A mathematical model for cell density and proliferation in squamous epithelium after single-dose irradiation

Abstract

Purpose: To establish a mathematical model describing changes in cell density in squamous epithelia induced by single-dose irradiation. Detailed data from previous studies in mouse tongue epithelium have been used for this study.

Materials and methods: The major mechanisms of the epithelial regeneration response, i.e. loss of division asymmetry and accelerated proliferation of stem cells, in combination with residual, abortive proliferation of sterilized cells, have been included in a tissue compartment model. These phenomena have been incorporated via three parameters; T(delay), the duration of the cell cycle block; T(min), the minimum stem cell cycle time due to acceleration; and T(stop), the duration of abortive proliferation. The compartments introduced in the model are normal stem cells, S1; sterilized stem cells, S2; and post-mitotic, functional cells, F. The flux rats between the tissue compartments were defined by autoregulation of the stem cell population, and by overall cell numbers. The model was applied to fit experimental data on changes in oral mucosal cell density after single-dose exposure with 13 and 20 Gy. The best-fit sets of parameters were identified by L2 norm error analysis based on the total cell count.

Results: For 13 Gy, the best fit was achieved with T(min) = 1.0 days, T(delay) = 1.2 days and T(stop) = 7.5 days. For 20 Gy, the parameters were, T(min) =0.7 days, T(delay)= 1.0 days and T(stop) =9.5 days. In both data sets, T(min) was the most influential parameter. The resulting fluctuations in stem cell numbers were in good accordance with changes in radiation tolerance after 13 Gy.

Conclusions: The model can be used to define dose-dependent parameters describing the morphological response of squamous epithelia to single-dose irradiation. Based on these parameters, post-irradiation fluctuations in radiosensitivity can be predicted. For developing more complex and reliable mathematical models, which could incorporate transit divisions or fractionated radiotherapy, further experimental data at various dose levels are required.