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# 1-Compartment Oral Dosing

1-Compartment Oral Dosing. 400 mg of moxifloxacin is administered orally to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that about 20% of a moxifloxacin dose is excreted in the

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## 1-Compartment Oral Dosing

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1. 1-Compartment Oral Dosing 400 mg of moxifloxacin is administered orally to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that about 20% of a moxifloxacin dose is excreted in the urine unchanged. A further 20% is excreted unchanged in the bile and the rest is metabolised to either M1 (sulpho) or M2 (acyl-glucuronide) • Questions to Consider • What model & equation best describes profile? • Calculate Cmax, Tmax, AUC, K, T½, V &Cl • Write an equation that will calculate • concentrations at anytime after the 1st dose. • Calculate the absorption rate – ka. • Comparison of Observed and Estimated [ ].

2. 1-Compartment Oral Dosing 400 mg of moxifloxacin is administered orally to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that about 20% of a moxifloxacin dose is excreted in the urine unchanged. A further 20% is excreted unchanged in the bile and the rest is metabolised to either M1 (sulpho) or M2 (acyl-glucuronide) Exam Questions and Problem Sets will ask practical, application questions Recommend that you take this data and attempt to reproduce the calculations on your own.

3. Graph Patient Data Using semi-log paper, or Excel graph the data following oral administration of 400 mg of moxifloxacin 10 6 3 1 0.6 0.4 0.2 0.1 0 4 8 10 14 18 22 24

4. Graph Patient Data What model best describes this profile? Terminal elimination phase is log-linear… 1 Compartment Model with first order absorption (ka) and first order elimination (K)

5. Graph Patient Data What model best describes this profile? It is known that about 20% of a moxifloxacin dose is excreted in the urine unchanged. A further 20% is excreted unchanged in the bile and the rest is metabolised to either M1 (sulpho) or M2 (acyl-glucuronide)

6. Graph Patient Data What model best describes this profile? It is known that about 20% of a moxifloxacin dose is excreted in the urine unchanged. A further 20% is excreted unchanged in the bile and the rest is metabolised to either M1 (sulpho) or M2 (acyl-glucuronide) kH = kM1 + kM2 KNR = 20% excreted into bile as unchanged drug.

7. Graph Patient Data What model best describes this profile? It is known that about 20% of a moxifloxacin dose is excreted in the urine unchanged. A further 20% is excreted unchanged in the bile and the rest is metabolised to either M1 (sulpho) or M2 (acyl-glucuronide) K = ke + kH + kNR

8. 1-Compartment Oral Dosing 400 mg of moxifloxacin is administered orally to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that about 20% of a moxifloxacin dose is excreted in the urine unchanged. A further 20% is excreted unchanged in the bile and the rest is metabolised to either M1 (sulpho) or M2 (acyl-glucuronide) • Questions to Consider • What model & equation best describes profile? • Calculate Cmax, Tmax, AUC, K, T½, V &Cl • Write an equation that will calculate • concentrations at anytime after the 1st dose. • Calculate the absorption rate – ka. • Comparison of Observed and Estimated [ ]. What do you calculate first? Cmax, Tmax, AUC, K, T½, V or Cl

9. 1-Compartment Oral Dosing 400 mg of moxifloxacin is administered orally to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that about 20% of a moxifloxacin dose is excreted in the urine unchanged. A further 20% is excreted unchanged in the bile and the rest is metabolised to either M1 (sulpho) or M2 (acyl-glucuronide) • Questions to Consider • What model & equation best describes profile? • Calculate Cmax, Tmax, AUC, K, T½, V &Cl • Write an equation that will calculate • concentrations at anytime after the 1st dose. • Calculate the absorption rate – ka. • Comparison of Observed and Estimated [ ]. What do you calculate first? Cmax, Tmax, ? Does the maximum concentration actually occur at 2 hours (Tmax)? Cmax and Tmax are sampling time (data) dependant.

