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The following plasma concentrations (in ug/ml) of a new drug were recorded in a patient
The following plasma concentrations (in ug/ml) of a new drug were recorded in a patient. Is this data best fit by a single or double compartment model?
Time (hr) conc.
0.26 0.6149
0.51 0.4299
0.77 0.3213
1.02 0.2203
1.25 0.1773
1.51 0.1242
1.76 0.1167
2.02 0.0928
2.25 0.0722
2.51 0.0658
2.76 0.0614
3.02 0.0607
4.02 0.0471
5.01 0.0505
6.01 0.0438
7.01 0.0379
8.01 0.0325
9 0. 0305
10 0 .0282
From my understanding, you just need to either do a single exponential fit or a more complex exponential fit to see which fits the points better and determine single vs. double compartment model.
I think that if a single exponential does not fit, then a "best-fit" model is used, and it can be called a double compartment.
Expert Solution
please see the attached file.
Let C = concentration
t = time
If we use a single exponential fit then we could write:
C = aebt
I have done so in Excel but a single fit is not adequate. So we can try with 2 exponential functions:
C = aebt + cedt
I have done the curve fitting in a software called Statistica. I don't think you'll have this software but you can also do it in Matlab. The parameters in the double-exponential fit were found to be:
A= 0.06373
B = -0.07580
C = 0.83030
D = -1.56689
So you can now graph the fit function in excel. And as you can see, they fit extremely well. So to conclude, the data could be better fit with double-exponential function.
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