Error propagation in the estimation of glomerular pressure from macromolecule sieving data

Abstract

The theoretical effects of the glomerular transmural hydraulic pressure difference (delta P) on the sieving coefficients (theta i) of macromolecules of varying size have led to a number of attempts to use sieving curves to estimate delta P noninvasively, with inconsistent results. The objective of this study was to determine the extent to which experimental errors and imperfections in the theoretical models limit the ability to obtain reliable estimates of delta P using this method. Our approach was to generate many sets of synthetic “experimental data” using computer simulations of glomerular sieving and to compute values of delta P by fitting models to those data in the presence of various types and magnitudes of errors. Unbiased experimental errors were simulated by adding random amounts to individual values of theta i, and systematic errors were investigated by using a model based on one type of pore-size distribution to fit “data” generated using a model of a different type. We found that with random errors in theta i only, the estimate of delta P was accurate to within +/- 4 mmHg nearly all of the time, provided that the standard deviation, sigma i, was < or = 5% of theta i. When there were also systematic errors arising from the use of an “incorrect” form of pore-size distribution, a useful predictor of success was the probability P that the residuals, the differences between the measured and predicted sieving coefficients, were randomly distributed. A value of P > 0.2, as calculated from the algebraic signs of the residuals, indicated a high likelihood that the pressure estimate was accurate, provided that the random errors were sufficiently small. When P > 0.2, the fitted value of delta P was within +/- 4 mmHg of the true value in about 90%, 80%, and 70% of the cases examined when sigma i was < or = 2%, 5%, or 10% of theta i, respectively. An analysis of published data from a number of experimental studies indicated, however, that the favorable conditions of small sigma i and large P are extremely difficult to achieve, making it unlikely that an accurate group-mean value of delta P will be estimated from any given set of sieving data. Significant experimental and theoretical advances will be needed to make this a reliable method for estimating glomerular pressure.