Post on 14-Jan-2017
Gent, 24 August 2007/avpeer 1
Basic Concepts of Pharmacokinetics
Achiel Van Peer, Ph.D.Clinical Pharmacology
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Some introductory Examples
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15 mg of Drug X in a slow release OROS capsuleadministered in fasting en fed conditions
in comparison to 15 mg in solution fasting
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Prediction of drug plasma concentrations before the first dose in a human
NOAEL in female rat
NOAEL in male rat
NOAEL in female dog
NOAEL in male dog
First dose 5 mg Fabs 100%Fabs 50%Fabs 20%
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Allometric Scaling
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Pharmacokinetics: Time Profile of Drug Amounts
Drug at absorption site
Drug in body
Metabolites
Excreted drug
Time (arbitrary units)
Per
cent
of d
ose
Rowland and Tozer, Clinical Pharmacokinetics: Concepts and Applications, 3rd Ed. 1995
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Definition of Pharmacokinetics ?
Pharmacokinetics is the science describing drug
absorption from the administration sitedistribution to
tissues, target sites of desired and/or undesired activity
metabolismexcretion
PK= ADME
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We will cover
Some introductory Examples Model-independent ApproachCompartmental ApproachesDrug Distribution and EliminationMultiple-Dose PharmacokineticsDrug Absorption and Oral BioavailabilityRole of Pharmacokinetics
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The simplest approach … observational pharmacokineticsThe Model-independent Approach
Cmax : maximum observed concentration
Tmax : time of Cmax
AUC : area under the curve
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Cmax, Tmax and AUC in Bioavailability and Bioequivalence Studies
Absolute bioavailability (Fabs)compares the amount in the systemic circulation after intravenous (reference) and extravascular (usually oral) dosing
Fabs = AUCpo/AUCiv for the same dose
between 0 and 100% (occasionally >100%)
Relative bioavailability (Frel)compares one drug product (e.g. tablet) relative to another drug product (solution)
Bioequivalence (BE): a particular FrelTwo drug products with the same absorption rate (Cmax, Tmax) and the same extent (AUC) of absorption
(90% confidence intervals for Frel between 80-125%)
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Absolute oral bioavailabilityflunarizine, J&J data on file
Other example: nebivolol: 10% in extensive metabolisers; 100% in poor metabolisers
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Area under the curve
)12).(2
21(AUC t2-t1 ttCC−
+=
Trapezoidal rule: divide the plasma concentration-time profile to several trapezoids, and add the AUCs of these trapezoidsConc
Time
zClastlatedAUCextrapoλ
=
00
Units, e.g. ng.h/mL
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Elimination half-life ?
Half-life (t1/2) : time the drug concentration needs
to decrease by 50%
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Elimination half-life ?visual inspection
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Elimination half-life ?visual inspection or alternatives ?
Half-life (t1/2) : time to decrease by 50%
T1/2 = 6 hrs
Derived from a semilog plot
T1/2 = 0.693/λz
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From Whole-Body Physiologically based Pharmacokinetics to Compartmental Models
Poggesi et al., Nerviano Medical Science
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Compartmental Approach
One-compartment PK model
Bodycompartment
Drug Absorption
Drug Elimination
drug distributes very rapidly to all tissues via the systemic circulation
an equilibrium is rapidly established between the blood and the tissues, the body behaves like
one (lumped) compartment
does not mean that the concentrations in the different tissues are the same
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One compartment behaviour more often observed after oral drug intake
1
10
100
1000
0 8 16 24 32 40 48Time, hours
Poor metabolisers
Extensive metabolisers
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Intravenous dose of 0.2 mg Levocabastine(J&J data on file)
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Depending on rate of equilibration with the systemic circulation, lumping tissues together,
