A mathematical model of dynamics of cell populations in squamous epithelium after irradiation

Classification of tolerable/intolerable mucosal toxicity of head-and-neck radiotherapy schedules with a biomathematical model of cell dynamics

Purpose

The purpose of this study is to present a biomathematical model based on the dynamics of cell populations to predict the tolerability/intolerability of mucosal toxicity in head‐and‐neck radiotherapy.

Methods and Materials

Our model is based on the dynamics of proliferative and functional cell populations in irradiated mucosa, and incorporates the three As: Accelerated proliferation, loss of Asymmetric proliferation, and Abortive divisions. The model consists of a set of delay differential equations, and tolerability is based on the depletion of functional cells during treatment. We calculate the sensitivity (sen) and specificity (spe) of the model in a dataset of 108 radiotherapy schedules, and compare the results with those obtained with three phenomenological classification models, two based on a biologically effective dose (BED) function describing the tolerability boundary (Fowler and Fenwick) and one based on an equivalent dose in 2 Gy fractions (EQD₂) boundary (Strigari). We also perform a machine learning‐like cross‐validation of all the models, splitting the database in two, one for training and one for validation.

Results

When fitting our model to the whole dataset, we obtain predictive values (sen + spe) up to 1.824. The predictive value of our model is very similar to that of the phenomenological models of Fowler (1.785), Fenwick (1.806), and Strigari (1.774). When performing a k = 2 cross‐validation, the specificity and sensitivity in the validation dataset decrease for all models, from ˜1.82 to ˜1.55–1.63. For Fowler, the worsening is higher, down to 1.49.

Conclusions

Our model has proved useful to predict the tolerability/intolerability of a dataset of 108 schedules. As the model is more mechanistic than other available models, it could prove helpful when designing unconventional dose fractionations, schedules not covered by datasets to which phenomenological models of toxicity have been fitted.