BIOPHARMACEUTICS AND PHARMACOKINETICS.pdf

B.PHARMACY VI SEM.
UNIT 4. PHARMACOKINETICS.

1. B.Pharmacy
Subject-BiopharmaceuticsandPharmacokinetics
SubCode-BP604T
MODULE-3,4
PHARMACOKINETIC
MODELS
M. BALASUNDARESAN,
ASSISTANT PROFESSOR,
ARUNAI COLLEGE OF PHARMACY,
TIRUVANNAMALAI.

2. Objectiveofcourse;
Understandvariouspharmacokineticparameters,theirsignificance
&applications.
LearningOutcomes;
Studentswilllearnaboutdifferenttype ofpharmacokineticmodelsused
todeterminevariouspharmacokineticparameterslikeVd,t1/2,AUC,Ka
etc.

3. OVERVIEW
•Basicconsiderationsinpharmacokinetics
•Compartmentmodels
•Onecompartmentmodel
•Assumptions
•Intravenousbolusadministration
•Intravenousinfusion
•Extravascularadministration(zeroorderandfirstorderabsorption
model)
•Multi-compartmentmodel

4. BASICCONSIDERATIONSIN
PHARMACOKINETICS
•Pharmacokineticparameters
•Pharmacodynamicparameters
•Zero,firstorder&mixedorderkinetic
•Ratesandordersofkinetics
•Plasmadrugconc.Timeprofiles
•Compartmentalmodels–physiologicalmodel
•Applicationsofpharmacokinetics
•Noncompartmentmodel

5. S.no Pharmacokineticparameter AbbreviationFundamental unitsUnitsexample
1. Areaunderthecurve AUC Concentrationxtime µgxhr/mL
2. Totalbodyclearance ClT Volumextime Litres/time
3. Renalclearance ClR Volumextime Litres/time
4. Hepaticclearance ClH Volumextime Litres/time
5. Apparentvolumeofdistribution VD Volume Litres
6. Vol.ofdistributionatsteadystate V
SS Volume Litres
7. Peakplasmadrugconcentration C
MAX Concentration mg/L
8. Plasmadrugconcentration CP Concentration mg/L
9. Steady-statedrugconcentration C
ss Concentration mg/L
10. Timeforpeakdrugconcentration T
MAX Time Hr
11. Dose DO Mass mg
12. Loadingdose DL Mass mg
13. Maintenancedose DM Mass mg
14. Amountofdrug inthebody DB Mass Mg
15. Rateofdruginfusion R Mass/time mg/hr
16. Firstorderrateconstant fordrugabsorption Ka 1/time 1/hr
17.Zeroorderrateconstantfordrugabsorption KO Mass/time mg/hr
18.Firstorderrateconstantfordrugelimination K 1/time 1/hr
19. Eliminationhalf-life t Time hr
CommonunitsinPharmacokinetics

6. ATYPICALPLASMADRUGCONC.ANDTIMECURVE
OBTAINEDAFTERASINGLEORALDOSEOFA
DRUG,SHOWINGVARIOUSP'KINETICAND
P’DYNAMICPARAMETERSDEPICTEDINBELOW
FIG

7. PHARMACOKINETIC PARAMETERS
Threeimportantparametersusefulinassessingthebioavailabilityof adrug
fromitsformulationare:
1.Peakplasmaconcentration(cmax)
thepointatwhich,maximumconcentrationofdruginplasma.
Units:µg/ml
•Peakconc.Relatedtotheintensityofpharmacologicalresponse,it
shouldbeaboveMECbutlessthanMSC.
•Thepeakleveldependsonadministereddoseandrateofabsorption
andelimination.

8. 2.Timeofpeakconcentration(tmax)
thetimeforthedrugtoreachpeakconcentrationinplasma
(after extravascularadministration).
Units:hrs
•Usefulinestimatingonsetofactionandrateofabsorption.
•Importantinassessingtheefficacyofsingledosedrugsusedtotreatacute
conditions(pain,insomnia).

