## PHARMACOKINETICS PROBLEMS

- Assuming first order kinetics what fraction of an IV drug dose remains in the body after 4 half-lives?
- The t
_{1/2}of a drug is 6 hours. What fraction is left in the body at 21h post drug administration? - Twenty percent of a drug dose remains in the body at t=10hours. What is the half-life of the drug?
- The plasma concentration of a drug administered by IV bolus injection may be described by the following equation:

C_{t }= 0.92e ^{-0.35t}

where C_{t} is in units of mg/L and the time (t) is in hours.

If the dose is 50mg calculate the following:

- The plasma concentration at 6.5h post dosing.
- The plasma half-life.
- The volume of distribution.
- The area under the plasma concentration versus time curve.
- The total clearance.

- Drug X is administered as an IV bolus dose of 100mg and the following plasma concentrations were obtained with time:

Time (h) | 0.25 | 0.5 | 1.0 | 3.0 | 5.0 | 7.0 | 10.0 |

Plasma Concentration (mg/L) | 2.6 | 2.4 | 2.1 | 1.2 | 0.75 | 0.45 | 0.2 |

Calculate the volume of distribution, plasma half-life and clearance of X.

X was subsequently administered via the oral route at a dose of 200mg as both an aqueous solution and as a formulated product. The measured areas under the plasma concentration time curves were 14.3 mg/L.h and 12.6 mg/L.h for the solution dose and formulated product respectively.

Using this data calculate the relative and absolute bioavailability of X.

- Drug W on IV administration to an experimental animal at a dose of 10mg/kg (animal weight 2.3kg) gave the following plasma concentrations with time:

Time (h) | 0.1 | 0.25 | 0.5 | 0.75 | 1.0 | 1,5 | 2.0 | 3.0 | 4.0 |

Plasma Concentration
(mg/L) |
4.2 | 3.2 | 2.3 | 1.8 | 1.5 | 1.2 | 1.09 | 0.88 | 0.71 |

Using the above data:

- Draw a diagram of a compartmental model that describes the plasma disposition of the drug and indicate any relevant rate constants.
- Write an equation describing the plasma concentration versus time curve (use numbers rather than symbols as much as possible).
- Calculate the values of the rate constants you have indicated in part (a).
- What is the terminal half-life of drug W?
- What is the volume of distribution of W and what is the initial dilution volume (volume of the central compartment)?
- Calculate the area under the plasma concentration versus time curve and compare this value with that obtained using the trapezoidal method.

- Drug Y is administered orally to a patient at a dose of 100mg and the following plasma concentrations were obtained with time:

Time (h) | 0.2 | 0.4 | 1.0 | 2.0 | 3.0 | 4.0 | 6.0 | 8.0 | 10.0 |

Plasma Concentration (mg/L) | 0.33 | 1.0 | 1.8 | 2.02 | 2.0 | 1.6 | 1.0 | 0.6 | 0.38 |

Calculate the absorption and elimination rate constants, the volume of distribution and clearance of Y assuming that F, the bioavailability, is equal to 0.75.

If the 100mg oral dose is repeated at 8 hourly intervals calculate the maximum, minimum and average steady-state plasma concentrations.

- Drug A is administered IV to a patient according to the following table:

Day | Time | Dose (mg) |

1 | 4.00pm | 80 |

11.00pm | 160 | |

2 | 7.00am | 120 |

1.30pm | 80 |

At 4.00pm on day 2 a plasma sample was analysed for A and a concentration of 6mg/L was obtained.

Is this measured concentration consistent with the expected value?

Volume of distribution of A is 14.5L and clearance is 40mL/min.