Evaluation of indirect damage and damage saturation effects in dose–response curves of hypofractionated radiotherapy of early-stage NSCLC and brain metastases

Abstract

Background and purpose: To investigate the possible contribution of indirect damage and damage saturation to tumour control obtained with SBRT/SRS treatments for early-stage NSCLC and brain metastases. Methods and materials: We have constructed a dataset of early-stage NSCLC and brain metastases doseresponse. These data were fitted to models based on the linear-quadratic (LQ), the linear-quadratic-linear (LQL), and phenomenological modifications of the LQ-model to account for indirect cell damage. We use the Akaike-Information-Criterion formalism to compare performance, and studied the stability of the results with changes in fitting parameters and perturbations on dose/TCP values.Results: In NSCLC, a modified LQ-model with a beta-term increasing with dose yields the best-fits for a/ b = 10 Gy. Only the inclusion of very fast accelerated proliferation or low a/b values can eliminate such superiority. In brain, the LQL model yields the best-fits, and the ranking is not affected by variations of fitting parameters or dose/TCP perturbations.Conclusions: For a/b = 10 Gy, a modified LQ-model with a beta-term increasing with dose provides better fits to NSCLC dose-response curves. For brain metastases, the LQL provides the best fit. This might be interpreted as a hint of indirect damage in NSCLC, and damage saturation in brain metastases. The results for NSCLC are strongly dependent on the value of a/b and may require further investigation, while those for brain seem to be clearly significant. Our results can assist in the design of improved radiotherapy for NSCLC and brain metastases, aiming at avoiding over/under-treatment.

Volumetric reduction of brain metastases after stereotactic radiotherapy: Prognostic factors and effect on local control

“…The formulas for these models are as follows: where n is the number of fractions, d is the dose per fraction, α/γ is 648 Gy 2 , δ is 0.14, and G( χ ) = (2/ χ2 )( χ -1+ e -χ ). 2,[14][15][16][17] In the univariate analysis, we used the Pearson correlation coefficient (r) to evaluate the correlation between the GTV parameters themselves, and we used the Spearman's correlation coefficient to evaluate the correlation between the clinical (treatment) parameters and the GTV parameters. When either coefficient for the candidate prognostic factors was >0.40 in the univariate analysis, we selected only one variable for the multivariate analysis.…”

“…It is highly debated which of the following models should be chosen when performing SRT for brain metastases: LQ: α/β = 10; LQ: α/β = 20; LQC: α/β = 12; or LQL: α/β = 10. 2 , 14 , 15 , 16 , 17 , 18 LQ: α/β = 10 is well suited for stereotactic body radiotherapy for early‐stage lung cancer. 14 However, it is not appropriate for late‐stage lung cancer with brain metastases, which are best treated using LQL: α/β = 10.…”

“…Doses were stratified according to the biological effective dose (BED). It is a matter of debate which formula should be used to calculate the BED for SRT for brain metastases 2 , 14 , 15 , 16 , 17 , 18 ; hence, we used four models: two linear‐quadratic (LQ) models: α/β = 10 and α/β = 20; the linear‐quadratic cubic (LQC) model: α/β = 12; and the linear‐quadratic linear (LQL) model: α/β = 10. The formulas for these models are as follows:…”

“…where n is the number of fractions, d is the dose per fraction, α/γ is 648 Gy 2 , δ is 0.14, and G( χ ) = (2/ χ2 )( χ ‐1+ e ‐χ ). 2 , 14 , 15 , 16 , 17 …”

A biomathematical model of tumor response to radioimmunotherapy with $α$PDL1 and $α$CTLA4

“…Several effects contribute to this: re-oxygenation (which leads to radiosensitization) depending on the dose per fraction [36], saturation [37], or vascular damage [15]. As those effects apply mostly to the LQ model's, yet it is still not known how much, we have checked whether a simple ad hoc modification of the quadratic term can change the goodness of the fit [38]:…”