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Bolus Dosing

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### Bolus Dosing

1. 1. I.V. Bolus Dosing CHAPTER 4 Author: Michael Makoid and John Cobby Reviewer: Phillip Vuchetich OBJECTIVES For an IV one compartment model plasma and urine: 1. Given patient drug and/or metabolite concentration, amount, and/or rate vs. time profiles, the student will calculate (III) the relevant pharmacokinetic parameters available from IV plasma, urine or other excreta data: e.g. V d, K, k m, k r, AUC, AUMC, CL, MRT, t 1 ⁄ 2 2. The student will provide professional communication regarding the pharmacoki- netic parameters obtained to patients and other health professionals. 3. The student will be able to utilize computer programs for simulations and data analysis. 4-1 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
2. 2. I.V. Bolus Dosing 4.1 I.V. Bolus dosing of Parent compound 4.1.1 PLASMA ln C p = – K ⋅ t + ln C p 0 Valid equations: (EQ 4-1) (Obtained from the ln X = – K ⋅ t + ln X0 LaPlace transforms (EQ 4-2) derived from the appropriate models – Kt derived from the C p = C p0 e (EQ 4-3) pharmacokinetic descriptions of the drug) D- C p 0 = ----- (EQ 4-4) Vd t ½ = 0.693 ------------ - (EQ 4-5) K ( ∞) ( Cp n + Cp n + 1 ) Cp last Cp dt = Σ  ------------------------------------- ⋅ ∆t + -------------- ∫ AUC =   (EQ 4-6) 2 K 0 ( ∞) t ( t n ⋅ Cp n ) + ( t n + 1 ⋅ Cp n + 1 ) ( t l ast ⋅ Cp last ) Cp l ast ∑  ------------------------------------------------------------------- ⋅ ∆t + --------------- + ---------------------------------- ∫ t ⋅ C p dt = - AUMC = (EQ 4-7)   2 2 K K 0 0 MRT = AUMC ----------------- - (EQ 4-8) AUC Cl = K ⋅ Vd (EQ 4-9) Utilization: Can you determine the • You should be able to plot a data set Concentration vs. time on semilog yielding a straight line slope and intercept from with slope = – K and an intercept of C p0 . a graph? Plot the data in table 4 -1.on semi-log graph paper. Extrapo- Nifedipine 25 mg IV bolus TABLE 4-1 late the line back to time = 0 to get Cp0. Find the Cp half life. Calculate the Time (hr) (mcg/L) elimination rate con- 2 139 stant. 4 65.6 6 31.1 8 14.6 FIGURE 4-1. 4-2 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
3. 3. I.V. Bolus Dosing Does your Graph look Nifedipine IV Bolus (25 mg IV Bolus) FIGURE 4-1 like this? 100 10 3 Concentration (mic/L) Cp0 = 295 mic/L -K1 = -0.375 hr -1 Concentration (ng/mL) 10 2 1.85 hr 50 10 1 0 2 4 6 8 Time (hr) Time (hours) • You should be able to determine K. A plot of the data in TABLE 4-1 results in FIGURE 4-1 dy Remember from high school algebra, the slope of any straight line is the rise over the run, ----- , - dx In the case of semi-log graphs dy is the difference in the logarithms of the concentrations. Thus, using the rules of logarithms, when two logs are subtracted, the numbers themselves are divided. i.e. ln ( C1 ) – ln ( C2 ) = ln  ------ . Thus if we are judicious in the concentrations that we C1 -  C2 take, we can set the rise to a constant number. So, if we take any two concentrations such that one concentration is half of the other (In FIGURE 4-1 above, we took 100 and 50), the time it takes for the concentration to halve is the half life (in the graph above, 1.85 hr). Then 0.693 0.693 –1 K = ------------ = --------------- = 0.375 hr - - 1.85hr t½ • You should be able to determine V d :. To do this, extrapolate the line to t = 0 . The value of Cp mic when t = 0 is C p0 (in the graph above, C p0 = 295 -------- which is equal to D ⁄ V d for an IV bolus - L dose only. Dose 25mg 1000mic Thus, Cp 0 = ------------ , V d = Dose = ------------------ ⋅ -------------------- = 85L - - ------------ - Vd mg Cp 0 295mic ----------------- - L The volume of distribution is a mathematical construct. It is merely the proportionality constant between two knowns - the C p0 which results from a given D 0 . It is, however, useful because it is patient specific and therefore can be used to predict how the patient will treat a subsequent dose of the same drug. You should be able to obtain the volume of distribution from graphical analysis of the data. Pay attention to the units! Make sure that they are consistent on both sides of the equation. NOTE: the volume of distribution is not necessarily any physiological space. For example the approximate volume of distribution of digoxin is about 600 L If that were a physiological space and I were all water, that would mean that I would weigh about 1320 pounds. I’m a little overweight (I prefer to think that I’m underheight), but REALLY! • Given any three of the variables of the IV bolus equation, either by direct information (the vol- ume of distribution is such and such) or by graphical data analysis, you should be able to find the fourth. 4-3 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
