1. 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

2. 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 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.)

3. Multiple ORAL Dosing – through addition of single dose concentrations
Time Conc
(hr) (mg/L)
Dose=1000 mg, V=10L
ka=2hr-1; K=0.0863hr-1;
T½=8hr; F=1

4. Multiple ORAL Dosing – through addition of single dose concentrations
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
= 52.3
= 78.4

5. Multiple ORAL Dosing – through addition of single dose concentrations
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
= 52.3
= 78.4
= 91.5

6. Multiple ORAL Dosing – through addition of single dose concentrations
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
= 52.3
= 78.4
= 91.5
= 98.0

7. Multiple ORAL Dosing – through addition of single dose concentrations
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
= 52.3
= 78.4
= 91.5
= 98.0
= 99.6 mg/L

8. -------- = 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 e -k
= MAF =

9. 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

10. 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?

11. Multiple ORAL Dosing – using the equation, Predicting SS
Predicts SS

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

13. Dosing Interval 8 hrs and t = 8 hrs.
Multiple ORAL Dosing – using the equation
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
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*( )
(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

14. Dosing Interval 8 hrs and t = 8 hrs.
Multiple ORAL Dosing – using the equation
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
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*( )
(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
x 10-21
x 10-7
Ct = x 10-7

15. Multiple ORAL Dosing – using the equation
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
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*( )
(1-e-3*0.086*8)
(1-e-0.086*8)
Ct=
e-0.086*8
- e-2*8
0.875
0.499
Ct =
= [(1.75)(0.5) – ( )]
= [0.875 – ]
= mg/L

16. Multiple ORAL Dosing – using the equation
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
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 = mg/L

17. Dosing Interval 8 hrs. and t = 8 hrs
Multiple ORAL Dosing – using the equation
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
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*( )
(1)
(1-e-0.086*8)
Ct=
e-0.086*8
- 1 e-2*8 1
0.499
Ct =
= [1 – ( )]
= [1 – ]
= mg/L

18. Multiple ORAL Dosing – using the equation
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
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 = mg/L

19. Multiple ORAL Dosing – using the equation
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
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 = mg/L
Cmin1 = mg/L
MAF = 1.997

20. -------- = MAF = -----------
Multiple ORAL Dosing
but will MAF always work following oral absorption?
Cmax ss 1
Cmax 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 to 10
and dosing interval is 8 hours.
Cmax and Cmin is calculated for each dose.

21. Multiple ORAL Dosing – through addition of single dose concentrations
Time Conc
(hr) (mg/L)
Dose=1000 mg, V=10L
ka=2hr-1; K=0.0863hr-1;
T½=8hr; F=1

22. Multiple ORAL Dosing – through addition of single dose concentrations
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
= 52.3
= 78.4

23. Multiple ORAL Dosing – through addition of single dose concentrations
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
= 52.3
= 78.4
= 91.5

24. Multiple ORAL Dosing – through addition of single dose concentrations
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
= 52.3
= 78.4
= 91.5
= 98.0

25. Multiple ORAL Dosing – through addition of single dose concentrations
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
= 52.3
= 78.4
= 91.5
= 98.0
= 99.6 mg/L

26. -------- = 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 e -k
= MAF =

27. 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

28. 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?

29. Multiple ORAL Dosing – using the equation, Predicting SS
Predicts SS

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

31. Dosing Interval 8 hrs and t = 8 hrs.
Multiple ORAL Dosing – using the equation
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
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*( )
(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

32. Dosing Interval 8 hrs and t = 8 hrs.
Multiple ORAL Dosing – using the equation
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
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*( )
(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
x 10-21
x 10-7
Ct = x 10-7

33. Multiple ORAL Dosing – using the equation
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
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*( )
(1-e-3*0.086*8)
(1-e-0.086*8)
Ct=
e-0.086*8
- e-2*8
0.875
0.499
Ct =
= [(1.75)(0.5) – ( )]
= [0.875 – ]
= mg/L

34. Multiple ORAL Dosing – using the equation
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
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 = mg/L

35. Dosing Interval 8 hrs. and t = 8 hrs
Multiple ORAL Dosing – using the equation
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
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*( )
(1)
(1-e-0.086*8)
Ct=
e-0.086*8
- 1 e-2*8 1
0.499
Ct =
= [1 – ( )]
= [1 – ]
= mg/L

36. Multiple ORAL Dosing – using the equation
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
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 = mg/L

37. Multiple ORAL Dosing – using the equation
SD MD
Time Conc Conc
(hr) (mg/L) (mg/L)
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 = mg/L
Cmin1 = mg/L
MAF = 1.997

38. -------- = MAF = -----------
Multiple ORAL Dosing
but will MAF always work following oral absorption?
Cmax ss 1
Cmax 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 to 10
and dosing interval is 8 hours.
Cmax and Cmin is calculated for each dose.