10. 1-Compartment Oral Dosing Does the maximum concentration actually occur at 2 hours? Cmax and Tmax are sampling time (data) dependant and observed. Could the true maximum concentration occur at 2.5 hr??

11. 1-Compartment Oral Dosing 400 mg of moxifloxacin is administered orally to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that about 20% of a moxifloxacin dose is excreted in the urine unchanged. A further 20% is excreted unchanged in the bile and the rest is metabolised to either M1 (sulpho) or M2 (acyl-glucuronide) • Questions to Consider • What model & equation best describes profile? • Calculate Cmax, Tmax, AUC, K, T½, V &Cl • Write an equation that will calculate • concentrations at anytime after the 1st dose. • Calculate the absorption rate – ka. • Comparison of Observed and Estimated [ ]. What do you calculate first? AUC, K and T½ can be easily calculated from available data. K from slope of log [ ] vs. time or Excel. AUC, trapezoidal rule.

12. 1-Compartment Oral Dosing Since the concentrations between 4 and 24 hr appear log-linear, ANY pair of points in the terminal phase can be used to calculate K and half-life, AFTER CONVERSION to LOG. In Excel this would likely result in K being calculated by log-linear regression (SLOPE) of all points (4, 8, 12 and 24 hr).

13. 1-Compartment Oral Dosing Using the concentrations at 4 and 24 hours calculate K (x1 = 4 hr and x2 = 24 hr) (y1 = log (C4) = 0.248) (y2 = log (C24) = -0.357) Slope = (y2 – y1) / (x2 – x1) = (-0.357 – 0.248)/(24-4) = (- 0.605) / (20) = -0.0302 - K = slope x 2.303 = - 0.0302 x 2.303 K = 0.06961 hr-1 T½ = 0.693 / K = 0.693 / 0.06961 = 9.955 hours

14. 1-Compartment Oral Dosing Slope = (y2 – y1) / (x2 – x1) = (-0.357 – 0.248)/(24-4) = (- 0.605) / (20) = -0.0302 - K = slope x 2.303 = - 0.0302 x 2.303 K = 0.06961 hr-1 T½ = 0.693 / K = 0.693 / 0.06961 = 9.955 hours

15. 1-Compartment Oral Dosing Selection of the points from the terminal phase for calculation of K. Accurate calculation of K (T½) and all other parameters which depend on K (AUC, Cl, etc) demand that the points used to calculate K be found in the terminal phase after absorption is complete. When is absorption complete?

16. 1-Compartment Oral Dosing If absorption occurs as a first order process (constant percentage per unit time), When does absorption stop? If we deal with ka as we would K, Assume ka = 0.693, then T½ka = 1 hour. This means that following a 400 mg dose, half of the dose (200 mg) will be absorbed in the first hour And half of the remaining dose (100 mg) in the second.

17. 1-Compartment Oral Dosing If absorption occurs as a first order process (constant percentage per unit time), When does absorption stop? Amount absorbed during each hour following the dose can be estimated as: 6.25 mg/hr Time Amount (hr) (mg) 1 200 2 100 3 50 4 25 5 12.5 6 6.25 25 mg/hr 100 mg/hr Peak

18. 1-Compartment Oral Dosing Amount absorbed during each hour following the dose can be estimated as: Time Amount (hr) (mg) 1 200 2 100 3 50 4 25 5 12.5 6 6.25 Peak 6.25 mg/hr 25 mg/hr • so … when does absorption • stop for this formulation? • (i) At the Tmax – 2.6 hrs • (ii) Prior to the peak • (iii) ~ 1 hr after the peak • Technically – never • It depends 100 mg/hr

19. 1-Compartment Oral Dosing Selection of the points from the terminal phase for calculation of K. In Excel®, selection of points in the terminal phase can be completed with statistics. Evaluate the correlation coefficient (r) & the number of points. A change in r value signals the end of absorption, with confirmation by “visual inspection”.

