Pharmacokinetics

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Pharmacokinetics

• Pharmacokinetics is the study of those rate
  processes involved in the absorption,
  distribution, metabolism, and excretion of drugs
  (drug disposition) and their relationship to the
  pharmacological, therapeutic or toxic response
  in animals and man.

Metabolism Excretion Elimination
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Absorption - Distribution-Metabolism-Excret
ion
ABSORPTION
DISTRIBUTION
i.v.
DISTRIBUTION
LIVER M BE KIDNEY Ur. E
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Pharmacokinetics techniques

• Pharmacokinetic techniques attempt
  to mathematically define the time
  course for drug in the body by assaying
  for drug and metabolites in readilly
  accesible fluids such as blood and urine.

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Pharmacokinetics techniques

• The goal is to quantitatively account for the
  amount of drug which has entered the body
  (bioavailable dose) and to estimate the rate
  by which it is cleared from the body.

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Pharmacokinetics techniques

• The mathematical descriptions use PK variables
  (PK parameters) for modelling of the time-course
  of a drug in plasma or other fluids
  (concentration versus time curves). PK parameters
  are than used to calculate the rate of dosing.

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Pharmacokinetic parameters

• apparent volume of distribution Vd
• total clearance Cl
• elimination half-life t1/2
• bioavailability F

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Distribution
Drug distribution means the reversible transfer
of drug from one location to another within the
body. Once a drug has entered the
vascular system it becomes distributed throughout
the various tissues and body fluids in a pattern
that reflects the physico-chemical nature of the
drug and the ease with which it penetrates
different membranes.
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Factors affecting drug distribution

• Rate of distribution
  - Membrane permeability
  - Blood
  perfusion of organs and tissues
• Extent of Distribution
  - Lipid Solubility
  - pH - pKa
  (pH-partition theory for
  ionizable molecules)
  - Plasma protein binding
  - Intracellular
  binding

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• Plasma protein binding
• Extensive plasma protein binding will cause more
  drug to stay in the blood compartment. Therefore
  drugs which bind strongly to plasma protein tend
  to have lower distribution.
  
• Of these plasma proteins, albumin, which
  comprises 50 of the total proteins binds the
  widest range of drugs. Acidic drugs
  commonly bind to albumin, while basic drugs often
  bind to alpha1-acid glycoproteins and
  lipoproteins.

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Apparent Volume of Distribution (Vd)

• Definition The apparent volume
  of distribution indicates into how large
  a volume the drug distributes if it were
  at the same concentration as that in plasma
  (or in other reference fluid
  which is sampled - blood, serum).

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Apparent Volume of Distribution (Vd)

• This apparent volume of distribution is not
  a physiological volume. It won't be lower
  than blood or plasma volume but it can be much
  larger than body volume for some drugs.
  It is a mathematical factor relating the
  amount of drug in the body and the
  concentration of drug in the measured
  compartment, usually plasma
• Vd AMOUNT of drug in the body
  CONCENTRATION in plasma

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Apparent volume of distribution

• Vd AMOUNT OF DRUG IN THE BODY
  CONCENTRATION IN PLASMA
• Vd F x Dose - AMOUNT eliminated
  CONCENTRATION IN PLASMA
• F. ..absolute bioavailability (bioavailable
  fraction of the dose)
• Units volume (L, L/kg of TBW)

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Rapid (bolus) i.v. injection and uniform mixing
of the amount administered throughout
the volume of total body water
VdDose/cplasma
VdVtotal body water
Vd 0.6 L/kg BW Dose cplasma . Vd
Fat !!!0,2-0,35 L water per 1 kg of weight
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Vd Amount / Concentration in plasma

• Most drugs are distributed unevenly into the
  body. Some drugs (digoxin) are extensively
  distributed and bound in tissues, leaving low
  concentrations in the plasma, thus the body as a
  whole appears to have a large volume of
  distribution.

