Week 5- Pharmacokinetics of drug absorption - Portal

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					Week 5- Pharmacokinetics of
     oral absorption
 Pn. Khadijah Hanim Abdul Rahman
    School of Biological Sciences
      Universiti Malaysia Perlis
• Systemic drug absorption from GI tract/other
   extravascular site depend on:
- Physicochemical properties of drug
-dosage form used
- Anatomy and physiology of absorption site
• Oral dosing, factors effect the rate and extent
  of drug absorption:
- Surface area of GI tract
- Stomach emptying rate
- GI mobility
- Blood flow to absorption site
• Rate of change in the amount of drug in the
  body, dDB/dt = dependent on relative rates of
  drug absorption and elimination

• The net rate of drug accumulation in the body:
Absorption phase- rate of drug
absorption greater than rate of drug

Elimination occurs whenever drug
present- even though absorption
 At peak drug conc in plasma:
                                               Plasma level-time curve of drug absorption and
                                               elimination rate processes

 Immediately after time of peak          Drug at absorption site- depleted, rate
 drug absorption, some drug may          of absorption approaches 0, dDGI/dt=0
 still be at absorption site ( e.g. GI   (now elimination phase)- represents
 tract.                                  only the elimination of drug from the
                                         body- 1st order process.
                                         Elimination phase- rate of change in
  Rate of drug elimination is            the amount of drug in the body-
  faster than rate of absorption-        described as 1st order process
  postabsorption phase.
    Zero-order absorption model
• Zero-order absorption- when drug is absorbed
  by saturable process/ zero order controlled
  release system

• DGI- absorbed systemically at a constant rate,
  k0. drug- immediately/simultaneously
  eliminated from body by 1st order process-
  defined by 1st order rate constant, k.
• Rate of 1st order elimination, at any time:

• Rate of input = ko. ∴, net change per unit time
  in the body:
• Integration of this equation, substitute DB=
  V DC P :             (1)

• Rate of drug absorption, remain constant until
  DGI depleted. Time for complete drug
  absorption = DGI/ko. After this time, drug is not
  available for absorption from gut, equation 1-
  not valid. Drug conc in plasma- decline
  according to 1st order process.
    First-order absorption model
• Absorption- assume to be 1st order.

• Applies mostly to oral absorption of drugs in
  solution/ rapidly dissolving dosage (tablets,
• Oral drug- disintegrate of dosage form (if
  solid)- drug dissolves into fluid of GI tract.
• Only drug in solution- absorbed in body
• Rate of disappearance of drug from GI:

-   ka- 1st order absorption rate constant from GI
-   F- fraction absorbed
-   DGI- amount of drug in GI at any time, t.
•   Integration of above equation,
• Rate of drug change in the body:
• =
• Drug in GI- 1st order decline (i.e. drug is
  absorbed across GI wall), amount of drug in GI
  at any time, t = D0e-kat.

• Value of F- vary from 0 (drug completely
  unabsorbed) to 1 (fully absorbed).
• Integrate the equation- oral absorption
  equation- to calculate drug conc (Cp) in plasma
  at any time, t:

•Max plasma conc after oral dosing –
•Time needed to reach max conc- tmax
•tmax- independent of dose, dependent
on rate constant for absorption, ka and
elimination, k
•At Cmax- peak conc
•Rate of drug absorbed= rate of drug
•Net rate of conc change = 0
•At Cmax- rate of conc change:
                                                plasma level-time curve for drug given in
                                          (3)   single dose

Can be simplified:

• In order to calculate Cmax- the value of tmax is
  determine by equation (4) and substitute to
  equation (2).
• Equation (2)- Cmax is proportional to dose of
  drug given (Do) and F.
• Elimination rate constant, k- may determined
  from elimination phase of plasma level-time
• At later time intervals, when drug absorption
  completed, e-kat ≈ 0, equation 2 reduce to

• ln this equation:

• Substitute to log:
• With equation (5), graph constructed by
  plotting log Cp vs. t will yield straight line with
  a slope of –k/2.3
• With similar approach, urinary drug excretion
  data may be used for calculation of first-order
  elimination rate constant, k
• Rate of drug excretion after single oral dose

• dDu/dt= rate of urinary drug excretion
- Ke = 1st order renal excretion constant
- F = fraction of dose absorbed
• Graph constructed by plotting dDu/dt vs. t,
  yield curve identical to plasma level-time
• After drug absorption virtually complete, -e-kat
  approaches zero, equation (6) reduces to

• Taking ln of both sides, substitute for log

• When log (dDu/dt) vs. t, graph of straight line
  is obtained with slope of –k/2.3.
• To obtain the cumulative drug excretion in
• Plot of Du vs t- give urinary drug excretion