20. 1-Compartment Oral Dosing Selection of the points from the terminal phase for calculation of K. Notice that as you select more points to be used in the calculation of K, the K value begins to shrink, the T½ begins to increase and the correlation coefficient (r) becomes smaller. As you use more points in the absorption phase Best choice? 4 points? or 5 points?

21. 1-Compartment Oral Dosing 5 points? r -0.9999 K 0.069 hr-1 T½ 10.04 hr

22. 1-Compartment Oral Dosing AUC trapezoid AUC (0-24hr) AUC (LP-) AUC (0-)

23. 1-Compartment Oral Dosing AUC Analysis following Oral Absorption At time zero, even immediately following ingestion of the dose, the plasma concentration is 0 mg/L. Back extrapolation to t=0 is not appropriate, and should not be done It will not aid in the calculation of volume.

24. 1-Compartment Oral Dosing AUC Analysis following Oral Absorption AUC(0-24hr) AUC should be calculated by trapezoidal rule between all concentrations. The sum of these partial areas will equal AUC 0-24hr or AUC 0-LP

25. 1-Compartment Oral Dosing AUC Analysis following Oral Absorption AUC(0-24hr) 26.623 mg*hr/L AUC from the last measured concentration should be calculated by the pharmacokinetic method ([ ]LP/K). = (0.44 mg/L) / 0.069 hr-1 = 6.377 mg*hr/L = AUC LP-

26. 1-Compartment Oral Dosing AUC Analysis following Oral Absorption AUC(0-24hr) 26.623 mg*hr/L AUC(24hr-) 6.377 mg*hr/L Total AUC (0-) is the sum = 26.623 + 6.377 mg*hr/L = 33.000 mg*hr/L

27. 1-Compartment Oral Dosing AUC trapezoid AUC (0-24hr) AUC (LP-) AUC (0-)

28. 1-Compartment Oral Dosing AUC trapezoid AUC (0-24hr) AUC (LP-) AUC (0-)

29. 1-Compartment Oral Dosing 400 mg of moxifloxacin is administered orally to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that about 20% of a moxifloxacin dose is excreted in the urine unchanged. A further 20% is excreted unchanged in the bile and the rest is metabolised to either M1 (sulpho) or M2 (acyl-glucuronide) Time Plasma Conc (hr) (mg/L) 0.0 0.00 0.25 0.88 0.5 1.40 1 1.86 1.5 1.98 2 1.99 4 1.77 8 1.34 12 1.02 24 0.44 • Questions to Consider • What model & equation best describes profile? • Calculate Cmax, Tmax, AUC, K, T½, V &Cl • Write an equation that will calculate • concentrations at anytime after the 1st dose. • Calculate the absorption rate – ka. • Comparison of Observed and Estimated [ ]. Now calculate Clearance. Use the formula: ClT = Dose / AUC Does this formula make any assumptions?

30. 1-Compartment Oral Dosing 400 mg of moxifloxacin is administered orally to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that about 20% of a moxifloxacin dose is excreted in the urine unchanged. A further 20% is excreted unchanged in the bile and the rest is metabolised to either M1 (sulpho) or M2 (acyl-glucuronide) Time Plasma Conc (hr) (mg/L) 0.0 0.00 0.25 0.88 0.5 1.40 1 1.86 1.5 1.98 2 1.99 4 1.77 8 1.34 12 1.02 24 0.44 Clearance Cl = Dose / AUC = 400 mg / 33.00 mg*hr/L = 12.12 L/hr

31. 1-Compartment Oral Dosing 400 mg of moxifloxacin is administered orally to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that about 20% of a moxifloxacin dose is excreted in the urine unchanged. A further 20% is excreted unchanged in the bile and the rest is metabolised to either M1 (sulpho) or M2 (acyl-glucuronide) Time Plasma Conc (hr) (mg/L) 0.0 0.00 0.25 0.88 0.5 1.40 1 1.86 1.5 1.98 2 1.99 4 1.77 8 1.34 12 1.02 24 0.44 Clearance Cl = Dose / AUC = K * V Assumption? that the entire dose of 400 mg was absorbed. If not what happens to V?

