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Extravascular
     Administration
  Anas Bahnassi PhD RPh



One compartment Model
LECTURE’S OBJECTIVES
• Upon completion of this lecture, the student will able to:
• Calculate plasma drug concentration at any given time after the
  administration of an extravascular dose of a drug, based on known or
  estimated pharmacokinetic parameters
• Interpret the plasma drug concentration versus time curve of a drug
  administered extravascularly as the sum of an absorption curve and an
  elimination curve
• Employ extrapolation techniques to characterize the absorption phase
• Calculate the absorption rate constant and explain factors that influence
  this constant
• Explain possible reasons for the presence of lag time in a drug’s absorption
• Calculate peak plasma drug concentration, (Cp)max, and the time, (tmax)at
  which this occurs
• Explain the factors that influence peak plasma concentration and peak time
• Decide when flip-flop kinetics may be a factor in the plasma drug
  concentration versus time curve of a drug administered extravascularly.
                                                                         2
                          Anas Bahnassi PhD 2011
Xa                 Ka
                                     X
We Need the following info:
                                                                      Xu
1.   Equation for determining the plasma concentration at any time t.
2.   Determination of the elimination half life (t½) and rate constant (K or
     Kel).
3.   Determination of the absorption half life (t½)abs and absorption rate
     constant (Ka).
4.   Lag time (t0), if any.




                                                                                   Anas Bahnassi PhD 2011
5.   Determination of the apparent volume of distribution (V or Vd) and
     fraction of drug absorbed (F).
6.   Determination of the peak time (tmax).
7.   Determination of the peak plasma or serum concentration, (Cp)max.
                                                                               3
Graph
                        2.50
Concentration (ng/mL)




                        2.00



                        1.50



                        1.00




                                                                      Anas Bahnassi PhD 2011
                        0.50



                        0.00
                               0   4   8    12     16   20   24
                                                                  4
                                           Hours
Amount Remaining in the
  First         Administration Site
 Order
 Process
             ������������������
           −        = ������������ (������������ )������
              ������������
                             −������������ ������                  −������������ ������
(������������ )������ = (������������ )������=0 ������              = ������������������ ������
                      Bioavailability                  Dose
  100% Absorbed

                                            −������������ ������
                   (������������ )������ = ������������ ������
Monitoring Drug in Site of
           First                    Measurement
          Order
          Process
                          ������������������
                        −        = ������������ (������������ )������ − ������������
                           ������������
       ������������ (������������ )������=0 −������������
������������ =                  ������    − ������ −������������ ������
          ������������ − ������
       ������������ ������������0 −������������
������������ =            ������    − ������ −������������ ������
       ������������ − ������
Elimination Half life (t1/2)
And Elimination Rate Constant(k)
                             ������������ ������������0
                  ������������������ =               ������ −������������ − ������ −������������ ������
                           ������(������������ − ������)
          10.00




           1.00
            Concentration




                                               t½


           0.10
                            0   4   8    12    16     20     24
                                        Time
Calculating Absorption Rate
                                            Constant (ka)
 Method of Residuals

  Feathering Method
Time (h)         Observed Plasma Extrapolated Plasma                    (������������)������������������������ = ������������������������������ − ������������������������������
                 Concentrations  Concentrations
                 (Cp)observed    (Cp)extrapolated
Time values      Values only from the        Values only from the      Differences between
corresponding    absorption phase            extrapolated portion of   extrapolated and observed
to observed      (i.e. all values prior to   the plot of plasma        values for each time in the
plasma           reaching maximum            concentration–time        absorption phase (units,
concentrations   or highest plasma           (units, e.g. (mgmL1)      e.g. mgmL-1)
for absorption   concentration) (units,
phase only       e.g. mgmL-1)



                                        ������������ ������������0
                     ������������������������������������   =               ������ −������������ ������
                                      ������(������������ − ������)
                                                                                                       8
                                                                                    Anas Bahnassi PhD 2011
Calculating Absorption Rate
                              Constant (ka)
Method of Residuals

Feathering Method




                                                ������������
                                   Slope=−
                                               2.303




                      Anas Bahnassi PhD 2011           9
Lag Time (t0)
Theoretically, intercepts of the terminal linear portion
and the feathered line should be the same; however,
sometimes, these two lines do not have the same
intercepts, Sometimes absorption starts after
administration, this delay may be contributed to:

  •    Slow tablet disintegration
  •    Slow and/or poor dissolution
  •    Incomplete wetting of drug particles
  •    Poor formula
  •    Delayed Release formula



                     Anas Bahnassi PhD 2011                10
Negative Lag Time (t0)
The presence of a negative lag time may be attributed to
inadequate data points in the absorption phase as well
as in the elimination phase. Another possible reason
may be that the absorption rate constant is not much
greater than the elimination rate constant.




