ESTRO 2024 - Abstract Book

S3509

Physics - Dose prediction, optimisation and applications of photon and electron planning

ESTRO 2024

2 + Φ -1 (1-NTCP) × SD(E

d true = -½α/β + √[(½α/β + d p )

p ) / (n f × β)]. (4)

For SD(E), assuming that β varies with α (i.e. α/β = constant, SD(β)=SD(α )), using propagation of errors on Eq.3 gives:

2 × SD(d) 2 + (d×(1+d/(α/β))) 2 × SD(α) 2 ], (5)

SD(E) = n f × √[(α+2αd/(α/β))

Similar expressions exist for cases where SD(β)=0 or where β varies independently from α. Combining Eq.4 and Eq.5 gives us d true as function of d p , α , β, SD(d p ), and SD(α).

For clarity and validation, we simulated dose-effect studies using a Monte-Carlo approach. Dose and sensitivity values are sampled from their means and SDs for 10000 patients and Eq.3 is used to determine E for each patient. From the resulting distribution of E’s, the threshold E true that separates worst NTCP% cases from the rest is detected, which subsequently yields d true by inversing Eq.1. The simulations will be compared to Eq.1 and Eq.4.

Results:

In the calculations, default SD(d p )=10%, which was estimated from simulating the effect of dosimetric and geometric uncertainties on critical doses for OARs in our hypo and regularly fractionated clinical plans. Default α =0.05/Gy, α/β=3Gy, and SD(α)=20% were estimated from the published data that could be found. In Fig.1, simulated α vs D p plots for three different scenarios are compared with Eq.1 and Eq.4. Fig.1a: Without variation in radio-sensitivity, only dose will determine whether a patient will develop toxicity and both recipes predict the same d true at the mean α . Fig.1b: When variation in α is added, patients with higher sensitivity need less dose to yield toxicity (and vice versa), tilting the border between toxicity yes/no. However, both recipes still predict the correct d true because dose variation SD(d p ) is dominating SD(E). Fig.1c: When β varies with α, SD(α) becomes relevant for SD(E), the border becomes more diagonal, and Eq.1 underestimates the correct d true because an extra margin is needed to cover for the radio-sensitivity uncertainty.