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- To understand and use the non compartmental approach to parameter estimation
- be able to define, use, and calculate the parameters:
- AUMC (area under the first moment curve)
- MRT (mean residence time)
- MAT (mean absorption time)
- MDT (mean dissolution time)

**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

- IV Bolus 107 mg/Kg
- Oral Solution 107 mg/Kg
- Oral Rapid Release Tablet 105 mg/Kg
- Oral Sustained Release Tablet 249 mg/Kg

**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

Want more practice with this type of problem!

- Bevill, R.F., Dittert, L.W. and Bourne, D.W.A. 1977 Pharmacokinetics of Sulfamethazine in Cattle following IV and Three Oral Dosage Forms,
*J. Pharm. Sci.*,**66**, 619-23

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