# Dose Calculation Algorithms for External Radiation Therapy: An Overview for Practitioners
## 4 Dose Calculation Algorithms for Hadrontherapy
### Relative Biological Effectiveness  
It is well known that slow ions such as alpha particles have a different radiobiological impact at the same absorbed dose as photons. The concept of relative biological effectiveness (RBE) relates the dose from a given type of radiation to a reference quality, typically high-energy photons:  
\[\text{RBE}=\frac{D_{\text{photon}}}{D_{\text{ion}}}\ \Big{|}\ \text{same effect} \tag{8}\]  
There is a complex relationship between RBE and LET, projectile species, dose level, outcome parameter, as well as cell or tissue type. A large database of cell survival experiments can be found in [71].  
Protons, with their comparably low LET, are considered from a radiobiological point of view to be similar to photons, with their RBE values in clinical practice fixed at 1.1. Recently, interest in proton RBE has increased, as rising LET values at the end of the range are typically placed outside of the target due to necessary margins. This might lead to an underestimated effect in OARs [72]. Explicitly considering RBE also shows an effective range increase of proton beams, as the RBE continues to rise after the end of the SOBP [73].  
For heavier ions, the RBE is significantly higher and also varies along the SOBP with respect to the mixed beam field, resulting from fragmentation. Its complex relationship to several input parameters requires explicit RBE modeling to achieve clinically valid outcomes. Several RBE models have been developed and published, with two in current clinical use: the microdosimetric kinetic model (MKM) [74] and the local effect model (LEM) [75]. LEM is used in all European centers as well as in China, whereas MKM is used in all Japanese centers. Without going into detail, both models use different assumptions and result in a different dose scale, so dose prescriptions are not directly comparable [76]. Historically, the MKM did not include a dose-dependence of RBE, so that for high-fraction doses, the RBE is over-estimated, and stated doses are higher, as would be expected for a comparable effect in photon therapy. On the other hand, this model has been in clinical use for 25 years, and has an excellent track record of treating patients with carbon ions [77]. Therefore, even after an updated version of the MKM included dose dependence as a necessary adaptation for PBS [78], the dose scale was retained in order to preserve the significant clinical experience gained in many dose finding studies and clinical routines.  
The LEM, in contrast, was developed directly for PBS as used in the GSI pilot therapy project, and aims to transfer clinical experience from photon therapy. RBE-weighted doses computed by LEM should therefore have the same effect as the same photon dose, but clinical experience in high-fraction doses is limited. Clinical routine still employs the first version of the LEM, whereas the current research version is LEM IV [79]. Recently, RayStation also implemented LEM IV to support helium therapy, and now features LEM I, LEM IV and MKM for the calculation of ion beam doses.  
RBE models in general require data on the spectral composition of the beam, which varies with initial energy and penetration depth. For RBE-weighted analytical calculations, these data were loaded as additional base data, and were also derived from Monte Carlo simulations and validated by measurements. This same spectral information can be derived directly through a Monte Carlo calculation of the treatment field, so the MC code for particle therapy supports a variety of RBE models--both in research versions and the above-mentioned version in clinical use [80,81].  
It should be noted that the RBE-weighted dose calculation is in general non-linear to the beam weights, with important implications for treatment planning, as efficient linear programming is not suitable for these plans.