                 Anas Bahnassi PhD 2011                    11
Analysis of Absorption
       ������������ ≫ ������         Rate Constant

 Quicker     Faster Onset   ������������ for a given drug can
Absorption     of Action    change as a result of:

                            • Changing the formulation
                            • Changing the dosage form
                              or the extravascular route
                              of administration.
                            • Administration of a drug
                              with or without food.
Apparent Volume of
Cannot be calculated from plasma   Distribution(Vd)
drug concentration data alone
WHY?
The fraction of drug absorbed (F) is
not known.
If the drug is 100 percent
absorbed; F=1 then
                        ������������ ������������0
 ������������������������������������������������������ =               If F is not known then it is best to
                      ������(������������ − ������)
                                                ������
                                    calculate
                                                   ������
                                        ������   ������������ ������0         1
                                           =          (                  )
                                        ������ (������������ −������) ������������������������������������������������������


                        Anas Bahnassi PhD 2011                               13
Calculating Peak Time(tmax)
������������
     = ������������ ������������ − ������������                  When t=tmax ������������ ������������ = ������������
������������
������������
     = ������������ (������������ )������������������������ − ������(������)������������������������ = 0
������������

   ������������ (������������ )������������������������ = ������(������)������������������������
           ������������ ������������0 −������������
 ������������ =                  ������   − ������ −������������ ������
          ������������ − ������
                 ������������ ������������0 −������������
������������������������������ =                ������ ������������������ − ������ −������������ ������������������������    ������������ ������        = ������������ −������������ ������������������������
                ������������ − ������                                          ������������������




                                    Anas Bahnassi PhD 2011                                      14
Calculating Peak Time(tmax)


Taking natural log of both sides:




              Anas Bahnassi PhD 2011   15
Significance of Peak Time(tmax)
•   To determine comparative bioavailability and/or
    bioequivalence
•   To determine the preferred route of drug administration and
    the desired dosage form for the patient
•   To assess the onset of action.

                                      Significance of Peak
                                      Concentration(Cmax)
• Used to determine the comparative bioavailability and/or the
  bioequivalence between two products.
• Used to determine the superiority between two different
  dosage forms or two different routes of administration
• Correlates with the pharmacological effect of a drug.
                     Anas Bahnassi PhD 2011                 16
Plot the data and, using the plot, determine


Question
                         the following.
                         a. The elimination half life (t1/2) for each dose.
                         b. The elimination rate constant (K) for each
                         dose.
                         c. The absorption half life, (t1/2)abs, for each
                         dose.
                         d. The absorption rate constant (Ka) for each
                         dose.
                         e. The observed and computed peak time (tmax)
                         for each dose.
                         f. The observed and computed peak plasma
                         concentrations, (Cp)max, for each dose.
                         g. The y-axis intercept for each dose.
                         h. The apparent volume of distribution (V).
                         i. The fraction of drug absorbed (F).
                         j. The characteristics of a plot on rectilinear
                         paper of peak time (tmax) against the
                         administered dose (then make an important
                         observation).
                         k. The characteristics of a plot on rectilinear
                         paper of peak plasma concentrations, (Cp)max,
                         i. Lag time if any.
                                                                 17
Anas Bahnassi PhD 2011
Pharmacokinetics

Anas Bahnassi PhD RPh

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Pharmacokinetics: Lecture four

