In cardiac cells, calcium is the mediator of excitation-contraction coupling. Dysfunctions in calcium handling have been identified as the origin of some cardiac arrhythmias. In the particular case of atrial myocytes, recent available experimental data has found links between these dysfunctions and structural changes in the calcium handling machinery (ryanodine cluster size and distribution, t-tubular network, etc). To address this issue, we have developed a computational model of an atrial myocyte that takes into account the detailed intracellular structure. The homogenized macroscopic behavior is described with a two-concentration field model, using effective diffusion coefficients of calcium in the sarcoplasmic reticulum (SR) and in the cytoplasm. The model reproduces the right calcium transients and dependence with pacing frequency. Under basal conditions, the calcium rise is mostly restricted to the periphery of the cell, with a large concentration ratio between the periphery and the interior. We have then studied the dependence of the speed of the calcium wave on cytosolic and SR diffusion coefficients, finding an almost linear relation with the former, in agreement with a diffusive and fire mechanism of propagation, and little dependence on the latter. Finally, we have studied the effect of a change in RyR cluster microstructure. We find that, under resting conditions, the spark frequency decreases slightly with RyR cluster spatial dispersion, but markedly increases when the RyRs are distributed in clusters of larger size, stressing the importance of RyR cluster organization to understand atrial arrhythmias, as recent experimental results suggest (Macquaide et al., 2015).

Policymakers need clear, fast assessment of the real spread of the COVID-19 epidemic in each of their respective countries. Standard measures of the situation provided by the governments include reported positive cases and total deaths. While total deaths indicate immediately that countries like Italy and Spain had the worst situation as of mid-April, 2020, reported cases alone do not provide a complete picture of the situation. Different countries diagnose differently and present very distinctive reported case fatality ratios. Similar levels of reported incidence and mortality might hide a very different underlying pictures. Here we present a straightforward and robust estimation of the diagnostic rate in each European country. From that estimation we obtain a uniform, unbiased incidence of the epidemic. The method to obtain the diagnostic rate is transparent and empirical. The key assumption of the method is that the infection fatality ratio of COVID-19 in Europe is not strongly country-dependent. We show that this number is not expected to be biased due to demography nor to the way total deaths are reported. The estimation protocol is dynamic, and it has been yielding converging numbers for diagnostic rates in all European countries as from mid-April, 2020. Using this diagnostic rate, policy makers can obtain Effective Potential Growth updated every day, providing an unbiased assessment of the countries at greater risk of experiencing an uncontrolled situation. The method developed has been and will be used to track possible improvements in the diagnostic rate in European countries as the epidemic evolves.

Policymakers need a clear and fast assessment of the real spread of the epidemic of COVID-19 in each of their respective countries. Standard measures of the situation provided by the governments include reported positive cases and total deaths. While total deaths immediately indicate that countries like Italy and Spain have the worst situation as of mid April 2020, on its own, reported cases do not provide a correct picture of the situation. The reason is that different countries diagnose diversely and present very distinctive reported case fatality rate (CFR). The same levels of reported incidence and mortality might hide a very different underlying picture. Here we present a straightforward and robust estimation of the diagnostic rate in each European country. From that estimation we obtain an uniform unbiased incidence of the epidemic. The method to obtain the diagnostic rate is transparent and empiric. The key assumption of the method is that the real CFR in Europe of COVID-19 is not strongly country-dependent. We show that this number is not expected to be biased due to demography nor the way total deaths are reported. The estimation protocol has a dynamic nature, and it has been giving converging numbers for diagnostic rates in all European countries as of mid April 2020. From this diagnostic rate, policy makers can obtain an Effective Potential Growth (EPG) updated everyday providing an unbiased assessment of the countries with more potential to have an uncontrolled situation. The method developed will be used to track possible improvements on the diagnostic rate in European countries as the epidemic evolves. : medRxiv preprint countries [1-3]. However, comparative assessment of the spread of the pandemic in 4 other European countries has been more difficult to assess. The reason is that the real 5 incidence of the epidemic in each country can not be known with certainty because each 6 country is not able to perform the same number of PCR and consequently the 7 comparison of the ratio of those infected is difficult [4]. Policy responses have also 8 differed, with some countries focusing tests in its clinical use in hospitals, while others 9 have tried to use them, at least partially, to know some local chains of 10 transmissions [5,6]. The lack of clear cross country comparison in Europe can have deep 11 implications for the future structure of the UE since a lot of decisions are taken with a 12 heavy influence on the sense of in-country gravity. For these reasons, it is important to 13 have, at least, a proper measure of the relative spread of the epidemic. Policymakers 14 must know what is the real situation in their own countries in comparison to others so 15 that their decisions on the future of reopening and economic reconstruction are taken 16 not from false impressions but data. In this sense, policymakers must perceive the 17 method as unbiased, simple and robust. Most importantly, the relative comparisons 18 between countries must be as shielded as possible from the hypothesis of the method. In 19...

