pharmacokinetics part ii lecture notes

PharmacokineticsPart II

Berhanemeskel W.G.Assistant Professor

Pharmaceutics DepartmentSchool of Pharmacy

College of Medicine and Health SciencesUniversity of Gondar

Gondar [email protected]

7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 2

IntroductionDefinition of Pharmacokinetics• Pharmacokinetics is a study which describes

quantitatively the uptake of drugs by the body, their distribution, metabolism, and elimination from the body. • Both total amounts and tissue and organ concentrations

are considered.• Pharmacokinetics provides a mathematical basis to

assess the time course of drugs and their effects in the body. It enables the following processes to be quantified:

• Absorption• Distribution• Metabolism• Excretion

• These pharmacokinetic processes, often referred to as ADME, determine the drug concentration in the body when medicines are prescribed.


Introd’n (2)

• A fundamental understanding of these parameters is required to design an appropriate drug regimen for a patient.

• The effectiveness of a dosage regimen is determined by the concentration of the drug in the body.


6. Kinetic Analysis of Data: order and rate constants

• To consider the processes of ADME the rates of these processes have to be considered; they can be characterized by two basic underlying concepts.

• The rate of a reaction or process is defined as the velocity at which it proceeds and can be described as either zero-order or first-order.


Kinetic Analysis… (2)Zero-order reaction• Consider the rate of elimination of drug A from the

body. If the amount of the drug, A, is decreasing at a constant rate, then the rate of elimination of A can be described as:

dA = -k* dC = -k * where k* the zero-order rate constant.

dt dtdC= -kodt C= Co – kot

• The reaction proceeds at a constant rate and is independent of the concentration of A present in the body.

• Drugs that show this type of elimination will show accumulation of plasma levels of the drug and hence nonlinear pharmacokinetics.


Kinetic Analysis… (3)First-order reaction• If the amount of drug A is decreasing at a rate that is

proportional to A, the amount of drug A remaining in the body, then the rate of elimination of drug A can be described as:

dA = -kA dC = -kC where k* the first-order rate constant.

dt dtdC= -kC dt => lnC= lnCo – kt

• The reaction proceeds at a rate that is dependent on the concentration of A present in the body.

• It is assumed that the processes of ADME follow first-order reactions and most drugs are eliminated in this manner.


Kinetic Analysis… (4)• Most drugs used in clinical practice at therapeutic

dosages will show first-order rate processes; that is, the rate of elimination of most drugs will be first-order. – However, there are notable exceptions, for example

phenytoin and high-dose salicylates. • In essence, for drugs that show a first-order elimination

process one can show that, as the amount of drug administered increases, the body is able to eliminate the drug accordingly and accumulation will not occur.

• if you continue to increase the amount of drug administered then all drugs will change from showing a first-order process to a zero-order process,– for example in an overdose situation.


Zero-order Kinetics First order Kinetics

t

Cp Slope= -k0

Cp0

Ln Cp Slope= -k

lnCp0

t

Cp

t


7. Concepts in Pharmacokinetics7.1. Basic Pharmacokinetic models for drug

absorption and disposition• Model is an approximation for the real.

– It is difficult to have real model because it is difficult to sample tissues.

• Models are useful in determining the rate processes of absorption, distribution and elimination.

• Pharmacokinetic models are hypothetical structures – that are used to describe the fate of a drug in a biological

system following its administration (rate processes of absorption, distribution and elimination).

• The hypothetical structures are called compartments – that represent all those organs, tissues, and cells for which

the rates of uptake and subsequent clearance of a chemical are sufficiently similar to lead up kinetic resolution.


Concepts in Ph’kinetics (2)• Assumption of compartment:

– With in each compartment the drug is considered uniformly distribution, mixing of drug is instantaneously e.g. in blood

– Drugs move dynamically in and out of compartmenttherefore one compartment is open

– Rate constants used to represent the over all rate process of drug enter and out

– The model is an open system since the drug can be eliminated from the system

• A body considered as a series of compartment according to blood perfusion:1. Compartments easily accessible to blood2. Compartments less accessible to the blood3. Compartments very less accessible to the blood (nails, hairs)


Concepts in Ph’kinetics (3)

Classification of Pharmacokinetic Models• A model may be

– empirically, – physiologically, or – compartmentally based.

