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Intravenous Bolus
   Administration
  Anas Bahnassi PhD RPh



One compartment Model
LECTURE’S OBJECTIVES

Upon the completion of this lecture the student should be able to:
• Describe the different pharmacokinetic parameters.
• Determine pharmacokinetic parameters from either plasma or
  urinary data.
• State the equation for plasma drug concentration as a function of
  time.
• Calculate the corresponding plasma drug concentration at time t
• Calculate the intravenous bolus dose of a drug that will result in
  a target (desired) plasma drug concentration at time t.
                       Anas Bahnassi PhD 2011                   2
X
Assumptions
           • One-compartment model.
                                              Xu
               • First-order process.
                • Passive diffusion.
          • No metabolism takes place
          (elimination is 100% via renal
                     excretion)
      • The drug is being monitored in blood
             (plasma/serum) and urine.
                                                           3
                                  Anas Bahnassi PhD 2011
Anas Bahnassi PhD 2011   4
IV Bolus Equations:




Anas Bahnassi PhD 2011    5
Pharmacokinetic Parameters

•   Apparent volume of distribution (Vd).
•   Elimination half-life (t1/2).
•   Elimination rate constant (K0 or Kel).
•   Systemic clearance (Cls).




                Anas Bahnassi PhD 2011       6
Apparent volume of distribution
                                   (Vd)
• Concentrations are usually measured not
  masses.
• Vd is a proportionality constant whose sole
  purpose is to relate the plasma
  concentration (Cp) and the mass of drug (X)
  in the body at a time.
• It is not a physical volume.


               Anas Bahnassi PhD 2011           7
Vd Concept
Drug Concentration in Beaker                   Drug Concentration in Beaker
                                                       with charcoal



    Dose = 10mg                                    Dose = 10mg
    Cp0 = 20mg/L                                   Cp0 = 2mg/L
    Vd= 500mL                                      Vd= 5000mL




 The concentration of KI is different although the volume of water
                   in both beakers is the same.

                      Anas Bahnassi PhD 2011                                  8
Calculating Vd
       ������                 Apparent volumes
 ������ =                     of distribution are
      ������������                given in units of
                          volume (e.g. mL) or
                          units of volume on a
                          body weight basis
                          (Lkg-1 body weight).




Anas Bahnassi PhD 2011                      9
Elimination Half life (t1/2)

   The time (h, min,
   day, etc.) at which
   the mass (or                                                Semi-logarithmic Paper
   amount) of
   unchanged drug
   becomes half (or
   50%) of the initial
   mass of drug.



                              Basic Pharmacokinetics: S. Jambhekar , Phillip Breen 2009
                                                                                          10
Anas Bahnassi PhD 2011
Elimination Half life (t1/2)


When Cp = 0.5 (Cp)0
     t = t1/2




                      Anas Bahnassi PhD 2011   11
Elimination Rate Constant (k)

Unit of k in first order process is reciprocal of time (h-1)

                           ������ = ������������ + ������������
    Elimination
       Rate
     Constant
                                                               Metabolism
                                                                 Rate
                                   Excretion                    Constant
                                     Rate
                                   Constant

                            Anas Bahnassi PhD 2011                    12
Elimination Rate Constant (k)
                                                                    X0=
     0.963
������ =       = 0.173ℎ������ −1                                           250mg
       4
                          125
  %������������������������������������������������ =         ������100 = 50%
                          250                              M1=
                           75                              75mg
%������������������������������������������������������������������ =     ������100 = 30%
                          250
                          50
%������������������������������������������������������������������ =     ������100 = 20%
                          250                                      M2=
                                                                   50mg
 ������������ = ������������%������������. ������������������ = ������. ������������������������������������−������
������������������ = ������������%������������. ������������������ = ������. ������������������������������−������

������������������ = ������������%������������. ������������������ = ������. ������������������������������������−������            Xu=
                                                           125mg
                                  Anas Bahnassi PhD 2011                   13
Drawing a best-fit line through the
                              Data




