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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.
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 3
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.
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 4
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.
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 5
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.
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 6
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.
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 7
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.
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 8
Zero-order Kinetics First order Kinetics
t
Cp Slope= -k0
Cp0
Ln Cp Slope= -k
lnCp0
t
Cp
t
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 9
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.
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 10
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)
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 11
Concepts in Ph’kinetics (3)
Classification of Pharmacokinetic Models• A model may be
– empirically, – physiologically, or – compartmentally based.
• Compartment model• Mammillary model• Catenary model
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 12
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.
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 13
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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 14
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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 15
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.
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 16
Concepts in Ph’kinetics (8)
Peripheral (2)
Central (1)
K21 K12
KaKe
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 17
Concepts in Ph’kinetics (9)
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 18
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
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Concepts in Ph’kinetics (11)
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 20
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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 21
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.
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 22
Concepts in Ph’kinetics (14)
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.
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 23
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.
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 24
Concepts in Ph’kinetics (16)
• 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.
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 25
Concepts in Ph’kinetics (17)
• 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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 26
Concepts in Ph’kinetics (18)
• 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.
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 27
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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 28
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.
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 29
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.
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 30
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.
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 31
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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 32
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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 33
Dose =Amount at the
absorp. site+
Amount in
the body+
Amount of
metabolites+
Amount
excreted
A
t
IVPO
Drug metabolized
Drug excreted
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 34
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?
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 35
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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 36
• 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.
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 37
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)
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 38
• 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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 39
• 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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 40
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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 41
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?
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 42
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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 43
• 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.
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 44
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)
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 45
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)
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 46
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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 47
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)
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 48
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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 49
Drug level time relationships
Cp
C ss
t
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 50
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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 51
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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 52
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)
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 53
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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 54
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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 55
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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 56
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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 57
• 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
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 58
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.
7/9/2009 Berhanemeskel W.Gerima Asst. Prof. 59
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
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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
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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
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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
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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
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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
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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
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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)
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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
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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
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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
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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
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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)
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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
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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?
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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