5.5 Deconvolution

When we know C(t) and one of f(t) or g(t), then we can know the remained f(t) or g(t).

In other words, if we know C(t) and f(t), we can get g(t).

And if we know C(t) and g(t), we can know f(t).

This technique to find the unknown function is called deconvolution.

This technique usually use the sigma(Sigma) notation.

Usage Example of This Concept

If we have the Laplace transformation of Input and Disposition functions,

Inverse Laplace transformation of the product is C(t).

\[ L(f(t)) = in(s) \] \[ L(g(t)) = d(s) \]

then

\[ L^{-1} \left( in(s) \cdot d(s) \right) = C(t) \]

This property is used in the Gibaldi’s Pharmacokinetics (See Appendix A of that book)