and simplification is possible
Multi-Tissue or Multi-Compartment
Whole Body Pharmacokinetic model
Tri-compartment model
Two-compartment model
One-compartment model
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Zero-order rate drug administration and first-order rate drug elimination
Infusion rate mg/min
Rate of elimination is proportional to
the Amount in blood/plasma
dDose/dt = Ko = mg/min dA/dt = -k.A
Amount A in blood, plasma
[Often K=Kel=K10]
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First-order rate of drug disappearance
Intravenous bolus
Amount A [or Concentration C]
in blood, plasma
Rate of elimination is proportional to
the Amount or Concentration in
blood, plasma
dA/dt = -k.A = -k.Vd.C
If A = Amount in plasma, then V= Plasma volume
If A = Remaining amount in the body, thenVd= Total volume of distribution
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A single iv dose of 5 mgfor a drug with immediate equilibration
(one compartment behaviour)
dC/dt = -k10.C
dA/dt = -k10.A = -k10.V.C
dA/dt = -k10.A = -CL.C
C = C0. e-k10.t
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A single iv dose of 5 mg
C = C0 e-k10.t
lnC = lnC0 - k10.t
Remark for log10 scale: slope = k10/2.303
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A single iv dose of 5 mg
ln C = lnC0 - k10.t
12693.0
122ln1ln10
ttttCCk
−=
−−
=
C2= half of
C1
Slope=k10= the elimination rate constant
Half-life = 0.693/k10
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A single iv dose of 5 mg
Vd = volume of distribution,
relates the drug concentration
to the drug amountin the body
LmLngng 9.30
/1625000000
CpodoseVd ===
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One-Compartment model after intravenous administration
Vd = volume of distribution,
relates the drug concentration at a particular time
to the drug amount in the body at that time
k10= (first-order) elimination rate constant
Clearance (CL) = Vd.K10
The volume of drug in the body cleared per unit time
Half-life = 0.693 . Vd/CL
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Compartmental Approachafter intravenous dosing
Rapidly equilibrating tissues:plasma, red blood cells, liver, kidney, …
Slower equilibrating:adipose tissues, muscle, …
Usually peripheral compartment
Slowly redistribution reason for long terminal half-life
Elimination
Distribution
Re-distribution
Central compartment
Peripheralcompartment
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Intravenous dose of 0.2 mg levocabastine
V1 = 44 L V2 = 35 L
K12= 0.84 h-1
K21= 1.05 h-1
K10 = 0.4 h-1
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Intravenous dose of 0.2 mg levocabastine
V1 = 44 L V2 = 35 L
Cld= k12.V1= 36.7 L/h
Cld= k21.V2= 36.7 L/h
Cl=K10 .V1=Dose/AUC= 1.77 L/h=30 mL/min
Vdss = V1 + V2
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Rates of drug exchange
DAp/dt = - K10.Vc.Cp - K12.Vc.Cp + K21.Vt.Ct
DAt/dt = K12.Vc.Cp - k12.Vt.Ct
Initially very fast decay due to distribution to tissues and elimination (“distribution phase”) until equilibrium is reached (influx into and efflux from tissue is equal)
After a pseudo-equilibrium is reached, there is only loss of drug from the body (“elimination phase”), but is in fact combination of redistribution from tissues and elimination
Rate of redistribution may differ significantly across drugs; long terminal half-life is compounds sticks somewhere
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Intravenous dose of 0.2 mg levocabastine
Cp=A.e-α.t+B.e-β.t
Cp=2.1.e-1.91 .t+2.5.e- 0.0224.t
hh
tt term 3110224.0
693.02/12/1 =
−=
0.693==
ββ
Vdβ = CL/β=Dose/(AUC. β)=Vdarea
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Two-compartmental model
Central
Compartment
Vc
Peripheral
CompartmentVt
K10
K12
K21
K10, K12, K21 are first order rate constants
hybrid first-order rate constants α and β for the so-called distribution phase and elimination phases, T1/2α and T1/2β
Vc, Vdss, Vdβ or Vdarea are Vd of central compartment, at steady-state, during elimination phase
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Compartmental approachafter intravenous dosing
Central compartment
Shallow Peripheralcompartment
Deep Peripheralcompartment
Compartments serve as reservoirs with different drug amounts (concentrations),
different volumes, and different rates of exchange of drug with the central compartment.
