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DistributionVolume = Amount (dose) / Concentration
Gave 60mg V = 60mg/1 mg/L
V = 60 L
6 mg
54mg
60 mg
Looks like your 60mgwas dissolved into 60Linstead of 6L due tounequal partitioning.
This is Apparent Vd!!
6 L
Concentration = 1 mg/L
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As a first approximation, the body behaves like a
well-stirred beaker, i.e., chemicals are dispersed
throughout the container (body) rather quickly.
MAJOR CONCEPT #1CONCEPT OF VOLUME OF DISTRIBUTION
(VD) OF DRUGS
(Stir)
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CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS:
DEFINITION OF VD
Add DRUG
to Beaker
Calculate Volume
Obtain Sample
Assay for [Drug]
(Stir)
[Drug] = Amount Added z Volume of Beaker
Volume of Beaker = Amount Added z [Drug]
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CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS:
DEFINITION OF VD
Dose Body
with DRUG
Calculate Volume
(This volume is called VD)
Obtain Plasma Sample
Assay for [D]P
By DEFINITION: VD = A/[D]P(where A is amount of drug in body and [D]P is concentration of drug in plasma)
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CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS:
DEFINITION OF VD
WARNING: VD is a calculated value that
should not be taken literally as
representing somereal volume!!!!!!
VD is:
1. a calculated value,2. a reproducible value,
3. a clinically useful value.
VD is not a real volume with
an independent existence. In Thisregard, the word volume is
used in a metaphorical sense.
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DISTRIBUTION INTO BODY
COMPARTMENTS
Plasma 3.5 litres, heparin, plasma expanders
Extracellular fluid 14 litres,tubocurarine, charged polar compounds
Total body water 40 litres,
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CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS:
INTRODUCTION TO VD
B
LD = VD x [D]P(target)
KEY EQUATION #1
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CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS:
INTRODUCTION TO VD
VD and [D]P(target) and B are THE determinants of loading
dose (LD)!!
In other words, the amount of drug that must be given to
achieve rapidly a target concentration
of drug in the plasma is solely determined by VD, B
and [D]P(target).
LD = (VD x [D]P(target))/B
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CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS:
DETERMINANTS OF VD
Distribution into Body Compartments
Restriction of Drug to
Limited Areas of Body Free Assess of Drug to
Many Areas of Body
vs Large VDSmall VD
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CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS:
DETERMINANTS OF VD
Tissue Binding
qq [D]P
oo VD
A
qq [D]P
=
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CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS:
DETERMINANTS OF VD
Plasma Protein Binding
oo[D]P
qqVDoo[D]P
=
A
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CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS:
DETERMINANTS OF VD
Distribution into Fat
qq [D]P
oo VDqq [D]P
=
A
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CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS:
OBTAINING VD
Time (hrs)
[D]P0 is [D]P at time 0 and
is obtained by extrapolationVD is usually easy to
obtain!
1. Give bolus
of drug.
2. Measure plasma
levels over time.
3. Extrapolate to find
plasma level at time 0.
VD = Amount in body at time 0/[D]p0 = DoseIV /[D]P
0
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CONCEPT OF VOLUME OF DISTRIBUTION OF DRUGS:
EXAMPLE OF USING VD TO CALCULATE LD
Pharmacokinetic
Parameters forDigoxin:
[D]P(target) = 1.5 g/L
VD = 580 L
Oral Bioavailability = 0.7
LD = (VD x [D]P(target))/B
Oral LD = (580 L x 1.5 g/L) /0.7
Oral LD = 1243 g ~ 1.2mg
Calculation of Oral LD
For Digoxin:
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Plasma drug proteinbinding
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Protein Interactions
affinity
binding
specificity
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Biological relevanceofdrugbinding
Thebindingofdrugto plasma (and tissue)
proteinsis a majordeterminantofdrug
disposition (distribution)
Bindinghas a veryimportanteffecton
drug dynamicssinceonlythefree(unbound) druginteracts withreceptors
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Relevanceofplasma and tissueproteinbinding
From a biological pointofview YES
From a clinical pointofview NO
problemofdruginteraction and
displacementhasbeenoverestimated
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The problemofdruginteraction
and displacementh
asbeenoverestimated
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Th
e classical example:Phenylbutazone/warfarininteraction
Interaction actually exists
Displacement actually exists
but the plasma binding displacement is
not the underlying mechanism of
interactionPBZ stereoselectivity inhibits the metabolism
of s-warfarin
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Why plasma bindingseldom
has clinical relevance
Because few drugs (so-called displacer) are
therapeutically used
Because when displacement exists, it has no
consequence on the receptor exposure to thefree fraction of the displaced drug which
generally remains unaffected
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Isthereoften displacementof
drugfromthebindingsite?