                                                    Du∞ -   max amount of active drug excreted

  Cumulative urinary drug excretion vs t, single oral
  dose. Urine samples are collected at various time
  The amount of drug excreted in each sample is
  added to amount of drug recovered in previous
  urine sample. Total amount of drug recovered after
  all drug excreted is Du∞
  Determination of Absorption rate
 constants from oral Absorption data
Method of residuals
• Assume ka>> k in equation (2), the value of 2nd
  exponential will become significantly small (e-
  kat ≈0)- can be omitted. When this happen=
  drug absorption is virtually complete.
• From this, can obtain the intercept at y-axis
• Value of ka can be obtained by using the
  method of residuals as described in chapter
• If drug absorption begins
Immediately after oral admin
the residual lines obtained
will intercept on the y axis at
point A
                 Lag time
• sometimes, absorption of drug after single
  dose does not start immediately, due to:
- Physiologic factors (stomach-emptying time
  and intestinal motility)
- Time delay prior to commencement of 1st
  order drug absorption- lag time
•Lag time- if 2 residual lines obtained by
feathering intersect at point greater than
•Lag time t0- beginning of drug absorption.
•Equation to describe lag time:

Second expression that describes the
curve omits lag time:
  Determination of ka by plotting % of
  drug unabsorbed vs. time (Wagner-
• After single oral dose:

• Ab = DB + Du = amount of drug absorbed
• Ab∞= amount of drug absorbed at t= ∞
• Amount of drug excreted at any time t:

• DB, at any time = CpVD. At any time t, Ab is
• At t = ∞, Cp∞= 0 (i.e. plasma conc is
  neglectable), total amount of drug absorbed:

• Fraction of drug absorbed at any time
• Fraction unabsorbed at any time is

• Drug remaining in GI at any time, t:

• Therefore, fraction of drug remaining
• DGI/D0 = fraction of drug unabsorbed = 1-(Ab/Ab∞)
• Plot of 1-(Ab/Ab∞) vs. t gives slope = -ka/2.3
• The following steps use in determination of ka:
1. Plot log conc of drug vs. t
2. Find k from terminal part of slope, -k/2.3
3. Find [AUC]t0
4. Find k[AUC]t0 by multiplying each [AUC]t0 by k
5. Find [AUC]∞0 by adding up all the [AUC], from t=0 to t=∞
6. Determine 1-(Ab/Ab∞) value corresponding to each time
   point t
7. Plot 1-(Ab/Ab∞) vs. t
•If fraction of drug unabsorbed, 1-(Ab/Ab∞)
gives linear line, then rate of drug
absorption, dDGI/dt- 1st order process
•Drug approaches 100% absorption,
Cp- becomes small- the terminal part
become scattered- not included for
estimation of slope.
                                              Fraction of drug uabsorbed vs time using Wagner-
                                              Nelson method
 Estimation of ka from urinary data
• Absorption rate constant, ka- can be estimated from
  urinary excretion data- %of drug unabsorbed vs time.
• For one-compartment model:
- Ab= total amount of drug absorbed
- DB= amount of drug in body
- Du= amount of unchanged drug excreted from urine
- Cp= plasma drug conc
- DE= total amount of drug eliminated
- Ab= DB + DE
• Differential equation for Ab= DB + DE:

• Assuming 1st order elimination with renal
  elimination constant ke:

• Assuming one-compartment model:
• Substitute VDCP into equation (7):

• Rearrange:

• Substitute dCp/dt into equation (8) and kDu/ke
  for DE:
• Integrate equation (9) from 0 to t:

• At t=∞ all drug is absorbed, expressed as Ab∞
  and dDu/dt=0. total amount of drug absorbed

• Du∞= total amount of unchanged drug
  excreted in urine
• Fraction of drug absorbed at any time t=

• Plot of fraction of drug unabsorbed, 1-Ab/Ab∞
  vs t gives slope = -ka/2.3, in which absorption
  rate constant, ka obtained.
    Determination of ka from two-
  compartment oral absorption data
      (Loo-Riegelman method)
• After oral administration of a dose of drug
  exhibit two-compartment model, amount of
  drug absorbed, Ab:
• Each can be expressed as:
• Substitute the above expression for Dp and

• Divide the above equation with Vp to express
  the equation on drug conc:

• At t=∞, this equation become
• Equation (10) divided by equation (11)-
  fraction of drug absorbed at any time:

• Plot of fraction of drug unabsorbed, 1-Ab/Ab∞
  vs time gives –ka/2.3 as a slope from which
  the value of ka is obtained.
• Cp and k[AUC]t0 calculated from Cp vs time.
• Values for (Dt/Vp) can be approximated by Loo
  -Riegelman method:

• Ct = Dt/Vp, apparent tissue conc.
• (Cp)tn-1 = conc of drug at central compartment
  for sample n-1.
Cumulative relative fraction absorbed
• Fraction of drug absorbed at any time- can be
  summed or cumulated
• From equation             , the term Ab/Ab∞
  becomes cumulative relative fraction
  absorbed (CRFA).
• In the Wegner-Nelson equation, Ab/Ab∞ or
  CRFA- eventually equal unity- 100% (even
  though drug may not be 100% bioavailable.
     Significance of absorption rate
• Overall rate of systemic absorption surrounded
  by many rate processes:
- Dissolution of drug
- GI motility (ability to move spontaneously)
- Blood flow
- Transport of drug across capillary membrane to
  systemic circulation
• Rate of drug absorption- net result of this
• Calculation of ka- important in designing
  multiple-dosage regimen
• Ka and k allows for prediction of peak and
  plasma drug conc following multiple dosing

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