Poincare plot: A simple and powerful expression of... : MGM Journal of Medical Sciences (2024)


Functioning of the living body is better described with the help of physiological parameters, measured by noninvasive or invasive means. Some are common such as body temperature, pulse rate, respiration rate, blood pressure, etc.; other parameters are better known to the medical community, such as stroke output, peripheral blood flow, peristalsis, secretion of endocrinal and salivary glands, glycogen–glucose conversion, motility of large and small intestines, secretion of urine, and so on. Some of these such as heart rate, respiration rate, and blood pressure can be easily measured for long time intervals, causing no harm or discomfort to the patient. These physiological parameters never remain constant but keep on changing continuously depending on the physical and mental state of the subject. An increase/decrease in their value due to the physical activity of the subject is perfectly understandable and physiological. However minor fluctuations in their value even when the subject is physically inactive have caught the interest of the scientific and medical community during the past six decades and are being explored for diagnostic and monitoring applications under the heading of physiological variability.[123]

The history of physiological variability goes back to 1965 when Hon and Lee[4] observed that a decrease in beat-to-beat variation in the fetal heart rate during labor indicated fetal distress and the need for rapid delivery. The clinical importance of heart rate variability (HRV) became more obvious in the late 1980s when it was confirmed that HRV was a strong independent predictor of mortality after an acute myocardial infarction.[5] Similarly, Hyndman et al.[6] have related broadly repetitive fluctuations in the mean arterial pressure with the spontaneous rhythms (typically of a period of 10 s) in physiological control systems. Yet another example is that of fluctuations in the peripheral blood flow (PBF) in a resting individual without any pharmaceutical intervention. [Figure 1] shows the blood flow index (BFI) plotted against the beat number from a control subject and a patient with systemic hypertension.[27] As evident from [Figure 1A], the normal subject shows prominent rhythmic fluctuations as compared with that in the patient shown in [Figure 1B]. All these observations led to an investigation of their origin and subsequent clinical applications.

A breakthrough in these investigations came from Akselrod et al.,[8] who have shown that power spectrum distribution (PSD) of heart rate fluctuations comprises peaks in four dominant frequency ranges. These peaks are labeled as very low frequency (VLF), low-frequency (LF), mid-frequency (MF), and high-frequency (HF) peaks, respectively. The high-frequency peak centered around 0.4 Hz coincides with that of respiration. Barring VLF, the subsequent three peaks are shown in [Figure 2]. Extensive research has been conducted into the PSD analysis of HRV. Selective blockage of different components of autonomic function with the help of suitable pharmaceuticals either abolishes or dampens some of these peaks. Presently, MF, LF, and VLF peaks are renamed as LF, VLF, and ultra-low frequency (ULF) peaks, respectively. Conclusive evidence of most of these studies supports the following general principles:[9]

  1. The respiratory rhythm of HRV named HF is a marker of vagal modulation.[1011]
  2. The low-frequency spectral component is a marker of sympathetic modulation and corresponds to the rhythm of vasomotor waves present in both heart rate and blood pressure variations.[1012]
  3. There exists a reciprocal relationship between these two rhythms, which is similar to that characterizing sympathovagal balance.[12]

In addition to PSD, other presentations of variability are in the time domain and nonlinear domain. All three presentations are connected and correlated to each other. In the time domain, the parameters derived from beat-to-beat raw variable array are mean (µ), variance (Va), standard deviation (σ), and root mean square of successive differences (RMSSD). The last parameter means that another array of successive differences is obtained from the raw array; they are squared, summed and averaged, and square rooted. More explicitly, let RR be the raw variable (where RRn is the time interval between nth and (n + 1)th R-waves in the electrocardiogram (ECG) in seconds) and let n be an integer such that 0 ≤ nN; time-domain parameters are obtained by using the following equations:

In the nonlinear domain, variability is represented by geometric indices such as TINN, HTI and, a geometric plot called Poincare Plot. It is also estimated by fractal measures and entropy quantifiers. Poincare plot is a simple and informative method for visual presentation of physiological variability and assessment of autonomic control. For instance, the length of each RR interval (RRi+1) is plotted against the preceding RR interval (RRi) for the study of HRV, as shown in [Figure 3]. It is also known as Scatter plot, Poincare plot, Lorenz plot, Next amplitude plot, and Return map. SD2 represents the range of HR variation, whereas SD1 represents the strength of the high frequency of RR variation.[2]

Parameters from various representations in physiological variability are interrelated to each other. For example, variance in the time domain is proportional to total power in the frequency domain and its square root is proportional to major axis diameter SD2 in the Poincare plot. Similarly, RMSSD in the time domain is proportional to the square root of HF power in the frequency domain and short-axis diameter SD1 in the Poincare plot. Clinical applications requiring sympathovagal balance estimation call for frequency domain analysis. Twenty-four-hour monitoring calls for time-domain analysis and so on. However, Poincare plots give a simple and holistic representation of physiological variability. Ease of interpretation and holistic view makes Poincare representation a powerful tool in variability analysis. Some of these aspects are briefly described next.


