1. The half-life
OCT 2010

2. The plasma half-life Synonymous half-life of elimination
half-life of the terminal phase

3. Half-life has the apparent advantage of being a familiar term
The half-life
Half-life has the apparent advantage of being a familiar term

4. The 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 !

5. The half-life Meaning in terms of drug elimination
(half-life vs mean residence time (MRT))
MRT = 16 h
Concentration
MRT = 4 h
t1/2 = 12 h
time (h)

6. The half-life Meaning in terms of drug elimination
monocompartmental model
t1/2 = time to eliminate half the dose
t1/2 = time to eliminate half the remaining dose

7. Pharmacokinetic meaning of half-life

8. Half-life vs. Clearance
Clearance : ability to eliminate
Half-life : overall elimination during the terminal phase which depends on both clearance and distribution

9. Clearance vs. half-life
Amiodarone
Clearance: 1.9 ml/kg/min
Half-life: 25 days
Amikacine
Clearance: 1.3 ml/kg/min
Half-life: 2.3 hours

10. Meaning in terms of elimination and distribution
The half-life
Meaning in terms of elimination and distribution

11. The half-life is a hybrid parameter
Distribution large small
Clearance high low
Half-life equal

12. Plasma clearance vs plasma half-life

13. 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

14. The half-life is a hybrid parameter
K12
t1/2
K21
K10
t1/2 = function of K10, K12 and K21

15. The half-life Hybrid parameter t 1/ 2 = t 1/ 2 = 2 k12 k21 k10 0.693
1/2 ( k12 + k21 + k10 ) - ( k12 + k21 + k10 ) k21 k10
0.693
t 1/ 2 = 2

16. Half-life is a hybrid parameter reflecting both clearance and volume of distribution
x Volume of distribution
t 1/ 2 =
Clearance

17. If half-life increases it is because
Volume of distribution  or
Clearance 

18. The half-life t1/2 Terminal half-life is a hybrid parameter : Q ClintQ
Vmax Km Pt Ka
fup
Clint
Clearance
t1/2
fuB VB Vt
fub
fuT
Volume of
Distribution
fup : fraction of the total number of sites of free fixation
Ka : affinity constant
Km : Michaelis constant

19. Time parameters
In pharmacokinetics, all the time parameters are hybrid parameters

20. Hybrid properties of time parameters
Hybrid parameters
k12 Vc Vp
k21
k12 = distribution clearance / Vc
k10 = plasma clearance / Vc
k 21 = redistribution clearance / Vp
t 1/2 vie = Varea / plasma clearance
MRT : Vss / plasma clearance
k10

21. Consequences of the hybrid properties of time parameters
Interpretation of rate constant

22. Interpretation of rate constant
Interpretation of K10
k10 = Cl / Vc
dependent
variable
2 independent variables !
Wrong interpretation of clearance
Cl = K10 x Vc
(computation technique)

23. The 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

24. Why calculate a half-life ?
Dosage regimen
Dose
Interval of administration
Half-life
Clearance

25. Half-life Volume of Clearance distribution Systemic exposure
Absorption
Volume of
distribution
Clearance
bioavailability
Half-life
Systemic
exposure
Dosage regimen
How much
Dosing regimen
How often?

26. Half-life defines the dosing interval
If half-life is short
Problem in maintaining steady-state drug concentration
requires dosage form with a low input rate

27. Half-life defines the dosage interval
If half-life is long
drug accumulation
long delay to reach steady state conditions
requires a loading dose

28. Why calculate a half-life?
In case of multiple administration :
to predict drug accumulation
to predict time of steady state

29. 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)

30. Why calculate a half-life ?
To predict drug accumulation
R = 1
1- e
x t
0.693
t1/2
AUCss
AUC1
Accumulation index
AUCss
AUC1
Half-life
Interval of administration R=
Mono-compartmental model or if drug is administered in the post distribution phase for a x-compartmental model

31. Why 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)

32. Why 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

33. Half-life and delay to reach steady state conditions
Monocompartmental
50% = half-life
90% = 3.3 half-life

34. Half-life, accumulation and steady-state concentration
Hypothetical drug:
half-life : 24h
dosage interval :  = 24h
maintenance dose = 50
R = = = 2 1
1- e /24h * 24h 1

35. Half-life, accumulation and steady-state concentration
Days Just after dosing 24h later
infinity
Ratio = 2

36. Half-life, accumulation and steady-state concentration
Hypothetical drug:
half-life : 24h
dosage interval :  = 12h
maintenance dose = 25
R = = 3.41 1
1- e /24h * 12h

37. Half-life, accumulation and steady-state concentration
Days Hours Just after dosing 12h later
infinity
Ratio= 3.42

38. Half-life Bicompartmental model

39. Half-life accumulation and delay to reach steady state conditions
Bicompartmental
Function of elimination fraction during initial and terminal phase
t1/2 l2 control drug accumulation if at least 50% of the drug is eliminated during the terminal phase

40. Half-life and delay to reach steady state conditions
Bicompartmental model : plasma concentrations
100
t1/2 = 5h
100
t1/2 = 5h 80
t1/2 = 48h
t1/2 = 48h 20
R = +++
day
R = +
day 2 4 8 2 4 8
Apparent steady state is more rapidly reached when most of the drug is eliminated during the distribution phase
t1/2 l2 control drug accumulation if at least 50% of the drug is eliminated during the terminal phase