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Volumes of some compartments of the adult human
body in relation to VD
Total body water 0.6 L/kg BW Intracellular
water 0.4 L/kg BW Extracellular water 0.2 L/kg
BW
Plasma 0.04 L/kg BW VD 0.05
L/kg the drug remains in the blood (heparine) VD
0.1-0.3 L/kg distribution from blood into
extracellular fluid
(gentamicin - polar drugs). VD 0.6
L/kg distribution from blood into intracelular
and extracellular fluid
(methotrexate) VD gtgt0.6 L/kg distribution
intracellularly and high binding in
tissues (amiodarone - 350 L/kg)
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Use of Vd

• 1/ Vd in conjunction with a target concentration
  CT can be used to compute a loading dose DL
• DL VD . CT

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Loading dose CP x VD
L. Dose
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Use of Vd
EXAMPLE J.K.(TBW 90 kg)was admitted to the
ICU for pneumonia caused by Gram-negative
bacteria. Calculate the loading dose of
tobramycin for this patient to achieve the target
average concentration of 4 mg/l. Tobramycin VD
is 0.2 l/kg of TBW. Loading Dose ? Loading
Dose 0.2 . TBW . Concentration Loading Dose
0.2 . 90 . 4 72 mg
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Use of Vd

• 2) It can be usefull in case of overdoses and in
  certain medico-legal cases to estimate the amount
  of drug in the body
• Amount in the body Vd . Cactual, measured

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Use of Vd

• 3/ To assess feasibility of using
  hemoperfusion or dialysis for drug removal from
  the body
• The larger the VD the smaller fraction of the
  dose is in plasma, the less is plasma
  concentration and the less efficient is any drug
  removal through extracorporeal mechanisms.

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Clearance (CL)

• Definition Clearance of a drug is the ratio of
  the rate of elimination by all routs to the
  concentration of drug in plasma.
• CL Rate of eliminination mg / h
• C in plasma mg /L
• Unit Volume/Time L/h or adjusted for body
  weight l/h/kg

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Clearance (CL)

• Rate of eliminination CL x C in plasma
• (Amount / Unit of time) (Volume / Unit of time)
  x Cin plasma
• Unit Volume/Time L/h

Another possible way of understanding clearance
Clearance is the volume of plasma completly
cleared of the drug per unit of time by all
routes - by the liver, the kidney).
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Rate of elimination
Elimination of most drugs from the body after
therapeutically relevant doses follows
first-order kinetics. To illustrate first order
kinetics we might consider what would happen if
we were to give a drug by i.v.
bolus injection, collect blood samples at various
times and measure the plasma
concentrations of the drug. We might see a
decrease in concentration as the drug is
eliminated.
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Rate of elimination
Elimination which follows first-order kinetics
dC/dt - kel . C kel . rate constant
of elimination rate of change
is proportional to concentration and is
therefore decreasing with time as the conc.
decreases
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Rate of elimination
monoexponential decay C(t) C0 . e- kel . t
half-life t1/2 C C0 / 2 t t1/2 ln2 / kel
0.693/ kel after 4 half-lives 6
remaining, 94 eliminated
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Rate of elimination
Elimination which follows first-order kinetics
semi-log graph.
t 1/2 0.693/ kel
kel can be estimated by means of the
linear-regression analysis
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Clearance (CL)

• Clearance has an additive character it is the
  sum of clearences in all eliminating
  organs
• CL CLRENAL CLHEPATIC CLpulmonary ...other
• renal nonrenal

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The principle of linear pharmacokinetics
Linear (first-order) pharmacokinetics For most
drugs, clearance is constant over the plasma
concentration range used in clinical practice.
Elimination is not saturable (non-capacity-limited
) and the rate of drug elimination is directly
proporcionate to the concentration Rate of
elimin. CL . Concentration
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Nonlinear pharmacokinetics
Nonlinear pharmacokinetics (capacity-limited,
dose or concentration dependent, saturable) CL
varies depending on the concentration of a drug.
Rate of elimination Vmax . C /Michaelis-
Menten/ Km C CL Vmax
Km C ethanol, phenytoin, theofylline
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Use of clearance

• 1/ Total clearance determines the average
  steady-state concentration of a drug during
  continuous drug administration (multiple
  intermittent dosing or constant rate i.v.
  infusion
• at the steady-state
• Rate of dosing Rate of elimination CL . Cpss
• continuous i.v. infusion Cpss Rate of inf./ CL

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Use of clearance

• 2/ Total clearance, when multiplied by a target
  steady-state concentration CSS,TARGET , can be
  used to calculate the dosing rate required to
  maintain plasma CSS,TARGET (the maintenance dose)
  
• Rate of dosing CSS,TARGET . CL
• Rate of dosing .. Rate of i.v. infusion (mg/h)
• Oral dose / Dosing interval
• i.v. dose / Dosing interval

