Multiple ORAL Dosing Objectives

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Multiple ORAL Dosing Objectives Calculate Concentrations following multiple doses Evaluate methods of predicting conc.at SS following oral doses Evaluate changes in Tmax as SS approaches Evaluate Sustain Release formulations

Multiple Dosing Summary … so far – IV dosing We have seen that: 1. [ ] following single doses can be Summed to create MD profile (Additivity of [ ]) 2. At Steady State In (Dose) = Out (elimination) 3. MAF, predicts the degree of accumulation (K and τ) 4. (1/1-e(-Kτ)), converts a single dose equation to multiple dose 5. (1-e(-nKτ))/(1-e(-Kτ)) allows Calculation of [ ] at any time 6. Time to Reach steady state determine by K (Cl/V) -3.3 T½ AUC(0-τ) over a dosing interval @ SS = AUC(0-) 1st dose. Just as AUC(0-) 1st dose can be use to estimate bioequiavalence so can AUC(0-τ), as long as you are at steady state (min3 T½ dosing) . 9. Using MAF we can design an IV dosing regimen that will achieve desired peak and trough concentrations at SS. At Steady state all other parameters remain unchanged (ClR,ClH, proportion metabolised.)

Multiple ORAL Dosing – through addition of single dose concentrations Time Conc (hr) (mg/L) 0 0.00 0.5 61.6 1 81.7 1.5 86.6 2 86.0 4 73.9 6 62.1 8 52.3 16 26.1 24 13.1 32 6.5 40 1.6 Dose=1000 mg, V=10L ka=2hr-1; K=0.0863hr-1; T½=8hr; F=1

Multiple ORAL Dosing – through addition of single dose concentrations SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 + 0.0 = 52.3 16 26.1 26.1 + 52.3 = 78.4

Multiple ORAL Dosing – through addition of single dose concentrations SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 + 0.0 = 52.3 16 26.1 26.1 + 52.3 = 78.4 24 13.1 13.1 +26.1 + 52.3 = 91.5

Multiple ORAL Dosing – through addition of single dose concentrations SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 + 0.0 = 52.3 16 26.1 26.1 + 52.3 = 78.4 24 13.1 13.1 +26.1 + 52.3 = 91.5 32 6.5 6.5 + 13.1 + 26.1 + 52.3 = 98.0

Multiple ORAL Dosing – through addition of single dose concentrations SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 + 0.0 = 52.3 16 26.1 26.1 + 52.3 = 78.4 24 13.1 13.1 +26.1 + 52.3 = 91.5 32 6.5 6.5 + 13.1 + 26.1 + 52.3 = 98.0 40 1.6 1.6 + 6.5 + 13.1 + 26.1 + 52.3 = 99.6 mg/L

-------- = MAF = ----------- Multiple ORAL Dosing – using the equation Recall that MAF was able to convert the single dose equation to a multiple dose equation Cmax ss 1 Cmax 1 1 - e -k -------- = MAF = -----------

MAF = ----------- … predicts accumulation Multiple ORAL Dosing – using the equation Recall that MAF was able to convert the single dose equation to a multiple dose equation 1 MAF = ----------- … predicts accumulation 1 - e -K 1 x ------------- 1 – e -K Dose V -Kt Ct = ---------- e First Dose Conc. Accumulation Steady State Equation

MAF = ----------- MAF for ka? 1 1 - e -k Multiple ORAL Dosing – using the equation However, the single oral dosing equation has two exponentials (K and ka) and each will have its own MAF. 1 1 - e -k MAF = ----------- MAF for ka?

Multiple ORAL Dosing – using the equation, Predicting SS Predicts Concentration-time @ SS

Multiple ORAL Dosing – using the equation, all concentrations Predicts Concentration-time at ANY time following an ORAL dose

Dosing Interval 8 hrs and t = 8 hrs. Multiple ORAL Dosing – using the equation SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 16 26.1 78.4 24 13.1 91.5 32 6.5 98.0 40 1.6 99.6 Verify 24 hour concentration [Cmin dose 3] Dose=1000 mg, V=10L ka=2hr-1; K=0.0863hr-1; T½=8hr; F=1 Dosing Interval 8 hrs and t = 8 hrs. 2*1*1000 10*(2-0.086) (1-e-3*0.086*8) (1-e-0.086*8) Ct= e-0.086*8 (1-e-3*2*8) (1-e-2*8) - e-2*8

Dosing Interval 8 hrs and t = 8 hrs. Multiple ORAL Dosing – using the equation SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 16 26.1 78.4 24 13.1 91.5 32 6.5 98.0 40 1.6 99.6 Verify 24 hour concentration [Cmin dose 3] Dose=1000 mg, V=10L ka=2hr-1; K=0.0863hr-1; T½=8hr; F=1 Dosing Interval 8 hrs and t = 8 hrs. 2*1*1000 10*(2-0.086) (1-e-3*0.086*8) (1-e-0.086*8) Ct= e-0.086*8 (1-e-3*2*8) (1-e-2*8) - e-2*8 0.875 1- 1.4 x 10-21 0.499 1- 1.1 x 10-7 Ct = 104.53 0.5 - 1.1 x 10-7

Multiple ORAL Dosing – using the equation SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 16 26.1 78.4 24 13.1 91.5 32 6.5 98.0 40 1.6 99.6 Verify 24 hour concentration [Cmin dose 3] Dose=1000 mg, V=10L ka=2hr-1; K=0.0863hr-1; T½=8hr; F=1 Dosing Interval 8 hrs. 2*1*1000 10*(2-0.086) (1-e-3*0.086*8) (1-e-0.086*8) Ct= e-0.086*8 - e-2*8 0.875 0.499 Ct = 104.53 0.50 - 1.0 0.000000113 = 104.53[(1.75)(0.5) – (0.000000113)] = 104.53 [0.875 – 0.000000113] = 91.46 mg/L