32. 1-Compartment Oral Dosing 400 mg of moxifloxacin is administered orally to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that about 20% of a moxifloxacin dose is excreted in the urine unchanged. A further 20% is excreted unchanged in the bile and the rest is metabolised to either M1 (sulpho) or M2 (acyl-glucuronide) Time Plasma Conc (hr) (mg/L) 0.0 0.00 0.25 0.88 0.5 1.40 1 1.86 1.5 1.98 2 1.99 4 1.77 8 1.34 12 1.02 24 0.44 Clearance Cl = Dose / AUC = K * V Clearance Following oral absorption Cl = F x Dose / AUC where F is the fraction absorbed. So…how much was absorbed?

33. Calculation of Clearance Clearance Cl = Dose / AUC = 400 /33.00 = 12.12 L/hr Agrees with Estimate Using Excel® =12.12 L/hr

34. 1-Compartment Oral Dosing 400 mg of moxifloxacin is administered orally to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that about 20% of a moxifloxacin dose is excreted in the urine unchanged. A further 20% is excreted unchanged in the bile and the rest is metabolised to either M1 (sulpho) or M2 (acyl-glucuronide) Time Plasma Conc (hr) (mg/L) 0.0 0.00 0.25 0.88 0.5 1.40 1 1.86 1.5 1.98 2 1.99 4 1.77 8 1.34 12 1.02 24 0.44 • Questions to Consider • What model & equation best describes profile? • Calculate Cmax, Tmax, AUC, K, T½, V &Cl • Write an equation that will calculate • concentrations at anytime after the 1st dose. • Calculate the absorption rate – ka. • Comparison of Observed and Estimated [ ]. Now calculate Volume. This can be done through the use of two equations: Cl = Dose / AUC and Cl = K x V This allows: K x V = Dose / AUC and so Volume = Dose /(K x AUC) but again F? Volume = F x Dose /(K x AUC)

35. Calculation of Volume Volume Volume = F x Dose /(K x AUC) But because we do not know F Volume/F = Dose /(K x AUC) V/F = 175.69 L Notes: A volume of 175 L is calculated when F = 1. If F = 0.9 (90%) V = 158.12 If F = 0.8 (80%) V = 140.55 If F = 0.7 (70%) V = 122.98 If F = 0.6 …. … but what is F and how would this be determined? Volume Volume = F x Dose /(K x AUC) But because we do not know F we will assume a value of 1 (completely absorbed). Volume/F = Dose /(K x AUC) =400 / (0.069 x 33.00) V/F = 175.69 L

36. Calculation of Volume Volume Volume = F x Dose /(K x AUC) But because we do not know F Volume/F = Dose /(K x AUC) V/F = 175.69 L Notes: A volume of 175 L is calculated when F = 1. If F = 0.9 (90%) V = 158.12 If F = 0.8 (80%) V = 140.55 If F = 0.7 (70%) V = 122.98 If F = 0.6 …. … but what is F and how would this be determined?

37. Calculation of Volume Volume Volume = F x Dose /(K x AUC) or because we do not know F Volume/F = Dose /(K x AUC) V/F = 175.69 L Notes: A volume of 175 L is calculated when F = 1. If F = 0.9 (90%) V = 158.12 Monograph (CPS) and literature indicates that the fraction absorbed is approximately 90%. Another way???

38. Calculation of Volume Volume Volume = F x Dose /(K x AUC) or because we do not know F Volume/F = Dose /(K x AUC) V/F = 175.69 L Notes: A volume of 175 L is close to that determined by back extrapolation and calculation of a concentration of 2.3 mg/L at time zero. This appears to have worked because (i) absorption was relatively quick and (ii) elimination relatively slow (T½=10 hr).

