Explicit reformulations of the Lambert W-omega function for calculations of the solutions to one-compartment pharmacokinetic models with Michaelis-Menten elimination kinetics.

The exact closed-form solutions to the integrated rate equations for one-compartment pharmacokinetic models that obey Michaelis-Menten elimination kinetics were derived recently (Tang and Xiao in J Pharmacokin Pharmacodyn 34:807-827, 2007). These solutions are expressed in terms of the Lambert W(x)-omega function; however, unfortunately, most of the available computer programs are not set up to handle equations that involve the W(x) function. Therefore, in this article, I provide alternative explicit analytical equations expressed in terms of elementary mathematical functions that accurately approximate exact solutions and can be simply calculated using any optional standard software.