Kansas City University, Kansas City, USA

*Corresponding Author: Glenn C Ma, Kansas City University, Kansas City, MO 64106, USA; Email: [email protected]

Received Date: September 18, 2023

Publication Date: October 18, 2023

Citation: Ma GC. (2023). Effect of Radiobiological Model Parameterization on Radiotherapy Dose Conversion. Mathews J Cancer Sci. 8(3):44.

Copyright: Ma GC. © (2023)

ABSTRACT

The parameterization of radiobiological models is essential to the conversion of the absorbed dose to biological effective dose (BED) and equivalent dose in 2 Gy fractions (EQD₂) for clinical radiotherapy applications. In this work, we investigated the uncertainties of the linear quadratic (LQ) model parameters and their effect on the conversion of absorbed dose to BED and EQD₂.

The LQ model parameters were fitted using a random sampling method for two experimental datasets, the melanoma and non–small-cell lung cancer (NSCLC) cell lines. Depending on the dose range used in the fitting process, the parameters for the LQ model were α = 0.13 Gy, α/b =2.35 Gy for the dose range 0 – 5.5 Gy and α = 0.22 Gy, α/b = 5.91 Gy for the dose range 0 – 10 Gy for the melanoma survival curve while for the NSCLC cell line, α = 0.33 Gy, α/b = 8.81 Gy for dose range 0 – 6.2 Gy and α = 0.47 Gy, α/b = 27.9 Gy for dose range 0 – 15 Gy, respectively. As a result, the BED and EQD₂ values were converted, based on these LQ parameters differed by up to 100% for a 5-fraction x 10 Gy/fraction hypofractionated dose scheme. It is concluded that radiobiological models should be parameterized based on the dose range and treatment fractionation to reduce the uncertainty of BED and EQD₂ conversion.

Keywords: Radiation therapy, radiobiological modeling, linear-quadratic (LQ) model, model parameterization, biological effective dose (BED), equivalent dose in 2Gy fractions (EQD₂)

INTRODUCTION

Radiobiological models are useful tools in the evaluation of therapeutic effects of different radiation treatment doses and fractionation schemes. In conventional radiation therapy the differential response between normal and cancerous tissues is maximized with a clinically achievable treatment dose and fractionation [1,2]. Recent advances in radiotherapy equipment and treatment techniques have also resulted in a paradigm shift from conventionally fractionated radiation therapy (CFRT) that employs small daily doses (1.8 - 4Gy) to hypo-fractionated radiation therapy (HFRT) or stereotactic body radiotherapy (SBRT) that employs ablative doses (8 - 30Gy/fraction). SBRT is an alternative to surgery or CFRT for some patients with early stage, localized disease [3-5]. For example, SBRT has been used for primary and metastatic lung and liver malignancies with superior local control and normal tissue toxicities [6-12].

The linear quadratic (LQ) model has been widely used in radiobiological modeling for both radiation research and clinical applications [13,14]. It approximates clonogenic cell survival data with two simple parameters α and b to determine the relative contributions from the linear and quadratic components of the cell survival curve, which have been related to radiation killing due to double and single strand DNA breaks [15]. It gives a good description of the low-dose portion of the cell-survival (the shouldered response) curve for CFRT but over predicts the potency and toxicity for SBRT due to its continuously bending curvature with increasing doses [16-18].

In this work, we investigated the uncertainty of the LQ model parameterization for different dose ranges and its effect on the conversion of absorbed dose to biological effective dose (BED) and equivalent dose at 2Gy fractions (EQD₂) that are used in clinical trial designs and clinical outcome studies [13,14]. A random sampling method is used to fit the LQ model for two experimental datasets, the melanoma and non–small-cell lung cancer (NSCLC) cell lines. For this purpose, a Python program is developed to read the experimental data and to calculate the cell survival based on the LQ model. Model parameters are randomly sampled and the model predictions are compared with the experimental results of the melanoma and NSCLC cell lines to achieve the best fit. The LQ model parameters are then used to convert the physical absorbed dose to BED and EQD₂ for different dose fractionation schemes, and the impact of the dose conversion uncertainties is analyzed.

MATERIALS AND METHODS

The LQ model

The LQ model [13,14] approximates clonogenic cell survival fraction S as:

S =