9. 3.Areaundercurve(AUC)
Itrepresentsthetotalintegratedareaundertheplasmalevel-timeprofileand
expressesthetotalamountofthedrugthatcomesintosystemiccirculationafter
itsadministration.
Units:µg/mlxhrs
•Representsextentofabsorption–evaluatingthebioavailabilityofdrugfromits
dosageform.
•Importantfordrugs administeredrepetitivelyfortreatmentofchronicconditions
(asthmaorepilepsy).

10. PHARMACODYNAMIC PARAMETERS
1.Minimumeffectiveconcentration(MEC)
Minimumconcentrationofdruginplasma/receptorsiterequiredtoproduce
therapeuticeffect.
•ConcentrationbelowMEC–subtherapeuticlevel
•Antibiotics-MEC
2.Maximumsafeconcentration(MSC)
Concentrationinplasmaabovewhichadverseorunwantedeffectsare
precipitated.
•ConcentrationaboveMSC–toxiclevel

11. 3.Onsettime
Timerequiredtostartproducingpharmacologicalresponse.
Timeforplasmaconcentrationtoreachmecafteradministratingdrug
4.Onset ofaction
Thebeginningofpharmacologicresponse.
Itoccurswhenplasmadrugconcentrationjustexceedstherequiredmec.
5.Durationofaction
ThetimeperiodforwhichtheplasmaconcentrationofdrugremainsaboveMEC
level.
6.Intensityofaction
Itistheminimumpharmacologicresponseproducedbythepeakplasmaconc.Of
drug.
7.Therapeuticrangethedrugconc.BetweenMECandMSC

12. CONCEPTOF“HALFLIFE”
½Life=howmuchtimeittakesforbloodlevelsofdrugtodecreasetohalf
ofwhatitwasatequilibrium
Therearereallytwokindsof½life…
“Distribution”½life=whenplasmalevelsfalltohalfwhattheywere
atequilibriumduetodistributionto/storageinbody’stissuereservoirs.
“Elimination”½life=whenplasmalevelsfalltohalfwhattheywere
atequilibriumduetodrugbeing metabolizedandeliminated.
Itisusuallytheelimination½lifethatisusedto determinedosing
schedules,todecidewhenitissafetoputpatientsonanewdrug.

13. PHARMACOKINETIC MODELSAND
COMPARTMENTS

14. PharmacokineticModelling
Compartment
Models
Non-Compartment
Models
Physiologic
Models
Caternary
Model
Onecompt
Mamillary
Model
Multicompt Twocompt
iv
bolus
SingleoralDose
iv
infusion
Intermittentivinfusion
Multiple
doses
ivbolus
Oraldrug
AUC,MRT,MAT,Cl

15. PHARMACOKINETIC MODELS
Meansofexpressingmathematicallyorquantitatively,timecourseofdrug
throughoutthebodyandcomputemeaningfulpharmacokineticparameters.
Usefulin:
•Characterizethebehaviorofdrugin patient.
•Predictingconc.Ofdruginvariousbodyfluidswithdosageregimen.
•Calculatingoptimumdosageregimenforindividualpatient.
•Evaluatingbioequivalencebetweendifferentformulation.
•Explainingdruginteraction.
Pharmacokineticmodelsarehypotheticalstructuresthatareusedtodescribethe
fateofadruginabiologicalsystemfollowingitsadministration.
Model
•Mathematicalrepresentationofthedata.
•Itisjusthypothetical

16. WHYMODELTHEDATA?
Therearethreemainreasonsduetowhichthedataissubjectedtomodelling.
1.Descriptive:todescribethedrugkineticsinasimpleway.
2.Predictive:topredictthetimecourseofthedrugaftermultipledosingbased
onsingledosedata,topredicttheabsorptionprofileofthedrugfromtheiv
data.
3.Explanatory:toexplainunclearobservations.

17. PHARMACOKINETIC MODELINGISUSEFUL
IN:-
•Predictionofdrugconcentrationinplasma/tissue/urineatanypointoftime.
•Determinationofoptimumdosageregimenforeachpatient.
•Estimationofthepossibleaccumulationofdrugs/metabolites.
•Quantitativeassessmentoftheeffectofdiseaseondrug’sadme.
•Correlationofdrugconcentrationwithpharmacologicalactivity.
•Evaluationofbioequivalence.
•Understandingofd/i.

