There is a vast literature on the analysis of optimal design of nonlinear mixed-effects models (NLMMs) described by ordinary differential equations (ODEs) with analytic solution. However, much less has been published on the design of trials to fit such models with nonanalytic solution. In this article, we use the "direct" method to find parameter sensitivities, which are required during the optimization of models defined as ODEs, and apply them to find D-optimal designs for various specific situations relevant to population pharmacokinetic studies using a particular model with first-order absorption and elimination. In addition, we perform two simulation studies. The first one aims to show that the criterion computed from the development of the Fisher information matrix expression is a good measure to compare and optimize population designs, thus avoiding a large number of simulations; In the second one, a sensitivity analysis with respect to parameter misspecification allows us to compare the robustness of different population designs constructed in this article.