PHARMACOKINETICS Multiple IV Bolus Dose Administration ١ Multiple IV Bolus Dose Administration Objectives: 1) To understand drug accumulation after repeated dose administration 2) To recognize and use the integrated equations used to describe plasma concentrations versus time after multiple IV. doses 3) To calculate appropriate multiple dose drug regimen ٢ ١
Multiple-Dosage Regimens: After single-dose drug administration, the plasma drug level rises above and then falls below the minimum i effective concentration (MEC) decline in therapeutic effect. To maintain prolonged therapeutic activity, many drugs are given in a multiple-dosage regimen. The plasma levels of drugs given in multiple doses must be maintained within the narrow limits of the therapeutic window ٣ Ideally, a dosage regimen is established for each drug to provide the correct plasma level without excessive fluctuation and drug accumulation outside the therapeutic window. Some drugs that have a narrow therapeutic range (eg, digoxin and phenytoin) require definition of the therapeutic minimum and maximum nontoxic plasma concentrations (MEC and MTC). ٤ ٢
٥ Drug Accumulation In multiple dose administration, giving a second dose or multiple doses before the drug is completely eliminated, will lead into accumulation of the drug in the body. Upon repeating the dose, a plateau to steady state can be reached (fluctuating between a maximum and minimum values). There is a limit to drug accumulation because as the plasma conc. increases, the amount of the drug eliminated during dosing interval will also increase. There are two approaches for predicting the conc. at steady state or after any number of doses. ٦ ٣
The principle of superposition: model independent approach: To calculate multiple-dose regimens, it is necessary to decide whether successive doses of drug will have any effect on the previous dose. The principle of superposition assumes that Early doses of drug do not affect the pharmacokinetics of subsequent doses each dose will have the same conc-time profile. The blood levels after the second, third, or n th dose will overlay or superimpose the blood level attained after the (n 1) th dose. ٧ The concentration after multiple doses can be calculated by adding the concentrations from each dose with time conc increases to reach steady state. The principle of superposition allows one to project the plasma drug concentration time time curve of a drug after multiple consecutive doses based on the plasma drug concentration time curve obtained after a single dose. The same time intervals for sampling should be considered after each dose. ٨ ٤
٩ Independent Doses ١٠ ٥
Accumulating doses ١١ ١٢ ٦
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١٧ Model-dependent Approach This approach requires finding a factor so that Cn (max)=co*factor C =C (1+ kτ +e 2kτ + + (n-1)kτ n (max) o e e ) C n (min) =C o (e kτ +e 2kτ + + e nkτ ) C n (max) -C n (min) =C o -Coe nkτ C n (min) = C n (max) e kτ C n (max) -C n (max) e kτ =C o -Coe nkτ (C o = C 1(max) ) ١٨ ٩
١٩ nk 1 e K ( Cn ) t t = rcoe r = 1 kτ e τ ( Css ) t = Co * Re ss X C av = KV o dτ K t 1 R = 1 e kτ nτ = 1.44 t0. 5 ln(1 fss) ٢٠ ١٠
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Important During continuous (infusion) or continuous intermittent dosing (IV-bolus & oral dosing): The steady-concentration depends on the rate of dosing (the dose/dosing interval) and the clearance. Time required to achieve steady-state depends on the half-life and is independent of the rate of dosing and the clearance.. ٢٥ ١٣
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The relationship between t 1/2 and dosing interval τ can be used to predict the degree of accumulation of a drug in the blood. The longer t 1/2 and the shorter t, the more drug accumulates. τ t 1/2 τ < t 1/2 τ > t 1/2 Moderate accumulation during dosing (2-times) Significant accumulation during dosing g( (> 2-times) Insignificant accumulation During dosing (< 2-times) ٣٣ Fluctuation t 1/2 (the relationship between t 1/2 and dosing interval τ) can be used to predict the degree of fluctuation of a drug concentration within a dosing interval. τ t 1/2 C ss,min levels at steady state are aprox. 50% of C ss,max. Moderate fluctuation. τ <t 1/2 C ss,min levels l at steady state t are more than 50% of C ss,max. Small fluctuation. τ > t 1/2 C ss,min levels at steady state are less than 50% of C ss,max. Wide fluctuation. ٣٤ ١٧
