Revisiting the formalism of equivalent uniform dose based on the linear-quadratic and universal survival curve models in high-dose stereotactic body radiotherapy

Abstract

Purpose: To examine the equivalent uniform dose (EUD) formalism using the universal survival curve (USC) applicable to high-dose stereotactic body radiotherapy (SBRT).

Materials and methods: For nine non-small-cell carcinoma cell (NSCLC) lines, the linear-quadratic (LQ) and USC models were used to calculate the EUD of a set of hypothetical two-compartment tumor dose–volume histogram (DVH) models. The dose was varied by ±5%, ±10%, and ±20% about the prescription dose (60 Gy/3 fractions) to the first compartment, with fraction volume varying from 1% and 5% to 30%. Clinical DVHs of 21 SBRT treatments of NSCLC prescribed to the 70–83% isodose lines were also considered. The EUD of non-standard SBRT dose fractionation (EUDSBRT) was further converted to standard fractionation of 2 Gy (EUDCFRT) using the LQ and USC models to facilitate comparisons between different SBRT dose fractionations. Tumor control probability (TCP) was then estimated from the LQ- and USC-EUDCFRT.

Results: For non-standard SBRT fractionation, the deviation of the USC- from the LQ-EUDSBRT is largely limited to 5% in the presence of dose variation up to ±20% to fractional tumor volume up to 30% in all NSCLC cell lines. Linear regression with zero constant yielded USC-EUDSBRT = 0.96 × LQ-EUDSBRT (r2 = 0.99) for the clinical DVHs. Converting EUDSBRT into standard 2‑Gy fractions by the LQ formalism produced significantly larger EUDCFRT than the USC formalism, particularly for low α/β ratios and large fraction dose. Simplified two-compartment DVH models illustrated that both the LQ- and USC-EUDCFRT values were sensitive to cold spot below the prescription dose with little volume dependence. Their deviations were almost constant for up to 30% dose increase above the prescription. Linear regression with zero constant yielded USC-EUDCFRT = 1.56 × LQ-EUDCFRT (r2 = 0.99) for the clinical DVHs. The clinical LQ-EUDCFRT resulted in median TCP of almost 100% vs. 93.8% with USC-EUDCFRT.

Conclusion: A uniform formalism of EUD should be defined among the SBRT community in order to apply it as a single metric for dose reporting and dose–response modeling in high-dose-gradient SBRT because its value depends on the underlying cell survival model and the model parameters. Further investigations of the optimal formalism to derive the EUD through clinical correlations are warranted.