Disturbance in the rhythm of the heartbeat is called arrhythmia. Depending on the source of disturbance, it has several classifications. Premature ventricular contraction (PVC), sinus tachycardia, sinus bradycardia, ventricular fibrillation, atrial fibrillation, sinus arrest, interpolated PVC, atrial premature beat, and R on T are some of the arrhythmia types observed clinically. Let us take the example of PVC and arrive at its Poincare plot. PVC is characterized by a ventricular contraction before the anticipated time in the rhythm, which is followed by a compensatory pause. In terms of RR-intervals, suppose PVC occurs after k number of normal beats, then k+1st will arrive before time. However, the next beat occurs at the scheduled time as follows:

RRk+1 < 0.9 [RRk], [RRk] is the average RR interval of preceding k beats and

RRk+2 + RRk+1 = 2 [RRk].

Considering the Poincare plot of such data, the central elliptical conglomeration pertaining to all normal beats is expected along with three scattered clusters about RRk–RRk+1, RRk+1–RRk+2, and RRk+2–RRk+3 for each of the PVC complex, as shown in [Figure 4].

R-on-T arrhythmia will exaggerate the distances of these peripheral clusters from the central conglomeration. Sinus bradycardia and sinus tachycardia will shift the central conglomeration to the top right and bottom left of the Poincare plots, respectively. Sinus arrest will cause only two peripheral clusters in the top left and mid-right of the central conglomeration. Interpolated PVC will cause two clusters in the mid-bottom and mid-left of the central conglomeration. Arrhythmia observed in second-degree heart block has regularly irregular QRS complexes and will cause top left and mid-right clusters around the central conglomeration similar to that of sinus arrest.

Ventricular fibrillation is an extreme kind of fatal arrhythmia requiring immediate emergency intervention. In this case, QRS detection by algorithms may turn a large number of false positives as well as false negatives. This may lead to a bizarre-looking Poincare plot, as shown in [Figure 5]. Atrial fibrillation may also cause a similar Poincare plot, with the difference that the left bottom conglomeration will shift a little up and toward the right.

Park et al.[13] have demonstrated the efficacy of the Poincare line plot in place of the point plot for the detection of atrial fibrillation. They have replaced (RRi, RRi+1) and (RRi+1, RRi+2) points in the Poincare plot by a line joining these two points, for all values of i. This line plot yields a kind of dynamics of the variability and can help understanding the dynamics of electro-physiology in arrhythmias. For instance, a subject with a few PVCs will have a Poincare line plot as shown in [Figure 6A], showing an arrow-like structure with vertices corresponding to premature (bottom), compensatory (top left), and regular after compensatory beats (mid-right), respectively; with regular beats occupying the concave vertex. In contrast, a similar plot from a subject with atrial fibrillation presents a chaotic line plot, as shown in [Figure 6B]. This kind of Poincare plot, thus, becomes specific for the detection of atrial fibrillation.


Satti et al.[14] have introduced the concept of an extended Poincare plot. In this case, RRi+k is plotted against RRi, where i varies from 1 to N-k and k varies from 1 to K (any number less than N, typically 20). For a particular variable, the method yields 20 plots in place of a single plot. This has helped in the diagnosis of uncontrolled asthma and in the prediction of survival and assessment of thermoregulation in patients with liver disease. Despite the theoretical limitation in the assumption of linear behavior, extended Poincare establishes immediate new knowledge, which can potentially be used to solve unmet clinical needs.

Tannus et al.[15] have shown in their study that short-term spectral analysis of HRV (VLF, LF, and HF), despite being a practical tool for screening cardiovascular autonomic neuropathy, demonstrates poor reproducibility. In contrast, the cardiovascular autonomic function determined by the Valsalva ratio (deep breathing ratio and maximum: minimum ratio during orthostatic) and some time-domain HRV indices (such as mean standard deviation of RR-interval and its coefficient of variation) provide good levels of reproducibility.

