- average plasma concentration,
equation to calculate or adjust an appropriate dosing regimen
return to the Course index
previous | next
equation to calculate or adjust an appropriate dosing regimen
return to the Course index
previous | next
Material on this website should be used for Educational or Self-Study Purposes Only
Copyright © 2001-2010 David W. A. Bourne (david@boomer.org)
return to the Course index
previous | next
Equation 15.2.1 Cp after a Single Oral Dose
This can be converted to an equation describing plasma concentration at any time following n equal doses with constant dosing interval t using a "multiple dose function".
Equation 15.2.2 Multiple Dose Function
Figure 15.2.1 Plot of Cp versus Time for Multiple Oral Doses showing Cpmax and Cpmin
Click on the figure to view the interactive graph
Interactive graph as a Semi-log Plot
The Cpmax value could be calculated at the time t = tpeak after many doses (as n approaches ∞) but it is complicated by the need to determine the value for tpeak.
return to the Course index
previous | next
Material on this website should be used for Educational or Self-Study Purposes Only
Copyright © 2001-2010 David W. A. Bourne (david@boomer.org)
return to the Course index
previous | next
Equation 15.3.1 Cpmin after Many Oral Doses - Version 1
This can be further simplified if we assume that the subsequent doses are given after the plasma concentration has peaked and e-ka • τ is close to zero. That is the next dose is given after the absorption phase is complete.
Figure 15.3.1 Plot Cp versus Time after a Single Dose showing Possible Time of Second Dose
Cpmin then becomes:
Equation 15.3.2 Cpmin after Many Oral Doses - Version 2
The relationship between loading dose and maintenance dose and thus drug accumulation during multiple dose administration can be studied by looking at the ratio between the minimum concentration at steady state and the concentration at the end of the first dosing interval,τ, after the first dose. [Assuming e-ka • τ is close to zero].
Equation 15.3.3 Ratio Between Cp after First and Last Dose
Which can be simplified to give:
Equation 15.3.4 Ratio Between Cp after First and Last Dose
This turns out to be the same equation as for the multiple IV bolus doses. Therefore we can estimate a loading dose just as we did for an IV multiple dose regimen.
Equation 15.3.5 Loading Dose Equation
This equation holds if each dose is given after the absorption phase of the previous dose is complete.
We can further simplify Equation 15.3.2 when ka is high if we assume that ka >> kel then (ka - kel) is approximately equal to ka and ka/(ka - kel) is approximately equal to one.
Equation 15.3.6 Cpmin after Many Oral Doses - Version 3
Equation 15.3.6 is an even more extreme simplification. However, it can be very useful if we don't know the ka value but we can assume that absorption is reasonably fast. Equation 15.3.6 will tend to give concentrations that are lower than those obtained with the full equation (Equation 15.3.1). Thus any estimated fluctuation between Cpmin and Cpmax will be overestimated using the simplified equation.
Click on the figure
to download and use this Excel spreadsheet
return to the Course index
previous | next
Material on this website should be used for Educational or Self-Study Purposes Only
Copyright © 2001-2010 David W. A. Bourne (david@boomer.org)
return to the Course index
previous | next
or Cp(bar).
The average plasma concentration is defined as the area under the plasma concentration versus time curve during the dosing interval at steady state divided by the dosing interval.
Thus:
Equation 15.4.1 Average Cp for a Dosing Interval at Steady State
Figure 15.4.1 Plot of Cp versus Time after Multiple Oral Administration showing AUC at Steady State
Since,
Equation 15.4.2 AUC Equation
from the equations developed during the Wagner-Nelson derivation or from the clearance (kel • V) equation.
Equation 15.4.3 Average Cp for a Dosing Interval at Steady State
This works because the AUC during one dosing interval at steady state is the same as the AUC from zero to infinity after one single dose.
An interesting result of this equation is that we get the same average plasma concentration whether the dose is given as a single dose every dosing interval, τ, or is subdivided into shorter dosing intervals. For example 300 mg every 12 hours will give the same average plasma concentration as 100 mg every 4 hours. However, the difference between the maximum and minimum plasma concentration will be larger with less frequent dosing.
We could now calculate the loading dose
To get some idea of the fluctuations in plasma concentration we could calculate the Cpmin value.
Assuming that ka >> kel and that e-ka • τ approaches 0 we can use Equation 26.2.6.
Therefore the plasma concentration would probably fluctuate between 7 and 23 mg/L (very approximate) with an average concentration of about 15 mg/L. [23 = 15 + (15 - 7), i.e. high = average + (average - low), very approximate!].