• Compartment model• Mammillary model• Catenary model


Concepts in Ph’kinetics (4)• Empirical model

– The model that simply interpolates the data and allows an empirical formula to estimate drug level over time is justified when limited information is available.

– Empirical models are practical but not very useful in explaining the mechanism of the actual process by which the drug is absorbed, distributed, and eliminated in the body.

• Physiological model– also known as blood flow or perfusion models, are

pharmacokinetic models based on known anatomic and physiologic data.

– The models describe the data kinetically, with the consideration that blood flow is responsible for distributing drug to various parts of the body.


Concepts in Ph’kinetics (5)• Compartment model

– A compartmental model provides a simple way of grouping all the tissues into one or more compartments where drugs move to and from the central or plasma compartment.

• Mammillary model– The mammillary model is the most common compartment

model used in pharmacokinetics. – The mammillary model is a strongly connected system,

because one can estimate the amount of drug in any compartment of the system after drug is introduced into a given compartment.

– consists of one or more compartments around a central compartment like satellites.

• Catenary model– The catenary model consists of compartments joined to one

another like the compartments of a train


Concepts in Ph’kinetics (6)Mammillary Model1. One compartment model• This assumes that the drug achieves

instantaneous distribution throughout the body and that the drug equilibrates instantaneously between tissues.IV administered drug Extra-vascular administered drug

Where: ka absorption rate constant (h1), ke elimination rate constant (h1).

C, V, t

IV KeC, V, t

Ka Ke


Concepts in Ph’kinetics (7)2. Two compartment model• The two-compartment model resolves the body into

a central compartment and a peripheral compartment.– The central compartment comprises tissues that are highly

perfused such as heart, lungs, kidneys, liver and brain. – The peripheral compartment comprises less well-perfused

tissues such as muscle, fat and skin.• A two-compartment model assumes that, following

drug administration into the central compartment, the drug distributes between that compartment and the peripheral compartment.

• However, the drug does not achieve instantaneous distribution, i.e. equilibration, between the two compartments.



Peripheral (2)

Central (1)

K21 K12

KaKe




Concepts in Ph’kinetics (10)3. Multi-compartment model• In this model the drug distributes into more than one

compartment and the concentration–time profile shows more than one exponential. Each exponential on the concentration–time profile describes a compartment.

1 23

K31Ka K12

K21K13

Ke




Concepts in Ph’kinetics (12)Pharmacokinetic parameters• Considering one compartment model and

IV bolus dose-– we have different parameters that can be

determined from data obtained i.e. Cp and time.

• The parameters are: – Elimination rate constant, – Volume of distribution, – Half life, – Drug clearance


Concepts in Ph’kinetics (13)Elimination rate constant• Consider a single IV bolus injection of drug

X. As time proceeds, the amount of drug in the body is eliminated.

• Thus the rate of elimination can be described (assuming first-order elimination) as:

dX/dt = -kX i.e X=Xo exp (-kt)• Where X= amount of drug X, X0-dose and

k- first-order elimination rate constant.



Volume of distribution• The volume of distribution (Vd) has no direct

physiological meaning; it is not a ‘real’volume and is usually referred to as the apparent volume of distribution.

• It is defined as that volume of plasma in which the total amount of drug in the body would be required to be dissolved in order to reflect the drug concentration attained in plasma.


Concepts in Ph’kinetics (15)• It is important to realize that the concentration of the

drug (Cp) in plasma is not necessarily the same in the liver, kidneys or other tissues.

• However, changes in the drug concentration in plasma (Cp) are proportional to changes in the amount of drug (X) in the tissues. Since

Cp (plasma) Cp (tissues) i.e. Cp (plasma) X (tissues)Then Cp (plasma) = 1/Vd x X (tissues)

• where Vd is the constant of proportionality and is referred to as the volume of distribution, which thus relates the total amount of drug in the body at any time to the corresponding plasma concentration.



• Thus Vd = X/Cp

• Vd can be used to convert drug amount X to concentration. Since

X = X0 exp (-kt) then X/Vd = X0 exp (-kt)/Vd

Thus, Cpt = Cpo exp( kt), where Cpt= plasma concentration at any time t.



