Multi-scale approaches for the simulation of cardiac electrophysiology: I – sub-cellular and stochastic calcium dynamics from cell to organ

Computational models of the heart at multiple spatial scales, from sub-cellular nanodomains to the whole-organ, are a powerful tool for the simulation of cardiac electrophysiology. Application of these models has provided remarkable insight into the normal and pathological functioning of the heart. In these two articles, we present methods for modelling cardiac electrophysiology at all of these spatial scales. In part one, presented here, we discuss methods and approaches for modelling sub-cellular calcium dynamics at the whole-cell and organ scales, valuable for modelling excitation–contraction coupling and mechanisms of arrhythmia triggers

A two-dimensional organic-exciton polariton lattice fabricated using laser patterning

Exciton-polaritons in 2D lattice geometries now attract considerable attention as systems in which to explore new physics. However, such structures are relatively difficult to fabricate as this can involve sophisticated milling or etching of cavity layers to create arrays of defects. Here, a straightforward technique is reported that allows rapid fabrication of 2D polariton lattices that operate at room temperature. Specifically, laser patterning has been used to write a 2D square lattice of defects into a sacrificial polymer layer. An organic microcavity structure is then built on top of the patterned polymer, with the morphology of the patterned polymer propagating through the subsequent layers and spatially modifying the optical path-length of the active cavity region. Using real- and momentum-space spectroscopy, the formation of gapped polaritonic band structures has been demonstrated at room temperature. The optical writing approach discussed here opens up the way for fabrication of more complex 2D-lattice geometries for studying topological physics at room temperature

Aspects of electrostatics in a weak gravitational field

Several features of electrostatics of point charged particles in a weak, homogeneous, gravitational field are discussed using the Rindler metric to model the gravitational field. Some previously known results are obtained by simpler and more transparent procedures and are interpreted in an intuitive manner. Specifically: (i) We show that the electrostatic potential of a charge at rest in the Rindler frame is expressible as A_0=(q/l) where l is the affine parameter distance along the null geodesic from the charge to the field point. (ii) We obtain the sum of the electrostatic forces exerted by one charge on another in the Rindler frame and discuss its interpretation. (iii) We show how a purely electrostatic term in the Rindler frame appears as a radiation term in the inertial frame. (In part, this arises because charges at rest in a weak gravitational field possess additional weight due to their electrostatic energy. This weight is proportional to the acceleration and falls inversely with distance -- which are the usual characteristics of a radiation field.) (iv) We also interpret the origin of the radiation reaction term by extending our approach to include a slowly varying acceleration. Many of these results might have possible extensions for the case of electrostatics in an arbitrary static geometry. [Abridged Abstract]Comment: 26 pages; accepted for publication in Gen.Rel.Gra

Far-field positive phase blast parameter characterisation of RDX and PETN based explosives

A significant amount of scientific effort has been dedicated to measuring and understanding the effects of explosions, leading to the development of semi-empirical methods for rapid prediction of blast load parameters. The most well-known of these, termed the Kingery and Bulmash method, makes use of polylogarithmic curves derived from a compilation of medium to large scale experimental tests performed over many decades. However, there is still no general consensus on the accuracy and validity of this approach, despite some researchers reporting consistently high levels of agreement. Further, it is still not known whether blast loading can be considered deterministic, or whether it is intrinsically variable, the extent of this variability, and the range and scales over which these variations are observed. This article critically reviews historic and contemporary blast experiments, including newly generated arena tests with RDX and PETN-based explosives, with a view to demonstrating the accuracy with which blast load parameters can be predicted using semi-empirical approaches

Considering discrepancy when calibrating a mechanistic electrophysiology model

Uncertainty quantification (UQ) is a vital step in using mathematical models and simulations to take decisions. The field of cardiac simulation has begun to explore and adopt UQ methods to characterize uncertainty in model inputs and how that propagates through to outputs or predictions; examples of this can be seen in the papers of this issue. In this review and perspective piece, we draw attention to an important and under-addressed source of uncertainty in our predictions—that of uncertainty in the model structure or the equations themselves. The difference between imperfect models and reality is termed model discrepancy, and we are often uncertain as to the size and consequences of this discrepancy. Here, we provide two examples of the consequences of discrepancy when calibrating models at the ion channel and action potential scales. Furthermore, we attempt to account for this discrepancy when calibrating and validating an ion channel model using different methods, based on modelling the discrepancy using Gaussian processes and autoregressive-moving-average models, then highlight the advantages and shortcomings of each approach. Finally, suggestions and lines of enquiry for future work are provided. This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’

Species abundance distributions: moving beyond single prediction theories to integration within an ecological framework

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75247/1/j.1461-0248.2007.01094.x.pd

Distinct clinical symptom patterns in patients hospitalised with COVID-19 in an analysis of 59,011 patients in the ISARIC-4C study

COVID-19 is clinically characterised by fever, cough, and dyspnoea. Symptoms affecting other organ systems have been reported. However, it is the clinical associations of different patterns of symptoms which influence diagnostic and therapeutic decision-making. In this study, we applied clustering techniques to a large prospective cohort of hospitalised patients with COVID-19 to identify clinically meaningful sub-phenotypes. We obtained structured clinical data on 59,011 patients in the UK (the ISARIC Coronavirus Clinical Characterisation Consortium, 4C) and used a principled, unsupervised clustering approach to partition the first 25,477 cases according to symptoms reported at recruitment. We validated our findings in a second group of 33,534 cases recruited to ISARIC-4C, and in 4,445 cases recruited to a separate study of community cases. Unsupervised clustering identified distinct sub-phenotypes. First, a core symptom set of fever, cough, and dyspnoea, which co-occurred with additional symptoms in three further patterns: fatigue and confusion, diarrhoea and vomiting, or productive cough. Presentations with a single reported symptom of dyspnoea or confusion were also identified, alongside a sub-phenotype of patients reporting few or no symptoms. Patients presenting with gastrointestinal symptoms were more commonly female, had a longer duration of symptoms before presentation, and had lower 30-day mortality. Patients presenting with confusion, with or without core symptoms, were older and had a higher unadjusted mortality. Symptom sub-phenotypes were highly consistent in replication analysis within the ISARIC-4C study. Similar patterns were externally verified in patients from a study of self-reported symptoms of mild disease. The large scale of the ISARIC-4C study enabled robust, granular discovery and replication. Clinical interpretation is necessary to determine which of these observations have practical utility. We propose that four sub-phenotypes are usefully distinct from the core symptom group: gastro-intestinal disease, productive cough, confusion, and pauci-symptomatic presentations. Importantly, each is associated with an in-hospital mortality which differs from that of patients with core symptoms