Multiple ORAL Dosing – using the equation SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 16 26.1 78.4 24 13.1 91.5 32 6.5 98.0 40 1.6 99.6 Calculate Cmin at steady state Dose=1000 mg, V=10L ka=2hr-1; K=0.0863hr-1; T½=8hr; F=1 Dosing Interval 8 hrs. Cdose 3- 8 hr = 91.46 mg/L

Dosing Interval 8 hrs. and t = 8 hrs Multiple ORAL Dosing – using the equation SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 16 26.1 78.4 24 13.1 91.5 32 6.5 98.0 40 1.6 99.6 Calculate Cmin at steady state Dose=1000 mg, V=10L ka=2hr-1; K=0.0863hr-1; T½=8hr; F=1 Dosing Interval 8 hrs. and t = 8 hrs 2*1*1000 10*(2-0.086) (1) (1-e-0.086*8) Ct= e-0.086*8 - 1 e-2*8 1 0.499 Ct = 104.53 0.50 - 1.00 0.000000113 = 104.53[1 – (0.000000113)] = 104.53 [1 – 0.000000113] = 104.45 mg/L

Multiple ORAL Dosing – using the equation SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 16 26.1 78.4 24 13.1 91.5 32 6.5 98.0 40 1.6 99.6 Calculate Cmin at steady state Dose=1000 mg, V=10L ka=2hr-1; K=0.0863hr-1; T½=8hr; F=1 Dosing Interval 8 hrs. CminSS = 104.45 mg/L

Multiple ORAL Dosing – using the equation SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 16 26.1 78.4 24 13.1 91.5 32 6.5 98.0 40 1.6 99.6 Calculate Cmin at steady state Dose=1000 mg, V=10L ka=2hr-1; K=0.0863hr-1; T½=8hr; F=1 Dosing Interval 8 hrs. CminSS = 104.45 mg/L Cmin1 = 52.3 mg/L MAF = 1.997

-------- = MAF = ----------- Multiple ORAL Dosing but will MAF always work following oral absorption? Cmax ss 1 Cmax 1 1 - e -k -------- = MAF = ----------- MAF does not consider ka … could this cause error in the estimation of accumulation? Evaluate initial conditions of: Dose =200; V = 20 L; half-life = 8 hr; ka is varied from 0.029 to 10 and dosing interval is 8 hours. Cmax and Cmin is calculated for each dose.

Multiple ORAL Dosing – through addition of single dose concentrations Time Conc (hr) (mg/L) 0 0.00 0.5 61.6 1 81.7 1.5 86.6 2 86.0 4 73.9 6 62.1 8 52.3 16 26.1 24 13.1 32 6.5 40 1.6 Dose=1000 mg, V=10L ka=2hr-1; K=0.0863hr-1; T½=8hr; F=1

Multiple ORAL Dosing – through addition of single dose concentrations SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 + 0.0 = 52.3 16 26.1 26.1 + 52.3 = 78.4

Multiple ORAL Dosing – through addition of single dose concentrations SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 + 0.0 = 52.3 16 26.1 26.1 + 52.3 = 78.4 24 13.1 13.1 +26.1 + 52.3 = 91.5

Multiple ORAL Dosing – through addition of single dose concentrations SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 + 0.0 = 52.3 16 26.1 26.1 + 52.3 = 78.4 24 13.1 13.1 +26.1 + 52.3 = 91.5 32 6.5 6.5 + 13.1 + 26.1 + 52.3 = 98.0

Multiple ORAL Dosing – through addition of single dose concentrations SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 + 0.0 = 52.3 16 26.1 26.1 + 52.3 = 78.4 24 13.1 13.1 +26.1 + 52.3 = 91.5 32 6.5 6.5 + 13.1 + 26.1 + 52.3 = 98.0 40 1.6 1.6 + 6.5 + 13.1 + 26.1 + 52.3 = 99.6 mg/L

-------- = MAF = ----------- Multiple ORAL Dosing – using the equation Recall that MAF was able to convert the single dose equation to a multiple dose equation Cmax ss 1 Cmax 1 1 - e -k -------- = MAF = -----------

MAF = ----------- … predicts accumulation Multiple ORAL Dosing – using the equation Recall that MAF was able to convert the single dose equation to a multiple dose equation 1 MAF = ----------- … predicts accumulation 1 - e -K 1 x ------------- 1 – e -K Dose V -Kt Ct = ---------- e First Dose Conc. Accumulation Steady State Equation

MAF = ----------- MAF for ka? 1 1 - e -k Multiple ORAL Dosing – using the equation However, the single oral dosing equation has two exponentials (K and ka) and each will have its own MAF. 1 1 - e -k MAF = ----------- MAF for ka?

