1. Selected Bioavailability and Pharmacokinetic Calculations
University of Sulaimani College of Pharmacy 2nd Stage Pharmaceutical Orientation
Selected Bioavailability and
Pharmacokinetic Calculations
Lecture (7)
Shahen S. Mohammed
BSc Pharmacy
MSc pharmaceutics

2. Bioavailability refers to the relative amount of drug from an administered dosage form that enters the systemic circulation.
Pharmacokinetics is the study and characterization of the time course of the absorption, distribution, metabolism, and elimination (ADME) of drugs.

3. Drug Availability from Dosage Forms and Delivery Systems
The availability of a drug from a dosage form or delivery system is determined by measuring its dissolution characteristics in vitro (outside the biologic system) and/or its absorption patterns in vivo (within the biologic system). Generally, data are collected that provide information on both rate and extent of drug dissolution and/or absorption.
The data collected may be plotted on graph paper to depict concentration versus time curves for the drug’s dissolution and/or absorption.

4. Example;
The following dissolution data were obtained from a 250-mg capsule of ampicillin. Plot the data on graph paper and determine the approximate percentage of ampicillin dissolved following 15, 30, and 45 minutes of the study.

5. Ploting data

6. Determining the intercepts at 15, 30, and 45 minutes:
At 15 minutes, approximately 50 mg or 20% of the ampicillin,
At 30 minutes, approximately 100 mg or 40% of the ampicillin,
At 45 minutes, approximately 125 mg or 50% of the ampicillin,

7. Example Calculations of Bioavailability and Bioequivalence
Amount of Drug Bioavailable from a Dosage Form
If drug dissolution or drug absorption studies demonstrate consistently that only a portion of a drug substance in a dosage form is ‘‘available’’ for biologic absorption, the drug’s bioavailability factor (F), which represents the decimal percentage of a drug substance available, may be used to calculate bioavailability.
The value of F may be zero, indicating no absorption, to a maximum of a value of 1, indicating complete absorption.

8. If the bioavailability factor (F) for a drug substance in a dosage form is 0.60, how many milligrams of drug would be available for absorption from a 100-mg tablet of the drug?
The bioavailability factor (F) indicates that only 60% of the drug present in the dosage form is available for absorption. Thus:
100 mg × 0.60 = 60 mg

9. ‘‘Bioequivalent’’ Amounts of ‘‘Bioinequivalent’’ Dosage Forms
The bioavailability of a given drug substance may vary when in different dosage forms or in the same dosage form but from a different manufacturer. Thus, it may be desired to calculate the equivalent doses for two bioinequivalent products.

10. If the bioavailability (F) of digoxin in a 0. 25-mg tablet is 0
If the bioavailability (F) of digoxin in a 0.25-mg tablet is compared to the bioavailability (F) of 0.75 in a digoxin elixir (0.05 mg/mL), calculate the dose of the elixir equivalent to the tablet.
First, calculate the amount of ‘‘bioavailable’’ digoxin in the tablet:
0.25 mg × 0.60 = 0.15 mg, bioavailable amount of digoxin in the tablet.
Next, calculate the amount of ‘‘bioavailable’’ digoxin per milliliter of the elixir:
0.05 mg × 0.75 = mg, bioavailable amount of digoxin per milliliter of the elixir

11. Finally, determine the quantity of elixir that will provide 0
Finally, determine the quantity of elixir that will provide 0.15 mg of ‘‘bioavailable’’ digoxin:
By proportion:

12. Plotting and Interpreting a Blood-Drug–Concentration-Time Curve
Following the administration of a medication, if blood samples are drawn from the patient at specific time intervals and analyzed for drug content, the resulting data may be plotted on ordinary graph paper to prepare a blood-drug–concentration-time curve.
The vertical axis of this type of plot characteristically presents the concentration of drug present in the blood (or serum or plasma) and the horizontal axis presents the times the samples were obtained after administration of the drug.

13. When the drug is first administered (time zero), the blood concentration of the drug should also be zero. As an orally administered drug passes into the stomach and/or intestine, it is released from the dosage form, fully or partially dissolves, and is absorbed.
As the sampling and analysis continue, the blood samples reveal increasing concentrations of drug, until the maximum (peak) concentration (Cmax) is reached.
Then the blood level of the `drug decreases progressively and, if no additional dose is given, eventually falls back to zero.