• ln Cpt vs t plot gives slope= -k, the elimination rate constant; and the y intercept= ln Cp0. Since

• then at zero concentration (Cp0), the amount administered is the dose, D, so that



• If the drug has a large Vd that does not equate to a real volume,– e.g. total plasma volume, this suggests that

the drug is highly distributed in tissues. • On the other hand, if the Vd is similar to

the total plasma volume – this will suggest that the total amount of drug

is poorly distributed and is mainly in the plasma.


7.2. Absorption• Drug absorption- is the process by which

unchanged drug proceeds from the site of administration to the site of measurement with in the body.

• Measurement of drug in the body is limited usually to the blood or the plasma because:

– Convenient sites of measurement– Most logical for determining drug concentration

in the body• Is the drug absorbed?

– if it survives destruction in the gut lumen?– If an in vitro experiment revealed that the drug

passes the GI membranes


7.3. Disposition• Once drug is absorbed, it is delivered

simultaneously to all tissues, including the site of elimination.

• Therefore, distinction between distribution and elimination is often difficult.

• Disposition is the term used when distinction is difficult.

• Disposition can be defined as all the processes that occur subsequent to the absorption of the drug.


Disposition (2)Distribution• It is the process of reversible transfer of a

drug to and from the site of measurement.• It refers to the movement of drug to and

from the blood and various tissues of the body and the relative proportions of drug in the tissues.


Disposition (3)Drug distribution patterns• Distribution can be thought of as following one of

four types of patterns.1. The drug may remain largely within the vascular

system. 2. Some low molecular weight water soluble

compounds such as ethanol and a few sulfonamides become uniformly distributed throughout the body water.

3. A few drugs are concentrated specifically in one or more tissues that may or may not be the site of action. Iodine- thyroid gland, chloroquine-liver

4. Most drugs exhibit a non-uniform distribution in the body with variations that are largely determined by the ability to pass through membranes and their lipid/water solubility.


Factors affecting drug distribution 1. Rate of distribution

• Membrane permeability• Blood perfusion

2. Extent of Distribution • Lipid Solubility • pH - pKa• Plasma protein binding • Intracellular binding


Elimination• It is irreversible loss of drug from the site of

measurement• It occurs by two process 1. Excretion- is irreversible loss of chemically

unchanged drug– The major routes of excretion include renal, biliary,

pulmonary, and salivary. 2. Metabolism- is a conversion of one chemical species

to another. Note- occasionally, drug metabolites are converted

back to the drug, therefore, metabolic inter-conversion is the route of elimination only if:

• The metabolite is excreted• The inter-conversion is irreversible


Dose =Amount at the

absorp. site+

Amount in

the body+

Amount of

metabolites+

Amount

excreted

A

t

IVPO

Drug metabolized

Drug excreted


Answer the following questions • Does a 100% recovery of unchanged drug in the urine

following oral administration indicate that the drug is completely absorbed and not metabolized?

• When does drug in the body reach a peak following oral dose?

• When does the rate of change of drug in the body equals the rate of elimination?

• When does the rate of change of drugs in the body approaches the rate of absorption?

• Following oral administration of drug labeled with a radioactive atom all the radioactivity was recovered in the urine, can you conclude that the drug was completely absorbed?


8. Disposition and Absorption Kinetics8.1. Intravenous doseConcept of bolus• Administration a drug through IV ensures

that all of the dose enters the general circulation

• A drug can be administered IV as a rapid injection (IV bolus) or as constant rate infusion

• By rapid injection, elevated concentration of drug in the blood can be prompt achieved

• By infusion, a constant concentration can be maintained for prolonged period of time


• For a given dose, the shorter the duration of an infusion, the earlier and higher is the Cmax– more rapid onset and greater intensity of

response.• When ever the intent is to administer a

drug as rapidly as possible, although infused, it is often said to be given as a bolus dose.


Disposition viewed form plasma onlyExample: Procainamide HCl infusion at a constant rate of

100mg/min for 10 minutes. Consider as IV bolus dose.• Graphical representation of the Cp vs t data

– Plot of Cp vs t on regular graph paper– Plot of the same data on semilog paper

Observations• Rapid decline of Cp after giving the bolus

=> distribution phase• Much slow decline after the first few minutes

=> elimination phase• Elimination phase is characterized by two parameters:

• The elimination half life (t1/2) and • The apparent volume of distribution (Vd)


• Half life (t1/2) – is the time taken for the plas ma concentration as well as the amount of the drug in the body, to fall by one half. t ½ is independent of the amount of drug in the body (1 st order). Less drug is eliminated in each successing half life.