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Case Study: To a patient 250 mg penicillin with t½ of 1 h and Vd of 25 L is administered every 6 h intravenously for 2 days. The dose is then increased to 500 mg gq.i.d. 1) Estimate Cmax and Cmin. Calculate Cav at steady state. 2) Has the objective of maintaining concentration above minimum inhibitory concentration (4 mg/1) been achieved in this therapy? Elaborate! 3) Is the idea of giving a bolus dose to achieve Css in a shorter time feasible with regard to this drug? 4) How long did it take to reach Css? ٣٧ 24 22 20 18 16 14 12 10 8 6 4 2 0 0 5 10 15 20 25 30 35 40 Time (hr) ٣٨ ١٩
100.0 10.0 1.0 0.1 0 5 10 15 20 25 30 35 40 Time (hr) ٣٩ Case 1 A drug (200 mg) is administered to a 70- kg male patient by multiple IV injections at 6-h intervals. The drug is water-soluble and has a distribution volume equivalent to that of total body water (50 liters). The drug has a biological half-lifelife of 6 h.calculate (i)c(max) (initial), (ii)(ii) C (max), (iii) C (min) and (iii)(iv) Cav(ss). ٤٠ ٢٠
Case 2 A drug (50 mg ) is administered to a 70-kg male patient by repeated bolus IV injections. The drug has a distribution volume of 5 L and a biological half-life life of 8 h, and is injected at intervals of 8 h. Calculate the following: (i) C (max) (ii) The time necessary to reach 95% of the steady-state concentration. (iii) The number of doses required to reach 95% of the steady-state concentration. ٤١ Case 3 Assuming a one compartment linear pharmacokinetic model, with K = 0.19 hr-1 and V = 18.2 L, calculate the plasma concentration at 0.5, 1, 2, 4, 6, 9, 12, and 24+ hours after 250 mg i.v. doses every 8 hours. ٤٢ ٢١
18 0.5 12.49 1 11.36 16 14 12 10 8 6 4 2 0 5 10 15 20 25 2 9.39 4 6.42 6 4.39 9 13.84 12 7.83 Time 24 17.47 ٤٣ Excel ٤٤ ٢٢
129/131 44/131 67/131 107/131 113/131 ٢٣
107/131 47/131 37/131 19/131 47/131 ٢٤
113/131 63/131 31/131 65/131 40/131 36/131 ٢٥
57/131 51/131 48/131 45/131 ٢٦
83/131 39/131 22/131 33/131 ٢٧
The figure below depicts drug elimination curves, plotted on a log scale, for 3 drugs (X, Y, and Z) after identical amounts were independently administered to the same patient in bolus doses. Answer the following questions 10000 1000 Y co oncentration in plasma 100 10 1 0.1 X Z 0.01 0 2 4 6 8 10 12 time (hours) Which of the following statements is correct? a) (Vd for X) = (Vd for Z) b) (T1/2 for X) = (T1/2 for Y) c) Clearance for X = clearance of Y d) Elimination rate constant for X < elimination rate constant for Y e) Half lives of X and Z are equal but their clearances are different If X, Y, and Z were independently infused in equal amounts at a constant rate, which of the following statements t t would be correct? a) The first drug to reach steady state is Z b) The last drug to reach steady state is Z c) Xss for both X and Z should be the same d) More than one choice is correct ٢٨
The figure below shows concentrations of drug GR103 after administration of identical amounts of a tablet, suspension and solution to the same patient. Answer the following questions 10 9 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 Time (hr) 15) The time for reaching the maximum concentration for the solution is around a) 1 hour b) 1.5 hours c) 2 hours d) 9.5 hours e) 7.8 hours 16) The maximum concentration attained after the tablet was a) 1 mg/l b) 1.5 mg/l c) 9.5 mg/l d) 8.6 mg/l e) 7.7mg/L ٢٩
19-23 The following table summarizes the pharmacokinetics of drug PK 475 after an IV dose of 300 mg and an oral dose of 500 mg Parameter IV bolus Oral dose Cmax (μg/ml) AUC (μg.hr/ml) 190 160 Residual T 1/2 (hr) 3 Terminal T 1/2 (hr) 3 9 Xu (mg) 110 19) The Bioavailability of the drug is a) 84.2 % b) 118.8 % c) 71.3 % d) 50.5 % e) 40.3 % 20) Renal elimination rate constant is equal to: a) 0.231 hr 1 b) 0.04620462 hr 11 c) 0.134 hr 1 d) 0.0847 hr 1 e) 0.028 hr 1 ٣٠
21) The absorption half life is equal to a) 1.73 hrs b)3 hours c)9 hours d)0.077 hrs e)cannot be estimated (no enough data) 22) The maximum concentration ti after the IV dose is a)300 mg/l b)16.2 mg/l c)12.4 mg/l d)43.9 mg/l e)22.8 mg/l 23) The amount of the drug that is expected to be excreted unchanged in urine after the oral dose is a)92 mg b)124 mg c)200 mg d)250 mg e)500 mg ٣١