Biological effectiveness of uniform and nonuniform dose distributions in radiotherapy for tumors with intermediate oxygen levels.

Objective. We propose a criterion of biological effectiveness of nonuniform hypoxia-targeted dose distributions in heterogeneous hypoxic tumors based on equivalent uniform aerobic dose (EUAD). We demonstrate the utility of this criterion by applying it to the model problems in radiotherapy for tumors with different levels of oxygen enhancement ratio (OER) and different degrees of dose nonuniformity.Approach. The EUAD is defined as the uniform dose that, under well-oxygenated conditions, produces equal integrated survival of clonogenic cells in radiotherapy for heterogeneous hypoxic tumors with a non-uniform dose distribution. We define the dose nonuniformity effectiveness (DNE) in heterogeneous tumors as the ratio of the EUAD(D_N) for a non-uniform distributionD_Nand the reference EUAD(D_U) for the uniform dose distributionD_Uwith equal integral tumor dose. The DNE concept is illustrated in a radiotherapy model problem for non-small cell lung cancer treated with hypoxia targeted dose escalation. A two-level cell population tumor model was used to consider the hypoxic and oxygenated tumor cells.Results. Theoretical analysis of the DNE shows that the entire region of the OER can be separated in two regions by a threshold OER_th: (1) OER > OER_thwhere DNE > 1 indicating higher effectiveness of nonuniform dose distributions and (2) OER < OER_thwhere DNE < 1 indicating higher effectiveness of uniform dose distributions. Our simulations show that the value of the threshold OER_thin radiotherapy with conventional fractionation is significant in the range of about 1.2-1.6 depending on selected radiotherapy parameters. In general, the OER_thincreases with reoxygenation rate, relative hypoxic volume and dose escalation factor. The threshold value of OER_this smaller of about 1.1 for hypofractionated radiotherapy.Significance. The analysis of dose distributions using the DNE shows that the uniform dose distributions may improve biological cell killing effect in heterogeneous tumors with intermediate oxygen levels compared to targeted nonuniform dose distribution.