half life- 1 the half-life oct 2010. half life- 2 the plasma half-life synonymous half-life of...
TRANSCRIPT
Half life- 1
The half-lifeThe half-life
OCT 2010
Half life- 2
The plasma half-lifeThe plasma half-life
• Synonymous
• half-life of elimination
• half-life of the terminal phase
Half life- 3
The half-lifeThe half-life
Half-life has the apparent
advantage of being a familiar term
Half life- 4
The half-lifeThe half-life
Definition• Time required to divide the plasma
concentration by two after reaching pseudo-equilibrium distribution
• Not the time necessary for the amount of administered drug in the body to fall by one-half
!
Half life- 5
The half-lifeThe half-life
• Meaning in terms of drug elimination
(half-life vs mean residence time (MRT))C
on
cen
trat
ion
MRT = 16 h
MRT = 4 h
t1/2 = 12 h 24 time (h)
Half life- 6
• Meaning in terms of drug elimination
t1/2 = time to eliminate half the dose
t1/2 = time to eliminate half the remaining dose
monocompartmental model
The half-lifeThe half-life
Half life- 7
Pharmacokinetic meaning of half-life
Pharmacokinetic meaning of half-life
Half life- 8
Half-life vs. ClearanceHalf-life vs. Clearance
• Clearance : ability to eliminate
• Half-life : overall elimination during the terminal phase which depends on both clearance and distribution
Half life- 9
Clearance vs. half-lifeClearance vs. half-life
AmiodaroneClearance: 1.9 ml/kg/min
Half-life: 25 days
AmikacineClearance: 1.3 ml/kg/min
Half-life: 2.3 hours
Half life- 10
The half-lifeThe half-life
Meaning in terms of elimination and distribution
Half life- 11
The half-life is a hybrid parameterThe half-life is a hybrid parameter
Distribution large small
Clearance high low
Half-life equal
Half life- 12
Plasma clearance vs plasma half-lifePlasma clearance vs plasma half-life
Half life- 13
Half-life (HL), Clearance (Cl) & volume of distribution (Vd) of Amiodarone vs. amikacin
Half-life (HL), Clearance (Cl) & volume of distribution (Vd) of Amiodarone vs. amikacin
Drugs HL
(h)
Cl
ml/kg/min
Vd
L/kg
amiodarone 600 1.9 95
amikacin 2.5 1.3 0.27
Half life- 14
The half-life is a hybrid parameterThe half-life is a hybrid parameter
• t1/2 = function of K10, K12 and K21
t1/2
K12
K21
K10
Half life- 16
t 1/ 2 =0.693 x Volume of distribution
Clearance
Half-life is a hybrid parameter reflecting both clearance and
volume of distribution
Half-life is a hybrid parameter reflecting both clearance and
volume of distribution
Half life- 17
If half-life increases it is becauseIf half-life increases it is because
Volume of distribution
or
Clearance
Half life- 18
Volume of Distribution
Volume of Distribution
Terminal half-life is a hybrid parameter :
ClintVmax
Km
Pt
Ka
fup
Clearancet1/2
°Q
fuB
VB
Vt
fub
fuT
fup : fraction of the total number of sites of free fixationKa : affinity constantKm : Michaelis constant
The half-lifeThe half-life
Half life- 19
In pharmacokinetics, all the time
parameters are hybrid parameters
Time parametersTime parameters
Half life- 20
k10
k12
k21
k12 = distribution clearance / Vck10 = plasma clearance / Vck 21 = redistribution clearance / Vpt 1/2 vie = 0.693 Varea / plasma clearanceMRT : Vss / plasma clearance
Vc Vp
Hybrid parameters
Hybrid properties of time parametersHybrid properties of time parameters
Half life- 23
The half-lifeThe half-life
• Consequence of its hybrid property
• a poor parameter to evaluate the
influence of a pathology (e.g.: renal
failure) in drug disposition
• dosage adaptation should be based on
clearance not half-life
Half life- 24
Why calculate a half-life ?Why calculate a half-life ?
• Dosage regimen
DoseDose
ClearanceClearance
Interval of administrationInterval of administration
Half-lifeHalf-life
Half life- 25
Half-life Systemic exposure
ClearanceVolume of distribution
bioavailability
Dosing regimenHow often?
