Pharmacokinetics

•Pharmacokinetics, (from Ancient Greek pharmakon "drug" and
kinetikos "moving, putting in motion’), is a branch
of pharmacology dedicated to determining the fate of substances
administered externally to a living organism.
•The substances of interest include pharmaceutical agents, hormones,
nutrients, and toxins.
• It attempts to discover the fate of a drug from the moment that it is
administered up to the point at which it is completely eliminated from the
body.
•Pharmacokinetics describes how the body affects a specific drug after
administration through the mechanisms of absorption and distribution, as
well as the chemical changes of the substance in the body (e.g. by
metabolic enzymes such as cytochrome P450 or
glucuronoyltransferase enzymes), and the routes of excretion of the
metabolites of the drug.

Drug Safety and Effectiveness
• Not all people respond to a similar dose of a drug in the
exact same manner, this variability is based upon
individual differences and is associated with toxicity.
This variability is thought to be caused by:
– Pharmacokinetic factors contribute to differing
concentrations of the drug at the target area.
– Pharmacodynamic factors contribute to differing
physiological responses to the same drug concentration.
– Unusual, idiosyncratic, genetically determined or allergic,
immunologically sensitized responses.

Pharmacokinetics
• Absorption
• Distribution
• Metabolism
• Elimination

Pharmacokinetics
• Drug molecules interact with target sites to effect the
nervous system
– The drug must be absorbed into the bloodstream and then
carried to the target site(s)
• Pharmacokinetics is the study of drug absorption,
distribution within body, and drug elimination over
time.
– Absorption depends on the route of administration
– Drug distribution depends on how soluble the drug
molecule is in fat (to pass through membranes) and on the
extent to which the drug binds to blood proteins (albumin)
– Drug elimination is accomplished by excretion into urine
and/or by inactivation by enzymes in the liver

DISPOSITION OF DRUGS
The disposition of chemicals entering the body (from C.D. Klaassen, Casarett and Doull’s Toxicology, 5th ed., New
York: McGraw-Hill, 1996).

Routes of Administration
• Routes of Administration:Orally:
• Rectally:
• Inhalation: Absorption through mucous
membranes:
• Parenterally:
– Intravenous:
– Intramuscular:
– Subcutaneous:

Drug Delivery Systems
• Tablets
• Injections (Syringe)
• Cigarettes
• Beverages
• Patches
• Candy
• Gum
• Implants
• Gas
• Creams

Membranes
• Types of Membranes:
• Cell Membranes: This barrier is permeable to many drug
molecules but not to others, depending on their lipid
solubility. Small pores, 8 angstroms, permit small
molecules such as alcohol and water to pass through.
• Walls of Capillaries: Pores between the cells are larger
than most drug molecules, allowing them to pass freely,
without lipid solubility being a factor.
• Blood/Brain Barrier: This barrier provides a protective
environment for the brain. Speed of transport across this
barrier is limited by the lipid solubility of the psychoactive
molecule.
• Placental Barrier: This barrier separates two distinct
human beings but is very permeable to lipid soluble drugs.

Drug Distribution
• Dependent upon its route of administration and target area, every
drug has to be absorbed, by diffusion, through a variety of bodily
tissue.
• Tissue is composed of cells which are encompassed within
membranes, consisting of 3 layers, 2 layers of water-soluble complex
lipid molecules (phospholipid) and a layer of liquid lipid,
sandwiched within these layers. Suspended within the layers are
large proteins, with some, such as receptors, transversing all 3 layers.
• The permeability of a cell membrane, for a specific drug, depends on
a ratio of its water to lipid solubility. Within the body, drugs may
exist as a mixture of two interchangeable forms, either water
(ionized-charged) or lipid (non-ionized) soluble. The concentration
of two forms depends on characteristics of the drug molecule (pKa,
pH at which 50% of the drug is ionized) and the pH of fluid in which
it is dissolved.
• In water soluble form, drugs cannot pass through lipid membranes,
but to reach their target area, they must permeate a variety of types
of membranes.

