PHA 5127

Problem Set
"Drug Distribution"

 

 

 

1. Mark whether the following statements are True or False.

Answer:

  • drugs which are very lipophilic tend to distribute well into body tissues.
  •  
  • drugs which are predominantly ionized at physiologic pH do not readily distribute into tissues when compared to drugs which are primarily unionized. (Assuming tight membrane)
  •  
  • drugs are generally less well distributed to highly perfused tissues.
  •  
  • the volume of distribution depends only on the degree of tissue binding.
  •  
    •

    2. The volume of distribution in a 70 kg man is observed to be 10 liters. Indicate which one (or more) of the following statements is (are) consistent with the observation when you consider that albumin has a volume of distribution of about 7 liters.

    highly bound to plasma proteins

    does not pass any membranes

    not bound to plasma proteins

    low extraction drug

    3. Select the correct answer(s). Due to the nature of biological membranes, drugs with the following properties are more likely to cross most membrane barriers:

    ionized and lipophilic

    ionized and hydrophilic

    nonionized and lipophilic

    Nonionized and hydrophilic

    4. Mark the following statements true or false.

    Answer:

    The larger the volume of distribution:

  • the larger the necessary loading dose for an i.v. infusion
  • (this, I do not expect you to know, yet)
  •  
    •
  • the larger the plasma albumin binding
  •  
  • the higher the clearance
  • (this, I do not expect you to know, yet)
    •
  • more drug is outside of the plasma

    •

    More Sample problems.

     

    (1) Draw a simple diagram to illustrate the equilibrium between drug in the plasma and the tissue including both free and bound fractions.

    Equilibrium between bound/unbound drug in plasma/tisue

    fb is the fraction bound where

     

     

    (2) For drug X, the volume of distribution is normally 35L and 80% of the drug is bound to plasma proteins. In patients with hypoalbuminemia, plasma protein binding is reduced to 60%. Calculate the expected volume of distribution.

    For drug x, Vd = 35L and 80% plasma protein binding. What is Vd if binding is reduced to 60% in plasma? In order to calculate this, it must be assumed that no change occurs in the tissue binding. Recall the equation relating Vd to plasma/tissue binding:

     

    In this problem fu changes from fu = 0.2 to fu = 0.4. However, before we can put this new value into the equation, we must find VT/fuT (or assume VT = VTW = 38L and solve for fuT).

    Solving for VT/fuT:

     

    For VT = VTW = 38L, fuT is

    Now we can put in the new fu and determin the change in Vd.

    thus, Vd increased by almost a factor of 2.

     

    (3) To obtain a plasma concentration of 10 mg/L for drug X in the question above, what dose would be required for the normal patient and the patient with lower plasma protein levels?

    Want to achieve Cp0 = 10 mg/L for each case in problem 2. Assume iv bolus.

    Normal: Vd = 35

    or

    Hypoalbuminemia: Vd = 67L

    Note: This adjustment in dosage is for a single dose given to reach a target plasma concentration. Nothing should be stated or assumed (yet) about the dosage for continued drug therapy. Steady-state levels in multiple dosing depend on clearance NOT Vd.

    (4) Determine the fraction of warfarin bound in tissue. Vd is 10L and the fraction unbound in plasma is 0.005.

    The Vd for warfarin is 10 L with the unbound fraction in plasma being 0.005. (Note: Handout stated "bound fraction". Make this correction). Determine the bound fraction in tissue. Returning to the equation:

     

    To determine the fraction bound, we must first find fuT. In order to do this, we assume VT = VTW. Solving this equation for fuT gives

     

    Putting in the values,

    The fraction bound is then

    Thus, 97% of the warfarin in tissues is bound.

     

    (5) Phenytoin and valproic acid have a high degree of plasma protein binding. When both drugs are given at the same time, valproic acid, which has a higher affinity for the binding site, displaces part of the bound phenytoin. What effect does this have on the volume of distribution of phenytoin?

    Let x = phenytoin, O = valproic acid

     

    (a)
    (b)

    If valproic acid displaces phenytoin at the binding sites on plasma proteins, fu of phenytoin increases. Thus, Vd  f pheytoin will also increase : (« ) = no change

     

    (6) Changes in fu are most important for highly bound drugs. How does an increase in fu effect Vd and/or the resulting Cp when fu is initially very small?

    Effects of a change in fu on Vd and Cp0 when drug is extensively bound to plasma proteins. The following diagram is from the book by Rowland and Tozer (p. 498)

    So what is this diagram telling us?

    -When there is a high degree of plasma protein binding, an increase in fu of 100 or 200% does not cause as much a change in Vd as is seen when plasma protein binding is less extensive. If Vd does not change dramatically, while there may be a slight decrease in overall concentration (recall: ), there will be more free drug. Thus a change in fu from fu = 0.01 to fu = 0.2 (due to e.g. displacement by another drug having a higher affinity for the binding sites on plasma proteins) could be compared to a doubling of the dose. Again, Vd is not the only consideration and the effects of binding will be addressed when we discuss clearance.

     

    Let’s put some numbers in the Vd expression to illustrate this. Consider a drug with high tissue binding, fuT = 0.1, and compare the Vd values which result when fu in plasma is 0.5, 0.1, 0.01, and 0.005 and when each is increased by a factor of 2.

    Recall:

    fu

    Vd(L)

    New fu

    New Vd(L)

    % increase in Vd*

    0.5

    193

    1.0

    383

    98.45

    0.1

    41

    0.2

    79

    92.68

    0.01

    6.8

    0.02

    10.6

    55.88

    0.005

    4.9

    0.01

    6.8

    38.78

    * %increase =

    Thus, when fu is very small, fluctuation in fu has less effect on Vd than when there is less initial binding to plasma proteins.

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