Transverse and axial tubules (TATS) are an essential ingredient of the excitation-contraction machinery that allow the effective coupling of L-type Calcium Channels (LCC) and ryanodine receptors (RyR2). They form a regular network in ventricular cells, while their presence in atrial myocytes is variable regionally and among animal species We have studied the effect of variations in the TAT network using a bidomain computational model of an atrial myocyte with variable density of tubules. At each z-line the t-tubule length is obtained from an exponential distribution, with a given mean penetration length. This gives rise to a distribution of t-tubules in the cell that is characterized by the fractional area (F.A.) occupied by the t-tubules. To obtain consistent results, we average over different realizations of the same mean penetration length. To this, in some simulations we add the effect of a network of axial tubules. Then we study global properties of calcium signaling, as well as regional heterogeneities and local properties of sparks and RyR2 openings. In agreement with recent experiments in detubulated ventricular and atrial cells, we find that detubulation reduces the calcium transient and synchronization in release. However, it does not affect sarcoplasmic reticulum (SR) load, so the decrease in SR calcium release is due to regional differences in Ca 2+ release, that is restricted to the cell periphery in detubulated cells. Despite the decrease in release, the release gain is larger in detubulated cells, due to recruitment of orphaned RyR2s, i.e, those that are not confronting a cluster of LCCs. This probably provides a safeguard mechanism, allowing physiological values to be maintained upon small changes in the t-tubule density. Finally, we do not find any relevant change in spark properties between tubulated and detubulated cells, suggesting that the differences found in experiments could be due to differential properties of the RyR2s in the membrane and in the t-tubules, not incorporated in the present model. This work will help understand the effect of detubulation, that has been shown to occur in disease conditions such as heart failure (HF) in ventricular cells, or atrial fibrillation (AF) in atrial cells.

The current worldwide pandemic produced by coronavirus disease 2019 (COVID-19) has changed the paradigm of mathematical epidemiology due to the high number of unknowns of this new disease. Thus, the empirical approach has emerged as a robust tool to analyze the actual situation carried by the countries and also allows us to predict the incoming scenarios. In this paper, we propose three empirical indexes to estimate the state of the pandemic. These indexes quantify both the propagation and the number of estimated cases, allowing us to accurately determine the real risk of a country. We have calculated these indexes' evolution for several European countries. Risk diagrams are introduced as a tool to visualize the evolution of a country and evaluate its current risk as a function of the number of contagious individuals and the empiric reproduction number. Risk diagrams at the regional level are useful to observe heterogeneity on COVID-19 penetration and spreading in some countries, which is essential during deconfinement processes. During the pandemic, there have been significant differences seen in countries reporting case criterion and detection capacity. Therefore, we have introduced estimations about the real number of infectious cases that allows us to have a broader view and to better estimate the risk. These diagrams and indexes have been successfully used for the monitoring of European countries and regions during the COVID-19 pandemic.