Pulse dynamics in a three-component system : stability and bifurcations

In this article, we analyze the stability and the associated bifurcations of several types of pulse solutions in a singularly perturbed three-component reaction-diffusion equation that has its origin as a model for gas discharge dynamics. Due to the richness and complexity of the dynamics generated by this model, it has in recent years become a paradigm model for the study of pulse interactions. A mathematical analysis of pulse interactions is based on detailed information on the existence and stability of isolated pulse solutions. The existence of these isolated pulse solutions is established in previous work. Here, the pulse solutions are studied by an Evans function associated to the linearized stability problem. Evans functions for stability problems in singularly perturbed reaction-diffusion models can be decomposed into a fast and a slow component, and their zeroes can be determined explicitly by the NLEP method. In the context of the present model, we have extended the NLEP method so that it can be applied to multi-pulse and multi-front solutions of singularly perturbed reaction-diffusion equations with more than one slow component. The brunt of this article is devoted to the analysis of the stability characteristics and the bifurcations of the pulse solutions. Our methods enable us to obtain explicit, analytical information on the various types of bifurcations, such as saddle-node bifurcations, Hopf bifurcations in which breathing pulse solutions are created, and bifurcations into travelling pulse solutions, which can be both subcritical and supercritical.

Increased sedation requirements in patients receiving extracorporeal membrane oxygenation for respiratory and cardiorespiratory failure

Critically ill patients receiving extracorporeal membrane oxygenation (ECMO) are often noted to have increased sedation requirements. However, data related to sedation in this complex group of patients is limited. The aim of our study was to characterise the sedation requirements in adult patients receiving ECMO for cardiorespiratory failure. A retrospective chart review was performed to collect sedation data for 30 consecutive patients who received venovenous or venoarterial ECMO between April 2009 and March 2011. To test for a difference in doses over time we used a regression model. The dose of midazolam received on ECMO support increased by an average of 18 mg per day (95% confidence interval 8, 29 mg, P=0.001), while the dose of morphine increased by 29 mg per day (95% confidence interval 4, 53 mg, P=0.021) The venovenous group received a daily midazolam dose that was 157 mg higher than the venoarterial group (95% confidence interval 53, 261 mg, P=0.005). We did not observe any significant increase in fentanyl doses over time (95% confidence interval 1269, 4337 µg, P=0.94). There is a significant increase in dose requirement for morphine and midazolam during ECMO. Patients on venovenous ECMO received higher sedative doses as compared to patients on venoarterial ECMO. Future research should focus on mechanisms behind these changes and also identify drugs that are most suitable for sedation during ECMO.