OBJECTIVE 1: TO UNDERSTAND THE GENERAL PRINCIPLE AND THE METHODS USED TO MEASURE RENAL FUNCTION.

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A. Measurement of the varied functions of the kidney depends almost entirely on the application of the principle of conservation. For substances that are not synthesized or metabolized by renal tissue, the amount entering the kidney via the renal artery equals the amount leaving in the renal vein and ureter. Similarly, the amount entering the nephrons by filtration and/or secretion equals the amount leaving by reabsorption and/or excretion. The use of this principle provides the means for indirectly measuring renal blood flow, glomerular filtration rate, and the rates of tubular reabsorption and secretion of various substances.

B. Renal plasma flow can be determined by the principle of conservation and the use of a substance that is not synthesized or metabolized by the kidney. The amount of such a substance entering the kidney per unit time via the renal artery equals the amount leaving via the ureter and the renal vein. The difficulty of obtaining renal venous plasma samples limits the usefulness of this approach to measuring RPF. However, it has been found that the tubular secretory system for para-aminohippurate (PAH) is so efficient that at low plasma concentrations it removes 90% or more of the PAH from the plasma as it flows through the kidney. Thus for practical reasons, the 10% that remains in the renal vein is ignored and it is assumed that the amount entering the kidneys, renal plasma flow (RPF) x arterial concentration (P_PAH), equals the amount leaving via the ureters, urine concentration (U_PAH) x urine flow rate (V, ml/min). That is,

RPF x P_PAH = U_PAH V              
and 
RPF = U_PAHV / P_PAH     (Eq. 1)

For the reason indicated above this is an approximation; it is a very useful approximation for physiological measurements, but its use in disease is limited for obvious reasons.

C. Renal blood flow (RBF) equals the flow of plasma (RPF) plus the flow of red cells (RCF). It may be calculated from measurement of the RPF and the hematocrit (Hct), the fraction of blood volume that is composed of cells ):

RBF = RPF + RCF       
RCF = (RBF x Hct)      
RBF = RPF + (RBF x Hct)         
RBF = RPF / (1-Hct)         (Eq. 2)

Units for both RPF and RBF are ml/min.

Fig. 4-1. Measurement of filtration rate.

One such substance is inulin, a fructose polysaccharide with a molecular weight of approximately 5000. The amount of inulin filtered per unit time by the glomeruli equals the volume of plasma filtered/time (GFR) times the plasma concentration (P_in) (Fig. 4-1). The amount exiting from the ureter per unit time equals the urine flow rate (V) times the urine concentration (U_in). Since the tubular cells do not add or remove inulin from the filtrate, the amount entering the nephrons equals the amount exiting and Eq. 3 applies (fig. 4-1). Plasma and urine concentrations and the urine flow rate can be measured so that GFR can be calculated using Eq. 4.

Fig. 4-2. Measurement of solute reabsorption rate.

1. Most substances handled by the kidney are freely filterable, so the amount filtered per unit time equals the GFR times the plasma concentration of the substance (P_s).

2. The rate of reabsorption (T, for tubular transport) of a solute by the tubules can be determined by calculating the difference between the rate at which it is filtered and the rate it is excreted (Eq. 6, Fig. 4-2).

3. The rate of secretion (T) of a solute can be determined by calculating the difference between the rate of its excretion and the rate it is filtered (Eq. 8, Fig. 4-3).

Fig. 4-3. Measurement of solute secretion rate.

4. The measurement of the maximum rate of transport (Tm) for a substance is sometimes useful in clinical experiments to determine the amount of functional tubular tissue. The criteria for accurate measurement of Tm are as follows: (1) Plasma levels must be high enough to saturate the transport system. (2) Two consecutive clearance determinations must be made in which the plasma concentration rises, but the calculated rate of transport of the substance does not. This ensures that the tubular maximum has been reached.

QUESTIONS: 
1. How is the principle of conservation applied to the measurement of RPF? Of GFR?

2. Why is PAH a substance of choice for measuring RPF? Why is inulin a substance of choice for measuring GFR? Theoretically inulin could be used to measure RPF. What additional value would be required for the calculation?

3. An anesthetized rat was given priming doses of PAH and inulin and then a constant infusion containing both substances in order to raise the plasma concentration of each to a low constant level. The urine was then collected over a 20 min period and a blood sample was obtained at the midpoint of the urine collection period. The urine flow rate was calculated in ml/min. Inulin, PAH and Na concentrations in plasma and urine were measured. P_in = 0.7 mg/ml, U_in = 20 mg/ml, P_PAH = 0.2 M, U_PAH = 23 M, P_Na = 141 mM, U_Na = 45 mM, V = 0.06 ml/min and Hct = 45%. Calculate GFR, RPF and RBF, T_PAH and T_Na

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