4. 4. I.V. Bolus Dosing • You should be able to calculate Area Under the Curve (AUC) from IV Bolus data (Time vs. Cp). From the above data in TABLE 4-1 the AUC is calculated using (EQ 4-6): (∞) Cpn + Cp n + 1 Cp = Σ  --------------------------------  + --------l which in this case is: ∫ Cp dt - AUC =   ∆t K 0  Cp o + Cp 1 Cp l ast  Cp 1 + Cp 2 Cp2 + Cp 3 Cp 3 + Cp last Σ  ------------------------- ⋅ ∆t 1 + ------------------------- ⋅ ∆t 2 + ------------------------- ⋅ ∆t 3 + ------------------------------ ⋅ ∆t last + --------------  - - - - - 2 2 2 2  K1   295 + 139 14.6 mcg 139 + 65.6 65.6 + 31.1 31.1 + 14.6 Σ  ----------------------- ⋅ 2 + ------------------------- ⋅ 2 + -------------------------- ⋅ 2 + -------------------------- ⋅ 2 + ------------ ---------- hr or - - - - 2 2 2 2 0.375  L  mcg mcg Σ { 434 + 204.6 + 96.7 + 45.7 + 38.9 } --------- hr = 819.9 ---------- hr . In tabular format, the AUC calculation - L L is shown in TABLE 4-2. TABLE 4-2 AUC t t AUC AUC TIME Cp t–1 0 0 295 2 139 434.0 434.0 4 65.6 204.6 638.6 6 31.1 96.7 735.3 8 14.6 45.7 781.0 ∞ 0 38.9 819.9 The AUC of a plot of plasma concentration vs. time, in linear pharmacokinetics, is a number which is proportional to the dose of the drug which gets into systemic circulation. The propor- tionality constant, as before, is the volume of distribution. It is useful as a tool to compare the amount of drug obtained by the body from different routes of administration or from the same route of administration by dosage forms made by different manufacturers (calculate bioavail- ability in subsequent discussions). The AUC of a plot of Rate of Excretion of a drug vs. time, in linear pharmacokinetics, is the mass of drug excreted into the urine, directly. • You should be able to calculate the AUMC from IV Bolus data (Time vs. Cp). The equation for AUMC is equation 4-7: ( ∞) t ( t n ⋅ Cp n ) + ( t n + 1 ⋅ Cp n + 1 ) ( t l ast ⋅ Cp last ) Cp l ast ∑  ------------------------------------------------------------------- ⋅ ∆t + --------------- + ---------------------------------- ∫ t ⋅ C p dt = - which in the AUMC =   2 2 K K 0 0 data given in TABLE 4-1 is: T0 ⋅ C po + T1 ⋅ C p1 T1 ⋅ C p1 + T2 ⋅ C p2 T 2 ⋅ C p 2 + T3 ⋅ C p3 Σ ---------------------------------------------- ⋅ ∆t 1 + ---------------------------------------------- ⋅ ∆t 2 + ---------------------------------------------- ⋅ ∆t 3 + - - - 2 2 2 4-4 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
5. 5. I.V. Bolus Dosing T 3 ⋅ C p 3 + T last ⋅ C p last T last ⋅ C p l ast Cplast --------------------------------------------------------- ⋅ ∆t l ast + ------------------------------ + -------------- and thus, - - - 2 2 K K  0 ⋅ 295 + 2 ⋅ 139 4 ⋅ 65.6 + 6 ⋅ 31.1 mcg 2 2 ⋅ 139 + 4 ⋅ 65.6 Σ  -------------------------------------- ⋅ 2 + ---------------------------------------- ⋅ 2 + ----------------------------------------- ⋅ 2 --------- hr + - - - 2 2 2 L   6 ⋅ 31.1 + 8 ⋅ 14.6 14.6  mcg 2 8 ⋅ 14.6  ----------------------------------------- ⋅ 2 + ----------------- + ---------------  ---------- hr or - - - 2 0.375  L 2  0.375 mcg 2 Σ { 278 + 540.4 + 449 + 303.4 + 311.47 + 103.82 } = 1986.1 --------- hr - L Thus in tabular format the AUMC for data given in TABLE 4-1 is TABLE 4-3 below. TABLE 4-3 AUMC t AUMC AUMC t TIME Cp Cp*T 0 0 295 0 2 139 278 278.0 278.0 4 65.6 262.4 540.4 818.4 6 31.1 186.6 449.0 1267.4 8 14.6 116.8 303.4 1570.8 ∞ 0 0 415.3 1986.1 The AUMC is the Area Under the first Moment Curve. A plot of T*Cp vs. T is the first moment curve. The time function buried in this plot, the Mean Residence Time (MRT), can be extracted using equation 4-8 below. It is the geometric mean time that the molecules of drug stay in the body. It has utility in the fact that, as drug moves from the dosage form into solution in the gut, from solution in the gut into the body, and from the body out, each process is cumulatively additive. That means if we can physically separate each of these processes in turn, we can calculate the MRT of each process. The MRT of each process is the the inverse of the rate constant for that process. • You should be able to calculate MRT from IV Bolus data (Time vs. Cp) using equation 4-8 AUMC 1986.1 MRT = ----------------- = --------------- = 2.42 - - AUC 819.9 Since there is only the process of elimination (no release of the drug from the dosage form, no absorption), the MRT is the inverse of the elimination rate constant, K. Thus MRT = 1/K. 4-5 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
