On the authors' and employers' webpages: There are no format restrictions; files prepared and/or formatted by AIP or its vendors (e.g., the PDF, PostScript, or HTML article files published in the online journals and proceedings) may be used for this purpose. If a fee is charged for any use, AIP permission must be obtained. An appropriate copyright notice must be included along with the full citation for the published paper and a Web link to AIP's official online version of the abstract. A dedicated nonlinear oscillator model able to reproduce the pulse shape, refractory time, and phase sensitivity of the action potential of a natural pacemaker of the heart is developed. The phase space of the oscillator contains a stable node, a hyperbolic saddle, and an unstable focus. The model reproduces several phenomena well known in cardiology, such as certain properties of the sinus rhythm and heart block. In particular, the model reproduces the decrease of heart rate variability with an increase in sympathetic activity. A sinus pause occurs in the model due to a single, well-timed, external pulse just as it occurs in the heart, for example due to a single supraventricular ectopy. Several ways by which the oscillations cease in the system are obtained ͑models of the asystole͒. The model simulates properly the way vagal activity modulates the heart rate and reproduces the vagal paradox. Two such oscillators, coupled unidirectionally and asymmetrically, allow us to reproduce the properties of heart rate variability obtained from patients with different kinds of heart block including sino-atrial blocks of different degree and a complete AV block ͑third degree͒. Human heart rate is not constant. In fact, heart rate variability is a major factor in the effective functioning of the cardiovascular system and an important factor in medical diagnosis. A large effort has gone into defining complexity measures using both chaos theory and statistical physics concepts in order to create tools for such diagnosis. In spite of this, the source of the variability is not completely understood and remains an open research subject. It is well known that the autonomous nervous system moderates heart rate in mammals. One way to understand how this occurs is to build models. A variety of models-including the so-called whole heart modelsexist today. However, usually such models are so complex that an investigation of the global dynamical properties of the heart is difficult. Consequently, very rarely do they address the problem of heart rate variability. In our approach, we return to the 20th Century attempts of van der Pol and van der Mark of using relaxation oscillators to study the conduction system of the heart and its interaction with the autonomous nervous system. Following the work of several groups in the field, we developed our own modified van der Pol oscillator. We show that it is able to reproduce certain phenomena that occur in clinically recorded human heart rate: irregular heart rate, asystole, sinus pause, vagal paradox, certai...
The coupled sino-atrial and atrio-ventricular nodes of the heart are discussed using a dedicated non-linear oscillator model. Several modes by which the oscillations cease in the system are obtained (asystole models). The oscillations of the model are compared with heart rate variability in heart block patients.
ObjectivesPresenting outcomes of patients hospitalised for COVID-19 should be put in context and comparison with other facilities. However, varied methodology applied in published studies can impede or even hinder a reliable comparison. The aim of this study is to share our experience in pandemic management and highlight previously under-reported factors affecting mortality. We present outcomes of COVID-19 treatment in our facility that will allow for an intercentre comparison. We use simple statistical parameters—case fatality ratio (CFR) and length of stay (LOS).SettingLarge clinical hospital in northern Poland serving over 120 000 patients annually.ParticipantsData were collected from patients hospitalised in COVID-19 general and intensive care unit (ICU) isolation wards from November 2020 to June 2021. The sample consisted of 640 patients—250 (39.1 %) were women and 390 (60.9 %) were men, with a median age of 69 (IQR 59–78) years.ResultsValues of LOS and CFR were calculated and analysed. Overall CFR for the analysed period was 24.8%, varying from 15.9 % during second quarter 2021 to 34.1% during fourth quarter 2020. The CFR was 23.2% in the general ward and 70.7% in the ICU. All ICU patients required intubation and mechanical ventilation, and 44 (75.9 %) of them developed acute respiratory distress syndrome. The average LOS was 12.6 (±7.5) days.ConclusionsWe highlighted the importance of some of the under-reported factors affecting CFR, LOS and thus, mortality. For further multicentre analysis, we recommend broad analysis of factors affecting mortality in COVID-19 using simple and transparent statistical and clinical parameters.
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