Multiple ORAL Dosing – using the equation, Predicting SS Predicts Concentration-time @ SS

Multiple ORAL Dosing – using the equation, all concentrations Predicts Concentration-time at ANY time following an ORAL dose

Dosing Interval 8 hrs and t = 8 hrs. Multiple ORAL Dosing – using the equation SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 16 26.1 78.4 24 13.1 91.5 32 6.5 98.0 40 1.6 99.6 Verify 24 hour concentration [Cmin dose 3] Dose=1000 mg, V=10L ka=2hr-1; K=0.0863hr-1; T½=8hr; F=1 Dosing Interval 8 hrs and t = 8 hrs. 2*1*1000 10*(2-0.086) (1-e-3*0.086*8) (1-e-0.086*8) Ct= e-0.086*8 (1-e-3*2*8) (1-e-2*8) - e-2*8

Dosing Interval 8 hrs and t = 8 hrs. Multiple ORAL Dosing – using the equation SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 16 26.1 78.4 24 13.1 91.5 32 6.5 98.0 40 1.6 99.6 Verify 24 hour concentration [Cmin dose 3] Dose=1000 mg, V=10L ka=2hr-1; K=0.0863hr-1; T½=8hr; F=1 Dosing Interval 8 hrs and t = 8 hrs. 2*1*1000 10*(2-0.086) (1-e-3*0.086*8) (1-e-0.086*8) Ct= e-0.086*8 (1-e-3*2*8) (1-e-2*8) - e-2*8 0.875 1- 1.4 x 10-21 0.499 1- 1.1 x 10-7 Ct = 104.53 0.5 - 1.1 x 10-7

Multiple ORAL Dosing – using the equation SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 16 26.1 78.4 24 13.1 91.5 32 6.5 98.0 40 1.6 99.6 Verify 24 hour concentration [Cmin dose 3] Dose=1000 mg, V=10L ka=2hr-1; K=0.0863hr-1; T½=8hr; F=1 Dosing Interval 8 hrs. 2*1*1000 10*(2-0.086) (1-e-3*0.086*8) (1-e-0.086*8) Ct= e-0.086*8 - e-2*8 0.875 0.499 Ct = 104.53 0.50 - 1.0 0.000000113 = 104.53[(1.75)(0.5) – (0.000000113)] = 104.53 [0.875 – 0.000000113] = 91.46 mg/L

Multiple ORAL Dosing – using the equation SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 16 26.1 78.4 24 13.1 91.5 32 6.5 98.0 40 1.6 99.6 Calculate Cmin at steady state Dose=1000 mg, V=10L ka=2hr-1; K=0.0863hr-1; T½=8hr; F=1 Dosing Interval 8 hrs. Cdose 3- 8 hr = 91.46 mg/L

Dosing Interval 8 hrs. and t = 8 hrs Multiple ORAL Dosing – using the equation SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 16 26.1 78.4 24 13.1 91.5 32 6.5 98.0 40 1.6 99.6 Calculate Cmin at steady state Dose=1000 mg, V=10L ka=2hr-1; K=0.0863hr-1; T½=8hr; F=1 Dosing Interval 8 hrs. and t = 8 hrs 2*1*1000 10*(2-0.086) (1) (1-e-0.086*8) Ct= e-0.086*8 - 1 e-2*8 1 0.499 Ct = 104.53 0.50 - 1.00 0.000000113 = 104.53[1 – (0.000000113)] = 104.53 [1 – 0.000000113] = 104.45 mg/L

Multiple ORAL Dosing – using the equation SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 16 26.1 78.4 24 13.1 91.5 32 6.5 98.0 40 1.6 99.6 Calculate Cmin at steady state Dose=1000 mg, V=10L ka=2hr-1; K=0.0863hr-1; T½=8hr; F=1 Dosing Interval 8 hrs. CminSS = 104.45 mg/L

Multiple ORAL Dosing – using the equation SD MD Time Conc Conc (hr) (mg/L) (mg/L) 0 0.0 0.0 0.5 61.6 61.5 1 81.7 81.7 1.5 86.6 86.6 2 86.0 86.0 4 73.9 73.9 6 62.1 62.1 8 52.3 52.3 16 26.1 78.4 24 13.1 91.5 32 6.5 98.0 40 1.6 99.6 Calculate Cmin at steady state Dose=1000 mg, V=10L ka=2hr-1; K=0.0863hr-1; T½=8hr; F=1 Dosing Interval 8 hrs. CminSS = 104.45 mg/L Cmin1 = 52.3 mg/L MAF = 1.997

-------- = MAF = ----------- Multiple ORAL Dosing but will MAF always work following oral absorption? Cmax ss 1 Cmax 1 1 - e -k -------- = MAF = ----------- MAF does not consider ka … could this cause error in the estimation of accumulation? Evaluate initial conditions of: Dose =200; V = 20 L; half-life = 8 hr; ka is varied from 0.029 to 10 and dosing interval is 8 hours. Cmax and Cmin is calculated for each dose.

10 “formulations” are shown here, each with different absorption rates (ka) K = 0.08663 hr-1 T½= 8 hr  = 8 hours; D=200mg V= 20 L;F=1; ka is varied Tmax ka ka/K Cmax1 CmaxSS CmaxSS Error dose 1 (hr-1) (actual) (predicted) (%) (hr) 19.0 0.029 0.33 [1.92]1.47 14.26 2.88 273 11.55 0.087 1.0 [3.68]3.47 14.68 7.36 99.55 8.00 0.173 2.0 5.00 14.99 10.00 50.00 4.65 0.433 5.0 6.69 15.78 13.38 17.95 4.14 0.519 6.0 6.99 16.00 13.98 14.46 3.43 0.693 8.0 7.43 16.39 14.86 10.33 2.95 0.866 10.0 7.74 16.72 15.49 7.95 2.02 1.50 17.3 8.40 17.52 16.80 4.31 1.22 3.00 34.6 9.00 18.37 18.00 2.05 0.48 10.0 115.4 9.59 19.25 19.19 0.34 Slow absorption Fast absorption