No
For a substantial displacement to take place, the
displacer must occupy most of the availablebinding site thereby lowering the binding siteavailable to the primary drug
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No
To take place, the molar concentration of the
drug in plasma must exceed the molar
concentration of albumin (150 g/mL for a a
drug with a MW of 250)
e.g.: PBZ, phenytoin, valproic acid
This is not true for a1-glycoprotein acid (basic
drug)
Isthereoften displacementof
drugfromthebindingsite?
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Why plasma protein displacement
seldomhas clinical relevance
Generally only the free (unbound) drug is
metabolized and can access to the receptorAND
the free drug concentration is controlled by the
free drug clearance which is independent of the
plasma binding
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Plasma drug proteinbindingPhysiological aspects
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Plasma binding proteins
Proteins MW Concentration
g/L mM
Albumin 67 000 35-50 500-700
E-glycoprotein 42 000 0.4-1.0 9-23acid
Lipoproteins 200 000 variableto2.4 106
Transcortin 53 000 0.03-0.07 0.6-1.4
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Thefreefraction
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Drug plasma proteinbinding
Expressed in % or by fu (free fraction)
>90% = highly bound
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Thefreefraction:fu
fu = =free concentration
total concentration
Cfree
Ctot
Definition:
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Thetotal concentration
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Ctot is a functionofCfree
Ctot = Cfree +Cbind
Ctot = Cfree +BmaxxCfree
Kd +Cfree
Dependentvariable Parameters Independentvariable
controlled byClfree
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Total concentration
Ctot
=
! When conceptualizing dependency and
functionality,thisequationshould notberearranged
Cfree
fu
!
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Total concentration:
a convenientbutillicitrearrangementwhich canbemisleading when
discussing druginteraction
Cfree = fuxCtotal
indirectlyestimated
knownfrominvitro assay
measured byanalytical technique
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Whatisthe consequenceoffuo
Ctotq = or Cfree o = fuo xCtotal
Total concentration:
a convenientbutillicitrearrangement
which canbemisleading when
discussing druginteraction
Cfree
fuo
NOYES
Displacement (fu)modifiesCtot,notCfree
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Caseforwhich weneed toknow in vivo free concentration
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Caseforwhich weneed to
know in vivo free concentration
Formechanistic purposes
Fordata analysis whenbindingto
proteinisnot linear
e.g.: cortisol,ACEI
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Forextrapolation
from in vitro to in vivo in vitro, Kd (binding) and EC50 (functional response) arefree concentrations but EC50 (for PK/PD) is total
concentration
CMI (free) vs effective plasma concentration (Ctot)
between species
comparison of EC50 between animals requires to take into
account free fraction
Caseforwhich weneed to know
in vivo freefraction
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RESTRICTIVE VS NONRESTRICTIVE
ELIMINATIONRESTRICTIVE:
ClearanceDEPENDSon Protein Binding
KIDNEY: Drug Filtration Rate = fU y GFRLIVER: CL = fU y Clint
NONRESTRICTIVE:
Clearance INDEPENDENTof Protein Binding
KIDNEY: CL = Q (renal blood flow)
LIVER: CL = Q (hepatic blood flow)
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Competitiveinteraction
Caseofrestrictivelyeliminated drug
Clfree = Clint = constant Cltot = fuxClint
perfusionrate: K0
redistribution
Ctot
CfreeClfree = cst
Cltot
Administrationofthe2nd ligand, displacement fuo
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in vitrovs.