Basic Parameters
• In the next few slides the basic concepts and
paramaters will be described and explained.
• In pharmacokinetics the body is represented
as a single or multiple compartments in to
which the drug is distributed.
• Some of the parameters are therefore a little
abstract as we know the body is much more
complicated !

V
Volume 100 L
Clearance
10 L/hr
Volume of Distribution, Clearance and
Elimination Rate Constant

V
Volume 100 L (Vi)
Clearance
10 L/hr
Volume of Distribution, Clearance and
Elimination Rate Constant
V2
Cardiac and
Skeletal Muscle

V
Volume 100 L (Vi)
Clearance
10 L/hr
V2
Cardiac and
Skeletal Muscle
Volume of Distribution =
Dose_______
Plasma Concentration

V
Volume 100 L (Vi)
Clearance
10 L/hr
V2
Cardiac and
Skeletal Muscle
Clearance =
Volume of blood cleared of drug per unit time

V
Volume 100 L (Vi)
Clearance
10 L/hr
V2
Cardiac and
Skeletal Muscle
Clearance = 10 L/hr
Volume of Distribution = 100 L
What is the Elimination Rate Constant (k) ?

CL = kV
k = 10 Lhr -1 = 0.1 hr -1
100 L
10 % of the “Volume” is cleared (of drug) per hour
k = Fraction of drug in the body removed per hour

CL = kV
If V increases then k must decrease as
CL is constant

Important Concepts
• VD is a theoretical Volume and
determines the loading dose.
• Clearance is a constant and determines
the maintenance dose.
• CL = kVD.
• CL and VD are independent variables.
• k is a dependent variable.

Volume of Distribution (Vd)
Apparent volume of distribution is the
theoretical volume that would have to be
available for drug to disperse in if the
concentration everywhere in the body were the
same as that in the plasma or serum, the place
where drug concentration sampling generally
done.

Volume of Distribution
• An abstract concept
• Gives information on HOW the drug is
distributed in the body
• Used to calculate a loading dose

Loading Dose
Dose = Cp(Target) x Vd

Question
• What is the loading dose required for
drug A if;
• Target concentration is 10 mg/L
• Vd is 0.75 L/kg
• Patients weight is 75 kg

Answer: Loading Dose of Drug A
• Dose = Target Concentration x VD
• Vd = 0.75 L/kg x 75 kg = 56.25 L
• Target Conc. = 10 mg/L
• Dose = 10 mg/L x 56.25 L
• = 565 mg
• This would probably be rounded to 560 or
even 500 mg.

Clearance (CL)
• Ability of organs of elimination (e.g.
kidney, liver) to “clear” drug from the
bloodstream.
• Volume of fluid which is completely
cleared of drug per unit time.
• Units are in L/hr or L/hr/kg
• Pharmacokinetic term used in determination
of maintenance doses.

Clearance
• Volume of blood in a defined region of the
body that is cleared of a drug in a unit time.
• Clearance is a more useful concept in reality
than t 1/2 or kel since it takes into account
blood flow rate.
• Clearance varies with body weight.
• Also varies with degree of protein binding.

Clearance
• Rate of elimination = kel D,
– Remembering that C = D/Vd
– And therefore D= C Vd
– Rate of elimination = kel C Vd
• Rate of elimination for whole body = CLT C
Combining the two,
CLT C = kel C Vd and simplifying gives:
CLT = kel Vd

Maintenance Dose
Calculation
• Maintenance Dose = CL x CpSSav
• CpSSav is the target average steady state
drug concentration
• The units of CL are in L/hr or L/hr/kg
• Maintenance dose will be in mg/hr so for total
daily dose will need multiplying by 24

Question
• What maintenance dose is required for
drug A if;
• Target average SS concentration is 10
mg/L
• CL of drug A is 0.015 L/kg/hr
• Patient weighs 75 kg

Answer
• Maintenance Dose = CL x CpSSav
• CL = 0.015 L/hr/kg x 75 = 1.125 L/hr
• Dose = 1.125 L/hr x 10 mg/L
= 11.25 mg/hr
• So will need 11.25 x 24 mg per day
= 270 mg

The area under the plasma drug concentration-time curve (AUC)
reflects the actual body exposure to drug after administration of a
dose of the drug and is expressed in mg*h/L.