In the study by Alva et al.,[16] only one spectral index of HRV, namely HR_AVLF (a very low-frequency component of HRV), is significantly increased in only one group of ischemic heart disease (IHD) out of seven patient groups. Other six groups comprising patients with lung cancer (LC), stomach cancer (SC), auto-immune deficiency syndrome (AIDS), hypertension, pulmonary tuberculosis (TB), and cirrhosis of the liver (CoL) have not shown any significance in the spectral components of HRV. However, all the groups have shown significant change in blood flow mean and BF_AHF (a high-frequency component of blood flow variability (BFV)), except the cirrhosis of the liver group, which showed a change only in BF_AHF. The amplitude of the high-frequency component of BFV (BF_aHF) was observed to increase in AIDS, CoL, SC, and LC groups. Another parameter of BFV, namely the amplitude of the very low-frequency spectral component (BF_aVLF), was observed to be significantly decreased in CoL and LC groups. Another common feature of these two groups was a significant increase in the amplitude and power of high-frequency spectral component of morphology index variability (MI_aHF and MI_AHF). Thus, these three spectral components BF_aVLF, MI_aHF, and MI_AHF have shown a selective change in CoL and LC groups of patients and can be considered specific for these two disorders. Other changes are more or less general and can be used to estimate the severity of different disorders. This study also observed that the spectral component analysis of variability had a large scatter in the data in agreement with that observed by Tannus et al.[15]

The data of Alva et al. cited earlier have been used to derive the Poincare plots and one representative from each of the control, hypertension, CoL, SC, and LC groups is shown in [Figure 7]. Interestingly, it is seen that the scatter in RR-intervals not only gets reflected in HRV but also gets reflected in BFV and MIV, causing poor reproducibility in spectral components. However, scattered points in the Poincare plot may not matter provided central conglomeration alone is considered for assessment. CoL shows a marked decrease in the area of central conglomeration for all three variabilities. Analysis of changes in the shape of the main plot in different conditions may enhance the diagnostic capability of Poincare plots; it requires proper quantification of the main cluster of the Poincare plots.

Monitoring applications of the Poincare plot are obvious from the illustration from Copie et al.[717] They have shown marked changes in the Poincare plot after the administration of bisoprolol to a patient with heart failure in comparison to that caused by placebo. This adds to the capability of reflecting dynamic changes of the Poincare plot.


The Poincare plot has been sparingly used in the past due to the domination of time- and frequency-domain analysis of physiological variability. The realization of the limitations of linear analysis caused by large scatter in the variability parameters has recently shifted the emphasis to nonlinear Poincare analysis, with interesting observations. Peripheral cluster formation in different kinds of arrhythmias such as PVC, R on T, sinus arrest, interpolated PVC, and second-degree heart block is unique and can be used for arrhythmia detection in intensive care monitoring. Similarly, the bizarre plot is specific to ventricular and atrial fibrillation and so is the shift of central conglomeration to bottom left or top right for sinus tachycardia and bradycardia. This powerful expression is furthered by the chaotic line Poincare plot in the case of atrial fibrillation.

The extended Poincare plot offers a substitute for frequency-domain analysis. The extension parameter k can be experimentally correlated with different rhythms of the frequency-domain analysis. This is not only simpler but also may be less noisy. It has now come to the light that arrhythmia is the main source of high scatter in linear domain variability parameters and therefore the editing of arrhythmic beats/complexes may bring down the scatter appreciably. It calls for revisiting physiological variability through the pathway of Poincare analysis for increasing the sensitivity and accuracy of its clinical manifestation.

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.


The authors are grateful to Dr. Geeta S Lathkar, Director, and Dr. VG Sayagavi, Vice Principal, MGM’s College of Engineering and Technology, Navi Mumbai, India, respectively for their continuous support and encouragement. The authors thank Ms. Jyoti Jethe for her valuable contribution in designing the figures and Shri Nazim Momin and Shri Bhaskar Gaikwad for their contribution in article preparation.