6. 6. I.V. Bolus Dosing IV Bolus Flow Chart 4-1 K X MRT(IV) = 1/K Suppose the drug were given in a solution. Then the drug would have to be absorbed and then eliminated. Since the MRTs are additive, the MRT of the oral solution would be made up of the MRTs of the two processes, thus: Oral Solution Flow Chart 4-2 Ka K Xa X MRT(os) = MAT(os)+MRT(IV) MRT(os) = 1/Ka + 1/K Consequently, if a drug has to be released from a dosage form for the drug to get into solution which is subsequently absorbed, a tablet for example, the MRT of the tablet will consist of the MRT(IV) and the MAT(os) and the Mean Dissolution Time (MDT), thus: Tablet Flow Chart 4-3 Kd Ka K Xd Xa X MRT(tab) = MDT + MAT(os) + MRT(IV) MRT(tab) = 1/Kd + 1/Ka + 1/K MRT(tab) = MAT(tab) + MRT(IV) MRT(tab) = 1/Ka (apparent) + 1/K 4-6 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
7. 7. I.V. Bolus Dosing Normally, we don’t have information from the oral solution, just IV and tablet. So in that case the information obtained about absorption from the tablet is bundled together into an apparent absorption rate constant consisting of both dissolution and absorption. It should be apparent that this is a reasonably easily utilized and powerful tool used to obtain pharmacokinetic parameters. 4-7 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
8. 8. I.V. Bolus Dosing 4.1.2 IV BOLUS, PARENT COMPOUND, PLASMA PROBLEMS 1. K = –slope from equation 4-3 Equations used in this section: ln 2 2. t 1 ⁄ 2 = ------- equation 4-5 - K 1 MRT = --- ( estimate ) MRT = AUMC equation 4-8 - 3. ----------------- - K AUC 4. Cp 0 = the y-intercept of the line from equation 4-3 Cp 0 ∞ ∫0 Cp dt 5. Estimate for AUC = AUC = --------- which is K (∞) ( Cp n + Cp n + 1 ) Cp last Cp dt = Σ  ------------------------------------- ( ∆t ) + -------------- ∫ AUC =   2 K 0 Trapezoidal rule applied to equation 4-6 Estimate for AUMC = AUMC = AUC ⋅ MRT from equation 4-8 6. ( ∞) t ( t n ⋅ Cp n ) + ( t n + 1 ⋅ Cp n + 1 ) ( t last ⋅ Cp l ast ) Cp last ∑  ------------------------------------------------------------------- ⋅ ∆tn + --------------- + ---------------------------------- ∫ - AUMC Cp dt =   2 2 K K 0 0 from equation 4-7 V d = Dose from equation 4-4 7. ------------ - Cp 0 Cp 0 Dose Cl = K1 ⋅ V d = ----------- ⋅ ------------ = Dose - - ------------ 8. - AUC Cp 0 AUC 4-8 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
9. 9. I.V. Bolus Dosing Acyclovir (Problem 4 - 1) Problem Submitted By: Maya Lyte AHFS 12:34.56 Antivirals Problem Reviewed By: Vicki Long GPI: 1234567890 Antivirals De Miranda and Burnette, “Metabolic Fate and Pharmacokinetics of the Acyclovir Prodrug Valaciclovir in Cynomolgus Mon- keys”, Drug Metabolism and Disposition (1994): 55-59. Acyclovir is an antiviral drug used in the treatment of herpes simplex, varicella zoster, and in suppressive therapy. In this study, three male cynomolgus monkeys were each given a 10 mg ⁄ kg intravenous dose. The monkeys weighed an average of 3.35 kg each. Blood samples were collected and the following data was obtained: Acyclovir PROBLEM TABLE 4 - 1. Serum concentration ( µg ⁄ mL ) Time (hours) 0.167 26.0 0.300 23.0 0.500 19.0 0.75 16.0 1.0 12.0 1.5 7.0 2.0 5.0 From the data presented in the Preceding table, determine the following: Find the elimination rate constant, k . 1. Find the half life, t ½ . 2. Find MRT . 3. Find ( C p )0 . 4. Find the Area Under the Curve, AUC . 5. Find the area under the first moment curve, AUMC . 6. Find the volume of distribution, V d 7. Find the clearance, Cl . 8. 4-9 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
10. 10. I.V. Bolus Dosing (Problem 4 - 1) Acyclovir: 2 10 CONCENTRATION (MIC/ML) 1 10 100 0.0 0.5 1.0 1.5 2.0 TIME (HR) –1 k = 0.93hr 1. t½ = 0.75hr . 2. MRT = 1.08hr . 3. ( C p )0 = 30.4ug ⁄ mL . 4. AUC = 32.75ug ⁄ mL ⋅ hr . 5. 2 AUMC = 35.2ug ⁄ mL ⋅ hr . 6. Vd = 1.1L 7. Cl = 1.02L ⁄ hr . 8. 4-10 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
