Calculation of Volume Distribution¶
The Volume of Distribution is calculated in the below written fashion:
Necessary Parameters¶
Parameters |
Insight |
|---|---|
\(X\) |
Dose Administered |
\(C\) |
Concentration dataset [provided] |
\(T\) |
Time dataset [provided] |
\(ln(C)\) |
The natural logarithm of concentration data |
\(CT\) |
The multiplication of \(C\) with \(T\) |
\(K_{el}\) |
Elimination constant |
\(AUC\) |
Area under \(C\) ~ \(T\) curve |
\(AUMC\) |
Area under \(CT\) ~ \(T\) curve |
\(MRT\) |
The ratio of \(AUMC\) to \(AUC\) |
Manipulating Necessary Parameters¶
\(X\) is taken from the Dose Data.
\(ln(C)\) is made by applying \(log\) to each element of \(C\).
\(CT\) is made by multiplying \(C\) with \(T\).
\(k_{el}\) is calculated by linear regression from \(ln(C)\) ~ \(T\) curve, and will be plotted later.
\(AUC\) is the area under \(C\) ~ \(T\) curve, calculated by trapizoidal rule.
\(AUMC\) is the area under \(CT\) ~ \(T\) curve, calculated by trapizoidal rule.
\(MRT\) is calculated by the ratio of \(AUMC\) to \(AUC\)
Note
If \(C\) and \(T\) starts from 0, then program will try to compute \(ln(0)\), which is undefined.
Calculating Volume Distribution¶
- \(V_{area}\) is calculated by the formula
- \[\frac{X}{K_{el} \times AUC}\]
- \(V_{ss}\) is calculated by the formula
- \[\frac{X}{AUC} \times MRT\]