Comparison of Correlation Dimension and Fractal Dimension in Estimating BIS index

Ahmadi, Behzad; Amirfattahi, Rassoul

doi:10.4236/wsn.2010.21010

Cited by 19 publications

(12 citation statements)

References 18 publications

(22 reference statements)

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“…Compared to other classical measures derived from chaos theory (e.g., correlation dimension), this algorithm is simpler and faster since the reconstruction of the attractor phase space is not essential. HFD has been widely used to quantify the complexity and self-similarity of a signal (Gómez et al 2009;Ahmadi and Amirfattahi 2010;Coyt et al 2013). Its principle to compute FD can be described as the following:…”

Section: Higuchi's Fractal Dimensionmentioning

confidence: 99%

Nonlinear characteristics of hydroclimate variability in the mid-latitude Asia over the past seven centuries

Zhou

Fang

et al. 2015

Theor Appl Climatol

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Hydroclimate variations in the mid-latitude Asia have received considerable attention due to its significance for the regional ecosystem and livelihood, while its nonlinear characteristics over the past centuries are not fully understood yet. Hydroclimate patterns for the mid-latitude Asia are classified into eastern and western modes based on a network of the reconstructed Palmer drought severity index (PDSI) of 197 grids spanning since 1300. The hydroclimate variations of western mode are more complex than that of eastern mode based on the Higuchi's fractal dimension (HFD) analysis, which may be related to the complex atmospheric circulation patterns that dominate them. The relationships of the hydroclimate variations between western and eastern modes at different time scales extracted by ensemble empirical mode decomposition method (EEMD) are detected. The anti-phase relationship of the hydroclimatic variations between western and eastern modes at the interdecadal variations occurs during the periods with the enhanced El Nino Southern Oscillation (ENSO) variance. Similarly, the multidecadal hydroclimate variations are anti-phase when the Pacific Decadal Oscillation (PDO) is in its warm phases. The inverse relationship between western and eastern modes is stable for the centennial scale.

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Section: Higuchi's Fractal Dimensionmentioning

confidence: 99%

Nonlinear characteristics of hydroclimate variability in the mid-latitude Asia over the past seven centuries

Zhou

Fang

et al. 2015

Theor Appl Climatol

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“…electrocardiograms (ECG)) in the time and frequency domains 2–4 . There is increasing evidence suggesting that nonlinear analysis can be used in conjunction with standard diagnostic methods to quantify individual physiological states 5 . Differences in the nonlinear indices can be monitored between healthy and sick individuals, including cases of emotional stress, environmental changes, or genetic cardiomyopathies.…”

Section: Introductionmentioning

confidence: 99%

Quantification of Contractile Dynamic Complexities Exhibited by Human Stem Cell-Derived Cardiomyocytes Using Nonlinear Dimensional Analysis

Hoang

Jacquir

Lemus

et al. 2019

Sci Rep

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Understanding the complexity of biological signals has been gaining widespread attention due to increasing knowledge on the nonlinearity that exists in these systems. Cardiac signals are known to exhibit highly complex dynamics, consisting of high degrees of interdependency that regulate the cardiac contractile functions. These regulatory mechanisms are important to understand for the development of novel in vitro cardiac systems, especially with the exponential growth in deriving cardiac tissue directly from human induced pluripotent stem cells (hiPSCs). This work describes a unique analytical approach that integrates linear amplitude and frequency analysis of physical cardiac contraction, with nonlinear analysis of the contraction signals to measure the signals’ complexity. We generated contraction motion waveforms reflecting the physical contraction of hiPSC-derived cardiomyocytes (hiPSC-CMs) and implemented these signals to nonlinear analysis to compute the capacity and correlation dimensions. These parameters allowed us to characterize the dynamics of the cardiac signals when reconstructed into a phase space and provided a measure of signal complexity to supplement contractile physiology data. Thus, we applied this approach to evaluate drug response and observed that relationships between contractile physiology and dynamic complexity were unique to each tested drug. This illustrated the applicability of this approach in not only characterization of cardiac signals, but also monitoring and diagnostics of cardiac health in response to external stress.

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“…Several studies employing SI and LZC are available in the current literature, where authors have assumed durations of epochs to fulfil quasistationarity requirements covering values between 1 and 300 seconds. 13,[15][16][17][18][19][20][21][22][23][24]26,[39][40][41][42][43][44][45][46][47] In addition to the search of quasi-stationarity conditions, the number of data points also affects the nonlinear deterministic dynamics of these epochs; this is proportional to the sampling rate utilized in the acquisition of the signal, and too short data sets imply errors in the calculation of nonlinear metrics. Although under certain conditions this length should be larger than 100 000 data points according to criterion proposed by Eckmann and Ruelle 48 for generic time series, Gallez and Babloyantz 49 established that data sets larger than 20 000 data points can be suitable for evaluation of Lyapunov exponents in alpha activity, which is a nonlinear measure that quantifies the chaoticity in a time series.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Recurrent Dynamics and Long-Term Nonstationarities in EEG Alpha Cortical Activity: Implications for Choosing Adequate Segment Length in Nonlinear EEG Analyses

2017

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Nonlinear analysis of EEG recordings allows detection of characteristics that would probably be neglected by linear methods. This study aimed to determine a suitable epoch length for nonlinear analysis of EEG data based on its recurrence rate in EEG alpha activity (electrodes Fz, Oz, and Pz) from 28 healthy and 64 major depressive disorder subjects. Two nonlinear metrics, Lempel-Ziv complexity and scaling index, were applied in sliding windows of 20 seconds shifted every 1 second and in nonoverlapping windows of 1 minute. In addition, linear spectral analysis was carried out for comparison with the nonlinear results. The analysis with sliding windows showed that the cortical dynamics underlying alpha activity had a recurrence period of around 40 seconds in both groups. In the analysis with nonoverlapping windows, long-term nonstationarities entailed changes over time in the nonlinear dynamics that became significantly different between epochs across time, which was not detected with the linear spectral analysis. Findings suggest that epoch lengths shorter than 40 seconds neglect information in EEG nonlinear studies. In turn, linear analysis did not detect characteristics from long-term nonstationarities in EEG alpha waves of control subjects and patients with major depressive disorder patients. We recommend that application of nonlinear metrics in EEG time series, particularly of alpha activity, should be carried out with epochs around 60 seconds. In addition, this study aimed to demonstrate that long-term nonlinearities are inherent to the cortical brain dynamics regardless of the presence or absence of a mental disorder.

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Comparison of Correlation Dimension and Fractal Dimension in Estimating BIS index

Cited by 19 publications

References 18 publications

Nonlinear characteristics of hydroclimate variability in the mid-latitude Asia over the past seven centuries

Nonlinear characteristics of hydroclimate variability in the mid-latitude Asia over the past seven centuries

Quantification of Contractile Dynamic Complexities Exhibited by Human Stem Cell-Derived Cardiomyocytes Using Nonlinear Dimensional Analysis

Nonlinear Recurrent Dynamics and Long-Term Nonstationarities in EEG Alpha Cortical Activity: Implications for Choosing Adequate Segment Length in Nonlinear EEG Analyses

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