11. 11. I.V. Bolus Dosing Aluminum (Problem 4 - 2) Problem Submitted By: Maya Lyte AHFS 12:34.56 Antivirals Problem Reviewed By: Vicki Long GPI: 1234567890 Antivirals Xu, Pai, and Melethil, quot;Kinetics of Aluminum in Rats. II: Dose-Dependent Urinary and Biliary Excretionquot;, Journal of Pharmaceu- tical Sciences, Oct 1991, p 946 - 951. A study by Xu, Pai, and Melethil establishes the pharmacokinetics of Aluminum in Rats. In this study, four rats with an average weight of 375g, were given an IV bolus dose of aluminum (1 mg/kg). Blood samples were taken at various intervals and the following data was obtained: Aluminum PROBLEM TABLE 4 - 2. ng Serum concentration, ------- - mL Time (hours) 0.4 19000 0.6 18000 1.4 15000 1.6 14500 2.3 12500 3.0 10500 4.0 8500 5.0 6500 6.0 5000 8.0 3250 10.0 2000 12.0 1250 From the data presented in the preceding table, determine the following: Find the elimination rate constant, k . 1. Find the half life, t ½ . 2. Find MRT . 3. Find ( C p )0 . 4. Find the Area Under the Curve, AUC . 5. Find the area under the first moment curve, AUMC . 6. Find the volume of distribution, V d 7. Find the clearance, Cl . 8. 4-11 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
12. 12. I.V. Bolus Dosing (Problem 4 - 2) Aluminum: 5 10 CONCENTRATION (NG/ML) 4 10 3 10 0 2 4 6 8 10 12 TIME (HR) –1 k = 0.234hr 1. t½ = 3hr . 2. MRT = 4.3hr . 3. ( C p )0 = 21000ng ⁄ mL . 4. AUC = 89285ng ⁄ mL ⋅ hr . 5. 2 AUMC = 383926ng ⁄ mL ⋅ hr . 6. Vd = 17.86mL 7. Cl = 4.18mL ⁄ hr . 8. 4-12 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
13. 13. I.V. Bolus Dosing Amgen (Problem 4 - 3) Problem Submitted By: Maya Lyte AHFS 12:34.56 Antivirals Problem Reviewed By: Vicki Long GPI: 1234567890 Antivirals Salmonson, Danielson, and Wikstrom, quot;The pharmacokinetics of recombinant human erythropoetin after intravenous and subcuta- neous administration to healthy subjectsquot;, Br. F. clin. Pharmac. (1990), p 709- 713. Amgen (r-Epo) is a form of recombinant erythropoetin. Erythropoetin is a hormone that is produced in the kidneys and used in the production of red blood cells. The kidneys of patients who have end-stage renal failure cannot produce erythropoetin; therefore, r-Epo is being investigated for use in these patients in order to treat the anemia that results from the lack of erythropoetin. In a study by Salmonson et al, six healthy volunteers were used to demonstrate that both IV and subcutaneous administration of erythropoetin have similar effects in the treatment of anemia due to chronic renal failure. The six volunteers were each given a 50 U/kg intravenous dose of Amgen. The average weight of the six volunteers was 79 kg. Blood samples were drawn at various times and the data obtained is summarized below: Amgen PROBLEM TABLE 4 - 3. mU Serum concentration, -------- - mL Time (hours) 2 700 4 600 6 400 8 300 12 150 24 40 From the data presented in the preceding table, determine the following: Find the elimination rate constant, k . 1. Find the half life, t ½ . 2. Find MRT . 3. Find ( C p )0 . 4. Find the Area Under the Curve, AUC . 5. Find the area under the first moment curve, AUMC . 6. Find the volume of distribution, V d 7. Find the clearance, Cl . 8. 4-13 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
14. 14. I.V. Bolus Dosing (Problem 4 - 3) Amgen: 103 CONCENTRATION (MU/ML) 102 Con (mU/mL) 101 0 5 10 15 20 25 TIME (HR) –1 k = 0.134hr 1. t½ = 5.2hr . 2. MRT = 7.46hr . 3. ( C p )0 = 900mU ⁄ mL . 4. AUC = 6945mU ⁄ mL ⋅ hr . 5. 2 AUMC = 49600 mU ⁄ mL ⋅ hr . 6. Vd = 4.44L 7. Cl = 0.6L ⁄ hr . 8. 4-14 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
15. 15. I.V. Bolus Dosing Atrial Naturetic Peptide (ANP) (Problem 4 - 4) Problem Submitted By: Maya Lyte AHFS 12:34.56 Antivirals Problem Reviewed By: Vicki Long GPI: 1234567890 Antivirals Brier and Harding, quot;Pharmacokinetics and Pharmacodynamics of Atrial Naturetic Peptide after Bolus and Infusion Administra- tion in the Isolated Perfused Rat Kidneyquot;, The Journal of Pharmacology and Experimental Therapeutics (1989), p 372 - 377. A study by Brier and Harding a dose of 45 ng was given by IV bolus to rats. Samples of blood were taken at various intervals throughout the length of the study and the following data was obtained: Atrial Naturetic Peptide (ANP) PROBLEM TABLE 4 - 4. pg Serum concentration, ------- - mL Time (minutes) 3 380 10 280 20 170 30 130 40 100 50 70 60 50 From the data presented in the preceding table, determine the following: Find the elimination rate constant, k . 1. Find the half life, t ½ . 2. Find MRT . 3. Find ( C p )0 . 4. Find the Area Under the Curve, AUC . 5. Find the area under the first moment curve, AUMC . 6. Find the volume of distribution, V d 7. Find the clearance, Cl . 8. 4-15 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
