Regional performance variation in external validation of four prediction models for severity of COVID-19 at hospital admission: An observational multi-centre cohort study

Background Prediction models should be externally validated to assess their performance before implementation. Several prediction models for coronavirus disease-19 (COVID-19) have been published. This observational cohort study aimed to validate published models of severity for hospitalized patients with COVID-19 using clinical and laboratory predictors. Methods Prediction models fitting relevant inclusion criteria were chosen for validation. The outcome was either mortality or a composite outcome of mortality and ICU admission (severe disease). 1295 patients admitted with symptoms of COVID-19 at Kings Cross Hospital (KCH) in London, United Kingdom, and 307 patients at Oslo University Hospital (OUH) in Oslo, Norway were included. The performance of the models was assessed in terms of discrimination and calibration. Results We identified two models for prediction of mortality (referred to as Xie and Zhang1) and two models for prediction of severe disease (Allenbach and Zhang2). The performance of the models was variable. For prediction of mortality Xie had good discrimination at OUH with an area under the receiver-operating characteristic (AUROC) 0.87 [95% confidence interval (CI) 0.79–0.95] and acceptable discrimination at KCH, AUROC 0.79 [0.76–0.82]. In prediction of severe disease, Allenbach had acceptable discrimination (OUH AUROC 0.81 [0.74–0.88] and KCH AUROC 0.72 [0.68–0.75]). The Zhang models had moderate to poor discrimination. Initial calibration was poor for all models but improved with recalibration. Conclusions The performance of the four prediction models was variable. The Xie model had the best discrimination for mortality, while the Allenbach model had acceptable results for prediction of severe disease

Early Embryonic Vascular Patterning by Matrix-Mediated Paracrine Signalling: A Mathematical Model Study

During embryonic vasculogenesis, endothelial precursor cells of mesodermal origin known as angioblasts assemble into a characteristic network pattern. Although a considerable amount of markers and signals involved in this process have been identified, the mechanisms underlying the coalescence of angioblasts into this reticular pattern remain unclear. Various recent studies hypothesize that autocrine regulation of the chemoattractant vascular endothelial growth factor (VEGF) is responsible for the formation of vascular networks in vitro. However, the autocrine regulation hypothesis does not fit well with reported data on in vivo early vascular development. In this study, we propose a mathematical model based on the alternative assumption that endodermal VEGF signalling activity, having a paracrine effect on adjacent angioblasts, is mediated by its binding to the extracellular matrix (ECM). Detailed morphometric analysis of simulated networks and images obtained from in vivo quail embryos reveals the model mimics the vascular patterns with high accuracy. These results show that paracrine signalling can result in the formation of fine-grained cellular networks when mediated by angioblast-produced ECM. This lends additional support to the theory that patterning during early vascular development in the vertebrate embryo is regulated by paracrine signalling

Modelling vascular morphogenesis: current views on blood vessels development

In this work we present a comprehensive account of our current knowledge on vascular morphogenesis, both from a biological and a mathematical point of view. To this end, we first describe the basic steps in the known mechanisms of blood vessel morphogenesis, whose structure, function and unfolding properties are examined. We then provide a wide, although by no means exhaustive, account of mathematical models which are used to describe and discuss particular aspects of the overall biological process considered. We finally summarize the approaches presented, and suggest possible directions for future research. Details about some of the major signalling molecules involved are included in a first Appendix at the end of the paper. A second Appendix provides a brief overview of design principles for vascular nets, a subject that has deserved considerable attention over the years

Cell elongation.

<p>Distribution of cell lengths at different time points during the simulation. Red line and inset depict early, blue depicts late in development. Lengths are normalized to isotropic cells given the target area (, where is the scaling factor per pixel). Cells become increasingly anisotropic and elongated during vascular patterning. Filled regions represent standard deviation.</p

Paracrine chemotaxis model for vasculogenesis.

<p>Angioblasts (endothelial progenitor cells) are derived from mesodermal cells and assemble into polygonal networks under instructive paracrine signalling provided by the endoderm. Endodermal cells express pro-vascular growth factors such as VEGF. Angioblasts are located in the space between endoderm and mesoderm, surrounded by extracellular matrix (ECM). Angioblasts produce ECM molecules (such as heparan sulphates and fibronectin) with VEGF binding domains (depicted in yellow). This matrix thus acts to store chemotactic growth factors, which provides spatial cues for cell migration.</p

Morphometric comparison.

<p>Comparison between experimental (in blue) and simulated (in red) vascular networks (after 3000 MCS). (A) Binary images over cellular structures (green) overlayed with skeletonized network (red), detected branching points (blue points) and corrected nodes (blue circles). (B) Morphometric statistics. Boxes show average values (n = 2 for experiments; n = 10 for simulation) and error bars indicate standard deviation. (C) Distributions of morphometric properties. Lines show average values; filled areas indicate standard deviations.</p

Sensitivity analysis of chemotactic signal strength.

<p>Sensitivity of morphometric parameters to relative strength of bound () and soluble () VEGF. Red points (lacunae) and blue points (nodes) show averages of measured quantities in simulations (n = 3), half-transparent regions represent standard deviations. Insets show portions of networks (200×200) where the relative signalling strength () is set to soluble-VEGF-only (, left), bound-VEGF-only (, right) and equal strengths (, center). Arrowhead indicates the reference value.</p