dM CL C dt

Making the assumption that CL is constant, the integration as a function of time gives eqn [16]:

And making the further assumption that: (1) the drug is administered by the intravascular route; (2) the drug is eliminated from the plasma without any reintroduction (no enterohepatic cycling, no reversible biotransformation regenerating the parent drug from metabolites); and (3) the total amount Mof excreted drug is equal to the dose, then:

When the drug is administered by an extravascular route, the total amount reaching the body is unknown and CL cannot be calculated.

The product of urinary concentration and urinary volume gives the amount eliminated in urine (MU). When the compound measured in plasma and urine is the same (parent or metabolite), eqns [14] and [15] apply and become eqns [18] and [19]:

where CLR is the renal clearance, which can be calculated from urine fractions collected during At (eqns [20] and [21]):

AMU is the amount eliminated in urine during At and AAUC is the area corresponding to At. The calculation can be made using the global kinetics; therefore, eqn [17] becomes eqn [22]:

The only assumption here is that CLR remains constant.

Hepatic and renal clearances are additive; lung clearance is multiplicative since it acts upstream of liver and kidneys. When neither the lungs nor any other organ plays a significant role in the overall clearing process, the total plasma clearance is the sum of hepatic and renal clearances:

and CLh can be obtained by difference.

Clearance of drugs occurs by blood perfusing the organ of extraction. Extraction refers to the proportion of the drug arriving at the organ and removed irreversibly by excretion or metabolism. Hepatic intrinsic clearance (CLint) refers to the global capacity of the hepatocytes to contribute to the processes of the hepatic elimination. CLint can be estimated from in vitro studies using hepatocytes and the drug as substrate and scaling up to whole liver dimensions:

^^ Vmax number of hepatocytes in the liver mt Km number of cultured hepatocytes

For drugs highly extracted by the liver (high CLint), clearance depends on the blood flow perfusing the liver, and causes a large hepatic first-pass effect. Conversely, for a drug with a low CLint, clearance depends on Cu, the free concentration of the drugs, which is only available for extraction, and on enzymatic activity. Equation [14] then becomes eqn [25]:

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