2006

Case Study VI Answers PHA 5127 – Fall 2006 Question 1. A patient is given a 250 mg immediate-release theophylline tablet (Tablet A). A week later, the same patient is given a 250 mg sustained-release theophylline tablet (Tablet B). The tablets follow a one-compartmental model and have a first-order absorption and elimination. The bioavailability is 90% for both tablets. The plasma drug concentration-time profiles for both tablets are as follows: Time (hrs) 0.5 1 2 3 6 12 18 24 36 48 72 96

Plasma Drug Conc. (mg/L) Tablet A Tablet B 2.52 0.11 4.04 0.21 5.36 0.39 5.56 0.55 4.47 0.90 2.38 1.23 1.26 1.28 0.66 1.20 0.18 0.93 0.68 0.34 0.16

Determine ke, ka, and Vd for both tablets. Formulation A: First plot the data on a semi-log scale: Tablet A

Plasma Conc. (mg/L)

10

1

0.1 0

10

20 Time (hrs)

30

40

Looking at the plot, we can deduce the following: 1

Case Study VI Answers PHA 5127 – Fall 2006 a) The last four data points are fairly linear and assumed to be the terminal phase b) Since the tablet is an immediate-release one, ka>>ke so the terminal phase reflects ke. F ⋅ D ⋅ ka e − ke ⋅t − e −ka ⋅t Cp = Vd ⋅ (k a − k e )

(

)

Determine ke: Tablet A: Terminal phase

Plasma Drug Conc. (mg/L)

10

y = 8.7116e-0.1077x R2 = 1

1

0.1 0

10

20 Time (hrs)

30

40

Based on the exponential regression of the last four data points: Cp" = C ⋅ e − k e ⋅t = 8.7116 ⋅ e −0.1077 ⋅t So ke = 0.11 hr-1 Determine ka: We can use the feathering method (also known as method of residuals) to find ka. Determine Cp” (as shown above) by extrapolating Cp (given in the table on page 1). Find the difference between Cp” and Cp, this will give you (Cp”-Cp). The absorption constant ka can be determined from the exponential regression of (Cp”–Cp).

Time (hrs) 0.5 1 2 3

Cp Cp" Cp"-Cp (mg/mL) (mg/mL) (mg/mL) 2.52 8.3 5.7 4.04 7.8 3.8 5.36 7.0 1.7 5.56 6.3 0.7

2

Case Study VI Answers PHA 5127 – Fall 2006

Tablet A: Feathering method for ka

(Cp"-Cp) {mg/L}

10

1 y = 8.5741e-0.8157x R2 = 0.9999

0 0

0.5

1

1.5 2 Time (hrs)

2.5

3

3.5

From the regression: (Cp"−Cp ) = C ⋅ e − k a ⋅t = 8.5741 ⋅ e −0.8157 ⋅t So, ka = 0.82 hr-1. Determine Vd: From the terminal phase regression line, Vd can be determined from the constant C. D ⋅ F ⋅ ka C= Vd ⋅ (k a − k e ) 8.71 mg Vd =

L

=

250mg × 0.9 × 0.82hr −1 260mg = −1 −1 Vd Vd ⋅ 0.82hr − 0.11hr

(

)

260mg = 30 L 8.71 mg L

3

Case Study VI Answers PHA 5127 – Fall 2006 Formulation B: First plot the data on a semi-log scale: Tablet B Plasma Drug Conc. (mg/L)

10

1

0.1 0

40

80

120

Time (hrs)

Looking at the plot, we can deduce the following: c) The last four data points are fairly linear and assumed to be the terminal phase d) Since the tablet is a sustained-release one, ka