Progression rate of radiation damage to the mouse kidney: a quantitative analysis of experimental data using a simple mathematical model of the nephron

Mouse kidneys were irradiated bilaterally with a range of single or fractionated X-ray doses. After an interval of 2 weeks or 26 weeks, the animals were reirradiated with a range of single X-ray doses. The rate of development of functional kidney damage was assessed repeatedly by the 51Cr-EDTA clearance assay. The rate at which the damage is expressed was found to depend on the primary dose, on the interval between primary treatment and retreatment, and on the retreatment dose. A subset of the data was analysed using a mathematical model of nephron function. In the model, the residual activity of 51Cr-EDTA depends on the glomerular filtration rate (GFR). The GFR is related to the cellularities of three target cell populations. The filtration capacity of the glomerulus is assumed to depend on the numbers of glomerular endothelial cells and mesangial cells. The reabsorption capacity of the tubule is related to the number of tubular epithelial cells. The impact of tubulo-glomerular feedback and the reserve capacity of the kidney on residual activity is considered. The target cell populations are assumed to be of a flexible type, i.e. to consist of cells which are all both functional and self-renewing. Free parameters of the model were optimized by minimizing the residual sum of squares. With the optimized parameter values, the measured and the model-predicted rates of progression of the functional damage correspond well for a wide range of irradiation schedules. The model analysis suggests a pronounced role of tubulo-glomerular feedback in the development of functional injury in the kidney. It is concluded that the model represents a good starting point for quantitative studies of the cellular basis of radiation nephropathy.