GCA in 2d

We make a detailed study of the infinite dimensional Galilean Conformal Algebra (GCA) in the case of two spacetime dimensions. Classically, this algebra is precisely obtained from a contraction of the generators of the relativistic conformal symmetry in 2d. Here we find quantum mechanical realisations of the (centrally extended) GCA by considering scaling limits of certain 2d CFTs. These parent CFTs are non-unitary and have their left and right central charges become large in magnitude and opposite in sign. We therefore develop, in parallel to the usual machinery for 2d CFT, many of the tools for the analysis of the quantum mechanical GCA. These include the representation theory based on GCA primaries, Ward identities for their correlation functions and a nonrelativistic Kac table. In particular, the null vectors of the GCA lead to differential equations for the four point function. The solution to these equations in the simplest case is explicitly obtained and checked to be consistent with various requirements.Comment: 45 pages; v2: 47 pages. Restructured introduction, minor corrections, added references. Journal versio

Universal time-dependent deformations of Schrodinger geometry

We investigate universal time-dependent exact deformations of Schrodinger geometry. We present 1) scale invariant but non-conformal deformation, 2) non-conformal but scale invariant deformation, and 3) both scale and conformal invariant deformation. All these solutions are universal in the sense that we could embed them in any supergravity constructions of the Schrodinger invariant geometry. We give a field theory interpretation of our time-dependent solutions. In particular, we argue that any time-dependent chemical potential can be treated exactly in our gravity dual approach.Comment: 24 pages, v2: references adde

Enhanced Supersymmetry of Nonrelativistic ABJM Theory

We study the supersymmetry enhancement of nonrelativistic limits of the ABJM theory for Chern-Simons level $k=1,2$. The special attention is paid to the nonrelativistic limit (known as `PAAP' case) containing both particles and antiparticles. Using supersymmetry transformations generated by the monopole operators, we find additional 2 kinematical, 2 dynamical, and 2 conformal supercharges for this case. Combining with the original 8 kinematical supercharges, the total number of supercharges becomes maximal: 14 supercharges, like in the well-known PPPP limit. We obtain the corresponding super Schr\"odinger algebra which appears to be isomorphic to the one of the PPPP case. We also discuss the role of monopole operators in supersymmetry enhancement and partial breaking of supersymmetry in nonrelativistic limit of the ABJM theory.Comment: 22 pages, references added, version to appear in JHE

Detection of focal source and arrhythmogenic substrate from body surface potentials to guide atrial fibrillation ablation

Focal sources (FS) are believed to be important triggers and a perpetuation mechanism for paroxysmal atrial fibrillation (AF). Detecting FS and determining AF sustainability in atrial tissue can help guide ablation targeting. We hypothesized that sustained rotors during FS-driven episodes indicate an arrhythmogenic substrate for sustained AF, and that non-invasive electrical recordings, like electrocardiograms (ECGs) or body surface potential maps (BSPMs), could be used to detect FS and AF sustainability. Computer simulations were performed on five bi-atrial geometries. FS were induced by pacing at cycle lengths of 120-270 ms from 32 atrial sites and four pulmonary veins. Self-sustained reentrant activities were also initiated around the same 32 atrial sites with inexcitable cores of radii of 0, 0.5 and 1 cm. FS fired for two seconds and then AF inducibility was tested by whether activation was sustained for another second. ECGs and BSPMs were simulated. Equivalent atrial sources were extracted using second-order blind source separation, and their cycle length, periodicity and contribution, were used as features for random forest classifiers. Longer rotor duration during FS-driven episodes indicates higher AF inducibility (area under ROC curve = 0.83). Our method had accuracy of 90.6±1.0% and 90.6±0.6% in detecting FS presence, and 93.1±0.6% and 94.2±1.2% in identifying AF sustainability, and 80.0±6.6% and 61.0±5.2% in determining the atrium of the focal site, from BSPMs and ECGs of five atria. The detection of FS presence and AF sustainability were insensitive to vest placement (±9.6%). On pre-operative BSPMs of 52 paroxysmal AF patients, patients classified with initiator-type FS on a single atrium resulted in improved two-to-three-year AF-free likelihoods (p-value < 0.01, logrank tests). Detection of FS and arrhythmogenic substrate can be performed from ECGs and BSPMs, enabling non-invasive mapping towards mechanism-targeted AF treatment, and malignant ectopic beat detection with likely AF progression