• The concentration after distri bution is complete, is a result of the dose and the ext ent of distribution of the drug (Vd)

• The apparent volume into which a drug distributes in the body at equilibrium is called apparent volume of distribution (Vd).

Concentration of drug in the body = Amount of drug in the body (A)Extent of distribution (Vd)

Volume of distribution (Vd) = Amount of drug in the body (A)Plasma drug Concentration


• If a drug has Vd > 70lt (volume of the body), we can say that the drug distribute more than the blood/plasma. If it is < 3lt, it is distributed inside the plasma.

• Volume of distribution is used in estimating– Cp when a known amount of drug is in the body or– Dose required to achieve a given Cp

• Calculation of Vd requires that distribution is achieved between the tissues and that in plasma

• The decline in Cp during elimination phase can be characterized by the linear equation

lnC= lnCo – kt• Co is estimated by extrapolating the linear line of the

elimination phase back to zeroDose= V. Co


First order Elimination lnC = lnCo – kt (1)C = Co e-kt (2)

Multiplying eq. 2 by VA= dose* e-kt (3)

Differential equation for eq. 3 givesdA/dt = -k dose* e-kt (4)dA/dt = -k A (5)

• After distribution equilibrium, dA/dt is the rate of elimination of drug from the body thus

k = rate of elimination (6)amount of drug in the body

• K is regarded as the fraction rate of drug removal or fractional rate of elimination


Fraction of dose remaining (FDR)• FDR = A/dose= e –kt (7) from eq. 3• The number of half lives (n) elapsed after the dose

administered is t/t1/2n= t/t½ (8)

FDR = exp. (-kt) = exp. (-0.693n)= (½)n (9)E.g.

1. How many percent of dose remaining after 2 half-lives?2. How much drug remains in the body after 4 half-lives of a

bolus dose?3. The half life of a drug is 6hrs. How much is left in the body

20hrs after a bolus dose?4. Twenty percent of a drug remains in the body 10hrs after

bolus dose. What is the half life of the drug?


Total Clearance (Cl T)• Clearance is one of the most important pharmacokinetic

parameters. • It is defined as the volume containing the amount of drug

eliminated per unit time by a specified organ; • It has the dimension of a flow• As V relates to C and A, So does Cl to relate C and rate

of drug eliminationRate of elimination = Cl . C (10)

• The unit of clearance is volume per unit time. Cl is independent of concentration

• Clearance may be influenced by:– Organ blood flow– Degree of plasma protein binding and– Whether the organ is healthy or diseased


• From eq. 6 Rate of elimination (re) = k.AThus, re = K . V. C (11)By combining eq. 10 and 11

Cl = kV (12) e.g. Clearance of procainamide is 33 lt/hr (0.5

lt/min) and at plasma concentration of 1mg/ml its rate of elimination is 0.5 gm/min.


CL and t1/2• Half life is related to clearance by (from equ. 12)

t ½ = 0.693V/Cl (13)• Half life and elimination rate constant reflect rather than control Vd

and Cl.Cl, AUC and Vd• Rearranging eq. 10 for small interval of time (dt), amount eliminated

in interval dt=> Cl.C.dt, where Cdt is the corresponding small area under Cp vs time curve

-dA/dt = Cl.Cp-dA = Cl Cp.dt (14)

• The total amount of drug eventually eliminated is the sum of theamount eliminated in each time interval from zero to infinite time. There fore,

Dose = Cl. AUC (15)From eq. 12,

V= Cl/K= Dose/AUC.K (16)


Disposition viewed from the plasma and urine• Useful pharmacokinetics information can be obtained from urinary dataRenal clearance (Clr)• It is defined as the proportionality term between urinary excretion rate

and plasma concentrationExcretion rate = Clr x Cp (17)

• Problems in estimating Clr from plasma and urine data– Plasma concentration is changing during the collection time interval (good

in narrow time interval)– Incomplete bladder emptying, if the interval is short

Amount excreted = Clr x C x dt (18)• Where Cdt is the corresponding small area under the

plasma drug concentration-time curve• The urine collection interval (dt) is composed of many such

increments of time.Amount excreted in dt = Clr x AUC with interval (19)


