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Finger Print Method

Inverse Laplace Transform

The so-called finger print method provides a quick and easy method for the back transformation of many of the Laplace equations found in pharmacokinetics. With a few limitations the method can be commonly applied. This method is derived from the explanation of the general partial fraction method presented by Benet and Turi (Benet, L.Z. and Turi, J.S. 1971. "Use of the General Partial Fraction Theorems for Obtaining Inverse Laplace Transforms in Pharmacokinetic Analysis", J. Pharm. Sci., 60: 1593-1594).

General Partial Fraction Method

The general partial fraction method is summarized with the equation:

General Partial Fraction Theorem equation

Equation 7.2.1 Equation demonstrating the General Partial Fraction Theorem

The function in 's' on the left is transformed into the function on the right in terms of 't' (time). The λ terms are the roots of the polynomial term in the denominator on the left. In pharmacokinetic equations these are usually zero or negative.

Limitations or Requirements

There are two requirements for this method to be applicable. Examples

Fractions which don't comply with requirements

Equation 7.2.2 Fractions which Don't Comply with the Limitations

Fractions which do comply

Equation 7.2.3 Fractions which Do Comply with the Limitations

General Procedure

The general procedure for this method is to:

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