Syllabus

Nonlinear Pharmacokinetics: a. Introduction, b. Factors causing Non-linearity. c. Michaelis-menton method of estimating parameters, Explanation with example of drugs.

Introduction:

• In most cases, at therapeutic doses, the change in the amount of drug in the body or the change in its plasma concentration due to absorption, distribution, binding, metabolism or excretion, is proportional to its dose, whether administered as a single dose or as multiple doses. 
• In such situations, the rate processes are said to follow first-order or linear kinetics and all semilog plots of C versus t for different doses, when corrected for dose administered, are superimposable. This is called as principle of superposition. The important pharmacokinetic parameters viz. F, K_a, K_E, V_d, Cl_R and Cl_H which describe the time-course of a drug in the body remain unaffected by the dose i.e. the pharmacokinetics is dose-independent.
• In some instances, the rate process of a drug’s ADME are dependent upon carrier or enzymes that are substrate-specific, have definite capacities, and susceptible to saturation at high drug concentration. In such cases, an essentially first-order kinetics transform into a mixture of first-order and zero-order rate processes and the pharmacokinetic parameters change with the size of the administered dose. The pharmacokinetics of such drugs are said to be dose-dependent. Other terms synonymous with it are mixed-order, nonlinear and capacity-limited kinetics. Drugs exhibiting such a kinetic profile are sources of variability in pharmacological response.
• Definition: Non-linear pharmacokinetics occurs when the relationship between a drug’s dose and its resulting concentration in the body is not proportional. If the dose is doubled, the concentration may disproportional spike or drop, because the body’s mechanisms for absorption, distribution, or clearing the drug become saturated. 
• Non-linear pharmacokinetics is called dose-dependent kinetics because pharmacokinetic parameters—like how fast a drug is processed, cleared, or removed from the body—change depending on the size of the dose you take.
• If you double the dose, the blood concentration might triple or quadruple. The drug processing systems get overloaded, meaning the body’s rate of eliminating or distributing the drug is not fixed, but instead depends heavily on how much drug is introduced. 
• There are several tests to detect nonlinearity in pharmacokinetics but the simplest ones are –
• Determination of steady-state plasma concentration at different doses. If thesteady-state concentrations are directly proportional to the dose, then linearity in the kinetics exists. Such proportionality is not observable when there is nonlinearity.
• Determination of some of the important pharmacokinetic parameters such asfraction bioavailable, elimination half-life or total systemic clearance at different doses of the drug. Any change in these parameters which are usually constant, is indicative of nonlinearity.

Causes of Non-Linearity

Nonlinearities can occur in drug absorption, distribution, metabolism and excretion.

Drug Absorption

Nonlinearity in drug absorption can arise from 3 important sources –

1. When absorption is solubility or dissolution rate-limited e.g. griseofulvin. At higher doses, a saturated solution of the drug is formed in the GIT or at any other extravascular site and the rate of absorption attains a constant value.
2. When absorption involves carrier-mediated transport systems e.g. absorption of riboflavin, ascorbic acid, cyanocobalamin, etc. Saturation of the transport system at higher doses of these vitamins results in nonlinearity.
3. When presystemic gut wall or hepatic metabolism attains saturation e.g. propranolol, hydralazine and verapamil. Saturation of presystemic metabolism of these drugs at high doses leads to increased bioavailability.

The parameters affected will be F, K_a, C_max and AUC. A decrease in these parameters is observed in the dissolution rate-limited and carrier-mediated transport system cases and an increase in the presystemic gut wall attains saturation case. Other causes of nonlinearity in drug absorption are changes in gastric emptying and GI blood flow and other physiologic factors. Nonlinearity in drug absorption is of little consequence unless availability is drastically affected.

Drug Distribution

Nonlinearity in distribution of drugs administered at high doses may be due to –

1. Saturation of binding sites on plasma proteins e.g. phenylbutazone and naproxen. There is a finite number of binding sites for a particular drug on plasma proteins and, theoretically, as the concentration is raised, so too is the fraction unbound.
2. Saturation of tissue binding sites e.g. thiopental and fentanyl. With large single bolus doses or multiple dosing, saturation of tissue storage sites can occur.

In both cases, the free plasma drug concentration increases but V_d increases only in the former case whereas it decreases in the latter. Clearance is also altered depending upon the extraction ratio of the drug. 

Drug Metabolism

Two important causes of nonlinearity in metabolism are –

1. Capacity-Limited Enzymes: Hepatic (liver) enzymes that metabolize drugs have a maximum processing capacity (𝑉_𝑚𝑎𝑥). At low doses, clearance is proportional to concentration. At higher doses, the enzyme system saturates, causing the drug to accumulate rapidly in the body.
2. Enzyme Induction or Inhibition: Certain drugs can cause the liver to produce more enzymes (auto-induction) or block enzyme activity, which decreases or increases drug concentrations respectively over time. 

Saturation of enzyme results in decreased Cl_H and therefore increased C_ss. Reverse is true for enzyme induction. 

Drug Excretion

The two active processes in renal excretion of a drug that are saturable are –

1. Active Renal Secretion: The kidneys actively secrete certain drugs into the urine via transporter systems. These carriers have a limited capacity and can become saturated at high drug loads. E.g. penicillin G
2. Active Renal Reabsorption: Carrier mediated transporters that pull useful substances back from the urine into the blood can also become saturated, an increase in renal clearance occurs.

Other sources of nonlinearity in renal excretion include forced diuresis, changes in urine pH, nephrotoxicity and saturation of binding sites.
Biliary secretion, which is also an active process, is also subject to saturation e.g. tetracycline and indomethacin.