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### Week 5- Pharmacokinetics of oralabsorption

Pn. KhadijahHanim 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

Elimination occurs whenever drug present- even though absorption predominates

At peak drug conc in plasma:

Plasma level-time curve of drug absorption and elimination rate processes

Immediately after time of peak drug absorption, some drug may still be at absorption site ( e.g. GI tract.

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

Rate of drug elimination is faster than rate of absorption- 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= 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)

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

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:

(2)

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:

plasma level-time curve for drug given in single dose

(3)

Can be simplified:

(4)

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.

At later time intervals, when drug absorption completed, e-kat≈ 0, equation 2 reduce to

- ln this equation:
- Substitute to log:

(5)

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 drug:
- dDu/dt= rate of urinary drug excretion
- Ke = 1st order renal excretion constant
- F = fraction of dose absorbed

(6)

Graph constructed by plotting dDu/dt vs. t, yield curve identical to plasma level-time curve

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:

Plot of Duvs t- give urinary drug excretion curve.

Du∞- max amount of active drug excreted

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∞

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.

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

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 t=0.

- 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-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

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:
- Plot log conc of drug vs. t
- Find k from terminal part of slope, -k/2.3
- Find [AUC]t0
- Find k[AUC]t0 by multiplying each [AUC]t0 by k
- Find [AUC]∞0 by adding up all the [AUC], from t=0 to t=∞
- Determine 1-(Ab/Ab∞) value corresponding to each time point t
- Plot 1-(Ab/Ab∞) vs. t

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∞)

Fraction of drug uabsorbedvs 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:

(7)

Substitute VDCP into equation (7):

- Rearrange:
- Substitute dCp/dt into equation (8) and kDu/ke for DE:

(8)

(9)

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

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.

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 Du:

- Divide the above equation with Vp to express the equation on drug conc:
- At t=∞, this equation become

(10)

(11)

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 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

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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