A comparison of mathematical models for regeneration in acutely responding tissues.

A mathematical model is presented to describe the regenerative response of mouse gut epithelal cells to radiation. The model, derived from radiobiological principles, predicts the cellular surviving fraction following any irradiation regimen. There are three basic elements to the model (a) a single dose survival curve, either the linear-quadratic or the two-component model, (b) a part to incorporate the regenerative response, either a Gompertzian or a logistic growth and (c) a part to accomodate the delayed onset of regeneration, including either a mitotic delay, a fixed time delay, both, or neither. The models are similar in spirit, but different in detail to the model proposed by Cohen. The various models are evaluated on three large datasets, where the response is cell survival in the jejunum or the colon measured using the crypt colony assay. The models were fit and the parameter estimates and standard errors were obtained from the raw observations using non-linear least squares. It is concluded that Gompertzian growth gives a better fit to the data than logistic growth; the delayed onset of regeneration in these tissues can be best accounted for by a mitotic delay or a mitotic delay plus a fixed time delay, and there is little to choose between the linear-quadratic and the two-component model. There was a strong relationship between the tissue cell cycle time and the regenerative response, the mitotic delay being longer and the rate of regeneration slower for the colon than for the jejunum.