View source for Mathematical description of pharmacokinetic processes

=== Renal clearance ===
Renal clearance ( '''CL<sub>R</sub>''' )  is the amount of drug eliminated per unit time by the kidneys, related to the concentration of the substance in the blood ( '''c''' ). The amount excreted per unit time is equal to the product of the volume of urine excreted per unit time (volumetric urine flow rate) and the concentration of the drug in the urine ( '''c<sub>U</sub>''' ).
<math>
CL_{R}=\frac{\dot{V}c_{U}}{c}=\frac{(\frac{V}{T})c_{U}}{c}=\frac{A_{U}}{AUC}
</math>


where is the volumetric flow rate of urine (ml/s), '''c<sub>U</sub>'''is the concentration of the drug (generally any substance) in the urine, '''c''' is the concentration in the blood. Renal drug clearance is obtained by the same procedure as creatinine clearance. During the collection interval '''T''' , a volume of urine '''V''' is collected . The average blood drug concentration within the urine collection interval is used in the denominator. If urine is collected long enough (from the time the drug is administered until the drug disappears from the blood), the relationship with '''A<sub>U</sub>'''  (total amount of drug excreted in urine) and '''AUC''' (area under the curve of blood drug concentration vs. time) is used. Rearranging the relation gives: 

<math>
CL_{R} c = \dot{V} c_{U}
</math>

Renal clearance can therefore also be understood as the volume of blood (plasma) that is completely cleared of the drug in the kidneys per unit of time.

Similarly, total clearance is the volume of blood (plasma) that is completely cleared of the drug (the volume from which the drug is completely removed) per unit time.

Renal excretion includes the processes of glomerular filtration (GF), active tubular secretion, and active and passive tubular reabsorption. GF and secretion increase renal clearance, while reabsorption decreases renal clearance.

The physiological range for glomerular filtration rate is 80−120 ml/min. In practice, GF is measured using the clearance of an endogenous substance - creatinine ( '''Cl<sub>KR</sub>'' ). Creatinine does not bind to plasma proteins, it is freely filtered into the primary urine and is not absorbed or secreted in the tubules (active secretion occurs only with pathologically elevated creatinineemia). With normal kidney function, the concentration of creatinine in the blood is relatively constant during the day. This simplifies the calculation:

:'''GF ≈ Cl<sub>kr</sub> = (c<sub>U</sub>. V) / (c.T)'''

where '''V''' is the volume of urine, '''T''' is the time interval of urine collection, '''c<sub>U</sub>''' and '''c''' are the concentrations of creatinine in urine and plasma.

The magnitude of renal clearance allows some consideration of the mechanism of drug excretion. E.g. the renal clearance of ampicillin (283 ml/min) greatly exceeds the amount of glomerular filtration, so we can consider a significant contribution of tubular secretion to the elimination of the drug by the kidneys.

The drug, which is largely excreted unmetabolized in the urine and has a high renal clearance value (≥ 0.1 l/min), accumulates in the body of patients with reduced kidney function. Dosing rate must be reduced (dosing interval extended or even individual dose reduced). There are several ways (tables, nomograms, computer programs) to adjust the dosage of these drugs based on GFR testing.