ExampleDose administered is 50 mgPlasma data

Urine data

• The time (hr) in plasma data should be the mid point time of the time interval of urine collection

• Assess– Cumulative amount of drug excreted in each time interval (0-2, 0-4, 0-6, 0-8, 0-

12,1-24)– Determine t1/2, v from plasma data

Time (hr) 1 3 5 7 10 18

Avg. Conc (mg/lt) 2 1.15 0.70 0.43 0.20 0.025

Time interval of Urine collection (hr)

0-2 2-4 4-6 6-8 8-12 12-24

Volume of Urine (ml) 120 180 89 340 178 950Conc. Of unchanged drug in the urine (mg/lt)

133 50 63 10 18 2


Disposition viewed from urine only• In practice, the interval of urine collection should be less than

elimination half life• Can be determine

– t ½ as well as k– fe (fraction of dose excreted unchanged)

• Rate of excretion = Clr .C (20)= Clr .A/V

Rate of Excretion = Clr. Dose e –kt /V (21)ln (rate of excretion) = ln (Clr. Dose/v) – kt (22)

• In the absence of plasma measure neither the volume of distribution nor the renal or total clearance can be determine

• fe = Total amount excreted unchanged/dose (23)• fe = rate of excretion/rate of elimination (24)

fe= Clr.C/Ct.C => fe= Clr/Clt (25)Clt= Clr + Clext (26)Clext = Clt –Clr = Clt (1-fe) (27)


8.2. Constant Rate of Infusion• A drug is said to be given as a constant

rate infusion when the intent is to maintain a stable plasma concentration or amount in the body

• Could be done with– Constant rate intravenous infusion or – Constant rate release devices (extra-vascular)

• In the latter case, absorption is a pre-requisite to attain effective plasma concentration


Drug level time relationships

Cp

C ss

t


At any time during an infusion, the rate of change in the amount of drug in the body is the difference between the rate of drug infusion (Ro) and elimination.

dA/dt = Ro – k.A (1)Or in terms of drug concentration in the plasma

dA/dt = Ro – Cl.C (2) At steady state or plateau, the rate of infusion and

rate of elimination are equal i.e. rate of change of drug in the body is zero

A ss = Ro/k (3)Css = Ro/Cl (4)

Ass is governed only by the rate of infusion and the elimination rate constant while Css is governed by the infusion rate and clearance


Time to reach plateau A delay always exists between the start of an infusion

and the establishment of plateau. The approach to the plateau is controlled only by the

half life of the drug not rate of infusion. Consider a situation in which a bolus dose is given at the

start of a constant infusion to immediately attain Ass. There is decline.

The amount associated with the bolus dose declines exponentially and at any time is

The decline is always match by the gain resulting from the infusion. Thus, the amount in the body will be maintained at Ass

Amount remaining in the body from bolus dose

= Ass . e-kt


The amount in body due to infusion is always the difference between Ass and the amount remaining from the bolus dose.

A inf = A ss – A ss e-kt (6)C inf = C ss (1- e-kt ) (7)

In-terms of number of half life (n)A inf = A ss (1- (1/2)n) (8)C inf = C ss (1- (1/2)n ) (9)


Example: Bolus + InfusionSituation 1- Changing IV bolus dose• Assumption infusion rate= 23.1mg/hr and t1/2= 6hrsCase 1: drug is infused alone and the amount rises reaching a

plateau of 200mg in approx. 4half-lifes

Case 2: first adm. IV dose 200mg followed by the infusion

Amount in body

200mg

t1/2

Amount in body

200mg

t1/2

t (n)

Amount (mg)

IV bolus

IV inf Total

1 0 100 100

2 0 150 = 100 + 50 150

3 0 175 = 100 + 50 + 25

175

4 0 187.5 187.5

5 0 193.75 193.75

t (n)

Amount (mg)

IV bolus

IV inf Total

1 100 100 200

2 50 150 = 100 + 50 200

3 25 175 = 100 + 50 + 25

200

4 12.5 187.5 200

5 6.25 193.75 200


Case 3: A bolus dose of 400mg was given with the infusion

400mg bolus + infusion= net effect decrease in conc.

Case 4: A bolus dose of 100mg was given with infusion100mg bolus + infusion= net effect increase in conc.