Different absorption rates (ka) produces different first dose Tmax K = 0.08663 hr-1 T½= 8 hr  = 8 hours; D=200mg V= 20 L;F=1; ka is varied Tmax ka ka/K Cmax1 CmaxSS CmaxSS Error dose 1 (hr-1) (actual) (predicted) (%) (hr) 19.0 0.029 0.33 [1.92]1.47 14.26 2.88 273 11.55 0.087 1.0 [3.68]3.47 14.68 7.36 99.55 8.00 0.173 2.0 5.00 14.99 10.00 50.00 4.65 0.433 5.0 6.69 15.78 13.38 17.95 4.14 0.519 6.0 6.99 16.00 13.98 14.46 3.43 0.693 8.0 7.43 16.39 14.86 10.33 2.95 0.866 10.0 7.74 16.72 15.49 7.95 2.02 1.50 17.3 8.40 17.52 16.80 4.31 1.22 3.00 34.6 9.00 18.37 18.00 2.05 0.48 10.0 115.4 9.59 19.25 19.19 0.34

10 “formulations” are shown here, each with different absorption rates (ka) K = 0.08663 hr-1 T½= 8 hr  = 8 hours; D=200mg V= 20 L;F=1; ka is varied Tmax ka ka/K Cmax1 CmaxSS CmaxSS Error dose 1 (hr-1) (actual) (predicted) (%) (hr) 19.0 0.029 0.33 [1.92]1.47 14.26 2.88 273 11.55 0.087 1.0 [3.68]3.47 14.68 7.36 99.55 8.00 0.173 2.0 5.00 14.99 10.00 50.00 4.65 0.433 5.0 6.69 15.78 13.38 17.95 4.14 0.519 6.0 6.99 16.00 13.98 14.46 3.43 0.693 8.0 7.43 16.39 14.86 10.33 2.95 0.866 10.0 7.74 16.72 15.49 7.95 2.02 1.50 17.3 8.40 17.52 16.80 4.31 1.22 3.00 34.6 9.00 18.37 18.00 2.05 0.48 10.0 115.4 9.59 19.25 19.19 0.34 Slow absorption Fast absorption

Different absorption rates (ka) produces different first dose Tmax K = 0.08663 hr-1 T½= 8 hr  = 8 hours; D=200mg V= 20 L;F=1; ka is varied Tmax ka ka/K Cmax1 CmaxSS CmaxSS Error dose 1 (hr-1) (actual) (predicted) (%) (hr) 19.0 0.029 0.33 [1.92]1.47 14.26 2.88 273 11.55 0.087 1.0 [3.68]3.47 14.68 7.36 99.55 8.00 0.173 2.0 5.00 14.99 10.00 50.00 4.65 0.433 5.0 6.69 15.78 13.38 17.95 4.14 0.519 6.0 6.99 16.00 13.98 14.46 3.43 0.693 8.0 7.43 16.39 14.86 10.33 2.95 0.866 10.0 7.74 16.72 15.49 7.95 2.02 1.50 17.3 8.40 17.52 16.80 4.31 1.22 3.00 34.6 9.00 18.37 18.00 2.05 0.48 10.0 115.4 9.59 19.25 19.19 0.34

Using MAF, CmaxSS is predicted from Cmax1. This prediction is reasonable in some cases, very poor in others K = 0.08663 hr-1 T½= 8 hr  = 8 hours; D=200mg V= 20 L;F=1; ka is varied Tmax ka ka/K Cmax1 CmaxSS CmaxSS Error dose 1 (hr-1) (actual) (predicted) (%) (hr) 19.0 0.029 0.33 [1.92]1.47 14.26 2.88 273 11.55 0.087 1.0 [3.68]3.47 14.68 7.36 99.55 8.00 0.173 2.0 5.00 14.99 10.00 50.00 4.65 0.433 5.0 6.69 15.78 13.38 17.95 4.14 0.519 6.0 6.99 16.00 13.98 14.46 3.43 0.693 8.0 7.43 16.39 14.86 10.33 2.95 0.866 10.0 7.74 16.72 15.49 7.95 2.02 1.50 17.3 8.40 17.52 16.80 4.31 1.22 3.00 34.6 9.00 18.37 18.00 2.05 0.48 10.0 115.4 9.59 19.25 19.19 0.34 poor close Very close

If Error less than 10% is acceptable, unacceptable deviations only occur with slower releasing formulations K = 0.08663 hr-1 T½= 8 hr  = 8 hours; D=200mg V= 20 L;F=1; ka is varied Tmax ka ka/K Cmax1 CmaxSS CmaxSS Error dose 1 (hr-1) (actual) (predicted) (%) (hr) 19.0 0.029 0.33 [1.92]1.47 14.26 2.88 273 11.55 0.087 1.0 [3.68]3.47 14.68 7.36 99.55 8.00 0.173 2.0 5.00 14.99 10.00 50.00 4.65 0.433 5.0 6.69 15.78 13.38 17.95 4.14 0.519 6.0 6.99 16.00 13.98 14.46 3.43 0.693 8.0 7.43 16.39 14.86 10.33 2.95 0.866 10.0 7.74 16.72 15.49 7.95 2.02 1.50 17.3 8.40 17.52 16.80 4.31 1.22 3.00 34.6 9.00 18.37 18.00 2.05 0.48 10.0 115.4 9.59 19.25 19.19 0.34

MAF fails with oral absorption, primarily slow absorption ? When does this occur (ka/K <10) K = 0.08663 hr-1 T½= 8 hr  = 8 hours; D=200mg V= 20 L;F=1; ka is varied Tmax ka ka/K Cmax1 CmaxSS CmaxSS Error dose 1 (hr-1) (actual) (predicted) (%) (hr) 19.0 0.029 0.33 [1.92]1.47 14.26 2.88 273 11.55 0.087 1.0 [3.68]3.47 14.68 7.36 99.55 8.00 0.173 2.0 5.00 14.99 10.00 50.00 4.65 0.433 5.0 6.69 15.78 13.38 17.95 4.14 0.519 6.0 6.99 16.00 13.98 14.46 3.43 0.693 8.0 7.43 16.39 14.86 10.33 2.95 0.866 10.0 7.74 16.72 15.49 7.95 2.02 1.50 17.3 8.40 17.52 16.80 4.31 1.22 3.00 34.6 9.00 18.37 18.00 2.05 0.48 10.0 115.4 9.59 19.25 19.19 0.34