AUC
• For IV bolus, the AUC represents the total
amount of drug that reaches the circulatory
system in a given time.
• AUC =Dose
CLT

Monocompartimental model presupposes
that blood plasma concentrations of the drug
are a true reflection of the drug’s
concentration in other fluids or tissues and
that the elimination of the drug is directly
proportional to the drug’s concentration in the
organism (first order kinetics).

Bioavailability
• The fraction of the dose of a drug (F) that
enters the general circulatory system,
F= amt. of drug that enters systemic circul.
Dose administered
F = AUC/Dose

Bioavailability
• A concept for oral administration
• Useful to compare two different drugs or different
dosage forms of same drug
• Rate of absorption depends, in part, on rate of
dissolution (which in turn is dependent on
chemical structure, pH, partition coefficient,
surface area of absorbing region, etc.) Also first-
pass metabolism is a determining factor

Factors affecting bioavailability
•Physical properties of the drug (hydrophobicity, pKa, solubility)
•The drug formulation (immediate release, excipients used, manufacturing
methods, modified release – delayed release, extended release, sustained
release,
•Whether the formulation is administered in a fed or fasted state
•Gastric emptying rate
•Interactions with other drugs (e.g., antacids, alcohol, nicotine)
•Interactions with other foods (grapefruit juice, pomello,
•Health of the GI tract
•Enzyme induction (↑ rate of metabolism), Phenytoin induces CYP1A2,
•Enzyme inhibition(↓ rate of metabolism), grapefruit juice inhibits CYP3A
•Age: drugs are metabolized more slowly in fetal, neonatal, and geriatric
populations
•Disease state; E.g., hepatic insufficiency, poor renal function

•Causes of low bioavailability
• Orally administered drugs must pass through the intestinal wall and
then the portal circulation to the liver; both are common sites of first-
pass metabolism (metabolism that occurs before a drug reaches
systemic circulation). Thus, many drugs may be metabolized before
adequate plasma concentrations are reached.
• Insufficient time for absorption in the GI tract is a common cause of
low bioavailability. If the drug does not dissolve readily or cannot
penetrate the epithelial membrane (eg, if it is highly ionized and polar),
time at the absorption site may be insufficient.
• Age, sex, physical activity, genetic phenotype, stress, disorders (eg,
achlorhydria, malabsorption syndromes), or previous GI surgery (eg,
bariatric surgery) can also affect drug bioavailability.

• Chemical reactions that reduce absorption can decrease
bioavailability. They include formation of a complex
(bet. tetracycline and polyvalent metal ions), hydrolysis by gastric
acid or digestive enzymes, conjugation in the intestinal wall (eg,
sulfoconjugation of isoproterenol), adsorption to other drugs
(eg, digoxin to cholestyramine), and metabolism by luminal
microflora.

Bioequivalence is a term in pharmacokinetics used to assess the
expected in vivo biological equivalence of two proprietary preparations
of a drug. If two products are said to be bioequivalent it means that they
would be expected to be, for all intents and purposes, the same.
Birkett (2003) defined bioequivalence by stating that, "two
pharmaceutical products are bioequivalent if they are pharmaceutically
equivalent and their bioavailabilities (rate and extent of availability) after
administration in the same molar dose are similar to such a degree that
their effects, with respect to both efficacy and safety, can be expected to
be essentially the same. Pharmaceutical equivalence implies the same
amount of the same active substance(s), in the same dosage form, for the
same route of administration and meeting the same or comparable
[1]

Half-Life and k
• Half-life is the time taken for the drug
concentration to fall to half its original
value
• The elimination rate constant (k) is the
fraction of drug in the body which is
removed per unit time.

Half-Life
• C = Co e - kt
• C/Co = 0.50 for half of the original amount
• 0.50 = e – k t
• ln 0.50 = -k t ½
• -0.693 = -k t ½
• t 1/2 = 0.693 / k

Steady-State
• Steady-state occurs after a drug has been given
for approximately five elimination half-lives.
• At steady-state the rate of drug administration
equals the rate of elimination and plasma
concentration - time curves found after each
dose should be approximately superimposable.