Chaste: an open source C++ library for computational physiology and biology

Chaste - Cancer, Heart And Soft Tissue Environment - is an open source C++ library for the computational simulation of mathematical models developed for physiology and biology. Code development has been driven by two initial applications: cardiac electrophysiology and cancer development. A large number of cardiac electrophysiology studies have been enabled and performed, including high performance computational investigations of defibrillation on realistic human cardiac geometries. New models for the initiation and growth of tumours have been developed. In particular, cell-based simulations have provided novel insight into the role of stem cells in the colorectal crypt. Chaste is constantly evolving and is now being applied to a far wider range of problems. The code provides modules for handling common scientific computing components, such as meshes and solvers for ordinary and partial differential equations (ODEs/PDEs). Re-use of these components avoids the need for researchers to "re-invent the wheel" with each new project, accelerating the rate of progress in new applications. Chaste is developed using industrially-derived techniques, in particular test-driven development, to ensure code quality, re-use and reliability. In this article we provide examples that illustrate the types of problems Chaste can be used to solve, which can be run on a desktop computer. We highlight some scientific studies that have used or are using Chaste, and the insights they have provided. The source code, both for specific releases and the development version, is available to download under an open source Berkeley Software Distribution (BSD) licence at http://www.cs.ox.ac.uk/chaste, together with details of a mailing list and links to documentation and tutorials

A Workflow for Probabilistic Calibration of Models of Left Atrial Electrophysiology

Atrial fibrillation is an increasingly common condition. Computational models that describe left atrial electrophysiology have the potential to be used to guide interventions such as catheter ablation. Calibration of these models to faithfully represent left atrial structure and function in a particular patient is challenging because electrophysiology observations obtained in the clinical setting are typically sparse and noisy, and can be difficult to register to a mesh obtained from imaging. Probabilistic approaches show promise as a way to obtain personalised models while taking account of noise, sparseness, and uncertainty. We have developed a workflow in which parameter fields are represented as Gaussian processes, and the posterior distribution is inferred using MCMC. Our workflow has been tested using synthetic data, generated from simulations where the spatial variation in model parameters is known, and we have shown that both features and parameters can be recovered from simulated sparse measurements

Prolonged progressive hypermetabolism during COVID-19 hospitalization undetected by common predictive energy equations