  • 1. Extravascular Administration Anas Bahnassi PhD RPh One compartment Model
  • 2. LECTURE’S OBJECTIVES • Upon completion of this lecture, the student will able to: • Calculate plasma drug concentration at any given time after the administration of an extravascular dose of a drug, based on known or estimated pharmacokinetic parameters • Interpret the plasma drug concentration versus time curve of a drug administered extravascularly as the sum of an absorption curve and an elimination curve • Employ extrapolation techniques to characterize the absorption phase • Calculate the absorption rate constant and explain factors that influence this constant • Explain possible reasons for the presence of lag time in a drug’s absorption • Calculate peak plasma drug concentration, (Cp)max, and the time, (tmax)at which this occurs • Explain the factors that influence peak plasma concentration and peak time • Decide when flip-flop kinetics may be a factor in the plasma drug concentration versus time curve of a drug administered extravascularly. 2 Anas Bahnassi PhD 2011
  • 3. Xa Ka X We Need the following info: Xu 1. Equation for determining the plasma concentration at any time t. 2. Determination of the elimination half life (t½) and rate constant (K or Kel). 3. Determination of the absorption half life (t½)abs and absorption rate constant (Ka). 4. Lag time (t0), if any. Anas Bahnassi PhD 2011 5. Determination of the apparent volume of distribution (V or Vd) and fraction of drug absorbed (F). 6. Determination of the peak time (tmax). 7. Determination of the peak plasma or serum concentration, (Cp)max. 3
  • 4. Graph 2.50 Concentration (ng/mL) 2.00 1.50 1.00 Anas Bahnassi PhD 2011 0.50 0.00 0 4 8 12 16 20 24 4 Hours
  • 5. Amount Remaining in the First Administration Site Order Process ������������������ − = ������������ (������������ )������ ������������ −������������ ������ −������������ ������ (������������ )������ = (������������ )������=0 ������ = ������������������ ������ Bioavailability Dose 100% Absorbed −������������ ������ (������������ )������ = ������������ ������
  • 6. Monitoring Drug in Site of First Measurement Order Process ������������������ − = ������������ (������������ )������ − ������������ ������������ ������������ (������������ )������=0 −������������ ������������ = ������ − ������ −������������ ������ ������������ − ������ ������������ ������������0 −������������ ������������ = ������ − ������ −������������ ������ ������������ − ������
  • 7. Elimination Half life (t1/2) And Elimination Rate Constant(k) ������������ ������������0 ������������������ = ������ −������������ − ������ −������������ ������ ������(������������ − ������) 10.00 1.00 Concentration t½ 0.10 0 4 8 12 16 20 24 Time
  • 8. Calculating Absorption Rate Constant (ka) Method of Residuals Feathering Method Time (h) Observed Plasma Extrapolated Plasma (������������)������������������������ = ������������������������������ − ������������������������������ Concentrations Concentrations (Cp)observed (Cp)extrapolated Time values Values only from the Values only from the Differences between corresponding absorption phase extrapolated portion of extrapolated and observed to observed (i.e. all values prior to the plot of plasma values for each time in the plasma reaching maximum concentration–time absorption phase (units, concentrations or highest plasma (units, e.g. (mgmL1) e.g. mgmL-1) for absorption concentration) (units, phase only e.g. mgmL-1) ������������ ������������0 ������������������������������������ = ������ −������������ ������ ������(������������ − ������) 8 Anas Bahnassi PhD 2011
  • 9. Calculating Absorption Rate Constant (ka) Method of Residuals Feathering Method ������������ Slope=− 2.303 Anas Bahnassi PhD 2011 9
  • 10. Lag Time (t0) Theoretically, intercepts of the terminal linear portion and the feathered line should be the same; however, sometimes, these two lines do not have the same intercepts, Sometimes absorption starts after administration, this delay may be contributed to: • Slow tablet disintegration • Slow and/or poor dissolution • Incomplete wetting of drug particles • Poor formula • Delayed Release formula Anas Bahnassi PhD 2011 10
  • 11. Negative Lag Time (t0) The presence of a negative lag time may be attributed to inadequate data points in the absorption phase as well as in the elimination phase. Another possible reason may be that the absorption rate constant is not much greater than the elimination rate constant. Anas Bahnassi PhD 2011 11
  • 12. Analysis of Absorption ������������ ≫ ������ Rate Constant Quicker Faster Onset ������������ for a given drug can Absorption of Action change as a result of: • Changing the formulation • Changing the dosage form or the extravascular route of administration. • Administration of a drug with or without food.
  • 13. Apparent Volume of Cannot be calculated from plasma Distribution(Vd) drug concentration data alone WHY? The fraction of drug absorbed (F) is not known. If the drug is 100 percent absorbed; F=1 then ������������ ������������0 ������������������������������������������������������ = If F is not known then it is best to ������(������������ − ������) ������ calculate ������ ������ ������������ ������0 1 = ( ) ������ (������������ −������) ������������������������������������������������������ Anas Bahnassi PhD 2011 13
  • 14. Calculating Peak Time(tmax) ������������ = ������������ ������������ − ������������ When t=tmax ������������ ������������ = ������������ ������������ ������������ = ������������ (������������ )������������������������ − ������(������)������������������������ = 0 ������������ ������������ (������������ )������������������������ = ������(������)������������������������ ������������ ������������0 −������������ ������������ = ������ − ������ −������������ ������ ������������ − ������ ������������ ������������0 −������������ ������������������������������ = ������ ������������������ − ������ −������������ ������������������������ ������������ ������ = ������������ −������������ ������������������������ ������������ − ������ ������������������ Anas Bahnassi PhD 2011 14
  • 15. Calculating Peak Time(tmax) Taking natural log of both sides: Anas Bahnassi PhD 2011 15
  • 16. Significance of Peak Time(tmax) • To determine comparative bioavailability and/or bioequivalence • To determine the preferred route of drug administration and the desired dosage form for the patient • To assess the onset of action. Significance of Peak Concentration(Cmax) • Used to determine the comparative bioavailability and/or the bioequivalence between two products. • Used to determine the superiority between two different dosage forms or two different routes of administration • Correlates with the pharmacological effect of a drug. Anas Bahnassi PhD 2011 16
  • 17. Plot the data and, using the plot, determine Question the following. a. The elimination half life (t1/2) for each dose. b. The elimination rate constant (K) for each dose. c. The absorption half life, (t1/2)abs, for each dose. d. The absorption rate constant (Ka) for each dose. e. The observed and computed peak time (tmax) for each dose. f. The observed and computed peak plasma concentrations, (Cp)max, for each dose. g. The y-axis intercept for each dose. h. The apparent volume of distribution (V). i. The fraction of drug absorbed (F). j. The characteristics of a plot on rectilinear paper of peak time (tmax) against the administered dose (then make an important observation). k. The characteristics of a plot on rectilinear paper of peak plasma concentrations, (Cp)max, i. Lag time if any. 17 Anas Bahnassi PhD 2011
  • 18. Pharmacokinetics Anas Bahnassi PhD RPh abahnassi@gmail.com http://twitter.com/abahnassi http://www.linkedin.com/in/abahnassi http://www.udemy.com/pharmacokinetics http://www.slideshare.net/abahnassi attribution – non-commercial – share alike