The central theme of this work is the use of the rate constant of the terminal exponential from the clearance of a tracer as a measure of glomerular filtration rate (GFR). This rate constant is an estimate of GFR divided by the distribution volume of the tracer and hence gives GFR normalised to extra cellular fluid volume (ECV). This may be an ideal measure of renal function because it indicates how quickly the kidneys can remove substances that are distributed in the ECV. Experimental data and modelling were used to derive corrections for the one pool assumption to give a better estimate of GFR/ECV from the rate constant calculated from blood samples taken at 2, 3 and 4 hours. Monte Carlo techniques were used to compare the effect of experimental errors on GFR derived from the rate constant and GFR conventionally derived from the rate constant and the intercept. Using normal volunteers a comparison was made of the appropriateness in adults of normalising GFR to ECV and estimated body surface area and additionally, in a small group, other whole body parameters including total body water, lean body mass and exchangeable potassium. The reproducibility of GFR derived by the two approaches was compared. Iohexol was compared with Cr-51 EDTA including an assessment of the performance of GFR derived from the rate constant with the different experimental errors encountered with iohexol. A comparison was made of how GFR derived by the two approaches performed in identifying changes in renal function as a result of changes in drug regime. The rate constant can be used as a near real time measure of renal function under changing conditions and in an extension of this, a study was performed using the rate constant as a measure of dialyser performance.