Dosage regimen How much
Absorption
Half life- 26
Half-life defines the dosing intervalHalf-life defines the dosing interval
If half-life is short
requires dosage form with a low input rate
Problem in maintaining steady-state drug concentration
Half life- 27
Half-life defines the dosage intervalHalf-life defines the dosage interval
If half-life is long
• drug accumulation
• long delay to reach steady state conditions
requires a loading dose
Half life- 29
Why calculate a half-life ?Why calculate a half-life ?
• To predict drug accumulation
• To predict the time of steady-state
• To determine the dosage interval• Essential to develop a new drug with
respect to compliance (eg: antibiotic)
Half life- 30
- x
Why calculate a half-life ?Why calculate a half-life ?• To predict drug accumulation
R = 1
1- e0.693t1/2
Accumulation index Half-life Interval of
administrationR= AUCss
AUC1
AUC1
AUCss
Mono-compartmental model or if drug is administered in the post distribution phase for a x-compartmental model
Half life- 31
Why calculate a half-lifeWhy calculate a half-life
• To predict the time of steady state
• it is independent of the dosing interval
• it is only a function of the terminal half-life (3-4 times)
Half life- 32
Why calculate a half-lifeWhy calculate a half-life
• Delay to reach steady state conditions
• if a drug is administered daily, the steady
state will be reached after the 2nd or 3rd
administration for all the drugs having a
terminal half-life < 12 h
Half life- 33
Half-life and delay to reach steady state conditions
Half-life and delay to reach steady state conditions
• Monocompartmental50% = half-life
90% = 3.3 half-life
Half life- 34
• Hypothetical drug:• half-life : 24h• dosage interval : = 24h• maintenance dose = 50
• R = = = 2
Half-life, accumulation and steady-state concentrationHalf-life, accumulation and steady-state concentration
1
1- e -0.693/24h * 24h
1
1 - 0.5
Half life- 35
Days Just after dosing 24h later
1 50 25
2 75 37.5
3 87.5 43.75
4 93.75 46.88
5 96.88 48.44
6 98.44 49.22
7 99.22 49.61
8 99.61 49.80
infinity 100 50
Half-life, accumulation and steady-state concentrationHalf-life, accumulation and steady-state concentration
Ratio = 2
Half life- 36
• Hypothetical drug:• half-life : 24h• dosage interval : = 12h• maintenance dose = 25
• R = = 3.41
Half-life, accumulation and steady-state concentrationHalf-life, accumulation and steady-state concentration
1
1- e -0.693/24h * 12h
Half life- 37
Days Hours Just after dosing 12h later
1 0 25.00 17.681 12 42.68 30.182 24 55.18 39.022 36 64.02 45.273 48 70.27 49.693 60 74.69 52.824 72 77.82 55.034 84 80.03 56.605 96 81.60 57.705 108 82.70 58.486 120 83.48 59.046 132 84.04 59.437 144 84.43 59.707 156 84.70 59.908 168 84.90 60.048 180 85.04 60.13
infinity 85.37 60.37
Half-life, accumulation and steady-state concentrationHalf-life, accumulation and steady-state concentration
Ratio= 3.42
Half life- 43
• Aim : to immediately reach the steady state conditions (Css)
LD = Vss x Css
Loading dose (LD)Loading dose (LD)
Half life- 45
Technical considerations for the calculation of half-life
Technical considerations for the calculation of half-life
Half life- 46
• Estimation
• Linear regression
• Peeling method (residuals)
• Non-linear regression
Half-lifeHalf-life
Half life- 47
z
100
10
1
Yz
How to calculate it
• t1/2 = 0.693 / z• a semilogarithmic plot representation
Half-lifeHalf-life
Half life- 48
Weighing factor and terminal half-lifeWeighing factor and terminal half-life
Half life- 52
Half-life and level of quantification (LOQ)Half-life and level of quantification (LOQ)
Half life- 53
(ng/ml)
10
1.0
0.1
20 50 100 Time (days)
5 h 33.3
2 days 66.6
20 days 100
half-life AUC(%)
C(t) = 100 e-0.139 t + 10 e-0.0139t + 1 e-0.00139t