Background & Aims: Indirect calorimetry (IC) is the gold-standard for determining measured resting energy expenditure (mREE) in critical illness. When IC is not available, predicted resting energy expenditure (pREE) equations are commonly utilized, which often inaccurately predict metabolic demands leading to over- or under-feeding. This study aims to longitudinally assess mREE via IC in critically ill patients with SARS-CoV-2 (COVID-19) infection throughout the entirety of, often prolonged, intensive care unit (ICU) stays and compare mREE to commonly utilized pREE equations. / Methods: This single-center prospective cohort study of 38 mechanically ventilated COVID-19 patients from April 1, 2020 to February 1, 2021. The Q-NRG® Metabolic Monitor was used to obtain IC data. The Harris-Benedict (HB), Mifflin St-Jeor (MSJ), Penn State University (PSU), and weight-based equations from the American Society of Parenteral and Enteral Nutrition – Society of Critical Care Medicine (ASPEN-SCCM) Clinical Guidelines were utilized to assess the accuracy of common pREE equations and their ability to predict hypo/hypermetabolism in COVID-19 ICU patients. / Results: The IC measures collected revealed a relatively normometabolic or minimally hypermetabolic mREE at 21.3 kcal/kg/d or 110% of predicted by the HB equation over the first week of mechanical ventilation (MV). This progressed to significant and uniquely prolonged hypermetabolism over successive weeks to 28.1 kcal/kg/d or 143% of HB predicted by MV week 3, with hypermetabolism persisting to MV week 7. Obese individuals displayed a more truncated response with significantly lower mREE versus non-obese patients in MV week 1 (19.5±1.0 kcal/kg/d vs 25.1±1.8 kcal/kg/d, respectively; p < 0.01), with little change in weeks 2-3 (19.5±1.5 kcal/kg/d vs 28.0±2.0 kcal/kg/d; p < 0.01). Both ASPEN-SCCM upper range and PSU pREE equations provided close approximations of mREE yet, like all pREE equations, occasionally over- and under-predicted energy needs and typically did not predict late hypermetabolism. / Conclusions: Study results show a truly unique metabolic response in COVID-19 ICU patients, characterized by significant and prolonged, progressive hypermetabolism peaking at 3 weeks’ post-intubation, persisting for up to 7 weeks in ICU. This pattern was more clearly demonstrated in non-obese versus obese patients. This response is unique and distinct from any previously described model of ICU stress response in its prolonged hypermetabolic nature. This data reaffirms the need for routine, longitudinal IC measures to provide accurate energy targets in COVID-19 ICU patients. The PSU and ASPEN-SCCM equations appear to yield the most reasonable estimation to IC-derived mREE in COVID-19 ICU patients, yet still often over-/under-predict energy needs. These findings provide a practical guide for caloric prescription in COVID-19 ICU patients in the absence of IC

Constructing a Human Atrial Fibre Atlas

Atrial anisotropy affects electrical propagation patterns, anchor locations of atrial reentrant drivers, and atrial mechanics. However, patient-specific atrial fibre fields and anisotropy measurements are not currently available, and consequently assigning fibre fields to atrial models is challenging. We aimed to construct an atrial fibre atlas from a high-resolution DTMRI dataset that optimally reproduces electrophysiology simulation predictions corresponding to patient-specific fibre fields, and to develop a methodology for automatically assigning fibres to patient-specific anatomies. We extended an atrial coordinate system to map the pulmonary veins, vena cava and appendages to standardised positions in the coordinate system corresponding to the average location across the anatomies. We then expressed each fibre field in this atrial coordinate system and calculated an average fibre field. To assess the effects of fibre field on patient-specific modelling predictions, we calculated paced activation time maps and electrical driver locations during AF. In total, 756 activation time maps were calculated (7 anatomies with 9 fibre maps and 2 pacing locations, for the endocardial, epicardial and bilayer surface models of the LA and RA). Patient-specific fibre fields had a relatively small effect on average paced activation maps (range of mean local activation time difference for LA fields: 2.67-3.60 ms, and for RA fields: 2.29-3.44 ms), but had a larger effect on maximum LAT differences (range for LA 12.7-16.6%; range for RA 11.9-15.0%). A total of 126 phase singularity density maps were calculated (7 anatomies with 9 fibre maps for the LA and RA bilayer models). The fibre field corresponding to anatomy 1 had the highest median PS density map correlation coefficient for LA bilayer simulations (0.44 compared to the other correlations, ranging from 0.14 to 0.39), while the average fibre field had the highest correlation for the RA bilayer simulations (0.61 compared to the other correlations, ranging from 0.37 to 0.56). For sinus rhythm simulations, average activation time is robust to fibre field direction; however, maximum differences can still be significant. Patient specific fibres are more important for arrhythmia simulations, particularly in the left atrium. We propose using the fibre field corresponding to DTMRI dataset 1 for LA simulations, and the average fibre field for RA simulations as these optimally predicted arrhythmia properties