100
187.5
194
175
150
75
87.5 94 97
50
200
100
…
…
Accumulation to Steady State
100 mg given every half-life

C
t
Cpav
Four half lives to reach steady state

What is Steady State (SS) ?
Why is it important ?
• Rate in = Rate Out
• Reached in 4 – 5 half-lives (linear
kinetics)
• Important when interpreting drug
concentrations in time-dependent
manner or assessing clinical response

Drug Elimination
C
t
 KC
dC
dt
 KC
Ct  C0eKt

Use of t ½ and kel
• If drug has short duration of action, design
drug with larger t ½ and smaller kel
• If drug too toxic, design drug with
smaller t ½ and larger kel

Drug Concentration
Time
C1
Exponential decay
dC/dt  C
= -k.C
C2

Log Concn.
Time
C0
C0/2
t1/2
t1/2
t1/2
Time to eliminate ~ 4 t1/2

Integrating:
Cp2 = Cp1.e-kt
Logarithmic transform:
lnC2= lnC1 - kt
logC2 = logC1 - kt/2.303
Elimination Half-Life:
t1/2 = ln2/k
t1/2 = 0.693/k

Therapeutic Drug Monitoring
Some Principles

Drug Concentrations may be
Useful when there is:
• An established relationship between
concentration and response or toxicity
• A sensitive and specific assay
• An assay that is relatively easy to perform
• A narrow therapeutic range
• A need to enhance response/prevent
toxicity

Why Measure Drug
Concentrations?
• Lack of therapeutic response
• Toxic effects evident
• Potential for non-compliance
• Variability in relationship of dose and
concentration
• Therapeutic/toxic actions not easily
quantified by clinical endpoints

Potential for Error when using TDM
• Assuming patient is at steady-state
• Assuming patient is actually taking the drug
as prescribed
• Assuming patient is receiving drug as prescribed
• Not knowing when the [drug] was measured in
relation to dose administration
• Assuming the patient is static and that changes in
condition don’t affect clearance
• Not considering drug interactions

Elimination by the Kidney
• Excretion - major
1) glomerular filtration, glomerular structure,
size constraints, protein binding
2) tubular reabsorption/secretion
- acidification/alkalinization,
- active transport, competitive/saturable,
organic acids/bases
- protein binding
• Metabolism - minor

Elimination by the Liver
• Metabolism - major
1) Phase I and II reactions
2) Function: change a lipid soluble to more
water soluble molecule to excrete in kidney
• Biliary Secretion – active transport

Liver P450 systems
• Liver enzymes inactivate some drug molecules
– First pass effect (induces enzyme activity)
• P450 activity is genetically determined:
– Some persons lack such activity  leads to higher drug
plasma levels (adverse actions)
– Some persons have high levels  leads to lower
plasma levels (and reduced drug action)
• Other drugs can interact with the P450 systems
– Either induce activity (apparent tolerance)
– Inactivate an enzyme system

How are [drug] measured?
• Invasive: blood, spinal fluid, biopsy
• Noninvasive: urine, feces, breath, saliva
• Most analytical methods designed for
plasma analysis
• C-14, H-3

Therapeutic Window
• Useful range of concentration over which a drug is
therapeutically beneficial. Therapeutic window
may vary from patient to patient
• Drugs with narrow therapeutic windows require
smaller and more frequent doses or a different
method of administration
• Drugs with slow elimination rates may rapidly
accumulate to toxic levels….can choose to give
one large initial dose, following only with small
doses

Shape different for IV injection

Distribution
• Rate & Extent depend upon
– Chemical structure of drug
– Rate of blood flow
– Ease of transport through membrane
– Binding of drug to proteins in blood
– Elimination processes

• Partition Coefficients: ratio of solubility of
a drug in water or in an aqueous buffer to its
solubility in a lipophilic, non-polar solvent
• pH and ionization: Ion Trapping

The Compartment Model
• We can generally think of the body as a
series of interconnected well-stirred
compartments within which the [drug]
remains fairly constant. BUT movement
BETWEEN compartments important in
determining when and for how long a drug
will be present in body.

