2. • Systemic drug absorption from GI tract/other
extravascular site depend on:
- Physicochemical properties of drug
-dosage form used
- Anatomy and physiology of absorption site
3. • 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
4. • 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:
5. Plasma level-time curve of drug absorption and
elimination rate processes
Absorption phase- rate of drug
absorption greater than rate of drug
elimination
Elimination occurs whenever drug
present- even though absorption
predominates
At peak drug conc in plasma:
Immediately after time of peak
drug absorption, some drug may
still be at absorption site ( e.g. GI
tract.
Rate of drug elimination is
faster than rate of absorption-
postabsorption phase.
Drug at absorption site- depleted, rate
of absorption approaches 0, dDGI/dt=0
(now elimination phase)- represents
only the elimination of drug from the
body- 1st order process.
Elimination phase- rate of change in
the amount of drug in the body-
described as 1st order process
6. 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.
7. • 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=
VDCP:
• 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.
(1)
8. First-order absorption model
• Absorption- assume to be 1st order.
• Applies mostly to oral absorption of drugs in
solution/ rapidly dissolving dosage (tablets,
capsules)
• Oral drug- disintegrate of dosage form (if
solid)- drug dissolves into fluid of GI tract.
• Only drug in solution- absorbed in body
9. • 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,
10. • 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).
11. • Integrate the equation- oral absorption
equation- to calculate drug conc (Cp) in plasma
at any time, t:
(2)
12. plasma level-time curve for drug given in
single dose
•Max plasma conc after oral dosing –
Cmax
•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
eliminated
•Net rate of conc change = 0
•At Cmax- rate of conc change:
Can be simplified:
(3)
(4)
13. • 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
curve.
14. • At later time intervals, when drug absorption
completed, e-kat ≈ 0, equation 2 reduce to
• ln this equation:
• Substitute to log:
(5)
15. • With equation (5), graph constructed by
plotting log Cp vs. t will yield straight line with
a slope of –k/2.3
16. • 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
drug:
• dDu/dt= rate of urinary drug excretion
- Ke = 1st order renal excretion constant
- F = fraction of dose absorbed
(6)
17. • Graph constructed by plotting dDu/dt vs. t,
yield curve identical to plasma level-time
curve
18. • 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
urine:
19. • Plot of Du vs t- give urinary drug excretion
curve.
Cumulative urinary drug excretion vs t, single oral
dose. Urine samples are collected at various time
period.
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∞
Du∞- max amount of active drug excreted
20. 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.
22. • Value of ka can be obtained by using the
method of residuals as described in chapter
before.
• If drug absorption begins
Immediately after oral admin
the residual lines obtained
will intercept on the y axis at
point A
23. 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
24. •Lag time- if 2 residual lines obtained by
feathering intersect at point greater than
t=0.
•Lag time t0- beginning of drug absorption.
•Equation to describe lag time:
Second expression that describes the
curve omits lag time:
25. Determination of ka by plotting % of
drug unabsorbed vs. time (Wagner-
Nelson)
• 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
26. • At t = ∞, Cp
∞= 0 (i.e. plasma conc is
neglectable), total amount of drug absorbed:
• Fraction of drug absorbed at any time
27. • Fraction unabsorbed at any time is
• Drug remaining in GI at any time, t:
• Therefore, fraction of drug remaining
28. • 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
29.
30. Fraction of drug uabsorbed vs time using Wagner-
Nelson method
•If fraction of drug unabsorbed,
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.
1-(Ab/Ab∞)
31. 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
32. • Differential equation for Ab= DB + DE:
• Assuming 1st order elimination with renal
elimination constant ke:
• Assuming one-compartment model:
(7)
33. • Substitute VDCP into equation (7):
• Rearrange:
• Substitute dCp/dt into equation (8) and kDu/ke
for DE:
(8)
(9)
34. • 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
is:
• Du∞= total amount of unchanged drug
excreted in urine
35. • Fraction of drug absorbed at any time t=
Abt/Ab∞.
• Plot of fraction of drug unabsorbed, 1-Ab/Ab∞
vs t gives slope = -ka/2.3, in which absorption
rate constant, ka obtained.
36. 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:
37. • Substitute the above expression for Dp and
Du:
• Divide the above equation with Vp to express
the equation on drug conc:
• At t=∞, this equation become
(10)
(11)
38. • 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.
39. • 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.
40. 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).
41. • In the Wegner-Nelson equation, Ab/Ab∞ or
CRFA- eventually equal unity- 100% (even
though drug may not be 100% bioavailable.
42. Significance of absorption rate
constant
• 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
processes
43. • Calculation of ka- important in designing
multiple-dosage regimen
• Ka and k allows for prediction of peak and
plasma drug conc. following multiple dosing