The shape of the plasma concentration-time profile empirically defines the number of compartmentsl
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Intravenous Sufentanil
Gepts et al., Anesthesiology, 83:1194-1204, 1995
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Three compartmental modelSufentanil Pharmacokinetics
Gepts et al., Anesthesiology, 83:1194-1204, 1995
Mixed-effects Population PK analysis (N =23)
Population Average CV (%)
Volume of distribution (L)Central (V1) 14.6 22
Rapidly equilibrating (V2) 66 31Slowly equilibrating (V3) 608 76
At steady-state 689Clearance (L/min)
Systemic (CL or CL1) 0.88 23Rapid distribution (CL2) 1.7 48Slow distribution (CL3) 0.67 78
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Three compartmental modelSufentanil Pharmacokinetics
Gepts et al., Anesthesiology, 83:1194-1204, 1995
Fractional Coefficients
Rate constants (min-1)
A 0.94 K10 0.06
B 0.058 K12 0.11
C 0.0048 K13 0.05
K21 0.025
K31 0.0011
Exponents (min-1) Half-lives (min)
α 0.24 t1/2 α 2.9
β 0.012 t1/2 β 59
γ 0.0006 t1/2 γ 1129
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Compartmental approachafter intravenous dosing
Central compartment
Shallow Peripheralcompartment
Central compartment
Deep Peripheralcompartment
Peripheralcompartment
Effect site
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Shafer and Varvel, Anesthesiology 74:53-63, 1991
Time profile of opioid concentrations in plasma and the predicted
concentrations at the effect site based upon an effect compartment
PK-PD model
(expressed as percentage of the initial plasma concentration)
Effect site concentration profile reflect difference
in onset time of analgesia
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Rate of Drug Distribution
perfusion-limited tissue distribution
immediate equilibrium of drug in blood and in tissueonly limited by blood flowhighly perfused : liver, kidneys, lung, brainpoorly perfused : skin, fat, bone, muscle
Permeability rate limitations or membrane barriers
blood-brain barrier (BBB)blood-testis barrier (BTB)placenta
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Unbound Fraction and Drug Disposition
Plasma Tissue
Protein-bounddrug
Protein-bounddrug
Free drug(non-ionized)
Free drug(non-ionized)
Ionized drug(free)
Ionized drug(free)
Cellmembrane
Receptor-bounddrug
Pka-pH, affinity for plasma and tissue proteins, permeability, …
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Physicochemistry, PK and EEG PD of narcotic analgesics
Alfen tan il F en tan yl S u fen tan il
pK a 6.5 8 .43 8 .01
% u n io n ized a t p H 7 .4 89 8 10
P o ct/w ater 130 810 1750
% u n b o u n d in p lasm a 8 16 8
V d ss (L ) 23 358 541
C l (L /m in ) 0 .20 0 .62 1.2
t1 /2 keo E E G (m in ) 1 .1 6 .6 6 .2
C e50, E E G (ng /m l) 520 8.1 0 .68
C e50, u n b (ng /m l) 41 1.2 0 .051
K i (n g /m l) 7 .9 0 .54 0 .039
Shafer SL, Varvel JR: Pharmacokinetics, pharmacodynamics, and rational opioid selection. Anesthesiology 1991; 74:53-63; DR Stanski, J Mandema (diverse papers)
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Localisation and Role of Drug TransportersZhang et al., FDA web site and Mol. Pharmaceutics 3, 62-69, 2006
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Apparent Volume of Distribution
Vd = Amount of drug in body/concentration in plasmaMinimum Vd for any drug is ~3L, the plasma volume in an adult, for ethanol: equal to body water For most basic drugs very high due to sequestering in specific organs (liver, muscle, fat, etc.)