Partitioning into body fat and
other tissues
 A large, nonpolar compartment. Fat has
low blood supply—less than 2% of cardiac output,
so drugs are delivered to fat relatively slowly
•For practical purposes: partition into body fat
important following acute dosing only for a few
highly lipid-soluble drugs and environmental
contaminants which are poorly metabolized and
remain in body for long period of time

IMPORTANT EFFECTS OF pH
PARTITIONING:
  urinary acidification will accelerate the
excretion of weak bases and retard that of weak
acids; alkalination has the opposite effects
  increasing plasma pH (by addition of
NaHCO3) will cause weakly acidic drugs to be
extracted from the CNS into the plasma; reducing
plasma pH (by administering a carbonic anhydrase
inhibitor) will cause weakly acidic drugs to be
concentrated in the CNS, increasing their toxicity

Renal Elimination
• Glomerular filtration: molecules below 20 kDa
pass into filtrate. Drug must be free, not protein
bound.
• Tubular secretion/reabsorption: Active transport.
Followed by passive and active. DP=D + P. As D
transported, shift in equilibrium to release more
free D. Drugs with high lipid solubility are
reabsorbed passively and therefore slowly
excreted. Idea of ion trapping can be used to
increase excretion rate---traps drug in filtrate.

Plasma Proteins that Bind Drugs
• albumin: binds many acidic drugs and a
few basic drugs
 b-globulin and an a1acid glycoprotein
have also been found to bind certain basic
drugs

A bound drug has no effect!
• Amount bound depends on:
• 1) free drug concentration
• 2) the protein concentration
• 3) affinity for binding sites
% bound: __[bound drug]__________ x 100
[bound drug] + [free drug]

% Bound
• Renal failure, inflammation, fasting,
malnutrition can have effect on plasma
protein binding.
• Competition from other drugs can also
affect % bound.

An Example
• Warfarin (anticoagulant) protein bound ~98%
• Therefore, for a 5 mg dose, only 0.1 mg of drug is
free in the body to work!
• If patient takes normal dose of aspirin at same
time (normally occupies 50% of binding sites), the
aspirin displaces warfarin so that 96% of the
warfarin dose is protein-bound; thus, 0.2 mg
warfarin free; thus, doubles the injested dose

Volume of Distribution
• C = D/V
Vd is the apparent volume of distribution
C= [drug] in plasma at some time
D= total [drug] in system
Vd gives one as estimate of how well the drug is
distributed. Vd < 0.071 L/kg indicate the drug is
mainly in the circulatory system.
Vd > 0.071 L/kg indicate the drug has entered specific
tissues.

Conc. vs. time plots
C = Co - kt ln C = ln Co - kt

Types of Kinetics Commonly Seen
Zero Order Kinetics
• Rate = k
• C = Co - kt
• Constant rate of
elimination regardless
of [D]plasma
• C vs. t graph is
LINEAR
First Order Kinetics
• Rate = k C
• C = Co e-kt
• Rate of elimination
proportional to plasma
concentration.
Constant fraction of
drug eliminated per
unit time.
• C vs. t graph is NOT
linear, decaying
exponential. Log C
vs. t graph is linear.

Example of Zero Order Elimination:
Pharmacokinetics of Ethanol
• Ethanol is distributed in total body water.
• Mild intoxication at 1 mg/ml in plasma.
• How much should be ingested to reach it?
Answer: 42 g or 56 ml of pure ethanol (VdxC)
Or 120 ml of a strong alcoholic drink like whiskey
• Ethanol has a constant elimination rate = 10 ml/h
• To maintain mild intoxication, at what rate must
ethanol be taken now?
at 10 ml/h of pure ethanol, or 20 ml/h of drink.

