Question

The following data are simulated for a 200 mg dose of a drug given p.o. and i.v. VD = 500L Rate of absorption (oral only) = 0.0096 min-1 (IV bolus was assumed 100% absorption immediately) Rate of elimination = ke = 0.0099 min-1 Therefore, elimination half-life (t1/2) = 0.693/ke = 70 min Calculate the AUC of both p.o. and i.v. doses. I suggest using the trapezoidal method for calculating AUC: sum of [{avg of two points}*{time between two points}]. Then calculate the bioavailable fraction (F).

Time (min)	Cp (ug/L)
1	3.78
5	17.8
10	33.2
15	46.2
30	74.4
45	89.9
60	96.7
90	94.9
120	83.4
180	55.4
240	33.5
360	11.0
420	6.14
540	1.90

Time (min)	Cp (ug/L)
1	396
5	381
10	362
15	345
30	297
45	256
60	221
90	164
120	122
180	67.3
240	37.2
360	11.3
420	6.26
540	1.91

Answer 1

For O.P.

STEP 1. Plot Average concentration (Cp) versus time

STEP 2: Calculate Area under the curve using the formula

AUC_n= [(c_n + c_n+1)/2] x Time interval

For P.O.

Time (min)	P.O. Cp	Avg conc	AUC
1	3.78
5	17.8	10.79	53.95
10	33.2	25.5	127.5
15	46.2	39.7	198.5
30	74.4	60.3	904.5
45	89.9	82.15	1232.25
60	96.7	93.3	1399.5
90	94.9	95.8	2874
120	83.4	89.15	2674.5
180	55.4	69.4	4164
240	33.5	44.45	2667
360	11	22.25	2670
420	6.14	8.57	514.2
540	1.9	4.02	482.4

Cp_max for P.O. is 96.6 and t_max= 60 min.

For I.V.

Step 1.

For I.V. Step 2.

Time (min)	i.v. Cp (ug/L)	Avg conc	AUC
1	396
5	381	388.5	1942.5
10	362	371.5	1857.5
15	345	353.5	1767.5
30	297	321	4815
45	256	276.5	4147.5
60	221	238.5	3577.5
90	164	192.5	5775
120	122	143	4290
180	67.3	94.65	5679
240	37.2	52.25	3135
360	11.3	24.25	2910
420	6.26	8.78	526.8
540	1.91	4.085	490.2

Cp_max for I.V. is 400 and t_max= 1 min.

Calculation of Bioavailability:

Bioavailability is known as the fraction or the percent of the drug that actually reaches the circulation.

The bioavailability can be calculated using the formulae:

F_oral = (AUC_oral/D^o_oral)/(AUC_IV/D^o_IV)

Time (min)	P.O. Cp	Oral Avg conc	AUC (Oral)	i.v. Cp (ug/L)	I.V. Avg conc	AUC (IV)	F oral
1	3.78			396
5	17.8	10.79	53.95	381	388.5	1942.5	1
10	33.2	25.5	127.5	362	371.5	1857.5	1
15	46.2	39.7	198.5	345	353.5	1767.5	1
30	74.4	60.3	904.5	297	321	4815	1
45	89.9	82.15	1232.25	256	276.5	4147.5	1
60	96.7	93.3	1399.5	221	238.5	3577.5	1
90	94.9	95.8	2874	164	192.5	5775	1
120	83.4	89.15	2674.5	122	143	4290	1
180	55.4	69.4	4164	67.3	94.65	5679	1
240	33.5	44.45	2667	37.2	52.25	3135	1
360	11	22.25	2670	11.3	24.25	2910	1
420	6.14	8.57	514.2	6.26	8.78	526.8	1
540	1.9	4.02	482.4	1.91	4.085	490.2	1

Thus, the bioavailability was calculated as 1 (100%)