18. COMPARTMENTAL MODELS
•Acompartmentisnotarealphysiologicaloranatomicregion
butanimaginaryorhypotheticaloneconsistingoftissue/group
oftissueswithsimilarbloodflow&affinity.
•Ourbodyisconsideredascomposedofseveralcompartments
connectedreversiblywitheachother.

19. ADVANTAGES
•Givesvisualrepresentationofvariousrateprocessesinvolvedindrug
disposition.
•Possibletoderiveequationsdescribingdrugconcentrationchangesineach
compartment.
•Onecanestimatetheamountofdruginanycompartmentofthesystemafter
drugisintroducedintoagivencompartment.
DISADVANTAGES
•DruggivenbyIVroute maybehave accordingtosinglecompartmentmodel
butthesame druggivenbyoralroutemayshow 2compartmentbehaviour.
•Thetypeofcompartmentbehaviouri.E.Typeofcompartmentmodelmay
changewiththerouteofadministration.

20. 1.Centralcompartment
Blood&highlyperfusedtissuessuchasheart,kidney,lungs,liver,etc.
2.Peripheralcompartment
Poorlyperfused tissues suchasfat,bone,etc.
MODELS:
“OPEN”and“CLOSED”models:
•Theterm“open”itselfmeanthat,theadministereddrugdoseisremovedfrom
bodybyanexcretorymechanism(formostdrugs,organsofexcretionofdrugis
kidney)
•Ifthedrug isnotremovedfromthebodythenmodelrefersas“closed”model.
TYPESOFCOMPARTMENT

22. LOADINGDOSE
•Adrugdosedoesnotshowtherapeuticactivityunlessitreachesthedesiredsteady
state.
•Ittakesabout4-5halflivestoattainitandthereforetimetakenwillbetoolongif
thedrughasalonghalf-life.
•Plateaucanbereachedimmediatelybyadministeringadosethatgivesthedesired
steadystateinstantaneouslybeforethecommencementofmaintenancedosex0.
•Suchaninitialorfirstdoseintendedtobetherapeuticiscalledasprimingdoseor
loadingdosex0,l.

23. CALCULATIONOFLOADING
DOSE
•Aftere.V.Administration,cmaxisalwayssmallerthanthatachievedafteri.V.
Andhenceloadingdoseisproportionallysmaller.
•Forthedrugshaving alowtherapeuticindices,theloadingdosemaybe
dividedintosmallerdosestobegivenatavariousintervalsbeforethefirst
maintenancedose.
•Asimpleequationforcalculatingloadingdoseis:
xo,l=css,avvd
F

24. CALCULATION….,
•Whenvdisnotknown,loadingdosemaybecalculatedbythefollowing
equation:
xo,l= 1_
Xo(1–e
-ket)(1–e
-kat)
•Givenequationapplieswhenka>>keanddrugisdistributedrapidly.
•Whendrugisgiveni.V.Orwhenabsorptionisextremelyrapid,the
absorptionphaseisneglectedandtheaboveequationreducesto
accumulation index:

25. ASSUMPTIONS
1.Onecompartment
Thedruginthebloodisinrapidequilibriumwithdrugintheextra-vascular
tissues.Thisisnotanexactrepresentationhoweveritisusefulforanumber
ofdrugstoareasonableapproximation.
2.Rapidmixing
Wealsoneedtoassumethatthedrugismixedinstantaneouslyinbloodor
plasma.
3.Linearmodel
Wewillassumethatdrugeliminationfollowsfirstorderkinetics.