400mg

Amount in body

200mg

t1/2

Amount in body

200mg

t1/2

100mg

t (n) Amount (mg)

IV bolus

IV inf Total

1 200 100 300

2 100 150 250

3 50 175 225

4 25 187.5 212..5

5 12.25 193.75 200

t (n) Amount (mg)

IV bolus

IV inf Total

1 50 100 150

2 25 150 175

3 12.5 175 187.5

4 6.25 187.5 193.75


Situation 2: The same bolus dose and infusion rate are administered to three patients with different half lives of 3, 6, and 9hrs. The t½ of the drug is 6hrs. Patient A has 3hrs, B has 6hrs and C has 9hrs.

200mg

Amount in body

100mg

t1/2

Patient A

Amount in body

300mg

t1/2

200mg

Patient C

Amount in body

200mg

t1/2Patient B


t (hrs) Amount (mg)

IV bolus

IV inf Total

0 200 0 200

3 100 50 150

6 50 75 125

9 25 87.5 112..5

12 12.25 93.75 100

Patient A with t ½ = 3hrs Patient C with t ½ = 9hrs

t (hrs) Amount (mg)

IV bolus

IV inf Total

0 200 0 200

9 100 150 250

18 50 225 275

27 25 262.5 287.5

35 12.25 251.25 293.75

Ainf = Ass (1- (½ )n) Ass = Ro/K

K = ln2/t½


• At any time t, the amount of the drug in the dody• Abolus = Dose. e –kt = Ass . e-kt

• Cbolus= Co e-kt=Co (½)n

• Cinf = Css (1- e-kt) = Css (1- (½)n)• Cp = Cbolus + Cinf

= Co (½)n + Css (1- (½)n)= Co (½)n + Css – Css (½)n

C –Css = (Co – Css) (½)n

(½)n =Cp –Css

=Css –Cp

= e-ktCo –Css

Css–Co


8.3. Extra-vascular Dose Absorption is a pre-requisite for therapeutic

activity of drugs when administered extra-vascularly. Absorption of drugs from extra-vascular

sites often approximated by first order kinetics and is characterized by an

absorption rate constant (Ka) and a corresponding half life (t½a)

The half lives for the absorption of drugs usually ranges from 15min to 1hr.


Body level time relationship Comparison with an IV dose

– Absorption delays and reduces the magnitude of the peak compared to that seen following an equal IV bolus dose after extra-vascular administration.

dA/dt = dAa/dt – k.A– As absorption is a first order process:

Rate of absorption (dAa/dt) = Ka Aa

Plots of plasma drug concentration- time after an IV dose vs after extra-vascular dose

Cp

t

Cp

t

Cmax IV

Cmax EV IV

EV


The peak plasma concentration is always lower following EV administration Some drug remains in the absorption site and some

eliminated Beyond the peak time the plasma concentration on the EV administration

exceeds that following IV dose If the drug is not fully available its concentration may remain lower at all times than

observed after IV administration


Availability (F) Availability is the fraction or percent of an

administered dose that actuall y reaches the systemic circulation

It is proportional to the total area under the plasma concentration time curve

From IV bolus doseTotal amount eliminated = Cl.AUC

For EV dose, the total eliminated is the amount absorbed (F. Dose), therefore;

F. Dose = Cl . AUCF = Cl. AUC/Dose


Changing Dose in EV Increases the dose, unless alters the

absorption t½ or F, produces a proportional increase in the plasma concentration at all times Doubling the dose

Double rate of absorption t max is unchanged Increase Cp


Alterations in either absorption or disposition produce changes in the time profiles of the amount of drug in the body and plasma drug concentration

Consider the following cases where only the absorption half life is changed

Case A: The absorption half-life is much shorter than the elimination half-life– Absorption is quite rapid and elimination occur

nearly after the drug absorbed– By the time the peak is reached, most of the drug has

been absorbed and little has been eliminated– After tmax, decline of drug is mainly determined by

disposition of the drug => disposition is the rate limiting step

Changing absorption kinetics


Case B: The absorption half life is longer than in case A but still shorter than the elimination half life– The peak occurs latter than case A– The peak amount is lower than case A– Absorption is still essentially completes before the

majority of the drug has been eliminated– Disposition remains to be the rate limiting step

