The Poincaré plot is a geometrical technique used to visualize and quantify the correlation between two consecutive data points in a time-series. Since the dynamics of fluctuations in physiological rhythms exhibit long-term correlation and memory, this study aimed to extend the Poincaré plot by calculating the correlation between sequential data points in a time-series, rather than between two consecutive points. By incorporating this so-called lag, we hope to integrate a temporal aspect into quantifying the correlation, to depict whether a physiological system holds prolonged association between events separated by time. In doing so, it attempts to instantaneously characterize the intrinsic behavior of a complex system. We tested this hypothesis on three different physiological time-series: heart rate variability in patients with liver cirrhosis, respiratory rhythm in asthma and body temperature fluctuation in patients with cirrhosis, to evaluate the potential application of the extended Poincaré method in clinical practice. When studying the cardiac inter-beat intervals, the extended Poincaré plot revealed a stronger autocorrelation for patients with decompensated liver cirrhosis compared to less severe cases using Pearson’s correlation coefficient. In addition, long-term variability (known as SD2 in the extended Poincaré plot) appeared as an independent prognostic variable. This holds significance by acting as a non-invasive tool to evaluate patients with chronic liver disease and potentially facilitate transplant selection as an adjuvant to traditional criteria. For asthmatics, employing the extended Poincaré plot allowed for a non-invasive tool to differentially diagnose various classifications of respiratory disease. In the respiratory inter-breath interval analysis, the receiver operating characteristic (ROC) curve provided evidence that the extension of the Poincaré plot holds a greater advantage in the classification of asthmatic patients, over the traditional Poincaré plot. Lastly, the analysis of body temperature from patients using the extended Poincaré plot helped identify inpatients from outpatients with cirrhosis. Through these analyses, the extended Poincaré plot provided unique and additional information which could potentially make a difference in clinical practice. Conclusively, the potential use of our work lies in its possible application of predicting mortality for the organ allocation procedure in patients with cirrhosis and non-invasively distinguish between atopic and non-atopic asthma.

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Chronic liver damage leads to scarring of the liver tissue and ultimately a systemic illness known as cirrhosis. Patients with cirrhosis exhibit multi-organ dysfunction and high mortality. Reduced heart rate variability (HRV) is a hallmark of cirrhosis, reflecting a state of defective cardiovascular control and physiological network disruption. Several lines of evidence have revealed that decreased HRV

An author name was incorrectly spelled as "Mohammad R. Rauofy." The correct spelling is "Mohammad R. Raoufy." The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way. The original article has been updated.