26. LINEARMODEL-FIRSTORDER
KINETICS
•FIRST-ORDER
KINETICS

27. MATHEMATICALLY
•Thisbehaviorcanbeexpressedmathematicallyas:

28. ONECOMPARTMENT MODEL
Onecompartmentmodelcanbedefined:
•One com.Openmodel–i.V.Bolus.
•One com.Openmodel-cont.Intravenousinfusion.
•One com.Openmodel-extravas.Administration (zero-orderabsorption)
•Onecom.Openmodel-extravas.Administration(First-orderabsorption)
•INTRAVENOUS(IV)BOLUSADMINISTRATION

29. RATEOFDRUGPRESENTATIONTOBODY
IS:
•Dx=ratein(availability)–rateout(Eli)
Dt
•Sincerateinorabsorptionisabsent, equationbecomes
dx= -rateout
dt
•Ifrateoutoreliminationfollowsfirstorderkinetic
Dx/dt=-kex (eq.1)
ELIMINATIONPHASE:
Eliminationphasehasthreeparameters:
•Eliminationrateconstant
•Eliminationhalflife
•Clearance

30. ELIMINATIONRATECONSTANT
•Integrationofequation(1)
•Inx=lnxo–ket (eq.2)
Xo=amtof druginjectedattimet=zeroi.E.Initial amountofdruginjected
X=xoe
-ket (eq.3)
•Logx=logxo–ket
2.303 (eq.4)
•Sinceitisdifficulttodirectlydetermineamountofdruginbodyx,weuserelationship
thatexistsbetweendrugconc.InplasmaCandX;thus
•X=vd C (eq.5)
•Soequation-8becomes
logc=logco– ket
2.303 (eq.6)

31. (Eq.7)KE=KE+KM+KB+KL+…..
(KEisoveralleliminationrateconstant)

32. ELIMINATIONHALFLIFE
T1/2=0.693
KE (eq.8)
•Eliminationhalflifecanbereadilyobtainedfromthegraphoflogc
versust
•Halflifeisasecondaryparameterthatdependsupontheprimary
parameterssuchasclearanceandvolumeofdistribution.
•T1/2=0.693Vd
ClT (eq.9)

33. APPARENTVOLUMEOF
DISTRIBUTION
•Definedasvolumeoffluidinwhichdrugappearstobedistributed.
•Vd=amountofdruginthebody=
Plasmadrugconcentration
x
C (eq.10)
Vd=xo/co
=I.V.Bolusdose/co (eq.11)
•Example:30mgi.V.Bolus,plasmaconc.=0.732mcg/ml.
=30000mcg/0.732mcg/ml
…….12.A
•Vol.Of dist.=30mg/0.732mcg/ml
=41liter.
•Fordrugsgiven asi.V.Bolus,
Vd(area)=xo/KE.Auc
•Fordrugsadmins.Extra.Vas.
Vd(area)=fxo/ke.Auc ……..12.B

34. CLEARANCE
Clearance=rate ofelimination
Plasmadrugconc.. (Or)cl=dx/dt
C……., (eq.13)
Thus,renalclearance
Hepaticclearance=
=rateofeliminationbykidney
C
rateofeliminationbyliver
C
Otherorganclearance=rateofeliminationbyorgan
C
Totalbodyclearance:
Clt=clr+clh+clother ……,(eq.14)

35. •Accordingtoearlierdefinition
cl= dx/dt
C
•Submittingeq.1dx/dt=KEX,aboveeq.Becomes,clt=KEX/C..,(Eq15)
•Byincorporatingequation1andequationforvol.Ofdist.(Vd= X/C)wecan
get
clt=KEvd (eq.16)
•Parallelequationscanbewrittenforrenalandhepaticclearance.
(eq.17)
(eq.18)
Clh=kmvd
Clr=kevd
•But,KE=0.693/t1/2
•So, clt =0.693vd (eq.19)
t
1/2

36. •Fornoncompartmentalmethodwhichfollowsonecompartmental
kinetic is:
•Fordruggivenbyi.V.Bolus
clt =xo …..20.A
Auc
•Fordrugadministeredbye.V.
Clt=fxo …..20.B
Auc
…….(eq.21)
•Fordruggivenbyi.V. Bolus
renalclearance=xu∞
auc

37. ORGANCLEARANCE
•Rateofeliminationbyorgan=rateofpresentationtotheorgan–rateofexit
fromtheorgan.
•Rateofelimination=q.Cin-Q.Cout
(Rateof extraction)=Q(cin-cout)
Clorgan=rateofextraction/cin
=q(cin-cout)/cin
…………….(eq 22)=Q.Er
•Extractionratio:
ER=(cin-cout)/cin
•ERisanindexofhowefficientlytheeliminatingorgancleartheblood
flowingthroughitofdrug.