Figure 15.4.2 Figure Illustrating Cpmax, Cpmin and Cp(average)
The would be the same
Thus the plasma concentration would fluctuate between about 10.4 to 20 with an average of 15 mg/L.
With F = 1.0, V = 30 liter, t1/2 = 6 hours or kel = 0.693/6 = 0.116 hr-1, a dose of 600 mg given every 12 hours will achieve an average plasma concentration of approximately 15 mg/L. Try simulating this regimen and also the alternate regimen of 1200 mg very 24 hours and 300 mg every 6 hours. Which regimen gives the least variation between Cpmax and Cpmin? Explore the problem as a Linear Plot - Interactive graph
Carbamazepine is a drug which can induce its own metabolism during the first few days of therapy (Hawkins Van Tyle and Winter, 2004). After the first dose, carbamazepine pharmacokinetic parameters include F = 0.8, V = 1.4 L/hr, CL = 0.028 L/Kg/hr. After 3 to 5 days carbamazepine metabolism is induced such that the CL becomes 0.064 L/Kg/gr. For a 70 Kg patients pre-induction (first-dose) parameter values are kel = 0.02 hr-1 and V = 100 L. After induction the kel changes to 0.045 hr-1. Dose adjustment during the first few days can be difficult. Using post induction parameters for initial dosage regimen could cause toxic concentrations. For example, try the simulation again with a dose regimen of 600 mg every 12 hours with both pre and post induction kel values. The typical therapeutic plasma concentration range is 4 - 12 mg/L. Explore the problem as a Linear Plot - Interactive graph
Theophylline is marketed in a number of oral dosage forms. Rapid release tablets generally are rapidly and completely absorbed with F close to 1.0 and ka values above 2 hr-1. The apparent volume of distribution is approximately 0.5 L/Kg (ideal body weight, IBW). Average values of theopylline clearance approximate 0.04 L/Kg/hr (based on IBW). A number of factors can influence this average clearance value. For example; smoking x 1.6, cimetidine co-administration x 0.6, phenytoin co-administration 1.6, congestive heart failure x 0.5 (depending on status), cystic fibrosis x 1.5, hepatic cirrhosis x 0.5. Considering a 70 Kg (IBW) non-smoker patient the expected V and kel might be 35 L and 0.08 hr-1. For a patient that smokes the kel would be expected to be approximately 0.125 hr-1. Try adjusting the parameter values according to these covariates and adjust the dosing regimen to maintain appropriate therapeutic concentrations. Explore the problem as a Linear Plot - Interactive graph
return to the Course index
previous | next
Material on this website should be used for Educational or Self-Study Purposes Only
Copyright © 2001-2010 David W. A. Bourne (david@boomer.org)
return to the Course index
previous | next
For example, calculate drug concentration at 24 hours after the first dose of 200 mg. The second dose of 300 mg was given at 6 hours and the third dose of 100 mg at 18 hours. The apparent volume of distribution is 15 L and the elimination rate constant is 0.15 hr-1.
The concentration from the first dose at 24 hours after the administration of the first dose
The concentration from the second dose at 24 hours after the administration of the first dose
The concentration from the third dose at 24 hours after the administration of the first dose
The total concentration from all three doses at 24 hours after the administration of the first dose. This method involved calculating the contribution from each dose at a time 24 hours after the first dose.
The result of this calculation is shown graphically in Figure 15.5.1.
Figure 15.5.1 Drug Concentration after Three IV Bolus Doses
Another approach is to work through the dosing regimen dose by dose.
Total drug concentration just after the first dose
Total drug concentration just before the second dose
Total drug concentration just after the second dose
Total drug concentration just before the third dose
Total drug concentration just after the third dose
Total drug concentration 6 hours after the third dose. This answer can also be calculated using an Excel spreadsheet illustrating the superposition principle.
Click on the figure
to download and use this Excel spreadsheet
Dosing three times a day may be interpreted as take with meals, the plasma concentration may then look like the plot in Figure 60. The ratio between Cpmax and Cpmin is seven fold (8.2/1.1 = 7.45) in this example.
Figure 15.5.3 Cp versus Time during Dosing at 8 am, 1 pm, and 7 pm
However this regimen may be acceptable if
1) the drug has a wide therapeutic index
2) there is no therapeutic disadvantage to low overnight plasma concentrations, e.g., analgesic if patient stays asleep.
This regimen can be explored further using an Excel spreadsheet illustrating the superposition principle.
Click on the figure
to download and use this Excel spreadsheet
return to the Course index
previous | next
Material on this website should be used for Educational or Self-Study Purposes Only
Copyright © 2001-2010 David W. A. Bourne (david@boomer.org)