Analytical solution of linear multi-compartment models with non-zero initial condition and its implementation with R

The analytical solution for multi-compartment models with a non-zero initial condition is complex because of the inter-compartmental transfer. An elegant solution and its implementation in the ‘wnl' R package can be useful in solving examples of textbooks and developing software of therapeutic drug monitoring, pharmacokinetic simulation, and parameter estimation. This solution uses Laplace transformation, convolution, matrix inversion, and the fact that the general solution of an inhomogeneous ordinary differential equation is the sum of a homogenous and a particular solution, together.