Dynamical complexity of discrete time regulatory networks

Genetic regulatory networks are usually modeled by systems of coupled differential equations and by finite state models, better known as logical networks, are also used. In this paper we consider a class of models of regulatory networks which present both discrete and continuous aspects. Our models consist of a network of units, whose states are quantified by a continuous real variable. The state of each unit in the network evolves according to a contractive transformation chosen from a finite collection of possible transformations, according to a rule which depends on the state of the neighboring units. As a first approximation to the complete description of the dynamics of this networks we focus on a global characteristic, the dynamical complexity, related to the proliferation of distinguishable temporal behaviors. In this work we give explicit conditions under which explicit relations between the topological structure of the regulatory network, and the growth rate of the dynamical complexity can be established. We illustrate our results by means of some biologically motivated examples.Comment: 28 pages, 4 figure

Weaning from mechanical ventilation in intensive care units across 50 countries (WEAN SAFE): a multicentre, prospective, observational cohort study

International audienceBackground: Current management practices and outcomes in weaning from invasive mechanical ventilation are poorly understood. We aimed to describe the epidemiology, management, timings, risk for failure, and outcomes of weaning in patients requiring at least 2 days of invasive mechanical ventilation. Methods: WEAN SAFE was an international, multicentre, prospective, observational cohort study done in 481 intensive care units in 50 countries. Eligible participants were older than 16 years, admitted to a participating intensive care unit, and receiving mechanical ventilation for 2 calendar days or longer. We defined weaning initiation as the first attempt to separate a patient from the ventilator, successful weaning as no reintubation or death within 7 days of extubation, and weaning eligibility criteria based on positive end-expiratory pressure, fractional concentration of oxygen in inspired air, and vasopressors. The primary outcome was the proportion of patients successfully weaned at 90 days. Key secondary outcomes included weaning duration, timing of weaning events, factors associated with weaning delay and weaning failure, and hospital outcomes. This study is registered with ClinicalTrials.gov, NCT03255109. Findings: Between Oct 4, 2017, and June 25, 2018, 10 232 patients were screened for eligibility, of whom 5869 were enrolled. 4523 (77·1%) patients underwent at least one separation attempt and 3817 (65·0%) patients were successfully weaned from ventilation at day 90. 237 (4·0%) patients were transferred before any separation attempt, 153 (2·6%) were transferred after at least one separation attempt and not successfully weaned, and 1662 (28·3%) died while invasively ventilated. The median time from fulfilling weaning eligibility criteria to first separation attempt was 1 day (IQR 0–4), and 1013 (22·4%) patients had a delay in initiating first separation of 5 or more days. Of the 4523 (77·1%) patients with separation attempts, 2927 (64·7%) had a short wean (≤1 day), 457 (10·1%) had intermediate weaning (2–6 days), 433 (9·6%) required prolonged weaning (≥7 days), and 706 (15·6%) had weaning failure. Higher sedation scores were independently associated with delayed initiation of weaning. Delayed initiation of weaning and higher sedation scores were independently associated with weaning failure. 1742 (31·8%) of 5479 patients died in the intensive care unit and 2095 (38·3%) of 5465 patients died in hospital. Interpretation: In critically ill patients receiving at least 2 days of invasive mechanical ventilation, only 65% were weaned at 90 days. A better understanding of factors that delay the weaning process, such as delays in weaning initiation or excessive sedation levels, might improve weaning success rates. Funding: European Society of Intensive Care Medicine, European Respiratory Society