Two-compartment mammillary model for intravenous administration using Laplace transform

6 Two-compartment mammillary model for intravenous administration using Laplace transform 

This model is an extension of the one-compartment model for intravenous injection (Section 39.1.1) which is now provided with a peripheral buffering compartment which exchanges with the central plasma compartment. Elimination occurs via the central compartment (Fig. 39.12). The model requires the estimation of the plasma volume of distribution and three transfer constants, namely for 

These equations form a set of first order linear differential equations with constant coefficients and with initial conditions  

While the simple linear models in the previous sections have been solved by straightforward integration, the present model (and more complicated ones) are more conveniently solved by means of the Laplace transform. 

In this section, we will outline only those properties of the Laplace transform that are directly relevant to the solution of systems of linear differential equations with constant coefficients. A more extensive coverage can be found, for example, in the text book by Franklin [6]. 

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