Session Item

Currently, types of objective functions to include LETdxDose (LD) in proton therapy planning are limited. A reason is that, as the effect of LET is still a topic of ongoing research, accepted threshold values to prevent side effects are not as readily available as they are for dose. Nonetheless, there is the danger of high LD values in organs at risk (OAR) leading to adverse effects, even if they only occur in a small volume[1] . Thus, we investigated a new type of objective functions. Contrary to previously introduced objectives, it considers the spatial orientation of the voxels.  The aim is to smooth the LD distribution and hence prevent hotspots.

We used convolution kernels for edge detection to obtain undesired structures of the LD distribution and consequently minimized them with a p-norm. The approach was tested with cases from the CORT [2]  dataset. MatRad [3] was used to obtain the dose and LD influence matrices and optimization was done in python. To compare the effects, optimization was performed with or without objective functions to minimize or smooth LD.

Table 1 shows the results for the OARs for the prostate case and the Laplace kernel.  Using objective functions for smoothing, the total variance was reduced by more than factor 3. Moreover, as Figure 1 shows, smoothing led to a reduction of the highest values. For the rectum this effect was stronger than by minimization of LD.

The introduced type of objective functions can smooth the LD distribution and consequently reduce hotspots. For future planning this enables the systematic avoidance of adverse effects. Due to the linearity of convolution, and the possibility to calculate it as a matrix multiplication, the presented type of functions is easy to handle in optimization. By including knowledge of the expected LD distribution for a specific case, a customization of the kernel might be beneficial.

[1] Yang Y, et al. (2022): Exploratory study of seed spots analysis to characterize dose and linear-energy-transfer effect in adverse event initialization of pencil-beam-scanning proton therapy. Medical physics 49 (9), DOI: 10.1002/mp.15859 .
[2] Craft D, et al. (2014): Shared data for intensity modulated radiation therapy (IMRT) optimization research: the CORT dataset, GigaScience, 3(1), DOI: 10.1186/2047-217X-3-37
[3] Wieser HP, et al. (2017): Development of the open-source dose calculation and optimization toolkit matRad. Medical physics 44 (6), . DOI: 10.1002/mp.12251