MAF works better (less error) with Cmin. K = 0.08663 hr-1 T½= 8 hr  = 8 hours; D=200mg V= 20 L;F=1; ka is varied Tmax ka ka/K Cmin1 CminSS CminSS Error dose 1 (hr-1) (actual) (predicted) (%) (hr) 19.0 0.029 0.33 1.47 14.09 2.95 380 11.55 0.087 1.0 3.47 13.87 6.93 100.0 8.00 0.173 2.0 5.00 13.33 10.00 33.4 4.65 0.433 5.0 5.86 12.10 11.72 3.23 4.14 0.519 6.0 5.81 11.81 11.63 1.59 3.43 0.693 8.0 5.67 11.39 11.34 0.39 2.95 0.866 10.0 5.54 11.10 11.09 0.1 2.02 1.50 17.3 5.31 10.61 10.62 0.001 1.22 3.00 34.6 5.15 10.30 10.30 ----- 0.48 10.0 115.4 5.04 10.09 10.09 -----

MAF fails with oral absorption, primarily slow absorption ? When does this occur K = 0.08663 hr-1 T½= 8 hr  = 8 hours; D=200mg V= 20 L;F=1; ka is varied Tmax ka ka/K Error Error dose 1 (hr-1) Cmax Cmin (hr) (%) (%) 19.0 0.029 0.33 273 380 11.55 0.087 1.0 99.55 100 8.00 0.173 2.0 50.00 33.4 4.65 0.433 5.0 17.95 3.23 4.14 0.519 6.0 14.66 1.59 3.43 0.693 8.0 10.33 0.39 2.95 0.866 10.0 7.95 0.1 2.02 1.50 17.3 4.31 0.001 1.22 3.00 34.6 2.05 ----- 0.48 10.0 115.4 0.34 ----- Error is greater in Cmax. Error is due to the failure to consider ka in MAF. When absorption has a greater effect on concentration, error is increased.

MAF fails with oral absorption, primarily slow absorption ? When does this occur K = 0.08663 hr-1 T½= 8 hr  = 8 hours; D=200mg V= 20 L;F=1; ka is varied Tmax ka ka/K Error Error dose 1 (hr-1) Cmax Cmin (hr) (%) (%) 19.0 0.029 0.33 273 380 11.55 0.087 1.0 99.55 100 8.00 0.173 2.0 50.00 33.4 4.65 0.433 5.0 17.95 3.23 4.14 0.519 6.0 14.66 1.59 3.43 0.693 8.0 10.33 0.39 2.95 0.866 10.0 7.95 0.1 2.02 1.50 17.3 4.31 0.001 1.22 3.00 34.6 2.05 ----- 0.48 10.0 115.4 0.34 ----- For immediate release formulations, error is generally ~ 10% or less. This occurs when absorption is faster than elimination ka/K > 5-10.

MAF fails with oral absorption, primarily slow absorption ? When does this occur K = 0.08663 hr-1 T½= 8 hr  = 8 hours; D=200mg V= 20 L;F=1; ka is varied MAF can be used to predict SS concentrations, but error increases as you move from Cmin to Cmax, as ratio of T½: increases and ratio of ka/K decreases. For immediate release formulations, error is generally ~ 10% or less. Red shaded area represent profiles with a Tmax occurring AFTER 4 hours. This occurs when absorption is slow (SR formulations) or ratio ka/K < 5 -10. T½:  = 0.5 T½:  = 0.5 T½: = 2 T½: = 2

Volume of Distribution Multiple ORAL Dosing Time to Achieve Steady State is Determined By? Dose Half-life Dosing Interval Volume of Distribution

Half-life Multiple ORAL Dosing – time to steady state Time to Achieve Steady State is Determined By? Dose Half-life Dosing Interval Volume of Distribution Time to SS is determined entirely by the half-life of the drug While steady–state is never actually reached You approach SS 1/2 way each half-life, you reach 90% of true steady state after 3.3 half-lives. Half-life Number Percent Of Of Half-lives Steady State 1 50 2 75 3 87.5 4 93.75 5 96.875 6 98.4375 7 99.21875 but sometimes … elimination of a drug is “rate-limited” by absorption. How does this affect the time to SS? Is time to SS is determined by the slowest exponential …?

Multiple ORAL Dosing – time to steady state Evaluate time to SS – look at Cmin for products with a different ka. Drug: T½ = 5 hr;  = 8 hr, Dose = 100 mg; V= 10 L; F=1. MAF = 1.492 ka = 0.05 ka=0.18 ka= 0.693 ka =13.86 ka/k=0.36 ka/k=1.3 ka/k=5 ka/k=100 Dose time [mg/L] [mg/L] [mg/L] 1 0 0.00 0.00 0.00 0.00 1 0.46 1.54 4.63 8.97 2 0.83 2.62 6.35 7.66 3 1.13 3.35 6.68 6.66 6 1.72 4.16 5.24 4.40 8 1.92 4.04 4.08 3.33 8 5.34 7.32 5.89 4.80 8 8 8.22 7.91 6.11 4.97 14 8 8.67 7.91 6.11 4.97 MAF predicts well for CminSS when ka/K >5-10 & or Tmax was less than 4 hr. So why does it not work with a ka of 0.05hr-1? 61.% ??? 92.5% 96.4% 96.6% SS achieved