14. For conventional dosage forms, such as tablets and capsules, the Cmax will usually occur at only a single time point, referred to as Tmax.
The quantity of a dose administered and its bioavailability, dissolution, and absorption characteristics influence the blood level concentration for a drug substance.
The rate or speed of drug absorption determines the Tmax, the time of greatest blood drug concentration after administration; the faster the rate of absorption, the sooner the Tmax.

15. In a blood-drug–concentration-time curve, the area under the curve (AUC) is considered representative of the total amount of drug absorbed into systemic circulation.

16. From the following data, plot a serum concentration-time curve and determine (a) the peak height concentration (Cmax) and (b) the time of the peak height concentration (Tmax).

17. Plotting the data and interpretation of the curve:

18. Determining the intercept for Cmax and Tmax:
Cmax = 4.0 µg/mL
Tmax = 2 hours

19. Calculation of the bioavailability (F) of a drug may be determined by comparison of the AUC data for the particular dosage form against the intravenous form;
It is recalled that the value F is the fraction of an administered dose that enters the systemic circulation. The intravenous route is the reference standard for comparison since the quantity of drug administered intravenously is considered to enter completely into the systemic circulation

20. If the AUC for an oral dose of a drug administered by tablet is 4
If the AUC for an oral dose of a drug administered by tablet is 4.5 mcg/mL and the intravenous dose is 11.2 mcg/mL, calculate the bioavailability of the oral dose of the drug.

21. Example Calculations of Pharmacokinetic Parameters
Plasma Concentration of Unbound Versus Bound Drugs
Once absorbed into the circulation, a portion of the total drug plasma concentration (CT) is bound to plasma proteins (usually albumin), and a portion remains unbound, or free. It is the unbound drug (CU) that is available for further transport to its site of action in the body.

23. The fraction of unbound drug in the plasma compared with the total plasma drug concentration, bound and unbound, is termed alpha (α). Thus;

24. If one knows the value of for α drug and the total plasma concentration (CT), the concentration of free drug in the plasma may be determined by a rearranged equation:

25. If the alpha (α) value for the drug digoxin is 0
If the alpha (α) value for the drug digoxin is 0.70, what would be the concentration of free drug in the plasma if the total plasma concentration of the drug were determined to be 0.7 ng/mL?

26. Apparent Volume of Distribution of a Drug Substance
The volume of distribution is an indicator of the extent of a drug’s distribution throughout the body fluids and tissues.
After a dose of a drug is administered intravenously, a change in the concentration of the drug in the blood means a corresponding change in the drug’s concentration in another body fluid or tissue. This sequence allows an understanding of the pattern of the drug’s distribution.

27. Different drugs administered in the same amount will show different volumes of distribution because of different distribution characteristics. For example, drugs that remain in the blood after intravenous administration because of drug binding to plasma proteins or to blood cells show high blood concentrations and low volumes of distribution. Conversely, drugs that exit the circulation rapidly and diffuse into other body fluids and tissues show low blood concentrations and high volumes of distribution.

28. The equation for determining the volume of distribution (Vd) is:
in which D is the total amount of drug in the body, and Cp is the drug’s plasma concentration.

29. A patient received a single intravenous dose of 300 mg of a drug substance that produced an immediate blood concentration of 8.2 µg of drug per milliliter. Calculate the apparent volume of distribution.

30. Four hours following the intravenous administration of a drug, a patient weighing 70 kg was found to have a drug blood level concentration of 10 µg/mL. Assuming the apparent volume of distribution is 10% of body weight, calculate the total amount of drug present in body fluids 4 hours after the drug was administered.

32. Elimination Half-Life and Elimination Rate Constant
The elimination half-life (t1⁄2) is the time it takes for the plasma drug concentration (as well as the amount of drug in the body) to fall by one half.
For example, if it takes 3 hours for the plasma concentration of a drug to fall from 6 to 3 mg/L, its half-life would be 3 hours. It would take the same period of time (3 hours) for the concentration to fall from 3 to 1.5 mg/ L, or from 1.5 to 0.75 mg/L.

33. Many drug substances follow first-order kinetics in their elimination from the body, meaning that the rate of drug elimination per unit of time is proportional to the amount present at that time.
When drug elimination occurs at a constant rate, we call this zero order kinetics
After five elimination half-lives, it may be expected that virtually all of a drug (97%) originally present will have been eliminated.

34. The elimination rate constant for a first-order process may be calculated using the equation:

35. Calculate the elimination rate constant for a drug that has an elimination half-life of 50 minutes.