Generalized methods for predicting biological response to mixed radiation types and calculating equieffective doses (EQDX)

Abstract

Background: Predicting biological responses to mixed radiation types is of considerable importance when combining radiation therapies that use multiple radiation types and delivery regimens. These may include the use of both low- and high-linear energy transfer (LET) radiations. A number of theoretical models have been developed to address this issue. However, model predictions do not consistently match published experimental data for mixed radiation exposures. Furthermore, the models are often computationally intensive. Accordingly, there is a need for efficient analytical models that can predict responses to mixtures of low- and high-LET radiations. Additionally, a general formalism to calculate equieffective dose (EQDX) for mixed radiations is needed.

Purpose: To develop a computationally efficient analytical model that can predict responses to complex mixtures of low- and high-LET radiations as a function of either absorbed dose or EQDX.

Methods: The Zaider-Rossi model (ZRM) was modified by replacing the geometric mean of the quadratic coefficients in the interaction term with the arithmetic mean. This modified ZRM model (mZRM) was then further generalized to any number of radiation types and its validity was tested against published experimental observations. Comparisons between the predictions of the ZRM and mZRM, and other models, were made using two and three radiation types. In addition, a generalized formalism for calculating EQDX for mixed radiations was developed within the context of mZRM and validated with published experimental results.

Results: The predictions of biological responses to mixed-LET radiations calculated with the mZRM are in better agreement with experimental observations than ZRM, especially when high- and low-LET radiations are mixed. In these situations, the ZRM overestimated the surviving fraction. Furthermore, the EQDX calculated with mZRM are in better agreement with experimental observations.

Conclusion: The mZRM is a computationally efficient model that can be used to predict biological response to mixed radiations that have low- and high-LET characteristics. Importantly, interaction terms are retained in the calculation of EQDX for mixed radiation exposures within the mZRM framework. The mZRM has application in a wide range of radiation therapies, including radiopharmaceutical therapy.

Keywords: Ionizing radiation; biologically effective dose; dose response; equieffective dose; linear energy transfer; linear quadratic model; radiation mixture.