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Equation 20.1.1 Equation of the last segment AUMC
Time (hr)  Cp (mg/L)  Cp • t (mg.hr/L)  AUC (mg.hr/L)  AUMC (mg.hr^{2}/L) 

0  8  0  0  0 
1  7.09  7.09  7.55  3.55 
2  6.29  12.58  14.24  13.39 
3  5.58  16.74  20.18  28.05 
4  4.95  19.80  25.45  46.32 
6  3.89  23.34  34.29  89.46 
9  2.71  24.39  44.19  161.06 
12  1.89  22.68  51.09  231.67 
18  0.92  16.56  59.52  349.39 
24  0.44  10.56  63.60  430.75 
∞  67.27  549.31  
These data, Cp versus time and Cp x time versus time, can be plotted on linear graph.
Figure 20.1.1 Plot of Cp versus Time (IV)
Figure 20.1.2 Plot of Cp x Time versus Time (IV)
and various parameters can be calculated as:
Equation 20.1.2 Equation for Mean Residence Time (MRT)
Equation 20.1.3 Equation for Apparent Elimination Rate constant (kel')
Equation 20.1.4 Equation for Total Body Clearance (TBC)
Equation 20.1.5 Equation for Apparent Volume of Distribution, Steady State (V_{ss})
From the AUC and AUMC values we can calculate the mean residence time, MRT. This is the average time that the drug stays in the body (or plasma as measured here). It can be related to the average elimination rate constant as 1/MRT. The values from the above data are
MRT = 549.31/67.27 = 8.17 hr
and
kel' = 1/8.17 = 0.12 hr^{1}
Remember we can also calculate the clearance,
CL = Dose/AUC = 100/67.27 = 1.49 L.hr^{1}
Finally a steady state volume can be calculated as
V_{ss} = CL • MRT = 1.49 x 8.17 = 12.14 L
Oral data can be analyzed by these methods as well.
Time (hr)  Cp (mg/L)  Cp • t (mg.hr/L)  AUC (mg.hr/L)  AUMC (mg.hr^{2}/L) 

0  0  0  0  0 
1  12.18  12.2  6.09  6.09 
2  14.12  28.24  19.24  26.30 
3  13.43  40.29  33.02  60.57 
4  12.16  48.64  45.82  105.04 
6  9.64  57.84  67.62  211.52 
9  6.73  60.57  92.18  389.14 
12  4.69  56.24  109.31  564.42 
18  2.28  41.22  130.25  856.92 
24  1.11  26.64  140.45  1060.50 
∞  149.70  1359.58 
These data, Cp versus time and Cp x time versus time, can be plotted on linear graph.
Figure 20.1.3 Plot of Cp versus Time (PO)
Figure 20.1.4 Plot of Cp x Time versus Time (PO)
and additional parameters can be calculated (NOTE: We don't calculate Clearance or V_{ss} using oral data).
Equation 20.1.6 Equation for Mean Absorption Time (MAT)
Equation 20.1.7 Equation for Apparent Absorption Rate Constant (ka')
Equation 20.1.8 Equation for Oral Bioavailability (F)
The data were calculated after a 250 mg oral dose of the same drug. From these data a MRT was calculated as
MRT = AUMC/AUC = 1361/149.8 = 9.08 hr
We can subtract from this MRT(PO) the MRT(IV) to get an idea of the absorption process, the mean absorption time (MAT). That is
MAT = MRT(PO)  MRT(IV) = 9.08  8.17 = 0.92 hr
From this we can calculate an average absorption rate constant
ka' = 1/MAT = 1/0.92 = 1.09 hr^{1}
Of course we can calculate the bioavailability of the oral dosage form using the dose adjusted AUC ratio. Thus
F = (149.70/67.27) x (100/250) = 0.89
Figure 20.1.5 The Average Data from Each Dosage Form
AUC  AUMC  MRT (hr)  MAT (hr)  MDT (hr)  

IV  437  6393  14.6     
Solution  431  9454  21.9  7.3   
Tablet  450  11303  25.1  10.5  3.2 
Slow Tablet  765  45484  59.5  44.9  37.6 
Rate Constant (hr^{1})  Non Linear Regression Analysis  Non Compartmental Analysis 

kel'  0.077  0.068 
ka'  0.11  0.14 
kd' (fast)  0.41  0.31 
kd' (slow)  0.026  0.027 
Non compartmental analysis:
kel' = 1/MRT
ka' = 1/MAT
kd' = 1/MDT
where MDT is the mean dissolution time
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