       Anas Bahnassi PhD 2011   14
40

                         X = 61.827e-0.526t
35


30


25


20


15


10
                                                           RL paper
5

                                                                       15
0
     0   1   2   3   4   5      6        7    8   9   10    Anas Bahnassi PhD 2011
Calculating PK Parameters

  From the SL graph                               ������0
  t½= 1.3h                                ������������ =
                                                 ������������0
  Cp0= 63mg/mL.
                                   600000
                            ������������ =        = 9523.8������������
                                     63
                                     = 9.5238������



                                                      ������. ������������������
                                               ������ =
                                                        ������. ������



                      Basic Pharmacokinetics: S. Jambhekar , Phillip Breen 2009



                                                                   16
                                                 Anas Bahnassi PhD 2011
Use of Urinary Data

Amount remained
       to
  be excreted                                               Rate of
                                                           Excretion
1.   Urine collection is a non-invasive technique.
2.   More convenient sample collection
3.   Sample size is not restricting.
4.   The sampling time reflects cumulative drug concentration
     in urine collected over a period of time, rather than a drug
     concentration at a discrete time.
5.   Urinary data allows direct measurement of bioavailability,
     both absolute and relative, without the need of fitting the
     data to a mathematical model.                                          17
                                                                Anas Bahnassi PhD 2011
Use of Urinary Data
                         X
              Cumulative amount              ������������������
                                                                       Xu
                                                    = ������������ ������
              In Urine at time (t)            ������������
                                             ������������ ������ = ������0 (1 − ������ −������������������ )

                           Administered dose
                               of drug
                                                           Excretion Rate
������������ ������ = ∞                                                  Constant
                   ������������ = ������0
                         Anas Bahnassi PhD 2011                                18
Amount Remaining
                                            To be excreted
������������ ∞ − ������������ ������ = ������������������������������������ ������������������������������������������������������ ������������ ������������ ������������������������������������������������
                = ������������������������������������ ������������ ������ℎ������ ������������������������
                           = ������������                                 Drug Totally
                                                                   Drug Totally
                                                             Removed Unchanged
                                                             Removed Unchanged




                                                            Can not calculate
                                                          Volume of Distribution
                                                                                 19
                                                        Anas Bahnassi PhD 2011
Limitations
1. Keep obtaining urine samples until no
additional drug practically appears in the urine,
(t = 7 t½)
2. Urine samples can not be lost, or urine from
any samples used in the determination of Xu
(the exact volume of urine at each time interval
must be known)
3. A time-consuming method for a drug with a
long elimination half life.
4. There is a cumulative build up of error.


                       Anas Bahnassi PhD 2011              20
Dose = 80mg

                    The plot represents the cumulative quantity




                                                                                  Anas Bahnassi PhD 2011
                    of the medication from the collected urine
   Drug Totally
Removed Unchanged
                               samples vs. the time.



                                                                       21
                             Basic Pharmacokinetics: S. Jambhekar , Phillip Breen 2009
The plot represents the amount remaining
  to be excreted of the medication vs. time




                       Drug Totally
                    Removed Unchanged

������ = ������������
                     Can not calculate




                                              Anas Bahnassi PhD 2011
                   Volume of Distribution




                                        22
Rate of Excretion
                                                      Method
   ������������������
          = ������������ ������               ������������������
    ������������                                 = ������������ ������������ ������−������������������
                                   ������������
   ������ = ������������ ������−������������������
                                                         average time
                                                           between
                                                            urine
                                                          collection
average rate
of excretion

                         Anas Bahnassi PhD 2011                         23
The plot represents average rate of
excretion within the time interval between
   samples collection vs. average time
    between urine samples collection

       Anas Bahnassi PhD 2011                24
25




Anas Bahnassi PhD 2011
0.693 0.693
������ = ������������ =      =      = 0.693ℎ������ −1




                                        Anas Bahnassi PhD 2011
             ������½    1



                                   26
Questions:
What is the concentration of drug 0, 2 and 4 hours after a dose of 500
mg. Known pharmacokinetic parameters are apparent volume of
distribution, Vd is 30 liter and the elimination rate constant, kel is 0.2
hr-1 ?