Rowland and Tozer, Clinical Pharmacokinetics: Concepts and Applications,
3rd Ed., 1995
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Vd (L/kg) after iv dosingin rat and human (J&J data)
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Multiple Dosing Concepts
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Dosing to Steady-stateOn continued drug administration, the amount in the body will initially increase but attain a steady-state, when the rate of elimination (drug loss per unit time) equals the amount administered per unit time
Amount A in body
Cplasma.Vdss
mg/dayFractional loss of A or Cp
First-order rate- K.A; - CL.Cp
1. Initial increase when ko > -K10.Abody
2. Steady state when ko = K.Abody= CL.C
3. Ass or Css constant as long ko constant and CL constant
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Time to steady-stateHalf-life of 24 hr and dosing interval of 24 hrs
Steady-state when drug loss per day equals drug intake per day
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Time to steady-stateHalf-life of 24 hr and dosing interval of 24 hrs
Cmax
Cmin
Cavg,ss
Cavg,ss = AUCssτ/ τ
AUCτ at steady state = AUC∞ single dose
AUCτss/ AUCτfirst dose= Accumulation Index
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Steady-state
The amount in the body at steady-state (Ass)
KelKoAss =
The plasma concentration at steady-state (Css,Cavgss)
ClKo
Kel.VdssKoCpss ==
Css is proportional to the dosing rate (zero-order input) and
inversely proportional to the first-order elimination rate or clearance
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Time to steady-stateHalf-life of 24 hr and dosing interval of 24 hrs
Cmax
Cmin
Cavg,ss
C=Css(1-e-k.t)
5-6 half-lives to reach steady-state
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An effective half-life reflects drug accumulationDrug A: A=20 ng/mL; B=80 ng/mL; T1/2α=3 h; T1/2β=24 h
Drug B: A=80 ng/mL; B=20 ng/mL; T1/2α=3 h; T1/2β=24 h
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An effective half-life reflects drug accumulation
).exp(11
0AUCss, ratioon Accumulati
τττ
KeffAUC −−=
−=
C=Css(1-e-keff.t)
Drug A: T1/2eff= 20 hDrug B: T1/2eff= 10 h
Boxenbaum, J Clin Pharmcol 35:763-766, 1995
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Mean residence time = MRT
MRT is the time the drug, on average,resides in the body.
MRT = Vdss/Cl
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Loading and Maintenance Dose
Maintenance Dose = desired Css x CL
Loading Dose = desired Css X Vd
Loading dose can be high for drugs with large Vd,
then LD divided over various administrations
(J&J data on file)
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Total body clearance (CL)
CL= Dose / AUCplasma
CL = k10.Vc = λz.Vdz= MRT.Vdss
A measure of the efficiency of all eliminating organs to metabolize or excrete the drug
Volume of plasma/blood cleared from drug per unit time
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Physiological approach to Clearance
Rate in
Q.Cpa
Amount A or Concentration C
in blood Rate outQ.Cpv
Clearance = QE
Low hepatic clearance if extraction ratio E <<1
eg. Risperidone (Fabs 85%)
High hepatic clearance if E ≅1
eg. Nebivolol (Fabs 10%)
fu.ClintQfu.Clint.Q
CpaCpv)-Q(Cpa Clearance
+==
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Bioavailability F
After oral administration, not all drug may reach the systemic circulation
The fraction of the administered dose that reaches the systemic circulation
is called the bioavailability F
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Oral drug absorption, Influx and Efflux Transporters, Drug Loss by First-passGut
lumen
Portal Vein
LiverGut wall
MetabolismHepatic Metabolism
Biliary secretion
Uptake and efflux transporters Into
faeces
Tablet disintegration
Drug dissolution
Systemic circulation
Uptake and efflux transporters
F= Fabsorbed.(1-Egut).(1-Eliver)
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Grapefruit inhibits gut-wall metabolism(J&J data on file)
0
20
40
60
80
100
120
140
0 8 16 24 32 40 48Time after morning dose on day 6 (hours)
Plas
ma
cisa
prid
e co
nc. (
ng/m
L)
Cisapride 10 mg q.i.d./ waterCisapride 10 mg q.i.d./ GFJ
Mean (N=13)
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Total body clearance (CL)
CL= Dose / AUCiv
Cl = k10.Vc = λz.Vdz = MRT.Vdss
Intravenous clearance
Apparent oral clearance
Oral clearance CL/F= Dose / AUCoral
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High Solubility Low SolubilityH
igh
Perm
eabi
lity
Low
Pe
rmea
bilit
y
Amidon et al., Pharm Res 12: 413-420, 1995; www.fda.gov
Class 2Low SolubilityHigh Permeability
Class 1High SolubilityHigh PermeabilityRapid Dissolution
Class 3High SolubilityLow Permeability
Class 4Low SolubilityLow Permeability
Biopharmaceutical Classification
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High Solubility Low SolubilityH
igh
Perm
eabi
lity
Low
Pe
rmea
bilit
yClass 1Transporter effects minimal
Class 3Absorptive transporter effects predominate
Class 4Absorptive and efflux transporter effects could be important
Predicting Drug Disposition via BCS Wu and Benet, Pharm Res 22:11-23, 2005
Class 2Efflux transporter effects predominate
Gent, 24 August 2007/avpeer 64
High Solubility Low SolubilityH
igh
Perm
eabi
lity
Low
Pe
rmea
bilit
yClass 1Metabolism
Class 3Renal & Biliary Elimination of Unchanged Drug
Class 4Renal & Biliary Elimination of Unchanged Drug
Predicting Drug Disposition via BCS Wu and Benet, Pharm Res 22:11-23, 2005
Class 2Metabolism
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Biliary Excretion: Enterohepatic Recycling
The drug in the GI tractis depleted.
