Studies of Renal Excretion of Creatinine. II. Volume of Distribution

Abstract

By studying the time change of the concentration of a substance in the plasma and of its simultaneous rate of excretion in the urine, the conclusion has been reached 1 ,² that both these quantities decrease exponentially to the pre-ingestion level and furthermore, that the coefficients of the time in both exponential functions are equal, on an average, for a given substance. From these 2 facts it follows that the rate of excretion of a substance obeying such laws is proportional to the plasma concentration at any time. The above statements have been verified so far only for creatinine and xylose.

In symbols we have

where y is the rate of excretion in mg. per minute, x the plasma concentration in mg. per 100 cc., y_e and x_e the mean pre-ingestion levels of y and x respectively, a, b, α, and β, constants determined from the experimental data, e the base of natural logarithms, and t the time in hours.

Equations 5, 6, and 7 are simply the definitions of A, ≠ and ζ; Equations 1 and 2 are the empirical laws mentioned above; Equation 3 is an empirical fact, proved so far for creatinine and xylose, and Equation 4 is the result of the elimination of t between Equations 1 and 2.

A has been called the excretion constant. 1 It has the dimensions of flow [l³t^-1], and is measured in units of 100 cc. per minute, β has the dimension [t^-1], and is, from Equation 2, the velocity constant of the disappearance of the substance from the body. It will be called, for the sake of brevity, the velocity constant.