Question

The most efficient way to administer a drug to its intended target site is to administer it intravenously (directly to the blood). If the drug is administered in any other way (for example orally, nasal inhalant, or skin patch), then some of the drug is typically lost due to absorption before it gets to the blood. By definition, the bio-availability of a drug (F) measures the effectiveness of a non-intravenous method compared to an intravenous method. The bio-availability of intravenous dosing is 100%, F = 1. Let the functions Ci and Co give the concentrations of a drug in the blood, for times , using intravenous and oral dosing, respectively. (These functions can be determined through clinical experiments.) Assuming the same about the drug is initially administered by both methods, the bioavailability for oral dose (F0) is defined to be :
Where UAC is used in the pharmacology literature to mean "Area Under the Curve"

Suppose the concentration of a certain drug in the blood in mg/L when given intravenously is:

Ci(t) = 100e-0.3t

whereis measured in hours.

Suppose that the concentration of the same drug when delivered orally is:

C0(t) = 90(e-0.3t - e-2.5t)

Find F, the bio-availability of the drug.

Answer 1

Answer:

 F = 0.792

Step-by-step explanation:

Given:

- The function C_o :

                               C_o (t) = 90*(e^-0.3t - e^-2.5t)

- The function C_i :

                               C_i (t) = 100*e^-0.3t

The function:

                               $F = UAC_o / UAC_i = \frac{\int\limits^n_0 {C_o} \, dt }{\int\limits^n_0 {C_i} \, dt }$

Find:

- The factor F.

Solution:

- Determine UAC_o from the function given:

                       UAC_o = integral ( 90*(e^-0.3t - e^-2.5t) ) dt

                       UAC_o = -300*e^(-0.3t) + 36*e^(-2.5t)

Evaluate integral from infinity to zero:

                      | UAC_o | = 300 - 36 = 264

- Determine UAC_i from the function given:

                       UAC_i = integral ( 100e-0.3t ) dt

                       UAC_i = -333.333*e^(-0.3t)

Evaluate integral from infinity to zero:

                      | UAC_i | =  0 + 333.333 = 333.3333

- Evaluate factor F:

                          F =  | UAC_o | / | UAC_i |

                          F = 264 / 333.3333

                         F = 0.792