Biliary excreted drugis reabsorbed
Drugin blood
Conjugatein bile
Conjugatein intestine
Drug inIntestine
Excretionin urine
Conjugatein
Liver
Metabolism
Dumped from
gall bladder
Enzymatic breakdownof glucuronide
Re-absorption
Excretionin feces
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Highly variable drugs and drug products
Drugs with high within-subject variability in Cmax and AUC (> 30% coefficient of variation) are called “highly-variable drugs”
Highly-variable drug products are pharmaceutical products in which the drug is not highly variable, but the product is of poor pharmaceutical quality
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From PK to relevant information for the patient Compound X ®
Tablets and oral solution
……Pharmacokinetics: The estimated mean ± SD half-life at steady-state of compound X after intravenous infusion was 35.4 ± 29.4 hours.Renal impairment: The oral bioavailability of compound X may be lower in patients with renal insufficiency. A dose adjustment may be considered.Other medicines: Do not combine compound X withcertain medicines called azoles that are given for fungal infections. Examples of azoles are ketoconazole, itraconazole, miconazole and fluconazole.
You should not take compound X with grapefruit juice.
……
Gent, 24 August 2007/avpeer 68
Useful MaterialHandbooks
Pharmacokinetics, 2nd Ed., by Milo GibaldiClinical Pharmacokinetics, Concepts and Applications, 3rd Ed., by Malcolm Rowland and Thomas N. TozerPharmacokinetic & Pharmacodynamic Data Analysis:Concepts and Applications, 4th Ed., by Johan Gabrielsson and Dan Weiner
WinNonLin software™, Pharsight®Noncompartmental and Compartmental analysisPharmacokinetic-pharmacodynamic analysisStatistical Bioequivalence analysisIn vitro-in vivo Correlation for drug products
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Thank for your attention !
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Rates and Orders of pharmacokinetic processes
The rate of a process is the speed at which it occursThe rate of drug elimination represents the amount (A) of drug absorbed, distributed or eliminated per unit time
Zero-order process or rate: constant amount per unit time Input rate of infusion: mg per h
dA/dt = ko = zero order rate constant
First-order process or rate: rate is proportional to the amount of drug available for the process
dA/dt = - k.A = -k.Volume.Concentration
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Rates of drug exchangeChange of the drug amount in central compartment
DAplasma/dt = - K10. Aplasma - K12. Aplasma + K21. AperipheralDAplasma/dt = - K10.Vc.Cplasma - K12.Vc.Cplasma + K21.Vt.CperipheralDAplasma/dt = - CL.Cplasma - CLd.Cplasma + CLd.CperipheralDCp/dt = - K10.Cplasma - K12.Cplasma + K21.Cperipheral
Change of the drug amount in peripheral compartment
DAperipheral/dt = - K12.Vc.Cplasma + K21.Vt.CperipheralDAperipheral/dt = - CLd.Cplasma + CLd.CperipheralDCperipheral/dt = - K12.Cplasma + K21.Cperipheral