Coarse Projective kMC Integration: Forward/Reverse Initial and Boundary Value Problems

In "equation-free" multiscale computation a dynamic model is given at a fine, microscopic level; yet we believe that its coarse-grained, macroscopic dynamics can be described by closed equations involving only coarse variables. These variables are typically various low-order moments of the distributions evolved through the microscopic model. We consider the problem of integrating these unavailable equations by acting directly on kinetic Monte Carlo microscopic simulators, thus circumventing their derivation in closed form. In particular, we use projective multi-step integration to solve the coarse initial value problem forward in time as well as backward in time (under certain conditions). Macroscopic trajectories are thus traced back to unstable, source-type, and even sometimes saddle-like stationary points, even though the microscopic simulator only evolves forward in time. We also demonstrate the use of such projective integrators in a shooting boundary value problem formulation for the computation of "coarse limit cycles" of the macroscopic behavior, and the approximation of their stability through estimates of the leading "coarse Floquet multipliers".Comment: Submitted to Journal of Computational Physic

Projective and Coarse Projective Integration for Problems with Continuous Symmetries

Temporal integration of equations possessing continuous symmetries (e.g. systems with translational invariance associated with traveling solutions and scale invariance associated with self-similar solutions) in a ``co-evolving'' frame (i.e. a frame which is co-traveling, co-collapsing or co-exploding with the evolving solution) leads to improved accuracy because of the smaller time derivative in the new spatial frame. The slower time behavior permits the use of {\it projective} and {\it coarse projective} integration with longer projective steps in the computation of the time evolution of partial differential equations and multiscale systems, respectively. These methods are also demonstrated to be effective for systems which only approximately or asymptotically possess continuous symmetries. The ideas of projective integration in a co-evolving frame are illustrated on the one-dimensional, translationally invariant Nagumo partial differential equation (PDE). A corresponding kinetic Monte Carlo model, motivated from the Nagumo kinetics, is used to illustrate the coarse-grained method. A simple, one-dimensional diffusion problem is used to illustrate the scale invariant case. The efficiency of projective integration in the co-evolving frame for both the macroscopic diffusion PDE and for a random-walker particle based model is again demonstrated

Variation in Structure and Process of Care in Traumatic Brain Injury: Provider Profiles of European Neurotrauma Centers Participating in the CENTER-TBI Study.

INTRODUCTION: The strength of evidence underpinning care and treatment recommendations in traumatic brain injury (TBI) is low. Comparative effectiveness research (CER) has been proposed as a framework to provide evidence for optimal care for TBI patients. The first step in CER is to map the existing variation. The aim of current study is to quantify variation in general structural and process characteristics among centers participating in the Collaborative European NeuroTrauma Effectiveness Research in Traumatic Brain Injury (CENTER-TBI) study. METHODS: We designed a set of 11 provider profiling questionnaires with 321 questions about various aspects of TBI care, chosen based on literature and expert opinion. After pilot testing, questionnaires were disseminated to 71 centers from 20 countries participating in the CENTER-TBI study. Reliability of questionnaires was estimated by calculating a concordance rate among 5% duplicate questions. RESULTS: All 71 centers completed the questionnaires. Median concordance rate among duplicate questions was 0.85. The majority of centers were academic hospitals (n = 65, 92%), designated as a level I trauma center (n = 48, 68%) and situated in an urban location (n = 70, 99%). The availability of facilities for neuro-trauma care varied across centers; e.g. 40 (57%) had a dedicated neuro-intensive care unit (ICU), 36 (51%) had an in-hospital rehabilitation unit and the organization of the ICU was closed in 64% (n = 45) of the centers. In addition, we found wide variation in processes of care, such as the ICU admission policy and intracranial pressure monitoring policy among centers. CONCLUSION: Even among high-volume, specialized neurotrauma centers there is substantial variation in structures and processes of TBI care. This variation provides an opportunity to study effectiveness of specific aspects of TBI care and to identify best practices with CER approaches

Variation in neurosurgical management of traumatic brain injury

Background: Neurosurgical management of traumatic brain injury (TBI) is challenging, with only low-quality evidence. We aimed to explore differences in neurosurgical strategies for TBI across Europe. Methods: A survey was sent to 68 centers participating in the Collaborative European Neurotrauma Effectiveness Research in Traumatic Brain Injury (CENTER-TBI) study. The questionnaire contained 21 questions, including the decision when to operate (or not) on traumatic acute subdural hematoma (ASDH) and intracerebral hematoma (ICH), and when to perform a decompressive craniectomy (DC) in raised intracranial pressure (ICP). Results: The survey was completed by 68 centers (100%). On average, 10 neurosurgeons work in each trauma center. In all centers, a neurosurgeon was available within 30 min. Forty percent of responders reported a thickness or volume threshold for evacuation of an ASDH. Most responders (78%) decide on a primary DC in evacuating an ASDH during the operation, when swelling is present. For ICH, 3% would perform an evacuation directly to prevent secondary deterioration and 66% only in case of clinical deterioration. Most respondents (91%) reported to consider a DC for refractory high ICP. The reported cut-off ICP for DC in refractory high ICP, however, differed: 60% uses 25 mmHg, 18% 30 mmHg, and 17% 20 mmHg. Treatment strategies varied substantially between regions, specifically for the threshold for ASDH surgery and DC for refractory raised ICP. Also within center variation was present: 31% reported variation within the hospital for inserting an ICP monitor and 43% for evacuating mass lesions. Conclusion: Despite a homogeneous organization, considerable practice variation exists of neurosurgical strategies for TBI in Europe. These results provide an incentive for comparative effectiveness research to determine elements of effective neurosurgical care

Risk factors for Nontuberculous Mycobacteria Infections in Solid Organ Transplant recipients: a multinational case-control study.

Risk factors for nontuberculous mycobacteria (NTM) infections after solid organ transplant (SOT) are not well characterized. Here we aimed to describe these factors. Retrospective, multinational, 1:2 matched case-control study that included SOT recipients ≥12 years old diagnosed with NTM infection from January 1, 2008, to December 31, 2018. Controls were matched on transplanted organ, NTM treatment center, and post-transplant survival greater than or equal to the time to NTM diagnosis. Logistic regression on matched pairs was used to assess associations between risk factors and NTM infections. Analyses included 85 cases and 169 controls; (59% male, 88% white, median age at time of SOT of 54 years (IQR 40-62)). NTM infection occurred in kidney (42%), lung (35%), heart and liver (11% each), and pancreas transplant recipients (1%). Time from transplant to infection was 21.6 months (IQR 5.3-55.2). Most underlying comorbidities were evenly distributed between groups; however, cases were older at the time of NTM diagnosis, more frequently on systemic corticosteroids and had a lower lymphocyte count (all P < 0.05). In the multivariable model, older age at transplant (adjusted odds ratio [aOR] 1.04; 95 confidence interval [CI] 1.01-1.07), hospital admission within 90 days (aOR, 3.14; [1.41-6.98]), receipt of antifungals (aOR, 5.35; [1.7-16.91]), and lymphocyte-specific antibodies (aOR, 7.73, [1.07-56.14]), were associated with NTM infection. Risk of NTM infection in SOT recipients was associated with older age at SOT, prior hospital admission, receipt of antifungals or lymphocyte-specific antibodies. NTM infection should be considered in SOT patients with these risk factors