The consequence of day-to-day stochastic dose deviation from the planned dose in fractionated radiation therapy

Radiation therapy is one of the important treatment procedures of cancer. The day-to-day delivered dose to the tissue in radiation therapy often deviates from the planned fixed dose per fraction. This day-to-day variation of radiation dose is stochastic. Here, we have developed the mathematical formulation to represent the day-to-day stochastic dose variation effect in radiation therapy. Our analysis shows that that the fixed dose delivery approximation under-estimates the biological effective dose, even if the average delivered dose per fraction is equal to the planned dose per fraction. The magnitude of the under-estimation effect relies upon the day-to-day stochastic dose variation level, the dose fraction size and the values of the radiobiological parameters of the tissue. We have further explored the application of our mathematical formulation for adaptive dose calculation. Our analysis implies that, compared to the premise of the Linear Quadratic Linear (LQL) framework, the Linear Quadratic framework based analytical formulation under-estimates the required dose per fraction necessary to produce the same biological effective dose as originally planned. Our study provides analytical formulation to calculate iso-effect in adaptive radiation therapy considering day-to-day stochastic dose deviation from planned dose and also indicates the potential utility of LQL framework in this context.