Multiple ORAL Dosing – time to steady state Evaluate time to SS – look at Cmin for products with a different ka. Drug: T½ = 5 hr;  = 8 hr, Dose = 100 mg; V= 10 L; F=1. MAF = 1.492 ka = 0.05 ka=0.18 ka= 0.693 ka =13.86 ka/k=0.36 ka/k=1.3 ka/k=5 ka/k=100 [mg/L] [mg/L] [mg/L] [mg/L] MAF predicts well for CminSS when ka/K >5-10 & or Tmax was less than 4 hr. So why does it not work with a ka of 0.05hr-1? ka/K = 0.5 K > ka 96% SS @ 24 hr 61% SS at 24 hr Cmin1 = Cmax1

Multiple ORAL Dosing – time to steady state Evaluate time to SS – look at Cmin for products with a different ka. Drug: T½ = 5 hr;  = 8 hr, Dose = 100 mg; V= 10 L; F=1. MAF = 1.492 ka = 0.05 ka=0.18 ka= 0.693 ka =13.86 ka/k=0.36 ka/k=1.3 ka/k=5 ka/k=100 [mg/L] [mg/L] [mg/L] [mg/L] K > ka so ka is the slowest exponential and appears in the terminal phase of the profile. ka determines time to achieve Steady-State. T½ = 13.86 hr. 3.3 T½ = 45.7 hr Cmin48hr = 8.0 mg/L CminSS = 8.69 mg/L 92% SS at 48 hr =3.46 T½ 61% SS at 24 hr

How long does it take to get to steady state? When did SS occur? Steady State is considered to have been achieved when the Concentration is within 10% of the true steady state concentration. 90% of true steady state will occur at ~ 3.3 half-lives. Number Percentage Of of Eventual T½ SS Achieved (%) 1 50 2 75 3 87.5 4 93.25 5 96.875 6 98.4375 SS 100 Sometimes, SS is not considered to have been achieved until concentrations exceed 95% of the true steady state concentrations. This occurs between 4 and 5 half-lives. This gives rise to the statement that steady state is achieved in 3-5 half-lives. Each T½ reduces the gap between current concentrations and SS by half. Dosing interval (τ) does not affect time to SS

When is 90% of true (eventual) e-Kt determines proportion lost How long does it take to get to steady state? When did SS occur? Steady State is considered to have been achieved when the Concentration is within 10% of the true steady state concentration. 90% of true steady state will occur at ~ 3.3 half-lives. Number Percentage Of of Eventual T½ SS Achieved (%) 1 50 2 75 3 87.5 4 93.25 5 96.875 6 98.4375 SS 100 When is 90% of true (eventual) Steady State Achieved? e-Kt determines proportion lost

How long does it take to get to steady state? When did SS occur? Steady State is considered to have been achieved when the Concentration is within 10% of the true steady state concentration. 90% of true steady state will occur at ~ 3.3 half-lives. Number Percentage Of of Eventual T½ SS Achieved (%) 1 50 2 75 3 87.5 4 93.25 5 96.875 6 98.4375 SS 100 When is 90% of true (eventual) Steady State Achieved? e-Kt determines proportion lost e-K# determines proportion lost for a set number (#) of half-lives Example: If K = 0.693 and # = 2 T½ = e (-0.693 x 2) = 0.25

How long does it take to get to steady state? When did SS occur? Steady State is considered to have been achieved when the Concentration is within 10% of the true steady state concentration. 90% of true steady state will occur at ~ 3.3 half-lives. Number Percentage Of of Eventual T½ SS Achieved (%) 1 50 2 75 3 87.5 4 93.25 5 96.875 6 98.4375 SS 100 When is 90% of true (eventual) Steady State Achieved? e-K# determines proportion lost … then 1 - e-K# will determine proportion of steady-state achieved. Example: If K = 0.693 and # = 2 T½ = 1 -e (-0.693 x 2) = 0.75 Or expressed as a % 75% of SS after 2 T½

How long does it take to get to steady state? When did SS occur? Steady State is considered to have been achieved when the Concentration is within 10% of the true steady state concentration. 90% of true steady state will occur at ~ 3.3 half-lives. Number Percentage Of of Eventual T½ SS Achieved (%) 1 50 2 75 3 87.5 4 93.25 5 96.875 6 98.4375 SS 100 When is 90% of true (eventual) Steady State Achieved? e-K# determines proportion lost and … 1 - e (-0.693 x #) determines proportion of steady-state achieved. and … 100 x (1 - e (-0.693 x #) ) determines percent of steady-state achieved, where # is the number of half-lives. % SS = 100 x (1 - e (-0.693 x #) )

When is 90% of true (eventual) Therefore, 90% of true SS is achieved… How long does it take to get to steady state? When did SS occur? Steady State is considered to have been achieved when the Concentration is within 10% of the true steady state concentration. 90% of true steady state will occur at ~ 3.3 half-lives. Number Percentage Of of Eventual T½ SS Achieved (%) 1 50 2 75 3 87.5 4 93.25 5 96.875 6 98.4375 SS 100 When is 90% of true (eventual) Steady State Achieved? % SS = 100 x (1 - e (-0.693 x #) ) Therefore, 90% of true SS is achieved… 90 = 100 x (1 - e (-0.693 x #) ) 0.9 = 1 - e (-0.693 x #) e (-0.693 x #) = 0.1 ln(e (-0.693 x #) = ln(0.1) -0.693 x # = -2.30259 # = 3.322

