Expanded Answers for Study Problems in: Rowland & Tozer's Clinical Pharmacokinetics: Concepts and Applications, 3rd edition.

Chapter 10 - Distribution

Study Problems on Page 153

1. Apparent volume of distribution - The volume of fluid into which the xenobiotic would need to be distributed to give rise to the measured plasma/blood concentration.

Remember that the volume of distribution is essentially a proportionality constant between the amount of drug in the body and the concentration in a reference fluid (e.g., blood, plasma or serum). Drug which is in the tissues is essentially inaccessible for sampling; which may lead to an apparent volume which is higher than all physiologic volumes combined. That is why volume of distribution is most appropriately referred to with the qualifier apparent

3.a) With a volume of distribution in a 70 kg subject of 8 L, the drug clearly has a volume of distribution which exceeds that of plasma volume. Certainly, this would be consistent with a drug which is highly bound to plasma proteins - which would restrict a significant portion of the drug from distributing into extracellular space (creating an apparent volume of distribution less than this value).

b) This is also consistent with the observation. While one tends to think of a drug which is bound to components outside blood as having a large volume of distribution, if a drug is also highly bound to plasma proteins, only a small portion of the drug will escape vascular space and distribute to other tissues.

c) This is not consistent with the observations. If the drug was not bound to plasma proteins you would expect it to have an apparent volume which was 1) equal to plasma volume (if physicochemical characteristics made it impermeable to capillary membranes, 2) equal to extracellular space (if it could access all extracellular sites but could not cross cell membranes) or 3) larger than extracellular space. Since this drug exhibits an apparent volume of distribution which is between vascular volume and extracellular volume, it must be restricted, to some degree, in its distribution by binding to plasma proteins.

4.a) The answer in the textbook is technically incorrect. You'll note in the answer on p. 523 that the control curve (solid) line is displaced from that shown on p. 153 (Actually, it appears that the control curves for 4a and 4b have been switched in the answer section). The y-intercept on the control curve on p. 153 is 10 mg/L, while that given in the answer on p. 523 is about 5 mg/L (Thus, the volume of distribution of drug A in the control state is 50 L, not 100 L as stated in the answer section of the text.). However, the directional change given in the answer is correct. If the tissue binding is decreased in the presence of drug B, f_ut will increase. Clearance is independent of tissue binding, thus it will not change. An increase in f_ut will result in a decrease in V_ss (see p. 107 of class handout). The decrease in volume of distribution will result in an increase in the initial concentration. A decreased V_ss in the face of an unchanged CL will result in a decrease in the half-life of the drug. Thus, the peak concentration will increase, but concentrations will decline more rapidly (as shown in the answer on p. 523). The concentration vs time curve for unbound drug will change in a similar manner for the same reasons.

b) A drop in albumin will cause an increase in the f_ub and f_up (see Eq. 53 on p. 104 of class handout). This will result in an increase in the volume of distribution, causing a decline in the initial concentration. If the agent is a low clearance drug (which the answer in the book assumes, but is nowhere stated in the question), an increase in the fraction unbound will result in an increase in the total clearance. The increase in volume and clearance are proportional, therefore, no change in t_1/2 will occur. This means that the curve for total drug (A) in the presence of drug B will display a lower peak concentration, but will decline in parallel to the control curve. On the other hand, the curve for unbound drug will not change compared to control since none of the parameters which affect unbound drug will be altered.

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