Limited sampling strategy and population pharmacokinetic model of mycophenolic acid in pediatric patients with systemic lupus erythematosus: application of a double gamma absorption model with SAEM algorithm.

INTRODUCTION: Mycophenolic acid (MPA), the active metabolite of mycophenolate mofetil (MMF), is widely used in the treatment of systemic lupus erythematosus (SLE). It has been shown that its therapeutic drug monitoring based on the area under the curve (AUC) improves treatment efficacy. MPA exhibits a complex bimodal absorption, and a double gamma distribution model has been already proposed in the past to accurately describe this phenomenon. These previous population pharmacokinetics models (POPPK) have been developed using iterative two stage Bayesian (IT2B) or non-parametric adaptive grid (NPAG) methods. However, non-linear mixed effect (NLME) approaches based on stochastic approximation expectation-maximization (SAEM) algorithms have never been published so far for this particular model. The objectives of this study were (i) to implement the double absorption gamma model in Monolix, (ii) to compare different absorption models to describe the pharmacokinetics of MMF, and (iii) to develop a limited sampling strategy (LSS) to estimate AUC in pediatric SLE patients. MATERIAL AND METHODS: A data splitting of full pharmacokinetic profiles sampled in 67 children extracted either from the expert system ISBA (n = 34) or the hospital Saint Louis (n = 33) was performed into train (75%) and test (25%) sets. A POPPK was developed for MPA in the train set using a NLME and the SAEM algorithm and different absorption models were implemented and compared (first order, transit, or simple and double gamma). The best limited sampling strategy was then determined in the test set using a maximum-a-posteriori Bayesian method to estimate individual PK parameters and AUC based on three blood samples compared to the reference AUC calculated using the trapezoidal rule applied on all samples and performances were assessed in the test set. RESULTS: Mean patient age and dose was 13 years old (5-18) and 18.1 mg/kg (7.9-47.6), respectively. MPA concentrations (764) from 107 occasions were included in the analysis. A double gamma absorption with a first-order elimination from the central compartment best fitted the data. The optimal LSS with samples at 30 min, 2 h, and 3 h post-dose exhibited good performances in the test set (mean bias - 0.32% and RMSE 21.0%). CONCLUSION: The POPPK developed in this study adequately estimated the MPA AUC in pediatric patients with SLE based on three samples. The double absorption gamma model developed with the SAEM algorithm showed very accurate fit and reduced computation time.

Clusters in nonsmooth oscillator networks.

For coupled oscillator networks with Laplacian coupling, the master stability function (MSF) has proven a particularly powerful tool for assessing the stability of the synchronous state. Using tools from group theory, this approach has recently been extended to treat more general cluster states. However, the MSF and its generalizations require the determination of a set of Floquet multipliers from variational equations obtained by linearization around a periodic orbit. Since closed form solutions for periodic orbits are invariably hard to come by, the framework is often explored using numerical techniques. Here, we show that further insight into network dynamics can be obtained by focusing on piecewise linear (PWL) oscillator models. Not only do these allow for the explicit construction of periodic orbits, their variational analysis can also be explicitly performed. The price for adopting such nonsmooth systems is that many of the notions from smooth dynamical systems, and in particular linear stability, need to be modified to take into account possible jumps in the components of Jacobians. This is naturally accommodated with the use of saltation matrices. By augmenting the variational approach for studying smooth dynamical systems with such matrices we show that, for a wide variety of networks that have been used as models of biological systems, cluster states can be explicitly investigated. By way of illustration, we analyze an integrate-and-fire network model with event-driven synaptic coupling as well as a diffusively coupled network built from planar PWL nodes, including a reduction of the popular Morris-Lecar neuron model. We use these examples to emphasize that the stability of network cluster states can depend as much on the choice of single node dynamics as it does on the form of network structural connectivity. Importantly, the procedure that we present here, for understanding cluster synchronization in networks, is valid for a wide variety of systems in biology, physics, and engineering that can be described by PWL oscillators.