39. 1-Compartment Oral Dosing 400 mg of moxifloxacin is administered orally to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that about 20% of a moxifloxacin dose is excreted in the urine unchanged. A further 20% is excreted unchanged in the bile and the rest is metabolised to either M1 (sulpho) or M2 (acyl-glucuronide) Time Plasma Conc (hr) (mg/L) 0.0 0.00 0.25 0.88 0.5 1.40 1 1.86 1.5 1.98 2 1.99 4 1.77 8 1.34 12 1.02 24 0.44 • Questions to Consider • What model & equation best describes profile? • Calculate Cmax, Tmax, AUC, K, T½, V &Cl • Write an equation that will calculate • concentrations at anytime after the 1st dose. • Calculate the absorption rate – ka. • Comparison of Observed and Estimated [ ].

40. Concentration-time Equation Equation must include F and ka in addition to parameters found in the IV equation. Profile for a 1 compartment model with first order input and first order elimination.

41. Concentration-time Equation How do you calculate ka?

42. 1-Compartment Oral Dosing 400 mg of moxifloxacin is administered orally to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that about 20% of a moxifloxacin dose is excreted in the urine unchanged. A further 20% is excreted unchanged in the bile and the rest is metabolised to either M1 (sulpho) or M2 (acyl-glucuronide) Time Plasma Conc (hr) (mg/L) 0.0 0.00 0.25 0.88 0.5 1.40 1 1.86 1.5 1.98 2 1.99 4 1.77 8 1.34 12 1.02 24 0.44 • Questions to Consider • What model & equation best describes profile? • Calculate Cmax, Tmax, AUC, K, T½, V &Cl • Write an equation that will calculate • concentrations at anytime after the 1st dose. • Calculate the absorption rate – ka. • Comparison of Observed and Estimated [ ].

43. Determining the Absorption Rate How can we find the rate constant associated with absorption - ka from the rising concentration time data?

44. Determining the Absorption Rate Absorption phase generally associated with absorption of the drug, but what is going on here? Absorption? Elimination? Terminal phase generally associated with elimination of the drug. But what is going on here? Absorption? Elimination?

45. Determining the Absorption Rate Absorption & Elimination How can we look only at absorption? Terminal phase generally associated with elimination of the drug.

46. Determining the Absorption Rate Absorption & Elimination How can we look only at absorption? We need to be able to subtract the elimination rate, to strip away one rate constant to reveal only the other. This is called the method of residuals …sometimes called feathering the curve or curve stripping.

47. Determining the Absorption Rate Since the terminal phase is <pure>, associated with only 1 rate constant we can back extrapolate the terminal phase to find extrapolated concentrations at each of the times where concentrations were observed during absorption. Same method used with IV 2C models.

48. Determining the Absorption Rate Estimation of Absorption Rate Using method of residuals 1. Back extrapolate terminal phase using best r-value to guide selection. 2. Determine difference between obs. [ ] & back extrapolated [ ]. 3. Plot differences 4. Slope estimates ka.

49. Determining the Absorption Rate Estimation of Absorption Rate Using method of residuals 1. Back extrapolate terminal phase using best r-value to guide selection. Recall we had a K value of 0.069 hr-1 based on the last 5 points or 0.0696 hr-1 using the 4 and 24 hr concentrations. Using the selected K value and a point that is in the terminal phase (8, 12 or 24 hr), calculate the concentrations at 0, 0.25, 0.5, 1.0, 1.5 and 2 hr.

50. Determining the Absorption Rate Estimation of Absorption Rate Using method of residuals 1. Back extrapolate terminal phase using best r-value to guide selection. Recall we had a K value of 0.069 hr-1 based on the last 5 points or 0.0696 hr-1 using the 4 and 24 hr concentrations. Using the selected K value and a point that is in the terminal phase (8, 12 or 24 hr), calculate the concentrations at 0, 0.25, 0.5, 1.0, 1.5 and 2 hr. Completed using the K value of 0.069 hr-1 determined from the last 5 points generate concentrations at every time point.

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