Case C: The absorption half life is much longer than the eliminated half life– The peak occurs later and is lower than the two previous

cases– The half life of the decline of drug in the body

corresponds to the absorption half life– Absorption is the rate limiting step


Changing the disposition kineticsA. When Clearance is reduced, but availability

remains constant– Increased in AUC and magnitude of peak

concentration– Tmax decreased

B. When an increase in volume of distribution is responsible for a longer elimination half life, but Cl and f remains constant– K decreases – Cp decreases– AUC remains unchanged– Peak occurs later and is lower


Assessment of pharmacokinetics parameters1. Plasma data aloneA. Availability (F)

– Supplemental data from IV administration is required from IV dose

Dose IV = Cl . AUC IV– From EV dose

F. Dose EV = Cl . AUCEV

– Therefore,F = (AUCEV/AUCIV) x (Dose IV/Dose EV)


B. Relative availability• It is used when there is no IV data due to cost, stability or

solubility• It is determined by comparing different dosage forms,

routes of administration or conditions (diet, disease state, etc

Dosage form AFA . DoseA = Cl. AUCA

Dosage form BFB . DoseB = Cl. AUCB

Relative Availability= FA/FB= (AUCA/AUCB) x (Dose B/Dose A)• The reference dosage form chosen is usually the one that

is most bioavailable, i.e. the one having the highest area to dose ratio


C. Absorption rate constant (ka)• Can be determined by method of residuals

D. Lag time• It is the delay between drug administration and the

beginning of absorptionLag time = F. Dose . Ka/V (Ka – k)

time

Slop= K/2.03 = can determine t ½ of elimination

Log C

logC’

Log C’- logCLog C

Slope= Ka = can determine t ½of absorption


Exercise• Plasma concentration time data following oral

administration a 100mg dose of a drug

a) Prepare a semi log curve of a data and determine the rate constants for absorption and elimination and the corresponding half life

b) Estimate when absorption began (lag time)

Time (hr) Plasma concentration (mg/lt)1 0.382 0.733 0.914 0.975 0.976 0.928 0.71

10 0.5312 0.4014 0.30


Plasma and urine data• Clr can be estimated by the same approach as IV dose• Since no knowledge of availability is required, the value of

Clr after extra-vascular administration is as accurate as that obtained following IV administration.

Urine data only• Urine excretion rate data are of the little use in estimating

the absorption kinetics of the drug. – It is because during the first collection of urine (1-2 hrs

after drug adm) absorption of well absorbed drug is complete

• But cumulative urine data can be used to estimate availability


Fe = Amt. of drug excreted unchanged Ae, F. Dose

Fe = Ae, F. Dose

FA . DoseA = Ae, Afe

FB . DoseB = Ae, Bfe

FA/FB = (Ae, A/Ae, B) x (Dose B/DoseA)


Exercise• Data obtained following adm. Of 500mg of a drug

in solution by different routes

• Determinea) The IM availability of the drugb) The per oral availability of the drugc) The relative availability of the drugd) Clearancee) Volume of distributionf) Renal clearance

Route Plasma data Urine data

AUC t1/2 decline phase (min)

Cumulative amt. excreted unchanged (mg)

IV 7.6 190 152IM 7.4 185 147

Oral 3.5 193 70


9. Dosage regimens Dosage regimen is the manner in which a drug is

taken Successful drug therapy involves optimally

balancing the desirable and undesirable effects To achieve optimal therapy, the appropriate “drug

of choice” must be selected. The selection requires

– An accurate diagnosis of the disease– Knowledge of the clinical state– Sound understanding of the pharmaco-therapeutic

management of the disease– Answering the questions: how much? How often? And

How long?


Dosage Regimens (2)• How much?

– Recognizes that the magnitudes of the therapeutic and toxic responses and are functions of the dose given.

• How often?– Recognizes the importance of time, as the

magnitude of the effect declines with time following a single dose

• How long?– Recognizes the cost (in terms of side effects, toxicity,

economics) incurred with continuous drug administration.

