Mathematical Model of Progressive Renal Disease

A simple mathematical model is proposed that predicts the dynamics of chronic progressive renal disease. The model consists of coupled linear differential equations formed from three state variables, four control parameters, and three parameters related to initial conditions. All have straightforward physical interpretations. Applied to a population of nephrons, the model predicted the hypertrophic and sclerotic features of parenchyma progressing towards end-stage renal disease. Simulation results compared favorably with measurements obtained from the literature involving the subtotal nephrectomy rat model for renal disease. The time course of disease progression and treatment were considered. Also, the implications of the model for designing new diagnostic techniques using ultrasonic analysis are discussed.