Half-life and the level of quantification (LOQ) of the analytical technique
Half-life and the level of quantification (LOQ) of the analytical technique
Half life- 54
Terminal half-life of gentamicinTerminal half-life of gentamicin
44h
129h
154h
142h
87h
53h
The very long terminal HL of gentamicin is due to its slow release from tissues and account for urinary excretion for 3 weeks after a dose in man and long withdrawal times in food producing animals
Half life- 55
Variability of half-lifeVariability of half-life
• Generally an analytical artefactC
on
cen
trat
ion
time (h)
LOQ
Half life- 56
C(t) = 100 e -0.139t + 10 e-0.0139t + 1 e-0.00139t
Time (h), Dose = 100
LOQ (ng/ml)
ClearanceVssMRT (day)Varea (L)t1/2 (h)
10.0695
2.7439.65.0
49.85
0.10.0464
12.426733.4
498.5
1/0.661/4.4661/6.71/6.61/10
Ratio
Bias in the estimation of PK parameters with respect to the LOQ
Bias in the estimation of PK parameters with respect to the LOQ
Half life- 57
Where to stop ? (1)Answer : calculate the AUC associated with each phase
Y(t) = Y1 exp(-1t) + Y2 exp(-2t)
AUC1 = Y1 / 1
AUC2 = Y2 / 2
Y1
Y2
1
2
Half-life and the LOQ of the analytical technique
Half-life and the LOQ of the analytical technique
Half life- 58
Where to stop ? (2)Examples :
Y(t) = 1000 exp(-1t) + 500 exp(-0.1t) + 1exp(-0.01t)
AUC = 1000 + 5000 + 100
(16.4%) (82%) (1.6%)
Y(t) = 1000exp(-1t) + 500exp(-0.1t) + 100exp(-0.01t)
AUC = 1000 + 5000 + 10000
(6.8%) (31.3%) (62.5%)
Half-life and the LOQ of the analytical technique
Half-life and the LOQ of the analytical technique
Half life- 59
Where to stop ? (3)•example of gentamicin
• phase 1 : t1/2 = 5 min
• phase 2 : t1/2 2 = 2 h
• phase 3 : t1/2 3 = 24 h
• AUC phase 1 and 2 = 98%
Conclusion : 98% of gentamicin has already been eliminated when the equilibrium of pseudo-distribution occurs
Half-life and the LOQ of the analytical technique
Half-life and the LOQ of the analytical technique
Half life- 60
Le cas des « Very late terminal phases »
Le cas des « Very late terminal phases »
0.0001
0.001
0.01
0.1
1
10
100
0 48 96 144 192 240 288 336 384 432 480 528 576 624 672
LOQLOQ
Benchmark concentrationBenchmark concentration
Half life- 61
The half-time for extravascular route of
administration
The half-time for extravascular route of
administration
Half life- 62
2
6101520
0 24 48 72 96 144
104
2 4
103
1010
0
102
6 8
IM
IV
Pla
sma
Co
nce
ntr
atio
n (
ng
/ m
l)
Pred. sodium succinate Pred. acetate
HoursToutain et al. Am.J.Vet.Res 1985, 46:719-725
Prednisolone (0.6mg/kg)Prednisolone (0.6mg/kg)
IM
HL=3.7h HL=48h
Half life- 63
Half-absorption or half-elimination ?
• a rate-limited absorption (flip-flop) must be recognized
EV: rate of elimination
EV: rate of absorption
time
(C)
IV
What is the meaning of the terminal half-life after an extravascular drug administration?What is the meaning of the terminal half-life after an extravascular drug administration?
0.1
1
10
100
0 5 10 15 20 25 30
Half life- 64
(ng/ml)
Terminal half-life and the flip-flop caseTerminal half-life and the flip-flop case
F% = 100%Ka1Ka1 + Ka2
Ka1
Ka2
negligible
K12
K21
K10
Time
Ka=Ka1+Ka2 # Ka1 = flip-flop
0.1
1
10
100
0 5 10 15 20 25 30
Slow process of absorption
elimination
Half life- 66
(Ka)
(K10)
Flip-flop: a pictural viewFlip-flop: a pictural view
Half life- 67
To measure the absorption rate using some special methods
IM route
k a1
k a2
k10
k a
k10
k a1 k 10 k a2
k 12
k 21
k a
? ?
What is the meaning of the terminal half-life after an extravascular drug administration?What is the meaning of the terminal half-life after an extravascular drug administration?
Half life- 68
Half-life: summaryHalf-life: summary
• Definition
• Interpretation• elimination
• distribution
• Usefulness• single dose
• multiple dose