16. 16. I.V. Bolus Dosing (Problem 4 - 4) Atrial Naturetic Peptide (ANP): 103 Con CONCENTRATION (PG/ML) 102 (pg/mL) 101 0 10 20 30 40 50 60 Time (min) –1 k = 0.0345min 1. t½ = 20.09min . 2. MRT = 28.95min . 3. ( C p )0 = 386.6pg ⁄ mL . 4. AUC = 11206.4pg ⁄ mL ⋅ min . 5. 2 AUMC = 324425.4pg ⁄ mL ⋅ min . 6. Vd = 116.4mL 7. Cl = 4.02mL ⁄ min . 8. 4-16 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
17. 17. I.V. Bolus Dosing Aztreonam (Problem 4 - 5) Problem Submitted By: Maya Lyte AHFS 12:34.56 Antivirals Problem Reviewed By: Vicki Long GPI: 1234567890 Antivirals Cuzzolim et al., quot;Pharmacokinetics and Renal Tolerance of Aztreonam in Premature Infantsquot;, Antimicrobial Agents and Chemo- therapy (Sept. 1991), p. 1726 - 1928. Aztreonam is a monolactam structure which is active against aerobic, gram-negative bacilli. The pharmacokinetic parameters of Aztreonam were established in a study presented in by Cuzzolim et al in which Aztreonam (100 mg/ kg) was administered intravenously to 30 premature infants over 3 minutes every 12 hours. The group of neonates had an average weight of 1639.6g. The following set of data was obtained: Aztreonam PROBLEM TABLE 4 - 5. µg Serum concentration, ------- - mL Time (minutes) 1 40.50 2 34.99 3 29.99 4 23.88 5 22.20 6 19.44 7 16.55 8 14.99 From the data presented in the preceding table, determine the following: Find the elimination rate constant, k . 1. Find the half life, t ½ . 2. Find MRT . 3. Find ( C p )0 . 4. Find the Area Under the Curve, AUC . 5. Find the area under the first moment curve, AUMC . 6. Find the volume of distribution, V d 7. Find the clearance, Cl . 8. 4-17 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
18. 18. I.V. Bolus Dosing (Problem 4 - 5) Aztreonam: 10 2 CONCENTRATION (UG/ML) Con (ug/mL) 10 1 0 2 4 6 8 TIME (MIN) –1 k = 0.144min 1. t½ = 4.81min . 2. MRT = 6.94min . 3. ( C p )0 = 45.75ug ⁄ mL . 4. AUC = 317.7ug ⁄ mL ⋅ min . 5. 2 AUMC = 2204.8ug ⁄ mL ⋅ min . 6. Vd = 3.58L 7. Cl = 0.516L ⁄ min . 8. 4-18 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
19. 19. I.V. Bolus Dosing Recombinant Bovine Placental Lactogen (Problem 4 - 6) Problem Submitted By: Maya Lyte AHFS 12:34.56 Antivirals Problem Reviewed By: Vicki Long GPI: 1234567890 Antivirals Byatt, et. al., quot;Serum half-life and in-vivo actions of recombinant bovine placental lactogen in the dairy cowquot;, Journal of Endocri- nology (1992), p. 185 - 193. Bovine placental lactogen (bPL) is a hormone similar to growth hormone and prolactin. It binds to both prolactin and growth hormone receptors in the rabbit and stimulates lactogenesis in the rabbit. In a study by Byatt, et. al., four cows (2 pregnant and 2 nonpregnant) were given IV bolus injections of 4 mg and the following data was obtained: Recombinant Bovine Placental Lactogen PROBLEM TABLE 4 - 6. µg Serum concentration ------ L Time (minutes) 3.8 117 6.8 72 12.0 43 16.0 27 20.0 18 From the data presented in the preceding table, determine the following: Find the elimination rate constant, k . 1. Find the half life, t ½ . 2. Find MRT . 3. Find ( C p )0 . 4. Find the Area Under the Curve, AUC . 5. Find the area under the first moment curve, AUMC . 6. Find the volume of distribution, V d 7. Find the clearance, Cl . 8. 4-19 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
20. 20. I.V. Bolus Dosing (Problem 4 - 6) Recombinant Bovine Placental Lactogen: 103 CONCENTRATION (MIC/L) 102 Con (ug/L) 101 0 5 10 15 20 Time (min) –1 k = 0.113min 1. t½ = 6.13min . 2. MRT = 8.85min . 3. ( C p )0 = 167.8ug ⁄ L . 4. AUC = 1484.9ug ⁄ L ⋅ min . 5. 2 AUMC = 13141.1ug ⁄ L ⋅ min . 6. Vd = 23.84L 7. Cl = 2.69L ⁄ min . 8. 4-20 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
21. 21. I.V. Bolus Dosing Caffeine (Problem 4 - 7) Problem Submitted By: Maya Lyte AHFS 12:34.56 Antivirals Problem Reviewed By: Vicki Long GPI: 1234567890 Antivirals Dorrbecker et. al., quot;Caffeine and Paraxanthine Pharmacokinetics in the Rabbit: Concentration and Product Inhibition Effects.quot;, Journal of Pharmacokinetics and Biopharmaceutics (1987), p.117 - 131. This study examines the pharmacokinetics of caffeine in the rabbit. In this study type I New Zealand White rabbits were given an 8 mg intravenous dose of caffeine. Blood samples were taken and the following data was obtained: Caffeine PROBLEM TABLE 4 - 7. µg Serum concentration ------- - mL Time (minutes) 12 3.75 40 2.80 65 2.12 90 1.55 125 1.23 173 0.72 243 0.37 From the data presented in the preceding table, determine the following: Find the elimination rate constant, k . 1. Find the half life, t ½ . 2. Find MRT . 3. Find ( C p )0 . 4. Find the Area Under the Curve, AUC . 5. Find the area under the first moment curve, AUMC . 6. Find the volume of distribution, V d 7. Find the clearance, Cl . 8. 4-21 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
