the quadratic component caused by two-track events. The parameters are found by fitting a regression to experimental data. The ratio (α/β) is widely used to describe the fractionation sensitivity of different tissue types.

Phenomenological models are based on empirical data from in vitro proton irradiation of various cell lines and utilize the LQ-model with cell inactivation as the biological endpoint. The majority of the RBE models that have been developed for proton therapy belong to this group of models. They are all based on the same mathematical reasoning, starting with the fact that the survival fraction for proton radiation and the reference photon radiation are equal:

where SF(D$$

where D$$

Now, the RBE of the proton beam is made a function of the LQ-model parameters and physical proton dose. In general, the RBE dependency on dose gives highest RBE for low doses and decreasing RBE with increasing doses. By evaluating Equation (5) at the upper and lower proton physical dose limits we get two equations for RBE values, one for very low doses, and one for very high doses:

Both the equations for the extreme RBE values are dependent on only one of the LQ-model parameters. Thus, they can be regarded as independent functions describing the extreme RBE at low and high doses. We can use equations (6) and (7) to reformulate equation (5) with respect to RBE$$

where (α/β)$$

The RBE$$

The code, along with the original database and an edited version needed to run the code are availeble here: project.tar.xz

* Figure 1: Range and distribution of (α/β)$$ _{x}, LET$$_{d} and RBE$$_{max}. *

The regression lines for RBE$$

* Figure 2: Regression lines for RBE$$ _{max} vs LET$$_{d}. *

Figures 3-9 show the regression lines, plotted together with the Rorvik-lines. The RÃ¸rvik-lines were obtained from Equation 9, using the mean-values of the (α/β)$$

We see that the Rorvik-line lies above the regression line for most values of LET$$

As an extention of this project, it would be interesting to use smaller intervals of (α/β)$$