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. 2013 Sep 5;8(9):e72854.
doi: 10.1371/journal.pone.0072854. eCollection 2013.

Quantifying memory in complex physiological time-series

Amir H Shirazi  1 , Mohammad R Raoufy, Haleh Ebadi, Michele De Rui, Sami Schiff, Roham Mazloom, Sohrab Hajizadeh, Shahriar Gharibzadeh, Ahmad R Dehpour, Piero Amodio, G Reza Jafari, Sara Montagnese, Ali R Mani
Affiliations

Quantifying memory in complex physiological time-series

Amir H Shirazi et al. PLoS One. .

Abstract

In a time-series, memory is a statistical feature that lasts for a period of time and distinguishes the time-series from a random, or memory-less, process. In the present study, the concept of "memory length" was used to define the time period, or scale over which rare events within a physiological time-series do not appear randomly. The method is based on inverse statistical analysis and provides empiric evidence that rare fluctuations in cardio-respiratory time-series are 'forgotten' quickly in healthy subjects while the memory for such events is significantly prolonged in pathological conditions such as asthma (respiratory time-series) and liver cirrhosis (heart-beat time-series). The memory length was significantly higher in patients with uncontrolled asthma compared to healthy volunteers. Likewise, it was significantly higher in patients with decompensated cirrhosis compared to those with compensated cirrhosis and healthy volunteers. We also observed that the cardio-respiratory system has simple low order dynamics and short memory around its average, and high order dynamics around rare fluctuations.

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Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. Schematic view of the algorithm used to obtain the probability distribution of the exit times (τ) needed to observe accelerating or decelerating events for a defined threshold (ρ) in the original as well as the shuffled time-series (Bt).
Figure 2
Figure 2. The probability distribution of the normalized exit times (τ) needed to observe an accelerating event that is ρ = 0.5σ second faster than a given point (t) within the time-series (ΔB = Bt+τ−Bt≤−0.5σ).
Respiratory inter-breath interval time-series were obtained from (a) 10 healthy volunteers, (b) 10 patients with controlled atopic asthma (CAA), (c) 10 patients with uncontrolled atopic asthma (UCAA) and (d) 10 patients with uncontrolled non-atopic asthma (UNAA). Blue solid lines represent probability distribution of τ of the original time-series and red dash-dot lines correspond to their shuffled time-series. Data are presented as mean ± standard error of mean.
Figure 3
Figure 3. Comparison of the memory length (τm) for observing accelerating events with varying thresholds (ρ = 0.25σ, 0.5σ, 0.75σ and σ, ΔB≤−ρ) between healthy volunteers and patients with different types of asthma.
Respiratory inter-breath interval time-series were obtained from 10 healthy volunteers, 10 patients with controlled atopic asthma (CAA), 10 patients with uncontrolled atopic asthma (UCAA) and 10 patients with uncontrolled non-atopic asthma (UNAA). Data are presented as mean ± standard error of mean. *P<0.05, **P<0.01 in comparison with healthy subjects, CAA and UCAA. +P<0.05, ++P<0.01 in comparison with healthy volunteers (Bonferroni post-hoc test).
Figure 4
Figure 4. The probability distribution of the normalized exit times (τ) needed to observe a decelerating event that is ρ = σ second slower than a given point (t) within the time-series (ΔB = Bt+τ−Bt ≥σ).
Cardiac inter-beat interval time-series were obtained from (a) 41 healthy volunteers and (b) 93 patients with liver cirrhosis. Blue solid lines represent probability distribution of τ of original time-series and red dash-dot lines correspond to their shuffled time-series. Data are presented as mean ± standard error of mean.
Figure 5
Figure 5. Comparison of the memory length (τm) for observing decelerating events with varying thresholds (ρ = 0.5σ, σ, 1.5σ and 2σ, ΔB≥ρ) between healthy volunteers and patients with different degree of hepatic failure.
Cardiac inter-beat interval time-series were obtained from 41 healthy volunteers, 26 patients with compensated cirrhosis and 67 patients with decompensated cirrhosis. Data are presented as mean ± standard error of mean. *** P<0.001 in comparison with healthy volunteers (at ρ = 1.5σ and 2σ) and patients with compensated cirrhosis (at ρ = 2σ).
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