22. 22. I.V. Bolus Dosing (Problem 4 - 7) Caffeine: CONCENTRATION (MIC/ML) Caffeine 101 100 10-1 Con (ug/L) 0 50 100 150 200 250 Time (min) –1 k = 0.00997min 1. t½ = 69.51min . 2. MRT = 100.3min . 3. ( C p )0 = 4.105ug ⁄ mL . 4. AUC = 411.7ug ⁄ mL ⋅ min . 5. 2 AUMC = 41293.5ug ⁄ mL ⋅ min . 6. Vd = 1.95L 7. Cl = 19.44mL ⁄ min . 8. 4-22 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
23. 23. I.V. Bolus Dosing Ceftazidime (Problem 4 - 8) Problem Submitted By: Maya Lyte AHFS 12:34.56 Antivirals Problem Reviewed By: Vicki Long GPI: 1234567890 Antivirals Demotes-Mainard, et. al., quot;Pharmacokinetics of Intravenous and Intraperitoneal Ceftazidime in Chronic Ambulatory Peritoneal Dyialysisquot;, Journal of Clinical Pharmacology (1993), p. 475 - 479. Ceftazidime is a third generation cephalosporin which is administered parenterally. In this study, eight patients with chronic renal failure were each given 1 g of ceftazidime intravenously. Both blood samples were taken the data obtained from the study is summarized in the following table: Ceftazidime PROBLEM TABLE 4 - 8. mg Serum concentration ------ - L Time (hours) 1 50 2 45 4 38 24 21 36 14 48 11 60 8 72 4 From the data presented in the preceding table, determine the following: Find the elimination rate constant, k . 1. Find the half life, t ½ . 2. Find MRT . 3. Find ( C p )0 . 4. Find the Area Under the Curve, AUC . 5. Find the area under the first moment curve, AUMC . 6. Find the volume of distribution, V d 7. Find the clearance, Cl . 8. 4-23 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
24. 24. I.V. Bolus Dosing (Problem 4 - 8) Ceftazidime: 102 CONCENTRATION (MG/L) 101 Con (mg/L) 100 0 20 40 60 80 Time (hours) –1 k = 0.0324hr 1. t½ = 21.39hr . 2. MRT = 30.86hr . 3. ( C p )0 = 47.57mg ⁄ L . 4. AUC = 1468.2mg ⁄ L ⋅ hr . 5. 2 AUMC = 45308.6mg ⁄ L ⋅ hr . 6. Vd = 21.02L 7. Cl = 0.681L ⁄ hr . 8. 4-24 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
25. 25. I.V. Bolus Dosing Ciprofloxacin (Problem 4 - 9) Problem Submitted By: Maya Lyte AHFS 12:34.56 Antivirals Problem Reviewed By: Vicki Long GPI: 1234567890 Antivirals Lettieri, et. al., quot;Pharmacokinetic Profiles of Ciprofloxacin after Single Intravenous and Oral Dosesquot;, Antimicrobial Agents and Chemotherapy (May 1992), p. 993 -996. Ciprofloxacin is a fluoroquinolone antibiotic which is used in the treatment of infections of the urinary tract, lower res- piratory tract, skin, bone, and joint. In this study, twelve healthy, male volunteers were each given 300 mg intravenous doses of Ciprofloxacin. Blood and urine samples were collected at various times throughout the day and the following data was collected: Ciprofloxacin PROBLEM TABLE 4 - 9. mg Serum concentration ------ - L Time (hours) 2 1.20 3 0.85 4 0.70 6 0.50 8 0.35 10 0.25 From the data presented in the preceding table, determine the following: Find the elimination rate constant, k . 1. Find the half life, t ½ . 2. Find MRT . 3. Find ( C p )0 . 4. Find the Area Under the Curve, AUC . 5. Find the area under the first moment curve, AUMC . 6. Find the volume of distribution, V d 7. Find the clearance, Cl . 8. 4-25 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
26. 26. I.V. Bolus Dosing (Problem 4 - 9) Ciprofloxacin: 101 CONCENTRATION (MG/L) 100 Con (mg/L) 10-1 0 2 4 6 8 10 Time (hours) –1 k = 0.1875hr 1. t½ = 3.7hr . 2. MRT = 5.33hr . 3. ( C p )0 = 1.57mg ⁄ L . 4. AUC = 8.395mg ⁄ L ⋅ hr . 5. 2 AUMC = 44.74mg ⁄ L ⋅ hr . 6. Vd = 190.6L 7. Cl = 35.74L ⁄ hr . 8. 4-26 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