From the plot seen calculate all
pharmacokinetic parameters that
you can calculate




                          Anas Bahnassi PhD 2011                             27
Pharmacokinetics

Anas Bahnassi PhD RPh

                          abahnassi@gmail.com

            http://www.linkedin.com/in/abahnassi

              http://www.slideshare.net/abahnassi

                  http://bahnassi.coursesites.com

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Pharmacokinetics: Lecture two

  • 1. Intravenous Bolus Administration Anas Bahnassi PhD RPh One compartment Model
  • 2. LECTURE’S OBJECTIVES Upon the completion of this lecture the student should be able to: • Describe the different pharmacokinetic parameters. • Determine pharmacokinetic parameters from either plasma or urinary data. • State the equation for plasma drug concentration as a function of time. • Calculate the corresponding plasma drug concentration at time t • Calculate the intravenous bolus dose of a drug that will result in a target (desired) plasma drug concentration at time t. Anas Bahnassi PhD 2011 2
  • 3. X Assumptions • One-compartment model. Xu • First-order process. • Passive diffusion. • No metabolism takes place (elimination is 100% via renal excretion) • The drug is being monitored in blood (plasma/serum) and urine. 3 Anas Bahnassi PhD 2011
  • 5. IV Bolus Equations: Anas Bahnassi PhD 2011 5
  • 6. Pharmacokinetic Parameters • Apparent volume of distribution (Vd). • Elimination half-life (t1/2). • Elimination rate constant (K0 or Kel). • Systemic clearance (Cls). Anas Bahnassi PhD 2011 6
  • 7. Apparent volume of distribution (Vd) • Concentrations are usually measured not masses. • Vd is a proportionality constant whose sole purpose is to relate the plasma concentration (Cp) and the mass of drug (X) in the body at a time. • It is not a physical volume. Anas Bahnassi PhD 2011 7
  • 8. Vd Concept Drug Concentration in Beaker Drug Concentration in Beaker with charcoal Dose = 10mg Dose = 10mg Cp0 = 20mg/L Cp0 = 2mg/L Vd= 500mL Vd= 5000mL The concentration of KI is different although the volume of water in both beakers is the same. Anas Bahnassi PhD 2011 8
  • 9. Calculating Vd ������ Apparent volumes ������ = of distribution are ������������ given in units of volume (e.g. mL) or units of volume on a body weight basis (Lkg-1 body weight). Anas Bahnassi PhD 2011 9
  • 10. Elimination Half life (t1/2) The time (h, min, day, etc.) at which the mass (or Semi-logarithmic Paper amount) of unchanged drug becomes half (or 50%) of the initial mass of drug. Basic Pharmacokinetics: S. Jambhekar , Phillip Breen 2009 10 Anas Bahnassi PhD 2011
  • 11. Elimination Half life (t1/2) When Cp = 0.5 (Cp)0 t = t1/2 Anas Bahnassi PhD 2011 11
  • 12. Elimination Rate Constant (k) Unit of k in first order process is reciprocal of time (h-1) ������ = ������������ + ������������ Elimination Rate Constant Metabolism Rate Excretion Constant Rate Constant Anas Bahnassi PhD 2011 12
  • 13. Elimination Rate Constant (k) X0= 0.963 ������ = = 0.173ℎ������ −1 250mg 4 125 %������������������������������������������������ = ������100 = 50% 250 M1= 75 75mg %������������������������������������������������������������������ = ������100 = 30% 250 50 %������������������������������������������������������������������ = ������100 = 20% 250 M2= 50mg ������������ = ������������%������������. ������������������ = ������. ������������������������������������−������ ������������������ = ������������%������������. ������������������ = ������. ������������������������������−������ ������������������ = ������������%������������. ������������������ = ������. ������������������������������������−������ Xu= 125mg Anas Bahnassi PhD 2011 13
  • 14. Drawing a best-fit line through the Data Anas Bahnassi PhD 2011 14