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Calculation of the maintenance dose
J.K.was admitted to the ICU for pneumonia caused
by Gram-negative bacteria. Calculate the
maintenance dose (i.v.-infusion in 6 h
intervals)of tobramycin for this patient to
achive the target average concentration of 4
mg/l. Clearance of tobramycin was estimated to be
70 ml/min. Rate of dosing Dose / Interval Rate
of dosing Rate of elimination CL.cT Rate of
dosing 4.70.60 / 1000 16.8 mg/h Dose
Rate of dosing . Interval 6 . 16.8 101 mg
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Multiple i.v. bolus dose administration drug
accu- mulation in plasma until the steady state
is achieved
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Use of clearance

• 3/ The numerical value of total clearance and its
  two principal components (hepatic and renal)
  provide important insights into the elimination
  processes and into the potential needs for dosage
  adjustments in case of liver or kidney
  impairment.

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Biliary clearance CLh
Q hepatic blood flow per 1 min 1.5
L/min,

Q . Cout
LIVER
Q . Cin
bile
Amount excreted in bile Amount extracted
Q.(Cin- Cout)
CLh rate of elimin. / Cin Q . (Cin- Cout) /
Cin
CL Q . E hepatic extraction ratio
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Hepatic extraction ratio (E)

• E (Cin- Cout) / Cin
• A/ High extraction Cout ? 0, E ? 1 (gt0.7)
• After oral administration, drug is efficiently
  extracted by the liver and less is available in
  the systemic circulation - high first-pass
  effect. The elimination of the drug from the
  systemic circulation is flow limited (clearance
  Q.E Q).
• B/ Low extraction Cout ? Cin , E ? 0 (lt0.3)
• Small first-pass, high systemic availability
  after oral administration, hepatic clearance is
  sensitive to change in E (inhibition and
  induction of metabolism).

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Renal clearance CLR
GFR , C in plasma


GFR 100 -150 ml/min
KIDNEY

URINE
VU , CU
VU volume collected / urine collection period
Amount excreted VU . CU

CLR rate of elim. / C in plasma VU .
CU/ C in plasma
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Renal clearance CLR
CLR rate of elim. / C in plasma VU . CU/ C in
plasma

Renal clearance of a drug is the ratio of the
rate of elimination of the drug by the kidney
divided by its concentration in plasma.



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Renal clearance of the drug
CLR GFR x funbound Tubular secretion -
Tubular
reabsorption Glomerular filtration rate is
measured using endogenous creatinine GFR ?
creatinine clearance 100 - 150 ml/min 1/ CLR
gt GFR x funbound filtration
Tubular secretion 2/ CLR lt GFR x
funbound filtration - Tubular
reabsorption 3/ CLR ? GFR x
funbound filtration





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Elimination half-life (t1/2)
Definition Elimination half-life is the time it
takes the drug concentration in the blood to
decline to one half of its initial value. It is
a secondary parameter The elimination
half-life is dependent on the ratio of VD
and CL. Unit time (min, h, day)
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Use of t1/2
1/ t1/2 can be used to predict how long it will
take for the drug to be eliminated from
plasma.

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Use of t1/2
2/ t1/2 can be used to predict how long it will
take from the start of dosing to reach
steady-state levels during multiple dosing or
continuous i.v. infusion. No. of t1/2
Concentration achieved ( of steady
conc.) 1 50 2 75 3 87.5 4
94 5 97

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Important
During continuous (infusion) or continuous
intermittent dosing (oral dosing) The
steady-concentration depends on the rate of
dosing (the dose/dosing interval) and the
clearance. Time required to achieve steady-state
depends on the half-life and is independent of
the rate of dosing and the clearance..
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Use of t1/2
3/ the relationship between t1/2 and dosing
interval t can be used to predict the degree of
accumulation of a drug in the blood. The
longer t1/2 and the shorter t, the more drug
accumulates. t ? t1/2 Moderate accumulation
during dosing 2-times) t lt
t1/2 Significant accumulation during dosing (gt
2-times) t gt t1/2 Insignificant accumulation
during dosing (lt 2-times)

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Use of t1/2
4/ t1/2 (the relationship between t1/2 and
dosing interval t) can be used to predict the
degree of fluctuation of a drug concentration
within a dosing interval. t ? t1/2 Css,min
levels at steady state are aprox. 50 of
Css,max. Moderate fluctuation. t lt t1/2 Css,min
levels at steady state are more than 50 of
Css,max. Small fluctuation. t gt t1/2 Css,min
levels at steady state are less than 50 of
Css,max. Wide fluctuation.

