Non-Linear Pharmacokinetics: Bioavailability and Absorption Processes

To be absorbed, a drug MUST be in solution. Generally, particles in a solid form (such as lumps or particles from tablets and capsules) are not absorbed by the body.
This lecture focuses specifically on gastrointestinal (GI) absorption following an oral dose, as this is the most common route of administration.
Most oral medications are solid dose forms, which requires the drug to dissolve within the GI tract before absorption can occur.
There is a limited window of time for absorption to take place following an oral dose due to the constant movement of material through the gastrointestinal tract (GI motility). Any drug that remains undissolved or unabsorbed by the time it completes its transit will be excreted in the faeces.

If a drug has poor aqueous solubility, increasing the dose increases the concentration of the drug within the gastrointestinal fluid.
At higher doses, this can lead to saturation of the dissolution process. Effectively, the GI fluid can only hold a certain amount of the drug in solution at once.
When saturation of dissolution occurs, a greater fraction of the higher dose remains undissolved compared to a lower dose.
Consequently, the extent of absorption decreases because only the dissolved drug can cross the biological membranes. This results in a decrease in the fraction absorbed ( $f_a$ ) and a corresponding decrease in bioavailability ( $F$ ).

Griseofulvin is a highly lipophilic drug with very poor aqueous solubility.
Principles of Linearity: In linear pharmacokinetics, dose-corrected concentration profiles (calculated as $\text{Concentration} / \text{Dose}$ ) should be superimposable regardless of the dose size.
Non-Linear Observation: When the dose of Griseofulvin is doubled, it results in only a $60\%$ increase in the amount of drug absorbed (rather than the expected $100\%$ increase).
In experimental data comparing two tablets versus four tablets, the concentration profile for the four-tablet dose (when divided by two to correct for the dose) is significantly lower than the two-tablet profile.
This discrepancy occurs because the fraction absorbed decreased as saturation of solubility prevented the entire higher dose from dissolving.

Once a drug is in solution, it must cross the membrane barrier. This can occur via passive diffusion or active transport.

Passive diffusion can be paracellular (moving between cell junctions, as seen in "leaky" blood vessels) or transcellular (moving directly through the cell membrane).
Transcellular diffusion is easier for lipophilic drugs.
Passive absorption is, by definition, a non-saturable process. Therefore, passive diffusion alone cannot result in non-linearity in bioavailability.

Active uptake involves specific transport proteins that facilitate the movement of drugs from the GI tract into the portal circulation.
Because these transporters are proteins with specific binding sites, they are saturable. There is a maximal rate at which they can transport molecules within the time the drug is present in the GI tract.
As the dose increases, the transporters become saturated, making the uptake process less efficient. A smaller fraction of the dose is transported as the dose increases.
Effect on Bioavailability: In cases of active uptake, the fraction absorbed ( $f_a$ ) and bioavailability ( $F$ ) both decrease as the dose increases.

Vitamin C (Ascorbic Acid): These transporters are highly selective for molecules essential for normal bodily function. At a dose of $100\,mg$ , Vitamin C is essentially entirely absorbed. However, at a dose of $5000\,mg$ ( $5\,g$ ), only about $1/5$ (one-fifth) of the dose is absorbed. The maximal uptake capacity is approximately $1\,g$ . Taking massive oral doses is self-limiting because the excess is not absorbed and is excreted in the faeces.
Amoxycillin (and other Beta-lactams): Penicillin-type antibiotics like amoxycillin are subject to active uptake. When doses are doubled (e.g., $375\,mg$ , $750\,mg$ , $1500\,mg$ , and $3000\,mg$ ), the dose-normalized concentration profiles ( $\text{Concentration} / \text{Dose}$ ) are not superimposable. The profiles for higher doses are progressively lower than those for lower doses. The Area Under the Curve ( $AUC$ ) increases in a less-than-proportionate manner relative to the dose, demonstrating non-linear bioavailability.

Efflux transporters (such as P-glycoprotein) act to pump drugs out of the intestinal wall and back into the duodenal lumen, preventing them from being absorbed into the systemic circulation.
Like uptake transporters, efflux transporters have a limited capacity and can be saturated as the concentration and dose of the drug increase.
Saturation of Efflux Effect: As the dose increases and these transporters become overwhelmed, a smaller fraction of the dose is pumped back out. This means more drug "escapes" efflux and is successfully absorbed.
Result: For drugs subject to active efflux, the fraction absorbed ( $f_a$ ) and the bioavailability ( $F$ ) will increase as the dose increases.

Certain drugs alter gastric emptying or GI transit time, affecting the absorption of other medications. While not purely "non-linearity" in the traditional sense, these interactions cause deviations from expected predictable patterns.
Opioids: Act on the enteric nervous system and opioid receptors to slow down gastrointestinal motility.
Tricyclic Antidepressants: Can also slow gastric emptying.
Example Comparison: Studies on Atenolol (alone vs. in combination with other drugs) show that the concentration profile changes. Drugs like metoclopramide or propantheline can speed up or slow down gastric emptying, leading to different concentrations at specific time points.
While these effects are predictable once a combination is established, the initial change in combination therapy mimics non-linear behavior.

Non-linearity can also occur regarding the time of day a dose is administered, rather than the size of the dose itself. This is often driven by circadian alterations in GI motility.
Example: Theophylline (Sustained Release Formulation):
- A morning dose administered at $8\,am$ is absorbed reasonably rapidly for a sustained release product, followed by a typical decline.
- An evening dose administered at $8\,pm$ or $9\,pm$ shows a very different profile. Absorption is significantly delayed throughout the night and begins much later.
- Result: If the concentration is measured at exactly $4\,hours$ post-dose, the morning concentration will be very different from the evening concentration.
While the total exposure ( $AUC$ ) may remain roughly the same, the shape of the time-concentration curve is vastly different, representing non-linearity with respect to the time of day.