  • 15. 40 X = 61.827e-0.526t 35 30 25 20 15 10 RL paper 5 15 0 0 1 2 3 4 5 6 7 8 9 10 Anas Bahnassi PhD 2011
  • 16. Calculating PK Parameters From the SL graph ������0 t½= 1.3h ������������ = ������������0 Cp0= 63mg/mL. 600000 ������������ = = 9523.8������������ 63 = 9.5238������ ������. ������������������ ������ = ������. ������ Basic Pharmacokinetics: S. Jambhekar , Phillip Breen 2009 16 Anas Bahnassi PhD 2011
  • 17. Use of Urinary Data Amount remained to be excreted Rate of Excretion 1. Urine collection is a non-invasive technique. 2. More convenient sample collection 3. Sample size is not restricting. 4. The sampling time reflects cumulative drug concentration in urine collected over a period of time, rather than a drug concentration at a discrete time. 5. Urinary data allows direct measurement of bioavailability, both absolute and relative, without the need of fitting the data to a mathematical model. 17 Anas Bahnassi PhD 2011
  • 18. Use of Urinary Data X Cumulative amount ������������������ Xu = ������������ ������ In Urine at time (t) ������������ ������������ ������ = ������0 (1 − ������ −������������������ ) Administered dose of drug Excretion Rate ������������ ������ = ∞ Constant ������������ = ������0 Anas Bahnassi PhD 2011 18
  • 19. Amount Remaining To be excreted ������������ ∞ − ������������ ������ = ������������������������������������ ������������������������������������������������������ ������������ ������������ ������������������������������������������������ = ������������������������������������ ������������ ������ℎ������ ������������������������ = ������������ Drug Totally Drug Totally Removed Unchanged Removed Unchanged Can not calculate Volume of Distribution 19 Anas Bahnassi PhD 2011
  • 20. Limitations 1. Keep obtaining urine samples until no additional drug practically appears in the urine, (t = 7 t½) 2. Urine samples can not be lost, or urine from any samples used in the determination of Xu (the exact volume of urine at each time interval must be known) 3. A time-consuming method for a drug with a long elimination half life. 4. There is a cumulative build up of error. Anas Bahnassi PhD 2011 20
  • 21. Dose = 80mg The plot represents the cumulative quantity Anas Bahnassi PhD 2011 of the medication from the collected urine Drug Totally Removed Unchanged samples vs. the time. 21 Basic Pharmacokinetics: S. Jambhekar , Phillip Breen 2009
  • 22. The plot represents the amount remaining to be excreted of the medication vs. time Drug Totally Removed Unchanged ������ = ������������ Can not calculate Anas Bahnassi PhD 2011 Volume of Distribution 22
  • 23. Rate of Excretion Method ������������������ = ������������ ������ ������������������ ������������ = ������������ ������������ ������−������������������ ������������ ������ = ������������ ������−������������������ average time between urine collection average rate of excretion Anas Bahnassi PhD 2011 23
  • 24. The plot represents average rate of excretion within the time interval between samples collection vs. average time between urine samples collection Anas Bahnassi PhD 2011 24
  • 26. 0.693 0.693 ������ = ������������ = = = 0.693ℎ������ −1 Anas Bahnassi PhD 2011 ������½ 1 26
  • 27. Questions: What is the concentration of drug 0, 2 and 4 hours after a dose of 500 mg. Known pharmacokinetic parameters are apparent volume of distribution, Vd is 30 liter and the elimination rate constant, kel is 0.2 hr-1 ? From the plot seen calculate all pharmacokinetic parameters that you can calculate Anas Bahnassi PhD 2011 27
  • 28. Pharmacokinetics Anas Bahnassi PhD RPh abahnassi@gmail.com http://www.linkedin.com/in/abahnassi http://www.slideshare.net/abahnassi http://bahnassi.coursesites.com attribution – non-commercial – share alike