27. 27. I.V. Bolus Dosing The effect of Probenecid on Diprophylline (DPP) (Problem 4 - 10) Problem Submitted By: Maya Lyte AHFS 12:34.56 Antivirals Problem Reviewed By: Vicki Long GPI: 1234567890 Antivirals Nadai et al, quot;Pharmacokinetics and the Effect of Probenecid on the Renal Excretion Mechanism of Diprophyllinequot;, Journal of Pharmaceutical Sciences (Oct 1992), p. 1024 - 1027. Diprophylline is used as a bronchodilator. A study by Nadai et al was designed to determine whether or not coadmin- istration of Diprophylline with Probenecid affected the pharmacokinetic parameters of Diprophylline. In this study, male rats (average weight: 300 g) were given 60 mg/kg of Diprophylline intravenously and a 3 mg/kg loading dose of Probenecid followed by a continuous infusion of 0.217 mg/min/kg of Probenecid. The following set of data was obtained for Diprophylline (DPP): The effect of Probenecid on Diprophylline (DPP) PROBLEM TABLE 4 - 10. µg Serum concentration ------- - mL Time (minutes) 16 40.00 31 27.00 60 13.00 91 6.50 122 3.50 From the data presented in the preceding table, determine the following: Find the elimination rate constant, k . 1. Find the half life, t ½ . 2. Find MRT . 3. Find ( C p )0 . 4. Find the Area Under the Curve, AUC . 5. Find the area under the first moment curve, AUMC . 6. Find the volume of distribution, V d 7. Find the clearance, Cl . 8. 4-27 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
28. 28. I.V. Bolus Dosing (Problem 4 - 10) The effect of probenecid on diprophylline (DPP): 102 CONCENTRATION (MIC/ML) 101 Con (ug/mL) 100 0 20 40 60 80 100 Time (min) –1 k = 0.023min 1. t½ = 30.13min . 2. MRT = 43.48min . 3. ( C p )0 = 55.13ug ⁄ mL . 4. AUC = 2396.96ug ⁄ mL ⋅ min . 5. 2 AUMC = 104219.8ug ⁄ mL ⋅ min . 6. Vd = 326.5mL 7. Cl = 7.5mL ⁄ min . 8. 4-28 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
29. 29. I.V. Bolus Dosing Epoetin (Problem 4 - 11) Problem Submitted By: Maya Lyte AHFS 12:34.56 Antivirals Problem Reviewed By: Vicki Long GPI: 1234567890 Antivirals MacDougall et. al., quot;Clinical Pharmacokinetics of Epoetin (Recombinant Human Erythropoetinquot;, Clinical Pharmacokinetics (1991), p 99 - 110. Epoetin is recombinant human erythropoetin. Erythropoetin is a hormone that is produced in the kidneys and used in the production of red blood cells. The kidneys of patients who have end-stage renal failure cannot produce erythropo- etin; therefore, Epoetin is used in these patients to treat the anemia that results from the lack of erythropoetin. Epoetin has also been used in the treatment of anemias resulting from AIDS. malignant disease, prematurity, rheumatoid arthri- tis, sickle-cell anemia, and myelosplastic syndrome. In a study by Macdougall et al, eight patients who were on perito- neal dialysis (CAPD) were given an IV bolus dose of 120 U/kg which decayed monoexponentially from a peak of 3959 U/L to 558 U/L at 24 hours. The following data was obtained: Epoetin PROBLEM TABLE 4 - 11. U Serum concentration --- - L Time (hours) 0.0 4000 0.5 3800 1.0 3600 2.0 3300 3.0 3000 4.0 2550 5.0 2350 6.0 2150 7.0 1900 From the data presented in the preceding table and assuming that the patient weighs 65 kg, determine the following: Find the elimination rate constant, k . 1. Find the half life, t ½ . 2. Find MRT . 3. Find ( C p )0 . 4. Find the Area Under the Curve, AUC . 5. Find the area under the first moment curve, AUMC . 6. Find the volume of distribution, V d 7. Find the clearance, Cl . 8. 4-29 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
30. 30. I.V. Bolus Dosing (Problem 4 - 11) Epoetin: 104 CONCENTRATION (U/L) Con (U/L) 103 0 1 2 3 4 5 6 7 Time (hours) –1 k = 0.107 hr 1. t½ = 6.5 hr . 2. MRT = 9.38 hr . 3. ( C p )0 = 4023 Units/L . 4. Units ⋅ hr AUC = 37775 ----------------------- . - 5. L 2 Units ⋅ hr - AUMC = 354697 -------------------------- . 6. L Vd = 1.9 L 7. L- Cl = 0.2065 ---- . 8. hr 4-30 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
31. 31. I.V. Bolus Dosing Famotidine (Problem 4 - 12) Problem Submitted By: Maya Lyte AHFS 12:34.56 Antivirals Problem Reviewed By: Vicki Long GPI: 1234567890 Antivirals Kraus, et. al., quot;Famotidine--Pharmacokinetic Properties and Suppression of Acid Secretion in Pediatric Patients Following Car- diac Surgeryquot;, Clinical Pharmacokinetics (1990), p 77 - 80. Famotidine is a histamine H2-receptor antagonist. The study by Kraus, et. al., focuses on the kinetics of famotidine in children. In the study, ten children with normal kidney function and a body weight ranging from 14 - 25 kg, were each given a single intravenous 0.3 mg/kg dose of famotidine. Blood and urine samples were taken providing the following data: Famotidine PROBLEM TABLE 4 - 12. µg Serum concentration ------ L Time (hours) 0.33 300 0.50 250 1.00 225 4.00 125 8.00 70 12.00 40 16.00 15 From the data presented in the preceding table, determine the following assuming that the patient weighs 17.2 kg: Find the elimination rate constant, k . 1. Find the half life, t ½ . 2. Find MRT . 3. Find ( C p )0 . 4. Find the Area Under the Curve, AUC . 5. Find the area under the first moment curve, AUMC . 6. Find the volume of distribution, V d 7. Find the clearance, Cl . 8. 4-31 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