in vivosituation
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fuvsCfree:in vitro situation
fu = 0.5
Cfree = 3/V
Ctot = 6/V
fu = 0.83
Cfree = 5/V
Ctot = 6/V
1 2
6
5
4
3
1 2
6
5
4
3
displacer
displacee
V= volumeof
thebaker
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fuvsCfree:in vivo situation:
initial steadystate
1
2
6
5
4
3
Infusion=A
A=MT-1
K12C
free
K21 Cfree
Plasma Extracellularfluid Intracellularfluid
Elimination = K10 xCfree (3) = Aequated byinfusion
TOTALCONCENTRATION = 6/V
FREECONCENTRATION = 3/V
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fuvsCfree:in vivo situation:just afteradministrationofdisplacer
1
2
65
4
3
Infusion=A
A=MT-1
K12
xCfree: increase
transitively
K21 xCfree
Plasma Extracellularfluid Intracellularfluid
K10 xCfree (5) > A
displacer
Just displaced
free drug IncreasetransitorilyTOTALCONCENTRATION = 6/V
FREECONCENTRATION = 5/V
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fuvsCfree:in vivo situation:
final steadystate
1
2
63
Infusion=A
A=MT-1
K12
xCfree
K21 xCfree
Plasma Extracellularfluid Intracellularfluid
Elimination = K10 xCfree (3) = A
displacer
TOTALCONCENTRATION = 4/V
FREECONCENTRATION = 3/V
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Competitiveinteraction
wheninteractionoccurs,
Ctot is altered notCfree
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Thethreemainexceptionstothe
general ruleforwhich druginteractionhasno clinical meaning
1. Rapid bolus IVinjection
2. Parenteral administrationofdisplaced drug
with a highextractionratio
3. Therapeutic drugmonitoring and drug
displacementfromthe plasma bindingsite
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Caseforwhich druginteraction
atthebindingsiteisrelevant
1. Rapid IVinjection
Ifthe displacing agentisgivenrapidly (IVbolus),theCfree could increase
dramatically duetorapid displacementof
the displaced drugbeforethe
compensatorymechanism (redistribution)takes place
p Sulfamide and bilirubin kernicterus
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Caseforwhich druginteraction at
the plasma bindingsiteisrelevant
2. Parenteral administrationofdisplaced
drug with a highextractionratio
currently,noexample
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3. Therapeutic drugmonitoring and drug
displacementfrom plasma binding Therapeutic drugmonitoringis performed for
drugs with a narrow concentrationrange
betweentherapeutic and toxic effect
Monitoringis carried outontotal plasma
concentrations
Caseforwhich druginteraction at
the plasma bindingsiteisrelevant
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Caseforwhich druginteraction at
the plasma bindingsiteisrelevant
3. Therapeutic drugmonitoring and drug
displacementfrom plasma binding Anexample:
Phenytoin alone: Ctot = 20 g/mL
Phenytoin+Valproic acid: Ctot = 15 g/mL
no dosage adjustmentisnecessarybecause
Ctot decreased butnotCfree duetofuincrease
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Algorithmfordetermining clinical significance
ofpotential binding displacementinteraction
Is drugofinterest >90%
proteinbound?
Yes
Doesthe drughave a
narrow therapeutic index?
Yes
Whatisthehepatic extraction
ratioofthe drug?
High
Isthe druggiven IV?
Clinicallysignificantinteraction likely.
Perform a clinical studytoquantifyeffects
Clinicallysignificant
interactionnot likely
Would a transientincrease
infree drug concentration
be clinicallyrelevant?
no
no
low
no
no
Yes
Yes
Roslan 1994, B.J.Clin Pharmacol. 37, 125
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Age groups V d (L/kg) t (hr)
Newborns
Infants
Children
Adults
Elderly people
0.47
0.36
0.20
0.22
0.26
136
54
51
63
98
Sulfamethoxypyridazine; Apparent volume of distribution and Half-Lives.
