Studies of Renal Excretion of Creatinine. III. Utilization Constant. ∗

Abstract

In the preceding paper it was shown that, when a substance disappears exponentially from the body, and the rate of excretion by the kidneys is proportional to the plasma concentration, the rate of utilization of the portion not excreted is also proportional to the plasma concentration. The latter factor of proportionality was called utilization constant (B), in contradistinction to the former, excretion constant (A). The constant A for creatinine and xylose on one human subject has been published elsewhere. The calculation of B' is as follows:

Let us call ζ_o the initial concentration at the time zero. Then the quantity initially present, 1W let us say, is

The amount excreted in the time t is, from (1),

the subscripts o and t meaning as usual the value of the variable at zero time and time t respectively.

The latter equation, written in terms of ζ, becomes,

Therefore, since α = β,

Since the integral in this equation has a limit, S say,

we see that

and concequently, that

or

An approximation to the ratios on the left side of (25) and (26) has usually been obtained experimentally by comparing an amount S′ excreted in a sufficiently long interval of time to a quantity M′ given orally, or to the quantity M, precisely, given intravenously. The ratio (S′/M′) after oral administration would be an approximate value of (S/M) in (26) if it could be assumed that all the quantity given is absorbed. The ratio (S′/M) after intravenous injection could also be used as an approximation if it were proved that the amount excreted before the equilibrium between plasma and tissues is established, is negligible in comparison with the total amount excreted.

Lacking definite information on these points, we shall use a few figures from the literature in order to get an idea of the order of magnitude of the volume of distribution of creatinine and xylose.