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Arrhythmia detection; blood flow variability; heart rate variability; morphology index variability; Poincare plot

© 2021 MGM Journal of Medical Sciences | Published by Wolters Kluwer – Medknow
Poincare plot: A simple and powerful expression of... : MGM Journal of Medical Sciences (2024)


What does a Poincaré plot tell us? ›

A Poincaré plot, named after Henri Poincaré, is a type of recurrence plot used to quantify self-similarity in processes, usually periodic functions. It is also known as a return map. Poincaré plots can be used to distinguish chaos from randomness by embedding a data set in a higher-dimensional state space.

What is the HRV Poincaré plot? ›

The Poincaré plot for heart rate variability analysis is a technique considered geometrical and non-linear, that can be used to assess the dynamics of heart rate variability by a representation of the values of each pair of R-R intervals into a simplified phase space that describes the system's evolution.

What is the extended Poincaré plot? ›

The extended Poincare plot offers a substitute for frequency-domain analysis. The extension parameter k can be experimentally correlated with different rhythms of the frequency-domain analysis. This is not only simpler but also may be less noisy.

What is the line of identity in the Poincaré plot? ›

The line of identity is the 45° imaginary diagonal line on the Poincaré plot and the points falling on the imaginary line has the property RRn = RRn+1. SD1 measures the dispersion of points perpendicular to the line of identity, whereas SD2 measures the dispersion along the line of identity.

What is the plot method used for? ›

A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be drawn by hand or by a computer. In the past, sometimes mechanical or electronic plotters were used.

What is the RR interval? ›

RR interval, the time elapsed between two successive R-waves of the QRS signal on the electrocardiogram (and its reciprocal, the HR) is a function of intrinsic properties of the sinus node as well as autonomic influences.

How do you analyze HRV? ›

The single most common way in which to analyse HRV is a time-domain method called RMSSD. This is the Root Mean Square of Successive Differences between each heartbeat. It is relatively simple to calculate (important for large-scale computation), and provides a reliable measure of HRV and parasympathetic activity.

How do you read HRV values? ›

HRV is a measure of the time between heartbeats and is measured by many wearable fitness devices. A higher HRV value is associated with positive health and performance outcomes. A lower HRV indicates less resilience and adaptability of the body to respond to physical stressors (like exercise).

Why is HRV so variable? ›

Your heart rate variability is determined by the balance between the responses in your sympathetic and parasympathetic nervous systems. A high average heart rate variability suggests your autonomic nervous system is working in a "rest-and-digest" mode more often than a "fight-or-flight" mode.

How do you calculate Poincaré maps? ›

In each case the procedure for computing the Poincaré map is straightforward, namely, (1) find the general solution of the diffeq, (2) find the solution with initial value a, (3) compute the value of that solution at time t=T, where T is the specified period.

What is the Poincaré conjecture question? ›

The question asked by Poincaré: Give an easy criterion that enables us to recognize that a given 3-manifold has the same shape as the 3-dimensional hypersphere. More generally Poincaré was looking for a classification of possible shapes of all 3-manifolds.

How was the Poincaré conjecture solved? ›

Perelman proved the conjecture by deforming the manifold using the Ricci flow (which behaves similarly to the heat equation that describes the diffusion of heat through an object).

What are some interesting facts about Henri Poincare? ›

Key Takeaways:
  • 01Jules Henri Poincaré was a renowned French mathematician.
  • 02Poincaré was born on April 29, 1854, in Nancy, France.
  • 03He formulated the Poincaré Conjecture, which remained unsolved for over a century.
  • 04Poincaré's work laid the foundation for chaos theory.

What is the concept of HRV? ›

Heart rate variability is where the amount of time between your heartbeats fluctuates slightly. Even though these fluctuations are undetectable except with specialized devices, they can still indicate current or future health problems, including heart conditions and mental health issues like anxiety and depression.

What is the explanation of HRV? ›

Heart rate variability is the measure of time between your heartbeats. Factors such as health, stress, sleep, age, gender, and lifestyle may affect your HRV. HRV is traditionally measured using an EKG. Today, you can get a measure of your HRV at home using a fitness tracker or smartwatch.

What do HRV values mean? ›

HRV is simply a measure of the variation in time between each heartbeat. This variation is controlled by a primitive part of the nervous system called the autonomic nervous system (ANS). It works behind the scenes, automatically regulating our heart rate, blood pressure, breathing, and digestion among other key tasks.

What does HRV determine? ›

Heart rate variability, or HRV, is the measure of the variation in time between heartbeats, measured in milliseconds. For example, sometimes your heart might beat every 1.2 seconds; other times, it might beat at 0.8 seconds. You need a device to measure that variance in timing (more on that below).


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