Question

An HPLC method was developed for the separation and determination of ibuprofen in rat plasma samples as part of a study of the time course of the drug in laboratory animals. Several standards were chromatographed and the following results obtained:

Ibuprofen Concentration $\mu g/mL$	Relative Peak Area
0.5	5.0
1.0	10.1
2.0	17.2
3.0	19.8
6.0	39.7
8.0	57.3
10.0	66.9
15.0	95.3

Next, a 10mg/kg sample of ibuprofen was administered orally to a laboratory rat. Blood samples were drawn at various times after administration of the drug and subjected to HPLC analysis. The following results were obtained:

Time, h	Peak Area
0	0
0.5	91.3
1.0	80.2
1.5	52.1
2.0	38.5
3.0	24.2
4.0	21.2
6.0	18.5
8.0	15.2

Find the concentration of ibuprofen in the blood plasma for each of the times given above and plot the concentration versus time. On a percentage basis, during what half-hour period (first, second, third, etc.) is most of the ibuprofen lost?

Short answer

HPLC is an analytical chemistry technique that isolates, identifies, and quantifies each component of a mixture.

Step-by-step solution

Analysis

The following two table are given below:

Ibuprofen Concentration (microgram/mL)	Relative Peak Area
0.5	5.0
1.0	10.1
2.0	17.2
3.0	19.8
6.0	39.7
8.0	57.3
10.0	66.9
15.0	95.3

Time, h	Peak Area
0	0
0.5	91.3
1.0	80.2
1.5	52.1
2.0	38.5
3.0	24.2
4.0	21.2
6.0	18.5
8.0	15.2

Let us plot the above points and obtain the slope and intercept to obtain the graph by using the relative peak area on the $y$-axis against the ibuprofen concentration on the $x$-axis.

Explanation

From the above graph, the values of the slope and the intercept are obtained as $6.2669\mu \mathrm{g}/\mathrm{mL}$and $3.2695$respectively. It can be also seen that these values can also be used to calculate the concentration of the ibuprofen at different time intervals.

Time (h)	Relative Peak Area
0	0
0.5	91.3
1.0	52.1
2.0	38.5
3.0	24.2
4.0	21.2
6.0	18.5
8.0	15.2

Explanation

Ibuprofen Concentration (microgram/mL)	Relative Peak Area
0.5	5.0
1	10.1
2	17.2
3	19.8
6	39.7
8	57.3
10	66.9
15	95.3
Slope	6.2669
Intercept	3.2695

Analysis

Time (h)	Relative Peak Area	Concentration(microgram/mL)	Percentage Change
0	0	14.05
0.5	91.3	12.28	12.61
1.0	52.1	7.79	36.53
2.0	38.5	5.62	27.85
3.0	24.2	3.34	20.29
4.0	21.2	2.86	7.17
6.0	18.5	2.43	3.76
8.0	15.2	1.9	5.42

Documentation

$C20=(B20-B12)/B11$

$D21=(C20-C21)/C20$

Analysis

Let us plot the above points and obtain the slope and intercept to obtain the graph by using the ibuprofen concentration on the $y$-axis against the time in hours on the $x$-axis.

So, finally based on the spreadsheet and graph given above it can be easily observed that the maximum percentage loss in the concentration of ibuprofen is during $1.0-1.5$hours.