Conceptos de juventud y de identidad

establish a dependency between the usage of a proton beamlet and the accuracy with which it is simulated. This can be achieved, for example, by creating an iterative system that calculates the optimization matrices without full accuracy, then optimizes the plan and keeps adding more histories to the beamlets depending on their assigned weight until the intended accuracy in a given region is reached. Such a system has already been proposed by Ma et al. [Ma+14]. A different option that has not yet been proposed to my best knowledge is to realize a hybrid ADC-MC system. In such a system, heterogeneity indices could be employed to select the beamlets in which ADC would perform well and only simulate the others with GPU-MC. In this case, the margin employed for range uncertainty would be position dependent as it would depend on which beamlets were calculated with ADC and which with GPU-MC. If robust optimization is intended with the hybrid system, dose-influence matrices could be generated forcing the beamlets generated with ADC to be recalculated in wider error scenarios than the ones calculated with GPU-MC. Such system would be beneficial in sites like head and neck, where some beamlets traverse fairly homogeneous tissues, while others do not. Of course, the most effective solution to improve the computational efficiency is to simply employ more GPUs.

In summary, gPMC is a good and flexible candidate to increase dose calculation accuracy routinely in the clinic.

8.2

Project 2: LET-based optimization

The clinical application of the LET-based biological optimization presented in chapter5

is intimately dependent on the clinical translation of GPU-MC for IMPT planning. In this case GPU-MC simulations are again encouraged mainly by the higher calculation accuracy, however, this is more important for LET because only recently analytical calculation algorithms have modeled the lateral LET distribution [Mar+16; San+16;Hir+18]. In this project a method to cope with the large biological uncertainties present in proton therapy was proposed, leveraging the well established proportionality1between the biological effect of a radiation field in a given location and the quantity LET×D to reduce the potential impact of the field in OARs. This method does not reduce the biological uncertainty globally, but it does reduce its potential effects locally, where they might matter the most.

The ultimate goal however, would be to exactly predict the biological impact of the field through the RBE. Until that goal is achievable (if ever), employing surrogates to take the impact into account in a conservative manner can improve clinical outcomes, reducing toxicities in OARs. The advantages of employing LET×D as surrogate are that (1) it is a

linear function of the fluence, allowing the application of well-known optimization algorithms, (2) it is readily available from MC simulations and recently from analytical calculations [Hir+18] and (3) it can be interpreted as the biological extra effect produced by elevated LET, to first approximation.

Robust optimization with range uncertainties has similar consequences for the final plan as LET×D-based optimization. The LET×D distribution is dominated by the Bragg peak present in the dose distribution, but the product with LET makes the peak position sit at slightly deeper depth. Because the high LET×D is slightly beyond the Bragg peak, the prioritized optimization penalizes beamlets that aim directly to an OAR, favoring those that deliver the dose to the target borders with the lateral profile in sensitive regions. This is also what robust optimization with range uncertainties does, as the lateral profiles are not sensitive to small shifts in the Bragg peak depth. This realization was confirmed in [Gia+17], observing that robust optimization with range uncertainty significantly lowered the median LET in OARs, although not as efficiently as a dedicated term dependent on LET×D in the objective function. A more involved analysis by Unkelbach and Paganetti on robust treatment planning with physical and biological uncertainties can be found in a recent publication [UP18].

The expected dependency on LET is not the only base of RBE models that have been proposed, as cited in section2.4.4[SS04;SS06;Ste+11;Ste+15;Fri+13;Fre+11;Car+08]. However, the same expected dependency of RBE on high ionization areas might be parame- terizable on other quantities. An alternative surrogate to LET is to employ the proton stop positions as this distribution should be correlated to the LET. This tally is also supported in gPMC (as reported in6in section3.1.2). No studies have been published so far on this topic to my best knowledge, but it could be used to drive high LET areas out of OARs. The theoretical advantage of this quantity is that it does not suffer the spikes the LET distribution presents when scored with MC methods in a voxelized geometry. Nevertheless, the quantity LET×D employed in this project is more robust to those spikes as the low dose value in the spikes regions lowers their impact.

In any case, GPU-MC would offers the necessary flexibility to score multiple quantities in a realistic manner without having to develop a dedicated algorithm for it, allowing systematic comparisons of different candidates. Ultimately, it would allow clinical translation of such techniques.