WHY BE CONCERNED ABOUT
VARIABILITY ?
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Premature
Newborn
4 mos
12 mos
24 mos
36 mos
Adult
Percentage of Total Body WeightPercentage of Total Body Weight
Extracellular WaterExtracellular Water Intracellular WaterIntracellular Water ProteinProtein FatFat OtherOther
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WHY BE CONCERNED ABOUT
VARIABILITY ?
Digoxin doses
For infants; 15-20g/kg
For children; 10-15g/kg
For adults; 4 - 5 g/kg
How Drugs Distribute: Determines dose
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The requirement for larger doses in children than
adults is related in part to the fact that TBW andECW make up larger percentage of the total
body weight in children than adults
Total body water Extra cellular water
78% 45%(N.b)
60% 20%(Adults)
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Drug Free fraction Volume (L/Kg)
Neonates Adults Neonates Adults
Digoxin
PhenobarbitolPhenytoin
Sulfamethoxy
- pyrazine
0.8
0.680.2
0.43
0.7
0.530.1
0.38
5 -10
1.01.3
0.47
7
0.550.63
0.24
Proteinbinding (fractionfreein plasma),Apparent volumeof
Distribution
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Pregnancy
The volume available for drug distribution
increases due to pregnancy, with the growth of
uterus,placenta,and fetus.
Maternal plasma volume and ECF volume also
increase.
The concentration of plasma proteins to fallduring pregnancy, leads to reduced binding.
Glomerular filtration rate increases
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BODY WEIGHT AND SIZE
The apparent volume of distribution of a drug is determined by theanatomic space into which it distributes and its relative degree of
vascular and extra vascular binding.
The TBW and ECF is directly proportional to body weight.
Weight adjustments are generally thought unnecessary unless theweight of an individual differs by more than 50% from average
adult weight(70kg).
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OBESITY
IBW (men)= 501kg/2.5 cmabove or below in 150 cm inheight.
IBW (women) =451kg/2.5cm above or below in 150cmin height.
Percent fat =
90-2( Height Girth )
Lean body mass =(100- Percent fat )x Weight
*Girth is measuredininchesusing theumbilicallevelatexhalation.
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There is no need of modification of dosageregimen for obese persons if the Vd ,Cl,t values
are similar to that normal adults.
The dose calculation for children is based on
surface area (weight & height).
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Total BodyWater
Individual variability
= F(leanbodymass) 55 - 60% ofbody weightin adultmales
50 - 55% ofbody weightin adultfemale
~42LFora 70 Kgman.
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MajorExtracellularFluid
Compartments (11LofECF)
Plasma (blood minusthered and white
cells)
~3 Lin a 70 Kgman
~4.5% ofbody weight.
Interstitial space (betweenorgan cells)
~8 Lin a 70 Kgman ~11.5% ofbody weight.
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Blood isComposed ofCells
and Plasma.
Hematocrit (Hct). Fractionofblood thatis cells.
Oftenexpressed as percentage.
Plasma volume
= Blood volumex (1-Hct).
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Ingress and Egress
Plasma water
Ingested nutrients passthrough plasma on
wayto cells
Cellularwaste products passthrough plasma
beforeelimination
Interstitial space.
Direct access pointforalmost all cellsofthe
body
Exception -- red and whiteblood cells
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SoluteOverview:
Intracellularvs. Extracellular
Ionic composition very different Total ionic concentration verysimilar
Total osmotic concentrations virtually
identical
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MajorIonic Species
Principlecations
Extracellular: Na+
Intracellular: K+
Principleanions Extracellular: chlorideand bicarbonate.
Intracellular: proteins, aas,and phosphates
inorganic (HPO42-,H2PO4
-)
organic (amino acids and ATP).