39. 10 “formulations” are shown here,
each with different absorption rates (ka)
K = hr-1 T½= 8 hr
 = 8 hours; D=200mg
V= 20 L;F=1; ka is varied
Tmax ka ka/K Cmax CmaxSS CmaxSS Error
dose 1 (hr-1) (actual) (predicted) (%)
(hr)
[1.92]
[3.68]
Slow absorption
Fast absorption

40. Different absorption rates (ka) produces different first dose Tmax
K = hr-1 T½= 8 hr
 = 8 hours; D=200mg
V= 20 L;F=1; ka is varied
Tmax ka ka/K Cmax CmaxSS CmaxSS Error
dose 1 (hr-1) (actual) (predicted) (%)
(hr)
[1.92]
[3.68]

41. 10 “formulations” are shown here,
each with different absorption rates (ka)
K = hr-1 T½= 8 hr
 = 8 hours; D=200mg
V= 20 L;F=1; ka is varied
Tmax ka ka/K Cmax CmaxSS CmaxSS Error
dose 1 (hr-1) (actual) (predicted) (%)
(hr)
[1.92]
[3.68]
Slow absorption
Fast absorption

42. Different absorption rates (ka) produces different first dose Tmax
K = hr-1 T½= 8 hr
 = 8 hours; D=200mg
V= 20 L;F=1; ka is varied
Tmax ka ka/K Cmax CmaxSS CmaxSS Error
dose 1 (hr-1) (actual) (predicted) (%)
(hr)
[1.92]
[3.68]

43. Using MAF, CmaxSS is predicted from Cmax1.
This prediction is reasonable in some cases,
very poor in others
K = hr-1 T½= 8 hr
 = 8 hours; D=200mg
V= 20 L;F=1; ka is varied
Tmax ka ka/K Cmax CmaxSS CmaxSS Error
dose 1 (hr-1) (actual) (predicted) (%)
(hr)
[1.92]
[3.68]
poor
close
Very close

44. If Error less than 10% is acceptable,
unacceptable deviations only occur
with slower releasing formulations
K = hr-1 T½= 8 hr
 = 8 hours; D=200mg
V= 20 L;F=1; ka is varied
Tmax ka ka/K Cmax CmaxSS CmaxSS Error
dose 1 (hr-1) (actual) (predicted) (%)
(hr)
[1.92]
[3.68]

45. MAF fails with oral absorption, primarily slow absorption
? When does this occur (ka/K <10)
K = hr-1 T½= 8 hr
 = 8 hours; D=200mg
V= 20 L;F=1; ka is varied
Tmax ka ka/K Cmax CmaxSS CmaxSS Error
dose 1 (hr-1) (actual) (predicted) (%)
(hr)
[1.92]
[3.68]

46. MAF works better (less error) with Cmin.
K = hr-1 T½= 8 hr
 = 8 hours; D=200mg
V= 20 L;F=1; ka is varied
Tmax ka ka/K Cmin CminSS CminSS Error
dose 1 (hr-1) (actual) (predicted) (%)
(hr)

47. MAF fails with oral absorption, primarily slow absorption
? When does this occur
K = 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) (%) (%)
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.

48. MAF fails with oral absorption, primarily slow absorption
? When does this occur
K = 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) (%) (%)
For
immediate release
formulations,
error is generally
~ 10% or less.
This occurs when
absorption
is faster
than elimination
ka/K > 5-10.

49. MAF fails with oral absorption, primarily slow absorption
? When does this occur
K = 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 <
T½:  = 0.5
T½:  = 0.5
T½: = 2
T½: = 2

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

51. 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
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 …?

52. 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= 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]
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.% ??? % % %
SS achieved

53. 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= 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% 24 hr
61% SS at 24 hr
Cmin1 = Cmax1

54. 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= 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 = 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

55. 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
(%) SS
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

56. 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
(%) SS
When is 90% of true (eventual)
Steady State Achieved?
e-Kt determines proportion lost

57. 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
(%) SS
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 = and # = 2 T½
= e ( x 2)
= 0.25

58. 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
(%) SS
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 = and # = 2 T½
= 1 -e ( x 2)
= 0.75
Or expressed as a %
75% of SS after 2 T½

59. 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
(%) SS
When is 90% of true (eventual)
Steady State Achieved?
e-K# determines proportion lost
and … 1 - e ( x #)
determines proportion of steady-state achieved.
and … 100 x (1 - e ( x #) )
determines percent of steady-state achieved,
where # is the number of half-lives.
% SS = 100 x (1 - e ( x #) )

60. 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
(%) SS
When is 90% of true (eventual)
Steady State Achieved?
% SS = 100 x (1 - e ( x #) )
Therefore, 90% of true SS is achieved…
90 = 100 x (1 - e ( x #) )
0.9 = 1 - e ( x #)
e ( x #) = 0.1
ln(e ( x #) = ln(0.1)
x # =
# = 3.322

61. 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
(%) SS
When is 90% of true (eventual)
Steady State Achieved?
After half-lives
… frequently stated as 3.3 half lives
When is 95% of true (eventual)
ln(e ( x #) = ln(0.05)
x # =
# = 4.322

62. 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?

63. 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= 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]
What will happen to TMAX in every case ?

64. 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= 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]

65. 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= ka =13.86
ka/k=0.36 ka/k=1.3 ka/k=5 ka/k=100
peak occurs at…..
1st dose hr (8) 6.31 hr 2.9 hr hr
3rd dose 7.25 hr hr 2.5 hr 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

66. 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) dose (hr)
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 = hr-1 T½= 5 hr
 = 8 hours
ka is varied

67. 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
Mean: 8.55 hr
Range:
So … for TDM,
is it reasonable
to measure the
concentration
at Tmax ?
toxicity ??
dosage adjustment ??
Recommend routine use of Cmin

68. 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 ?

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

70. 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…?

71. 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
= hr-1

72. 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 = 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® = hr-1
ka for Kadian® = hr-1

73. 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. ?

74. 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?

75. 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

76. 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 = ng/mL
Trough = 4.7 ng/mL

77. 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

78. 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 [rec]
MS-Contin 200 q24H
Kadian q12H
Kadian q24H [rec]
For ANY formulation, giving a smaller dose more frequently
will ALWAYS reduce peak-trough fluctuations

79. 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?

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