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Multiple short i.v. infusions of amikacin
the rate of dosing is constant but interdose
interval is changing, t1/2 6 h
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Multiple short i.v. infusions of amikacin
the rate of dosing is constant but interdose
interval is changing, t1/2 6 h
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Use of t1/2
5/ t1/2 can be used to predict how long it will
take a drug concentration to decline from one
specific value to another. t t1/2 . ln(C1/C2)
/ 0.7 It can be usefull in overdoses and
dosage adjustments.

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Fundamental relationships between various PK
parameters
Elimination which follows first-order kinetics
can be described by rate constants (or
half-lives). If we assume rapid transfer of drug
from other parts of the body into plasma, the
drug is cleared from its total distribution
volume in the body
Rate of elimination VD . Rate of removal from
the unit volume VD . dC/dt Vd . kel . C CL
Rate of elimination / C Vd . kel Vd . 0.7 /
t1/2
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Fundamental relationships between various PK
parameters
Elimination which follows first-order kinetics
can be described by rate constants (or
half-lives). If we assume rapid transfer of drug
from other parts of the body into plasma, the
drug is cleared from its total distribution
volume in the body
Rate of elimination Distr. Volume . Rate of
removal from the unit volume Vd . dC/dt Vd .
kel . C Clearance Rate of elimination / C Vd
. kel Vd . 0.7 / t1/2 AUC Dose / (Vd . kel)
? Clearance Dose / AUC
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Area under the curve, AUC
C C0 . e- k.t monoexponential decay AUC is an
integral AUC Dose / (V . kel) AUC Dose /
CL CL Dose / AUC (i.v.) CL F. Dose / AUC

The AUC value is very useful for calculating the
amount of drug which reaches the systemic
circulation (the absolute bioavailability F)
after administration of different drug products.
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Pharmacokinetics after extravascular
administration
Most of the routes of administration are
extravascular for example IM, SC, and most
importantly oral. With this type of drug
administration the drug isn't placed in the
systemic circulation but must be absorbed through
at least one membrane. This has a considerable
effect on drug pharmacokinetics and may cause
a reduction in the actual amount of
drug which is absorbed and reaches the systemic
circulation.

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Pharmacokinetics after extravascular
administration
Bioavailable dose F . Dose Fabsolute
bioavailability (0 ltF lt 1) .after i.v.
administration F 1 Most commonly the
absorption process follows first order kinetics.
Even though many oral dosage forms are solids,
which must dissolve before being absorbed,
the overall absorption process can often be
considered to be a single first order process.

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Pharmacokinetics after extravascular
administration. Bioavailability
AUC Cmax Tmax
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Absorption rate constant (ka)

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Bioavailable fraction of the dose (F)

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Bioavailability
F must be determined by comparison with another
dose administration. If the other dosage form is
an intravenous form then the F value is termed
the absolute bioavailability. In the case where
the reference dosage form is another oral
product, the value for FR is termed the relative
bioavailability. CL (D/AUC) i.v. F.
(D/AUC)oral
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Bioavailability
Bioavailability indicates a measurement of the
rate and extent (amount) of therapeutically
active drug which reaches the general
circulation. Absolute bioavailability is the
absolute fraction of dose which is available from
a drug formulation in general circulation. It is
measured by comparing AUC after i.v. and
extravascular administration. Relative
bioavailability is a relative amount and relative
rate of availability if two formulations (other
than i.v.) are compared.
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Bioequivalence
Two drug formulations are bioequivalent if the
extent and rate of bioavailability of a drug is
comparable (within certain limits). Bioequivalence
study new drug formulation of a known
active drug is compared to the reference
(original formulation or another marketed
formulation) in a study with healthy
volunteers. Original product, Generic copies
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Bioequivalence
Two drug formulations are bioequivalent if the
extent and rate of bioavailability of a drug is
comparable (within certain limits). Cross-over
study with 2 periods Group 1 Test
Reference Group 2 Reference Test AUC,
cmax, Tmax,
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Some definitions
Brand Name is the trade name of the drug.
Chemical Name is the name used by the organic
chemist to indicate the chemical structure of the
drug. Drug Product means a finished dosage
form, e.g., tablet, capsule, or solution,
that contains the active drug ingredient,
generally, but not necessarily, in association
with inactive ingredients. Generic Name is the
established, common name of the active drug
in a drug product.