Estimation of radiobiological parameters and repopulation dose equivalents using classical cell kinetics with hypotheses concerning cellular changes during radiotherapy

Purpose To study tumour responses and the changes in radiobiological parameters which may better inform decision making applied to overall time issues and treatment delays in a variety of histological tumour types during radiotherapy. Methods Classical cell kinetic equations and radiobiological principles have been combined to study changes in effective doubling time ( T eff ) and repopulation dose equivalents ( Krepop ) during radiotherapy in a model which includes a non-proliferating radioresistant hypoxic fraction, reoxygenation, and a reducing cell loss factor (φ) governed by the tumour volume doubling time ( T D ), such that longer T D times will have longer apparent onset times of AR (accelerated repopulation). Results The model found shortening of T eff at a time commensurate with the onset of accelerated repopulation in well-defined histological tumour types with their typical cell kinetic characteristics, along with diminishing extents of tumour hypoxia with time. The Krepop values show a steady increase during treatment and become closer to the constant Krepop values normally used in treatment interruption assessments for each histological class. Tumour classes with lower initial φ values show a greater persistence of hypoxia; those with very long initial T D values do not develop accelerated repopulation during or closely after radiotherapy, their Krepop values remaining low. Conclusions The current use of constant Krepop values only after critical AR onset time durations may be sub-optimal in treatment interruption compensations since Krepop probably varies continuously with time due to progressive shortening of T eff . For shorter schedules, use of high K values (as used for longer schedules) could result in compensatory overdosage; lower compensatory doses obtained by using lower Krepop values should be preferred with no lag time to AR onset. Very prolonged interruptions probably require the highest Krepop values appropriate for the time at which compensation occurs.