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Half life- 1 The half-life OCT 2010

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

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

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Half life- 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 !

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Half life- 5 The half-life Meaning in terms of drug elimination (half-life vs mean residence time (MRT)) Concentration MRT = 16 h MRT = 4 h t1/2 = 12 h 24 time (h)

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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-life

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Half life- 7 Pharmacokinetic meaning of half-life

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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

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Half life- 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

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

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

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Half life- 12 Plasma clearance vs plasma half-life

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Half life- 13 Half-life (HL), Clearance (Cl) & volume of distribution (Vd) of Amiodarone vs. amikacin DrugsHL (h) Cl ml/kg/min Vd L/kg amiodarone6001.995 amikacin2.51.30.27

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Half life- 14 The half-life is a hybrid parameter t 1/2 = function of K 10, K 12 and K 21 t 1/2 K 12 K 21 K 10

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Half life- 15 t 1/ 2 = 0.693 1/2 ( k 12 + k 21 + k 10 ) - ( k 12 + k 21 + k 10 ) 2 - 4 k 21 k 10 k 10 k 12 k 21 Hybrid parameter t 1/ 2 = 0.693 2 The half-life

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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

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Half life- 17 If half-life increases it is because Volume of distribution or Clearance

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Half life- 18 Volume of Distribution Volume of Distribution Terminal half-life is a hybrid parameter : Clint Vmax Km P t Ka fu p Clearance t 1/2 ° Q fu B V B V t fu b fu T fu p : fraction of the total number of sites of free fixation Ka : affinity constant Km : Michaelis constant The half-life

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Half life- 19 In pharmacokinetics, all the time parameters are hybrid parameters Time parameters

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Half life- 20 k 10 k 12 k 21 k 12 = distribution clearance / Vc k 10 = plasma clearance / Vc k 21 = redistribution clearance / Vp t 1/2 vie = 0.693 V area / plasma clearance MRT : Vss / plasma clearance Vc Vp Hybrid parameters Hybrid properties of time parameters

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Half life- 21 Consequences of the hybrid properties of time parameters Interpretation of rate constant

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Half life- 22 Interpretation of K 10 k 10 = Cl / Vc dependent variable 2 independent variables Wrong interpretation of clearance Cl = K 10 x Vc (computation technique) ! Interpretation of rate constant

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Half life- 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

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

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

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Half life- 26 Half-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

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Half life- 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

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

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Half life- 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)

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

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Half life- 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)

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Half life- 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

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

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Half life- 34 Hypothetical drug: half-life : 24h dosage interval : = 24h maintenance dose = 50 R = = = 2 Half-life, accumulation and steady-state concentration 1 1- e -0.693/24h * 24h 1 1 - 0.5

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Half life- 35 DaysJust after dosing24h later 15025 27537.5 387.543.75 493.7546.88 596.8848.44 698.4449.22 799.2249.61 899.6149.80 infinity10050 Half-life, accumulation and steady-state concentration Ratio = 2

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Half life- 36 Hypothetical drug: half-life : 24h dosage interval : = 12h maintenance dose = 25 R = = 3.41 Half-life, accumulation and steady-state concentration 1 1- e -0.693/24h * 12h

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Half life- 37 DaysHoursJust after dosing12h later 1025.0017.68 11242.6830.18 22455.1839.02 23664.0245.27 34870.2749.69 36074.6952.82 47277.8255.03 48480.0356.60 59681.6057.70 510882.7058.48 612083.4859.04 613284.0459.43 714484.4359.70 715684.7059.90 816884.9060.04 818085.0460.13 infinity85.3760.37 Half-life, accumulation and steady-state concentration Ratio= 3.42

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Half life- 38 Half-life Bicompartmental model

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Half life- 39 Bicompartmental Function of elimination fraction during initial and terminal phase t 1/2 2 control drug accumulation if at least 50% of the drug is eliminated during the terminal phase Half-life accumulation and delay to reach steady state conditions

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Half life- 40 Half-life and delay to reach steady state conditions Bicompartmental model : plasma concentrations Apparent steady state is more rapidly reached when most of the drug is eliminated during the distribution phase t 1/2 2 control drug accumulation if at least 50% of the drug is eliminated during the terminal phase 100 80 t1/2 = 5h t1/2 = 48h 100 20 t1/2 = 5h t1/2 = 48h day 248 248 R = +++ R = +

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Half life- 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 z (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 z

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

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

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

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Half life- 45 Technical considerations for the calculation of half-life

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

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

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Half life- 48 Weighing factor and terminal half-life

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Half life- 49 Rate constant K el = = 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.: K el = 0.01 h -1 1% per h Rate of elimination Amount in body Cl V

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Half life- 50 Sampling conditions for the appropriate estimation of t 1/2 At least 3 times the expected t 1/2 if 24 hours = sampling are over at least 3 days

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Half life- 51 Half-life and sampling times 10 100 010203040506070 Time (hours) Concentrations t 1/2 =20 hours t 1/2 = 28 hours t 1/2 = 48.7 hours +20% = +20% -20%

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

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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

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Half life- 54 Terminal 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

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

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Half life- 56 C(t) = 100 e -0.139t + 10 e -0.0139t + 1 e -0.00139t Time (h), Dose = 100 LOQ (ng/ml) Clearance Vss MRT (day) Varea (L) t1/2 (h) 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 Ratio Bias in the estimation of PK parameters with respect to the LOQ

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Half life- 57 Where to stop ? (1) Answer : calculate the AUC associated with each phase Y(t) = Y 1 exp(- 1 t) + Y 2 exp(- 2 t) AUC 1 = Y 1 / 1 AUC 2 = Y 2 / 2 Y1Y1 Y2Y2 1 2 Half-life and the LOQ of the analytical technique

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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

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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

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Half life- 60 Le cas des « Very late terminal phases » LOQ Benchmark concentration

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Half life- 61 The half-time for extravascular route of administration

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Half life- 62 2 6 10 15 20 024487296 144 10 4 24 10 3 10 0 10 2 68 IM IV Plasma Concentration (ng / ml) Pred. sodium succinatePred. acetate Hours Toutain et al. Am.J.Vet.Res 1985, 46:719-725 Prednisolone (0.6mg/kg) IM HL=3.7h HL=48h

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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? 0.1 1 10 100 051015202530

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Half life- 64 (ng/ml) Terminal half-life and the flip-flop case F% = 100% Ka1 Ka1 + Ka2 K a1 K a2 negligible K 12 K 21 K 10 Time Ka=K a1 +K a2 # K a1 = flip-flop 0.1 1 10 100 051015202530 Slow process of absorption elimination

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Half life- 65 Flip-flop: a pictural view Baignoire avec réserve d’eau (dose), un robinet (ka) et une bonde (K 10, clairance) (Ka) (K 10 )

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Half life- 66 (Ka) (K 10 ) Flip-flop: a pictural view

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Half life- 67 To measure the absorption rate using some special methods IM route k a1 k a2 k 10 k a k 10 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?

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

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

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