Box 51 Physicochemical Properties Of Pharmaceuticals Physiologic Variables And Pharmacokinetic Parameters

Regardless of the mathematical model— noncompartmental or compartmental —used to estimate pharmacokinetic parameters, absorption and disposition of a pharmaceutical depend on physiochemi-cal properties such as hydrophobicity, molecular diameter, and substrate recognition by exsorption or absorption transporter molecules at absorption and distribution sites. While plasma protein binding of protein-based biopharmaceuticals may not be a significant factor, binding of therapeutic proteins to circulating receptors may have a significant impact on distribution and elimination. Gastrointestinal (GI) absorption could also be influenced by gastric emptying rate, gastrointestinal motility, and blood flow rate. Distribution of a pharmaceutical in the body may also depend on the amount of body fat, typically measured by weight-to-volume ratio. Elimination of pharmaceuticals through renal excretion may depend on activity of secretion processes such as active transport and tubular reabsorption, which is often influenced by pH, electrolytes, and urine flow rate. Many of these physiological processes may be influenced by diseases and concurrent drug therapy. The following table lists pharmacokinetic parameters, mathematical relationships, and physiologic variables that may have an impact on these parameters.

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BOX 5.1. Continued

Pharmacokinetic Parameter

Mathematical Relationship

Physiological Variables

Absorption rate

ka

Vmax^[Drug]absorption sitea Km + [Drug]absorption site

Absorption site blood-flow rate; gastric emptying and intestinal motility rate for orally administered drugs; GI pH, precipitation at absorption site

Clearance, hepatic

CLh

Blood flow • Fraction of drug extracted by liver

Liver blood flow; protein binding; liver metabolism

Clearance, renal

CLr

Blood flow • Fraction of drug extracted by kidney

Renal blood flow; protein binding; active secretion, transport and reabsorption; glomerular filtration; urine pH; urine flow

Volume of distribution

Vd

Amount of drug in body [DrUg]plasma

Binding and partition to blood, tissues, and fat; body composition and size

Half-life, elimination

tl/2

0.693 • Volume of distribution Clearance

Blood flow, protein and tissue binding, metabolism, renal excretion

Elimination rate constant

ke

Clearance Volume of distribution

Blood flow, protein and tissue binding, metabolism, renal excretion

Fraction excreted unchanged

Renal clearance Total clearance

Renal blood flow; protein binding; active secretion, transport and reabsorption; glomerular filtration; urine pH; urine flow; metabolism

Area under the curve, IV dosing

AUCv

Dose Clearance

Protein and tissue binding, metabolism, renal excretion

Steady state plasma concentration, IV dosing

Css

Infusion rate Clearance

Metabolism, renal excretion

Area under the curve, oral dosing

AUCpa

Dose • Oral bioavailability Clearance

Fraction of dose absorbed, first pass metabolism, dosage formulation

Mean residence time

MRT

Volume of distribution Clearance

Route of administration; rate of absorption; IV infusion rate, metabolism and renal excretion

'Expression based on capacity-limited absorption (e.g., enzyme degradation) processes. Passive absorption processes can be approximated by first order kinetics. Under the usual therapeutic conditions:

\ ka = Vmax^[Drug] = ki .[Drug], Km

Which is a first-order process.

■TABLE 5.2. Volume of distribution for selected therapeutic proteins

Therapeutic Protein

Molecular Weight (kDa)

Volume of Distribution (Liter)

Erythropoietin

30.4

2.8-3.5

Human monoclonal antibody

150

5.6

Superoxide dismutase

~32

7

■TABLE 5.3. Dose-dependent effects on volume of distribution

Therapeutic Protein

Dose

Volume of Distribution (L)

Human recombinant tumor

25 mg/m2

66 ± 30

necrosis factor-a (rhTNF-a)

100mg/m2

12 ± 4

Human recombinant

10IU/kg

7.1 + 1.8

erythropoietin

50 IU/kg

3.2 ± 0.3

1000IU/kg

5.0 ± 1.8

Human recombinant DNAse

0.01 mg/kg

5.4

1 mg/kg

12.1

marketed for the treatment of cystic fibro-sis, increases with dose (Table 5.3).

The decrease in the distribution volume of TNF with an increase in dose is thought to be due to capacity-limited extravascular transport processes (Table 5.3). The increase in volume of distribution of DNase with an increase in dose is thought to be due to capacity limited protein binding to actin in plasma (possibly an actin-vitamin D-DNase ternary complex).

Small molecules are eliminated from the body largely by means of drug metabolism enzymes in the liver and other tissues and by urinary excretion. Large molecules are also eliminated by renal and hepatic mechanisms. Proteins that are less than 40 to 50kDa are cleared by renal filtration with little or no tubular reabsorption. Larger proteins are less likely to be filtered but may be subject to phagocytosis in hepa-tocytes and Kupfer cells in the liver. Protein biotransformation—denaturation, proteolysis, and oxidative metabolism—is also important.

Elimination from the body is described quantitatively in terms of drug half-life and clearance. As a first approximation, the fall in drug concentrations in plasma after absorption is complete can usually be described as a first-order process. Therefore, a plot of log drug concentration versus time is usually linear. The slope of this line is called the elimination rate constant with units of reciprocal time. The reciprocal of the elimination rate constant is called the half-life, the time required to eliminate 50% of the drug from the body. Drugs with short half-lives are rapidly eliminated from the body, while drugs with long half-lives may persist for days or weeks or even longer.

Drug clearance integrates the concepts of organ perfusion (flow rate) and the organ's ability to eliminate a drug (i.e., extraction ratio). A small-molecule drug that is completely filtered in the kidneys and totally extracted in the urine without tubular reabsorption has a clearance of 125ml/min, the same as the glomerular filtration rate. In theory, clearance can be estimated across all eliminating organs. The sum of these organ clearances is called the total body clearance of a drug.

Clearance may vary widely across individuals, especially for drugs largely eliminated by drug metabolizing enzymes, because of genetic variability or poly

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