9.1. Empirical and kinetic approaches to drug therapy

In the past, the answers to many important therapeutic questions were obtained by trial and error

The dose, the interval between doses and the route of administration were selected by the clinical investigator.– The desired effects and signs of toxicity were

carefully noted if necessary, dosage regime was adjusted empirically until an acceptable balance between the desired and undesired effects was achieved

– The empirical approach contributes little towards a safe and effective dosage regimen for another drugs

The advent of pharmacokinetics• Studies showed that the magnitude of a

response is a function of the concentration of a drug in the fluid bathing the site (s) of them

• The necessity of studying the processes undertaken for a drug to reach from the site of administration to the site of action are– Mechanisms of ADME– Kinetics of ADME– Relations ship of ADME with the intensity and time

course of therapeutic and toxicological effects of drugs

Advantages of kinetics over the empirical approach

• Distinction can be made between the ph.kineticsand pharmacodynamic causes of unusual of drug response

• Information gained about the ph.kinetics of one drug can help in anticipating the ph.kinetics of other drug

• Understanding the ph.kinetics of a drug often explains the manner of its use

• Knowing th ph’kinetics of a drug aids the clinician in – Anticipating the optimal dosage regimen for an

individual patient– Predicting what will happen when a dosage regimen is

changed

9.2. Therapeutic dosage regimen• The same dose of a drug may produce a

different intensity of effect in different individuals

• Reasons for the differences could be– Pharmacokinetic variability– Pharmacodynamic variability

Multiple Dosage Regimen• After single-dose drug administration, the plasma drug

level rises above and then falls below the minimum effective concentration (MEC), resulting in a decline in therapeutic effect.

• To maintain prolonged therapeutic activity, many drugs are given in a multiple-dosage regimen.

• The plasma levels of drugs given in multiple doses must be maintained within the narrow limits of the therapeutic window to achieve optimal clinical effectiveness.

• Ideally, a dosage regimen is established for each drug to provide the correct plasma level without excessive fluctuation and drug accumulation outside the therapeutic window.

• In calculating a multiple-dose regimen, the desired or target plasma drug concentration must be related to a therapeutic response, and the multiple-dose regimen must be designed to produce plasma concentrations within the therapeutic window.

• There are two main parameters that can be adjusted in developing a dosage regimen: 1. size of the drug dose and 2. frequency of drug administration (ie, the time

interval between doses).

TimeAmount of drug remaining after each dose

1st dose 2nd dose 3rd dose 4th dose

0 Dose

Dose. e-k Dose

2 Dose. e-2k Dose . e-k Dose

3 Dose. e-3k Dose . e-2k Dose . e-k Dose

Where is dosing interval At = Dose. e -kt

A4 max= Dose (1 + r + r2+ r3) where r = e-k (1)AN max = Dose (1 + r + r2+ r3 + …… + r N-2 + rN-1) (2)AN max

.r = Dose (r + r2+ r3 + …… + r N-1 + rN) (3)Subtracting eq. 2 from 3

AN max (1- r) = Dose (1 - rN) (4)AN max = Dose (1 - rN) /1-rAN max = Dose (1 - e-Nk )/1- e-k (5)AN min = AN max e-k (6)

At steady state Ass max = Dose/1- e-k (7)Ass min= Ass max e-k = Ass max – Dose (8)

At steady state (plateau)Average rate in = average rate out

For EVF. Dose/ = k. Assav

F. Dose/ = Cl.Cssav

Assav = F. Dose /k = F.Dose.1.44 t½ /

Rate of accumulation to plateau• The approach to plateau depends solely on the drug

half life• The approach to plateau N doses expressed as

• Accumulation index- accumulation of drugs at first dose. It expresses how many times the maximum amount and minimum amount at plateau with respect to the corresponding value after single dose

ANmax =ANmin =

AN av = 1- e -NkAssmax Assmin Ass av

Ac.Index =Assmax

=Assmin

=Assav = 1

A1max A1min A1av 1- e -k

Relationship between DL and DM

• After drug absorption, the drug plasma concentration decline– Decreases therapeutic concentration

• Thus, to replace the amount lost during dosing interval maintenance dose administration is necessary.

DM = DL – DL. e -k= DL(1 – e -k )

Acc. Index = DL/DM = 1/1- e-k

• DL can be calculated if Dm is knownDL= DM/1- e-k

• The accumulation index depend on– Dosing interval and– t½

• Example: Tetracycline has a t1/2 of 8hrs, dose range which gives antimicrobial effect is 250 -500mg, = t1/2 = 8hrs, MD= 250mg, Case 1 having LD= 500, Case 2 having LD = 250

500mg

250mg

125mg

8hrs 16hrs 24hrs

500mg500mg 500mg

250mg

125mg

375mg