3 - Fractionation with Multiple Organs-at-Risk

Summary

This chapter extends the formulation from the previous chapter by including multiple organs-at-risk. The four analytical solution methods from the previous chapter are generalized to this case. Again, the structure of the solution depends on the relative values of the LQ dose-response parameters of the tumor and the organs-at-risk. The four solution methods are only adequate in two of the three possibilities that can arise regarding these relative parameter values. While these two possibilities are natural extensions of similar scenarios from the previous chapter, the third one is unique to this chapter. The chapter thus includes a fifth solution method to tackle this third possibility. That approach relies on reformulating the quadratically constrained quadratic program as an equivalent linear program with two variables. Clinical insights are obtained via numerical experiments.