To reiterate: Comparison
• First Order Elimination
– [drug] decreases
exponentially w/ time
– Rate of elimination is
proportional to [drug]
– Plot of log [drug] or
ln[drug] vs. time are
linear
– t 1/2 is constant regardless
of [drug]
• Zero Order Elimination
– [drug] decreases linearly
with time
constant
independent of [drug]
– No true t 1/2

Route of Administration Determines
Bioavailability (AUC)

AUC: An Indicator of Bioavailability
• Dose is proportional to [drug] in tissues.
• [drug], in turn, is proportional to the Area Under
the Curve in a Concentration-decay curve.
• Thus, we have k = dose/AUC
• Because oral administration is full of barriers,
the fraction, F, that is available by entering the
general circulation, may not be significant.
• Thus, FD = k(AUC)
or k = FD/AUC

• Combining these 2 equations gives us:
FDpo/AUCpo = Div/AUCiv
• And thus, F = AUCpoDiv
AUCivDpo
• More generally, the relative bioavailability,
F = AUCADoseB
AUCBDoseA

AUC
• For IV bolus, the AUC represents the total
amount of drug that reaches the circulatory
system in a given time.
• Dose = CLT AUC

The Effect of the Liver First Pass
• F = 1-E, where E is fraction of the dose elim
via the liver.
• Cltot = D/AUC
• Clhep = Cltot-Clren
• Clhep = E × LBF, which is liver blood flow
or E = Clhep/LBF
• Combining the 1st eq with the last gives
F = 1-E = 1 - Clhep
LBF

Rowland’s Equation
• F = 1-E = 1 - Clhep
LBF
This very useful equation calculates the
magnitude of the effect of the liver’s 1st
pass of an oral dose and, more precisely, to
predict it from and i.v. test.
Thus, if E < 0.10, then, clearly, bioavailability
F > 0.90.

P450 Interactions
• Substrate: Is the drug metabolized via a specific
hepatic isoenzyme?
• Inhibitor: does a specific drug inhibit a specific
hepatic isoenzyme?
– Would expect this to interfere with drug inactivation
• Inducer: does a specific drug enhance a specific
hepatic isoenzyme?
– Would expect this to speed up drug inactivation

Drug-CYP Interactions
Enzyme (CYP) Substrate Inhibitor Inducer
1A2 Clozapine, haloperidol Cimetidine Tobacco smoke
2B6 Bupropion Thiotepa Phenobarbital
2C19 Citalopram Fluoxetine
Prednisone
2C9 Fluoxetine Paroxetine Secobarbital
2D6 Most ADs, APs CPZ, ranitidine Dexamethasone
2E1 Gas anesthetics Disulfiram Ethanol
3A4,5,7 Alprazolam Grapefruit juice Glucocorticoid
–http://www.georgetown.edu/departments/pharmacology/clinlist.html

Drug Enantioners
• A drug molecule may be organized in such a way
that the same atoms are mirror images
– Enantioners represent drug molecules that are
structurally different (spatial configutation)
• Different physical properties
– Light rotation (levo = left; dextro = right)
– Melting points
• Different biological activities (typically: dextro > levo)
– Fenfluramine = racemic mix of
• dextro-fenfluramine
• levo-fenfluramine
• Enantiomers often have different affinity for
receptors

Drug Effectiveness
• Dose-response (DR) curve:
Depicts the relation between
drug dose and magnitude of
drug effect
• Drugs can have more than one
effect
• Drugs vary in effectiveness
– Different sites of action
– Different affinities for receptors
• The effectiveness of a drug is
considered relative to its safety
(therapeutic index)

Therapeutic Index
This is a figure of two different
dose response curves. You can
obtain a different dose response
curve for any system that the drug
effects. When you vary the drug,
this is the Independent variable,
what you are measuring is the % of
individuals responding to the drug.
Here we see the drugs effects on
hypnosis and death. Notice that the
effective dose for 50 % of the
people is 100 mg and if you double
the dose to 200 mg then 1 % of
your subjects die. Thus, if you
want to use this drug to hypnotize
99 % of your subjects, in the
process you will kill 2-3 % of your
subjects.

Pharmacokinetics

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