A novel fast strategy to calculate equieffective doses under different dose rate conditions

Radiopharmaceutical therapy (RPT) has gained notable attention for its potential in treating difficult cancers, with [¹⁷⁷Lu]Lu-DOTATATE being a notable example. However, the radiobiology of RPT is less understood compared to external beam radiotherapy (EBRT), and dosimetry protocols are not standardized. Organ dose limits and tumor dose-response correlations are often based on radiobiologically motivated equieffective doses (EQDX). On top of absorbed dose, these measures are also functions of the absorbed dose rate and radiobiological parameters that quantify tissue radiosensitivity and damage repair rate. Typically, the absorbed dose and repair rates are assumed to follow a monoexponential pattern, although describing the dose rate function often requires two or more phases to describe the data.

Here we present novel expressions for calculating the equieffective dose in 2 Gy fractions (EQD2) for RPT, considering various absorbed dose rate scenarios and the rate of sublethal DNA damage repair. We aimed to establish an approach that is scalable, robust, and can be used alongside various absorbed dose integration methods.

By assuming a simple exponential decay for DNA damage repair and employing a biexponential function for absorbed dose rate decay, we have re-established the solutions for EQDX in a concise analytical form. Additionally, we have devised a novel hybrid solution applicable to piecewise-defined absorbed dose-rate functions, leveraging both numerical and analytical methodologies. To validate these expressions, simulated measurements were utilized, and comparisons were made with a fully numerical approach. We also investigated the reliability of three methodologies-fully numerical, fully analytical, and a hybrid approach-when simplifying comprehensive dosimetry protocols. Utilizing publicly available clinical data from two patients undergoing [¹⁷⁷Lu]Lu-DOTATATE therapy, we defined the baseline absorbed dose rate model based on the best biexponential fit to four post-injection SPECT measurements at the organ level. We then explored variations in EQD2 values resulting from the omission of the final measurement.

The proposed expressions were found to be accurate and scalable, providing a reliable alternative to fully numerical methods. The results of the fully numerical method converged to our solutions with increasing accuracy as the extrapolation time after injection was increased. However, we found that to achieve an accuracy in EQD2 to within 2%, the numerical method had to extrapolate for up to 890 h in some cases, at which point overflow errors are likely to occur. Our hybrid method also achieved a significant decrease in computation time compared to the fully numerical method.Using data from two patients, we found that the numerical, hybrid, and analytical approaches underestimated the baseline EQD2 to tumors by 15.6 ± 9.4 %, 5.0 ± 4.2 %, and 1.5 ± 2.9 %, respectively.

Comprehensive dosimetric studies are often preferred in RPT when increased measurement accuracy is desired. Correspondingly, it is vital for radiobiological models to maintain a level of accuracy commensurate with comprehensive studies. Our proposed methods are accurate, scalable, and suitable for radiobiologically motivated RPT dosimetry.