38. AccordingtoER,drugscanbeclassifiedas
•DrugswithhighER(above0.7)
•DrugswithintermediateER(between0.7-0.3)
•DrugswithlowER(below0.3)
•Thefractionofdrugthatescapesremovalbyorganisexpressedas
F=1-ER
•Wheref=systemicavailabilitywhentheeliminatingorganisliver.

39. HEPATICCLEARANCE
Clh=clt–clr
Canalsobewrittendownfromeq22
Clh=QHERH
QH=hepaticbloodflow.ERH=hepaticextractionratio.
Hepaticclearanceofdrugcanbedividedintotwogroups:
1.Drugswithhepaticbloodflow rate-limitedclearance
2.Drugswith intrinsiccapacity-limitedclearance

40. HEPATICBLOODFLOW
•F=1-erh
=AUCoral
AUCi.V

41. INTRINSIC CAPACITYCLEARANCE
•Denotedasclint,itisdefinedastheinherentabilityofanorganto
irreversiblyremoveadrugintheabsenceofanyflowlimitation.

42. ONECOMPARTMENT OPENMODEL:
INTRAVENOUSINFUSION
•Modelcanberepresentas:(i.vinfusion)
Drug
…eq23
…eq24
Dx/dt=ro-kex
X=ro/ke(1-e
-ket)
SinceX=vdc
C=ro/kevd(1-e
-ket)…eq25
=Ro/clt(1-e
-ket)…eq26
Blood&other
Bodytissues
R0
Zeroorder
Infusion
rate
KE

43. •Atsteadystate.Therateofchangeofamountofdruginthebodyiszero,eq
23becomes
Zero=ro-kexss
Kexss=ro
Css=ro/kevd
=Ro/clti.E
…27
…28
…29
infusionrate....30
…31
Clearance
Substitutingeq.30ineq.26
•C=css(1-e
-ket)
Rearrangementyields:
• [Css-c]=e
-ket
. ...32
…33
C
ss
LogCSS-C
C
ss
=-ket
2.303

44. •Ifnistheno.Ofhalflivespassedsincethe startofinfusion(t/t1/2)
•Eq.Canbewrittenas
•C=CSS[1-(1/2)
n] …34

45. INFUSIONPLUSLOADING
DOSE
XO,L=CSSVD …35
…36
•SUBSTITUTIONOFCSS=RO/KEVD
•XO,L=RO/KE
•C=XO,L/VDE
-KET+RO/KEVD(1-E
-KET)…37

46. ONECOMPARTMENT OPENMODEL
EXTRAVASCULARADMINISTRATION
•Whendrugadministeredbyextravascularroute(e.G.Oral,i.M,rectal),
absorptionisprerequisiteforitstherapeuticactivity.

47. ONECOMPARTMENT MODEL:EXTRAVASCULAR
ADMIN (ZEROORDERABSORPTION)
•Thismodelissimilartothatforconstantrateinfusion.
Drugatsite
zeroorderelimination
n
oRateofdrugabsorptionasincaseofCDDS ,isconstant andcontinuesuntil
theamountofdrugattheabsorptionsite(Ex.GIT)isdepleted.
oAllequationsforplasmadrugconc.Profileforconstantratei.V.Infusion
arealsoapplicabletothismodel.
Blood&other
Bodytissues
R0
Absorptio

48. ONECOMPARTMENT MODEL:EXTRA
VASCULARADMIN(FIRSTORDER
ABSORPTION)
Blood&other
Bodytissues
Drugat
site
KEKa
Firstorder
absorption
elimination
•Drugthatentersthebodybyfirstorderabsorptionprocessgetsdistributedin
thebodyaccordingtoonecompartmentkineticandiseliminatedbyfirst
orderprocess.
•Themodelcanbedepictedasfollowsandfinalequationisasfollows
C=KaF Xo/Vd(Ka-KE)[e
-Ket-e
-Kat]…41