How long does it take to get to steady state? When did SS occur? Steady State is considered to have been achieved when the Concentration is within 10% of the true steady state concentration. 90% of true steady state will occur at ~ 3.3 half-lives. Number Percentage Of of Eventual T½ SS Achieved (%) 1 50 2 75 3 87.5 4 93.25 5 96.875 6 98.4375 SS 100 When is 90% of true (eventual) Steady State Achieved? After 3.322 half-lives … frequently stated as 3.3 half lives When is 95% of true (eventual) ln(e (-0.693 x #) = ln(0.05) -0.693 x # = -2.9957 # = 4.322

Multiple ORAL Dosing – Effect of ka. Absorption rate affects a number of things with multiple doses It can determine time to steady state It can affect the accuracy of MAF Can it affect anything else ? ka is the rate at which a drug is absorbed. ka and k are two determinants of Tmax. Tmax = [ln(ka/k) / (ka-k)] This is the equation for Tmax after 1 dose What is the effect of ka on Tmax on the way to steady state?

Multiple ORAL Dosing – Effect of ka on Tmax. Steady State & the Effect on Tmax Consider a drug with a 5 hour half-life, administered every 8 hours Dose time ka = 0.05 ka=0.18 ka= 0.693 ka =13.86 ka/k=0.36 ka/k=1.3 ka/k=5 ka/k=100 # hr [mg/L] [mg/L] [mg/L] [mg/L] 1 0 0.00 0.00 0.00 0.00 1 0.46 1.54 4.63 8.97 2 0.83 2.62 6.35 7.66 3 1.13 3.35 6.68 6.66 6 1.72 4.16 5.24 4.40 8 1.92 4.04 4.08 3.33 What will happen to TMAX in every case ?

Steady State & the Effect on Tmax Consider a drug with a 5 hour half-life, administered every 8 hours Dose time ka = 0.05 ka=0.18 ka= 0.693 ka =13.86 ka/k=0.36 ka/k=1.3 ka/k=5 ka/k=100 # hr [mg/L] [mg/L] [mg/L] [mg/L] 1 0 0.00 0.00 0.00 0.00 1 0.46 1.54 4.63 8.97 2 0.83 2.62 6.35 7.66 3 1.13 3.35 6.68 6.66 6 1.72 4.16 5.24 4.40 8 1.92 4.04 4.08 3.33 3 0 3.84 6.34 5.44 4.43 1 4.30 7.50 9.38 12.65 2 4.67 8.19 10.49 11.01 4 5.13 8.57 9.55 8.35 7 5.35 7.76 6.72 5.51 8 5.34 7.32 5.89 4.80

Steady State & the Effect on Tmax Consider a drug with a 5 hour half-life, administered every 8 hours Dose time ka = 0.05 ka=0.18 ka= 0.693 ka =13.86 ka/k=0.36 ka/k=1.3 ka/k=5 ka/k=100 1 0 0.00 0.00 0.00 0.00 1 0.46 1.54 4.63 8.97 2 0.83 2.62 6.35 7.66 3 1.13 3.35 6.68 6.66 6 1.72 4.16 5.24 4.40 8 1.92 4.04 4.08 3.33 peak occurs at….. 1st dose 11.5 hr (8) 6.31 hr 2.9 hr 0.336 hr 3rd dose 7.25 hr 3.75 hr 2.5 hr 0.34 hr 14th dose 3.5 hr 3.1 hr 2.2 hr 0.31 Steady migration of the Tmax to occur earlier most pronounced with SR products

Multiple ORAL Dosing – Effect of ka on Tmax. Does Tmax really move regardless of ka magnitude? ka Tmax Tmax Tmax Error (hr-1) ka/k (obs at SS) after (equation) (%) (hr) 1dose (hr) 0.0138 0.01 3.59 18.46 18.46 14.87 0.05 0.36 3.50 11.50 11.50 8.01 0.10 0.72 3.10 8.40 8.40 5.30 0.20 1.44 2.40 5.85 5.85 3.45 0.55 3.97 2.40 3.33 3.33 0.93 1.00 7.22 1.85 2.29 2.29 0.44 2.00 14.43 1.22 1.43 1.43 0.21 4.98 35.93 0.65 0.74 0.74 0.91 100. 721.0 0.062 0.066 0.66 0.004 Equation predicts first dose … but Tmax at SS moves in! Movement is greatest for SR products … but also occurs with IV bolus when accumulation occurs. K = 0.1385 hr-1 T½= 5 hr  = 8 hours ka is varied

have any relevance to the patient ? When does the Tmax actually occur? Does a shifting Tmax have any relevance to the patient ? YES When does the Tmax actually occur? Do you really know? We commonly see single dose kinetic data. If we are told that the Tmax is (on average) 8 hours … what is it in an individual patient at SS? Subject Tmax 1 8.5 2 12.25 3 12.16 4 8.16 5 6.58 6 4.00 7 10.33 8 12.00 9 7.66 10 6.08 11 6.28 Mean: 8.55 hr Range: 4.0-12.25 So … for TDM, is it reasonable to measure the concentration at Tmax ? toxicity ?? dosage adjustment ?? Recommend routine use of Cmin

FAQ 1. What is the purpose of and SR Product ? To reduce the peak-trough fluctuation …? Or allow the product to be given less frequently ?