32. 32. I.V. Bolus Dosing (Problem 4 - 12) Famotidine: 10 3 ConCONCENTRATION (MIC/L) 10 2 (ug/mL) 10 1 0 5 10 15 20 Time (hours) –1 k = 0.17 hr 1. t½ = 3.9 hr . 2. MRT = 5.7 hr . 3. µg ( C p )0 = 285 ------ . 4. L µg ⋅ hr AUC = 1600 ---------------- . - 5. L 2 µg ⋅ hr AUMC = 9000 ------------------ . 6. L Vd = 18 L 7. Cl = 3.2L . 8. 4-32 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
33. 33. I.V. Bolus Dosing Ganciclovir (Problem 4 - 13) Problem Submitted By: Maya Lyte AHFS 12:34.56 Antivirals Problem Reviewed By: Vicki Long GPI: 1234567890 Antivirals Trang, et. al., quot;Linear single-dose pharmacokinetics of ganciclovir in newborns with congenital cytomegalovirus infectionsquot;, Clin- ical Pharmacology and Therapeutics (1993), p. 15 - 21. Ganciclovir (mw: 255.23) is used against the human herpes viruses, cytomegalovirus retinitis, and cytomegalovirus infections of the gastrointestinal tract. In this study, twenty-seven newborns with cytomegalovirus disease were given 4 mg/kg of ganciclovir intravenously over one hour. Blood samples were taken and the data obtained is summarized in the following table: Ganciclovir PROBLEM TABLE 4 - 13. Time (hours) Serum concentration 1.50 4.50 2.00 4.00 3.00 3.06 4.00 2.40 6.00 1.45 8.00 0.87 From the data presented in the preceding table and assuming the patient weighs 3.6 kg, determine the following : Find the elimination rate constant, k . 1. Find the half life, t ½ . 2. Find MRT . 3. Find ( C p )0 . 4. Find the Area Under the Curve, AUC . 5. Find the area under the first moment curve, AUMC . 6. Find the volume of distribution, V d 7. Find the clearance, Cl . 8. 4-33 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
34. 34. I.V. Bolus Dosing (Problem 4 - 13) Ganciclovir: 10 CONCENTRATION (MICMOLE/L) 10 10 0 2 4 6 8 TIME (HR) –1 k = 0.288hr 1. t½ = 2.4hr . 2. MRT = 3.5hr . 3. µmole ( C p )0 = 23 --------------- . - 4. mL µmole ⋅ hr AUC = 80 ------------------------- . - 5. mL 2 µmole ⋅ hr - AUMC = 280 ---------------------------- . 6. mL mg 1000µg 4 ------ ⋅ 3.6kg ⋅ ------------------ - - Dose ------------------------------------------------------------ kg mg - Vd = ------------ = - = 2.45L 7. µmole µg - Cp 0 --------------- ⋅ 255.23 --------------- - 23 µmole L L- Cl = 0.7 ---- . 8. hr 4-34 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
35. 35. I.V. Bolus Dosing Imipenem (Problem 4 - 14) Problem Submitted By: Maya Lyte AHFS 12:34.56 Antivirals Problem Reviewed By: Vicki Long GPI: 1234567890 Antivirals Heikkila, Renkonen, and Erkkola, quot;Pharmacokinetics and Transplacental Passage of Imipenem During Pregnancyquot;, Antimicrobial Agents and Chemotherapy (Dec. 1992), p 2652 - 2655. Imipenem is a beta-lactam antibiotic which is used in combination with cilastin and is active against a broad spectrum of bacteria. The pharmacokinetics of Imipenem in pregnant women is established in this study. Twenty women (six of which were non-pregnant controls) were given a single intravenous dose of 500 mg of imipenem-cilastin (1:1). Blood samples were taken at various intervals and the data obtained is summarized in the following table: Imipenem PROBLEM TABLE 4 - 14. mg Serum concentration ------ - L Time (minutes) 10 27.00 15 23.50 30 15.50 45 9.50 60 6.50 From the data presented in the preceding table, determine the following: Find the elimination rate constant, k . 1. Find the half life, t ½ . 2. Find MRT . 3. Find ( C p )0 . 4. Find the Area Under the Curve, AUC . 5. Find the area under the first moment curve, AUMC . 6. Find the volume of distribution, V d 7. Find the clearance, Cl . 8. 4-35 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf
36. 36. I.V. Bolus Dosing (Problem 4 - 14) Imipenem: 2 10 CONCENTRATION (MG/L) 1 10 0 10 0 10 20 30 40 50 60 TIME (MIN) –1 k = 0.029 min 1. t½ = 24 min . 2. MRT = 34.5 min . 3. mg ( C p )0 = 36.2 ------ . - 4. L mg ⋅ min AUC = 1250 --------------------- . 5. L 2 mg ⋅ min - AUMC = 43125 ----------------------- . 6. L Dose 500mg Vd = ------------ = ------------------ = 13.8L - 7. Cp 0 mg 36.2 ------ - L L- Cl = 0.4 -------- . 8. min 4-36 Basic Pharmacokinetics REV. 00.1.27 Copyright © 1996-2000 Michael C. Makoid All Rights Reserved http://pharmacy.creighton.edu/pha443/pdf