41. Half-life and delay to reach steady state conditions
Peripheral compartment
delay to reach steady state conditions in the deepest tissular compartment is always controlled by t1/2 lz (residues,doping).
a "pseudo-plateau" can be reached earlier in plasma and shallow tissues than in deep tissues compartment
rate of accumulation is associated with Kz1 and Kz1 is a major determinant of lz

42. Half-life and delay to reach steady state conditions
Plasma vs shallow and deep compartment
0.137
0.0869
shallow
(2) 1
deep
(3)
0.518
0.0479 3
0.0558
Amount 1 2
Time

43. Loading dose (LD) LD = Vss x Css
Aim : to immediately reach the steady state conditions (Css)
LD = Vss x Css

44. Loading dose (LD) (first dose=LD)
maintenance dose
1- e x t
LD =
0.693 l1 or
LD =
maintenance dose x accumulation index
LD for the first example =50x2=100
LD for the second example=25X3.42=85.5

45. Technical considerations for the calculation of half-life

46. Half-life Estimation Linear regression Non-linear regression
Peeling method (residuals)
Non-linear regression

47. Half-life How to calculate it t1/2 = 0.693 / z
a semilogarithmic plot representation
100 z 10 Yz 1

48. Weighing factor and terminal half-life

49. Rate constant
Rate of elimination
Amount in body Cl V
Kel = =
Fractional rate of drug elimination can be viewed as the fraction of the volume of distribution from which drug is removed by unit of time
e.g.: Kel = 0.01 h-1  1% per h

50. Sampling conditions for the appropriate estimation of t1/2
At least 3 times the expected t1/2
if 24 hours = sampling are over at least 3 days

51. Half-life and sampling times
100
t1/2= 48.7 hours
-20%
+20%
Concentrations
t1/2= 28 hours
t1/2=20 hours
D = +20% 10 10 20 30 40 50 60 70
Time (hours)

52. Half-life and level of quantification (LOQ)

53. Half-life and the level of quantification (LOQ) of the analytical technique
C(t) = 100 e t + 10 e t + 1 e t
(ng/ml)
half-life AUC(%) 10
5 h
2 days
1.0
20 days 100
0.1
Time (days)

54. Terminal half-life of gentamicin
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

55. Variability of half-life
Generally an analytical artefact
Concentration
LOQ
time (h)

56. Bias in the estimation of PK parameters with respect to the LOQ
C(t) = 100 e t + 10 e t + 1 e t
Time (h), Dose = 100
LOQ (ng/ml)
Ratio 1
0.0695
2.74
39.6
5.0
49.85
0.1
0.0464
12.4
267
33.4
498.5
1/0.66
1/4.466
1/6.7
1/6.6
1/10
Clearance
Vss
MRT (day)
Varea (L)
t1/2 (h)

57. Half-life and the LOQ of the analytical technique
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 1 Y1 Y2 2

58. Half-life and the LOQ of the analytical technique
Where to stop ? (2)
Examples :
Y(t) = 1000 exp(-1t) exp(-0.1t) + 1exp(-0.01t)
AUC =
(16.4%) (82%) (1.6%)
Y(t) = 1000exp(-1t) + 500exp(-0.1t) + 100exp(-0.01t)
AUC =
(6.8%) (31.3%) (62.5%)

59. Half-life and the LOQ of the analytical technique
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

60. Le cas des « Very late terminal phases »
LOQ
Benchmark concentration

61. The half-time for extravascular route of administration

62. Prednisolone (0.6mg/kg) Pred. sodium succinate Pred. acetate HL=3.7h
104
HL=3.7h 20
HL=48h 15
103 10 IV
Plasma Concentration (ng / ml) IM 6
102 IM 10 2 2 4 6 8 10 24 48 72 96
144
Hours
Toutain et al. Am.J.Vet.Res 1985, 46:

63. Half-absorption or half-elimination ?
What is the meaning of the terminal half-life after an extravascular drug administration?
Half-absorption or half-elimination ?
• a rate-limited absorption
(flip-flop) must be recognized
100
(C) 10
EV: rate of absorption IV
EV: rate of elimination 1
0.1
time 5 10 15 20 25 30

64. Terminal half-life and the flip-flop case
Slow process of absorption
K12
Ka1
K21
Ka2
negligible
K10
(ng/ml)
100
Ka=Ka1+Ka2 # Ka1 = flip-flop 10
elimination 1
Ka1
Ka1 + Ka2
F% =  100%
0.1
Time 5 10 15 20 25 30

65. Flip-flop: a pictural view
Baignoire avec réserve d’eau (dose), un robinet (ka) et une bonde (K10, clairance)
(Ka)
(K10)

66. Flip-flop: a pictural view
(Ka)
(K10)

67. What is the meaning of the terminal half-life after an extravascular drug administration?
To measure the absorption rate using some special methods
IM route
k a1
k 10
k a 
k a2  ? ?
k a1
k 12
k a
k 21
k a2
k10
k10

68. Half-life: summary Definition Interpretation Usefulness elimination
distribution
Usefulness
single dose
multiple dose

69. Drug elimination expressed in terms of amount in the body
- dA/dt A
dA/dt = - l  A or l =
Rate of elimination
Amount in the body
l =
Elimination rate constant is regarded as the fractional rate of drug removal