Time Evolution of the Number of Functional Murine Eccrine Sweat Glands after Irradiation: A Quantitative Analysis of Experimental Data Using a Model of Proliferative and Functional Organization

Abstract

The function of eccrine sweat glands in the β-pad of the mouse foot after irradiation was followed over time. Graded doses of X-rays were given to the foot, either as single doses or in two equal fractions separated by a 24-h interval. A quantitative, non-invasive, functional assay was used allowing repeated evaluations of the animals. Sweat gland function was assessed once a week for the first 6 weeks, and at 8, 10, 14, 18, 28, 38 and 45 weeks after irradiation. The β-pad of the unirradiated foot was used as a control. The function dropped to a nadir within 8–10 weeks after irradiation, whereafter it gradually recovered, reaching a stable level 20–25 weeks after irradiation. These data were analyzed using a mathematical model of proliferative and functional organization of the sweat pore. The model provides a description of the time evolution of pore function, and its basic features were as follows. The functional subunit is a single sweat pore, which will be assayed as functional provided that it contains a number of functional cells above a critical threshold. The functional cells are capable of self renewal (a so-called ‘flexible’ tissue), and the proportion of proliferating cells is subject to homeostatic control. Irradiation is assumed to transfer a certain fraction of the cells into a state with a limited probability of successful division. This fraction is assumed to have a linear—quadratic dependence on dose. The values of all free model parameters were optimized by a maximum-likelihood fit to the experimental data. With optimized parameter values, the initial decrease, nadir, and long-term level of tissue function estimated from the model were in close agreement with the experimental observations for all the 28 dose groups. Some of the estimated model parameters are: growth fraction 4·2 ± 0·2%; cell cycle time, 0·95 ± 0·04 days; number of functional cells in a single pore in the unirradiated animal, 9·9 ± 0·5; and α/β ratio, 4·3 Gy (95% confidence interval 3·1–5·0 Gy). It is concluded that the present model, despite its relative mathematical simplicity, provides a close description of the postirradiation kinetics of functional cells in the mouse sweat gland.