Urinary formation by the kidneys, as outlined in Equation 33.3, involves the production of an ultrafiltrate of plasma across the glomerulus. The process of glomerular filtration and the regulation of glomerular filtration rate (GFR) and renal blood flow (RBF) are discussed in later chapters. The concept of renal clearance, which serves as the theoretical basis for measuring GFR and RBF, is presented in the following section. Subsequent chapters delve into the topics of reabsorption and secretion.

Renal clearance is based on the Fick principle, which involves mass balance or conservation of mass. Fig. 33.12 illustrates the factors required to describe the mass balance relationships within the kidney. The renal artery serves as the input source for substances that are not synthesized by the kidney. On the other hand, the renal vein and ureter act as the principal output routes. In other words, a nonmetabolized substance entering the renal circulation through the renal artery can only exit via the renal vein (including the unfiltered fraction and any reabsorbed amount) or the ureter (comprising the combined filtered and secreted fractions minus any tubular reabsorption). The mass balance relationship is defined by the following equation (Equation 33.1):

Equation 33.1: Renal artery plasma concentration (Px) = Renal vein plasma concentration (Pv) + Urinary excretion concentration (U)

Assuming that the concentration of substance x in renal artery plasma (Px) is identical to its concentration in a plasma sample from any peripheral blood vessel, the following relationship is obtained (Equation 33.4):

Equation 33.4: Px = Pv + U

Clearance is expressed in terms of volume per unit time and represents the volume of plasma from which all the substance has been removed and excreted into urine. To illustrate this point, consider an example where a substance is present in urine at a concentration of 100 mg/mL and the urine flow rate is 1 mL/min. The excretion rate for this substance can be calculated using Equation 33.5:

Equation 33.5: Excretion rate = Urine concentration × Urine flow rate

If the same substance is present in plasma at a concentration of 1 mg/mL, its clearance can be calculated using Equation 33.6:

Equation 33.6: Clearance = (Px - Pv) × Renal plasma flow rate

In Equation 33.6, Px and Pv represent the concentrations of substance x in renal artery and renal vein plasma, respectively, while Renal plasma flow rate in the artery and vein is denoted as RPFa and RPFv, respectively. Therefore, 100 mL of plasma will be completely cleared of substance x every minute.

Figure 33.13 illustrates the renal handling of creatinine. Creatinine is freely filtered across the glomerulus and is not reabsorbed, secreted, or metabolized by the nephron. It should be noted that not all the creatinine delivered to the kidney via the renal artery is filtered at the glomerulus (normally, 15%–20% of plasma creatinine is filtered). The portion that is not filtered returns to the systemic circulation through the renal vein. PCr represents plasma creatinine concentration, RPF stands for renal plasma flow, Ucr denotes urinary concentration of creatinine, and V signifies urine flow rate.

Although the concept of clearance suggests the removal and excretion of a substance from plasma per unit time, it is important to understand that it is not an actual volume of plasma but rather a virtual volume. Clearance is a crucial concept as it enables the measurement of GFR and RPF and facilitates the determination of whether a substance is reabsorbed or secreted along the nephron.

GFR represents the sum of the filtration rates of all functioning nephrons and serves as an aggregate index of kidney function. A decline in GFR generally indicates the progression of kidney disease, while an improvement typically suggests recovery. Therefore, serial assessment of a patient's GFR is vital for evaluating the severity and progression of kidney disease.
Equation 33.3 the substance from blood into tubule fluid. The first step in P × C = U × V˜ urine formation by the kidneys is production of an ultrafil-xa x x trate of plasma across the glomerulus. The process of glo-If
Eq. 33.3 is rearranged and the concentration of merular filtration and regulation of GFR and RBF substance x in renal artery plasma ( ) is assumed to beare discussed later in this chapter. The concept of renal clearance, which is the theoretical basis for measurement of GFR and RBF, is presented in the following section. Reabsorption and secretion are discussed in subsequent chapters.
The concept of renal clearance is based on the Fick principle (i.e., mass balance or conservation of mass).
Fig.
33.12 illustrates the various factors required to describe the mass balance relationships of a kidney. The renal artery is the single input source to the kidney for substances not synthesized by this organ, whereas the renal vein and ureter constitute the two principal output routes. In other words a nonmetabolized substance entering the renal circulation via the renal artery may only exit this circulation via the renal vein (i.e., the unfiltered fraction plus any filtered amount subsequently reabsorbed back into blood) or the ureter (the combined filtered and secreted fractions less any tubular reabsorption). The following equation defines the mass balance relationship:
Equation 33.1 where identical to its concentration in a plasma sample from any peripheral blood vessel (Px), the following relationship is obtained:
Equation 33.4
Clearance has the dimensions of volume/time, and it represents a volume of plasma from which all the substance has been removed and excreted into urine per unit time. This last point is best illustrated by considering the following example. If a substance is present in urine at a concentration of 100 mg/mL and the urine flow rate is 1 mL/min, the excretion rate for this substance is calculated as follows:
Equation 33.5
If this substance is present in plasma at a concentration of 1 mg/mL, its clearance according to
Eq. 33.4 is as follows:
Equation 33.6 are the concentrations of substance x in the renal artery and renal vein plasma, respectively
RPFa and RPFv are renal plasma flow rates in the artery and vein, respectively In other words, 100 mL of plasma will be completely Ux is the concentration of substance x in urine cleared of substance x each minute. The definition of clearV̇ is the urine flow rate ance as a volume of plasma from which all the substance . UCr x V
Amount filtered PCr x GFR = Amount excreted UCr x V .
• Fig. 33.13 Renal handling of creatinine. Creatinine is freely filtered across the glomerulus and is, to a first approximation, not reabsorbed, secreted, or metabolized by the nephron. Note that all the creatinine coming to the kidney in the renal artery does not get filtered at the glomerulus (normally, 15%–20% of plasma creatinine is filtered). The portion that is not filtered is returned to the systemic circulation in the renal vein. PCr, plasma creatinine concentration; RPF, renal plasma flow; Ucr, urinary concentration of creatinine; V., urine flow rate.
has been removed and excreted into urine per unit time is somewhat misleading because it is not a real volume of plasma; rather it is a virtual volume.
The concept of clearance is important because it can be used to measure GFR and RPF and determine whether a substance is reabsorbed or secreted along the nephron.
The GFR is equal to the sum of the filtration rates of all functioning nephrons. Thus it is an aggregate index of kidney function. A fall in GFR generally means the kidney disease is progressing, whereas recovery generally suggests recuperation. Thus serial assessment of a patient’s GFR is essential to evaluate the severity and course of kidney disease.