What Is the Formula for Calculating Bioavailability?

Bioavailability is a fundamental concept in pharmacology, representing the fraction or percentage of an administered drug dose that reaches the systemic circulation in an unchanged form. Understanding this value is important because it directly impacts the concentration of the active substance available to produce a therapeutic effect. This measurement is used to determine correct dosing regimens and ensure both the safety and efficacy of a medication.

The calculation of bioavailability is a core component of pharmacokinetics, the study of how a drug moves through the body. Since the drug must be in the bloodstream to be distributed to its target tissues, the amount reaching systemic circulation is the standard measure of exposure, quantified by calculating the Area Under the Curve (AUC) from a plasma concentration-time graph.

Calculating Absolute Bioavailability

The calculation for absolute bioavailability, represented by \(F\), compares the drug’s exposure from a non-intravenous (non-IV) route to the exposure from a standard intravenous (IV) injection. An IV dose is administered directly into the bloodstream, bypassing all barriers, meaning its bioavailability is defined as 100%, or \(F=1\). Any other route of administration, such as oral or transdermal, will have an absolute bioavailability less than or equal to this standard.

The standard formula for calculating absolute bioavailability is a ratio of dose-normalized exposures: \(F = \frac{(AUC_{non-IV} / Dose_{non-IV})}{(AUC_{IV} / Dose_{IV})}\).

The Area Under the Curve (AUC) is the definite integral of the drug concentration in the blood plasma over time. AUC represents the total drug exposure the body receives and is expressed in units like \(\text{mg} \cdot \text{h}/\text{L}\). Using AUC accounts for the entire time the drug is present in the body, not just the peak concentration.

The AUC is determined by measuring drug concentration in blood samples taken at various time points after administration, often using mathematical techniques like the trapezoidal rule. The formula requires a correction for the administered dose because the amounts given via the two routes are often different. This calculation compares the amount of drug absorbed per milligram of dose for the non-IV route against the amount absorbed per milligram of dose for the IV route. Absolute bioavailability varies widely, but a successful oral drug often has a value of at least 20%.

Understanding Relative Bioavailability

Relative bioavailability is calculated when comparing two different non-intravenous formulations of the same drug. This measurement is frequently used during drug development or regulatory studies to compare a new formulation against a previously approved reference formulation. It helps determine if two products are bioequivalent, meaning they deliver the active substance to the systemic circulation at a similar rate and extent.

The formula for relative bioavailability (\(F_{rel}\)) is: \(F_{rel} = \frac{(AUC_{test} / Dose_{test})}{(AUC_{reference} / Dose_{reference})}\). If the doses are the same, the calculation simplifies to a direct ratio of the AUCs.

If \(F_{rel}\) is close to 1 (or 100%), it suggests that the test formulation will provide a similar therapeutic effect to the reference. This concept is important for generic drugs, which must demonstrate bioequivalence to the original brand-name drug by showing their absorption falls within an acceptable range of the reference product.

Key Factors That Influence Bioavailability

The final bioavailability value (\(F\)) is determined by physiological and chemical barriers that prevent the entire administered dose from reaching the systemic circulation.

First-Pass Metabolism

One of the most significant obstacles for orally administered drugs is first-pass metabolism. This is the process where a drug is metabolized in the gut wall or liver before it reaches the rest of the body. After absorption from the intestine, the drug is transported via the portal vein directly to the liver, where enzymes can break down a large fraction of the dose, effectively lowering the systemic exposure.

Solubility and Dissolution Rate

Factors related to the physical and chemical properties of the drug include its solubility and dissolution rate. For a solid drug to be absorbed in the gastrointestinal (GI) tract, it must first dissolve into the GI fluids. If a drug has poor water solubility, it will dissolve slowly, resulting in insufficient time for complete absorption before elimination. Pharmaceutical formulations, including inactive ingredients, are often engineered to enhance the dissolution rate and improve absorption.

Membrane Permeability

The drug’s ability to cross biological barriers, known as membrane permeability/absorption, also affects bioavailability. To enter the bloodstream, the drug must pass through the lipid membranes of the cells lining the GI tract. Factors like the drug’s size, its ability to dissolve in fats (lipophilicity), and its charge (ionization state) all influence how easily it can permeate the gut wall. Additionally, the intestinal cell membrane contains transport proteins that can actively pump the drug back into the gut lumen, reducing the net amount absorbed.