PHARMACOKINETICS AND BIOPHARMACEUTICS (46:138)

LECTURE TUTORIAL

Dose- and Time-Dependent Pharmacokinetics

Key Terms:

 

Dose-dependent pharmacokinetics: For drugs whose elimination follows first-order kinetics, the CL and Vss are independent of dose – meaning that as dose is increased these parameters are constant. For some compounds, CL and Vss increase or decrease as dose is increased. Such compounds are said to display dose-dependent pharmacokinetics. While commonly referred to as ‘dose-dependent’, they are really ‘concentration-dependent’ … since it is the concentration and not the dose that is really important.

 

Time-dependent pharmacokinetics: For drugs eliminated via first-order kinetics, CL and Vss do not change with time. For a few compounds, the CL and/or Vss will change as a function of time after dosing, resulting in time-dependent pharmacokinetics. Some drugs will appear to display time-dependent kinetics, when the actual cause is dose dependent kinetics. For example, immediately after the administration of a high dose of phenytoin, the clearance is lower than it is 8 hrs after dose administration. But this ‘time-dependent’ effect is actually due to the fact that the concentration of the drug has decreased during that time period. Thus, the kinetics are not really time-dependent, but rather dose-dependent. A true example of time-dependent kinetics is autoinduction.

 

Capacity-limited metabolism: There are a finite number of drug metabolizing enzymes. As a consequence, if you increase the concentration of any substrate you will saturate the enzyme. This is theoretically possible with any drug that is metabolized. However, only a few compounds approach this concentration within the normal therapeutic range of the drug.

 

Autoinduction: This occurs when a compound increases its own metabolism. Carbamazepine is the most potent agent resulting in autoinduction in man.

 

Co-substrate depletion: Conjugation reactions require an endogenous co-substrate. At high doses of the drug, depletion of the co-substrate may occur, resulting in a reduced elimination of the compound compared to that seen after lower doses.

 

Key Principles:

 

            Any pharmacokinetic process that depends upon the interaction of a drug with an endogenous protein has the potential to be saturated and to display dose- or time-dependent pharmacokinetics. There are obviously a limited number of enzymes, transporters, and binding proteins. Therefore, any drug that binds to such endogenous macromolecules can exhibit dose-dependent pharmacokinetics. However, for most drugs, this does not occur within the normal therapeutic doses of the drug. Even if such saturation does not occur after normal doses, it may occur after an inadvertent or intentional overdose. This is important to keep in mind as the kinetics of a drug after an overdose may differ from that seen after therapeutic doses of the drug.

 

            A key step in determining whether or not dose- or time-dependent pharmacokinetics occurs is to determine whether or not key pharmacokinetic parameters (especially CL  and Vss) change with dose or time. For this reason, it is important to understand the relationship between important pharmacokinetic parameters and dose or time. The mechanism of dose- or time-dependency gives us insight into what pharmacokinetic parameters change with dose or time.

 

            Co-substrate depletion and simple capacity-limited metabolism can be differentiated by the appearance of their concentration versus time relationship after several doses. After administration of high doses of drugs exhibiting capacity-limited elimination and co-substrate depletion, the clearance of the drug will be lower than that seen after low doses. However, for drug eliminated by the capacity-limited metabolism, the clearance will increase as the concentration decreases. This does not occur after a high dose of a drug given via co-substrate depletion. With the high dose the co-substrate concentrations drop, which reduces the clearance of the drug. As a consequence, the clearance remains reduced even as the concentration decreases. This results in clear difference in the concentration-time relationship. Shown below is the concentration versus time curve after several doses of a drug that exhibits capacity-limited elimination. Notice that at high concentrations of the drug after a large dose the drug concentration declines with a ‘half-life’ that is longer than that seen after a low dose of the drug. However, when the concentration declines to levels similar to that seen after the low dose, the drug now declines in parallel with that seen after the lower dose (i.e., same half-life during this portion of the curve). This results in a curvilinear decline in drug concentration after a high dose.

 


           

 

           

The picture with a drug that exhibits co-substrate depletion is very different. As shown in the figure below, when dose is increased, the half-life is increased. However, it does not decline to a more rapid rate when the concentration declines to a level similar to that seen after a low dose. This results in a linear decline in drug concentration regardless of dose, though the slope of the line changes with dose.

 


Practice Problems:

 

 

1.      Draw a plot illustrating the relationship between t1/2 and dose for a drug that exhibits capacity-limited metabolism and one that displays first-order elimination throughout the dose range. Answer

 

2.      Draw a plot illustrating the relationship between t1/2 and dose for a drug that is eliminated by two pathways. One pathway exhibits capacity-limited metabolism while the other pathway displays first-order elimination throughout the dose range. Answer

 

3.      Draw a plot illustrating the relationship between Vss and dose for a drug that displays saturable plasma protein binding and an initial volume of distribution of 18 L/kg.  Answer

 

4.      Draw a plot illustrating the relationship between Vss and dose for a drug that displays saturable tissue binding and an initial volume of distribution of 18 L/kg.  Answer

 

5.      Draw a plot illustrating the relationship between AUCoral and dose for a drug that displays saturable first-pass metabolism. On the same plot show the relationship between AUCiv and dose for the same drug.  Answer

 

6.      Draw a plot illustrating the relationship between CL and dose for a drug that is administered intravenously, exhibits a high intrinsic hepatic clearance, and displays significant negative inotropic effects. Answer

 

7.      Patients receiving amitriptyline chronically have been have elevated levels of alpha1-acid glycoprotein. The average pharmacokinetic parameters for amitriptyline are as follows:

 

Vss = 15 L/kg      CLT = 15 ml/min/kg      Urinary Excretion (%) = <2     fup = <0.1

 

           Additionally, amitriptyline is a basic, lipophilic compound. With this knowledge of the pharmacokinetics of amitriptyline, as well as the knowledge that alpha1-acid glycoprotein concentration will increase with time during chronic dosing with the drug, draw a plot showing the relationship between Vss and time. Draw another plot showing the relationship between CLT and time. Answer

 

8.      Metabolism of phenylbutazone results in the formation of a metabolite that inhibits the metabolism of phenylbutazone in a process referred to as product inhibition. Draw a graph showing the relationship between the clearance of phenylbutazone and time after a dose. Assume that the metabolite exhibits elimination rate-limited elimination.  Answer

 

 

                    

 

Last revised 07/13/05

 

ă 2005 - Craig K. Svensson, Pharm.D., Ph.D.

 

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