FAQ 1. What is the purpose of and SR Product ? Smallest Peak / trough fluctuation provided by product with smallest Ka/K ratio [SR product]

FAQ Mr BB requires 200 mg/day of morphine for chronic cancer pain. There are several morphine formulations available for use, but it is decided that a sustained release formulations would provide Mr. BB with convenience and a smooth concentration-time profile that should provide good pain control. Kadian® and MS Contin® are 2 sustained release formulations. Kadian® is recommended for Q24 hr dosing and peaks at 10 hr. MS-Contin® is recommended for Q12 hr dosing and peaks 4-5 hr. Which formulation will yield the smallest peak-trough difference? Kadian® giving 200 mg q24 hours (recommended) Kadian® giving 100 mg q12 hours (100 mg/day) MS-Contin® giving 200 mg q24 hours MS-Contin® giving 100 mg q12 hours (recommended) What do we need to calculate? K, ka, AUC, F, V, Cmax, Tmax, Cl…?

FAQ There are two modified release morphine formulations. Your patient requires 200 mg per day. Which formulation will yield the smallest peak-trough difference? Kadian® is recommended for Q24 hr dosing and peaks at 10 hr. MS-Contin® is recommended for Q12 hr dosing and peaks 4-5 hr. We will answer this question assuming a 1C model with first order absorption and first order elimination. The half-life of morphine should fall between 2 and 4 hours in most individuals with normal liver function. We will assume a half-life of 3 hours to solve our question. Half-life of 3 hr corresponds to a K value of … ? K = 0.693/ 3 hr = 0.231 hr-1

FAQ There are two modified release morphine formulations. Your patient requires 200 mg per day. Which formulation will yield the smallest peak-trough difference? Kadian® is recommended for Q24 hr dosing and peaks at 10 hr. MS-Contin® is recommended for Q12 hr dosing and peaks 4-5 hr. K = 0.231 hr-1 for Kadian® and MS-Contin® formulations Estimate ka …! Using the 1C single dose Excel® spread sheet, knowing that the Tmax for Kadian® is 10hr and Tmax for MS-Contin® is 4.5hr. Volume for morphine is ~4 L/kg. Assume 280 L. ka for MS-Contin® = 0.27011 hr-1 ka for Kadian® = 0.031399 hr-1

FAQ There are two modified release morphine formulations. Your patient requires 200 mg per day. Which formulation will yield the smallest peak-trough difference? Kadian® is recommended for Q24 hr dosing and peaks at 10 hr. MS-Contin® is recommended for Q12 hr dosing and peaks 4-5 hr. ?

FAQ There are two modified release morphine formulations. Your patient requires 200 mg per day. Which formulation will yield the smallest peak-trough difference? Kadian® is recommended for Q24 hr dosing and peaks at 10 hr. MS-Contin® is recommended for Q12 hr dosing and peaks 4-5 hr. Kadian Single Dose Profile Tmax = 10 hr Cmax = 28 ng/mL AUC = 1.24 mg*hr/L V = 240 L F = 0.4 MS-Contin Profile Tmax = 4.5 hr Cmax = 113 ng/mL AUC = 1.24 mg*hr/L V = 240 L F = 0.4 Which formulation will yield the smallest peak-trough difference?

FAQ There are two modified release morphine formulations. Your patient requires 200 mg per day. Which formulation will yield the smallest peak-trough difference? Kadian® is recommended for Q24 hr dosing and peaks at 10 hr. MS-Contin® is recommended for Q12 hr dosing and peaks 4-5 hr. Which formulation will yield the smallest peak-trough difference? Kadian® giving 200 mg q24 hours (recommended) Kadian® giving 100 mg q12 hours (100 mg/day) MS-Contin® giving 200 mg q24 hours MS-Contin® giving 100 mg q12 hours (recommended) Take the single dose kinetic parameters and move to a multiple dose Excel® sheet Kadian Single Dose Profile Tmax = 10 hr Cmax = 28 ng/mL AUC = 1.24 mg*hr/L V = 240 L F = 0.4 MS-Contin Profile Tmax = 4.5 hr Cmax = 113 ng/mL AUC = 1.24 mg*hr/L V = 240 L F = 0.4

MS Contin® Recommended MS-Contin® 100 mg Q12 H Peak = 70.0 ng/mL Trough = 25.7 ng/mL MS Contin® Recommended to be given every 12 hours. MS-Contin® 200 mg Q24 H Peak = 115.5 ng/mL Trough = 4.7 ng/mL

Kadian® Recommended to be given every 24 hours. Kadian® 100 mg Q12 H Peak = 53.4 ng/mL Trough = 47.4 ng/mL Kadian® Recommended to be given every 24 hours. Kadian® 200 mg Q24 H Peak = 58.9 ng/mL Trough = 39.6 ng/mL

Questions There are two modified release morphine formulations. Your patient requires 200 mg per day. Which formulation will yield the smallest peak-trough difference? Kadian® is recommended for Q24 hr dosing and peaks at 10 hr. MS-Contin® is recommended for Q12 hr dosing and peaks 4-5 hr. Which formulation will yield the smallest peak-trough difference? Regimen Peak Trough Range ng/mL ng/mL ng/mL MS-Contin 100 q12H 70.0 25.7 44.3 [rec] MS-Contin 200 q24H 115.5 4.7 110.8 Kadian 100 q12H 53.4 47.4 6.0 Kadian 200 q24H 58.9 39.6 19.3 [rec] For ANY formulation, giving a smaller dose more frequently will ALWAYS reduce peak-trough fluctuations

Questions 3. A patient receives a drug every 12 hours. The drug has a half-life of ~5.7 hour the patient misses a dose … but remembers half way through the interval. Should the patient take the next scheduled dose (forget missed dose) or … take the missed dose immediately and resume normal dosing take two doses at the next scheduled time?

relationships between concentration & toxicity, Correct Answer is drug dependant based on relationships between concentration & toxicity, risk of sub-therapeutic concentrations, half-life & dosing interval.