Recurrence Quantification Analysis Variables Research Articles

Recurrence Quantification Analysis of Ankle Kinematics During Gait in Individuals With Chronic Ankle Instability.

PurposeAn investigation of the ankle dynamics in a motor task may generate insights into the etiology of chronic ankle instability (CAI). This study presents a novel application of recurrence quantification analysis (RQA) to examine the ankle dynamics during walking. We hypothesized that CAI is associated with changes in the ankle dynamics as assessed by measures of determinism and laminarity using RQA.MethodsWe recorded and analyzed the ankle position trajectories in the frontal and sagittal planes from 12 participants with CAI and 12 healthy controls during treadmill walking. We used time-delay embedding to reconstruct the position trajectories to a phase space that represents the states of the ankle dynamics. Based on the phase space trajectory, a recurrence plot was constructed and two RQA variables, the percent determinism (%DET) and the percent laminarity (%LAM), were derived from the recurrence plot to quantify the ankle dynamics.ResultsIn the frontal plane, the %LAM in the CAI group was significantly lower than that in the control group (p < 0.05. effect size = 0.86). This indicated that the ankle dynamics in individuals with CAI is less likely to remain in the same state. No significant results were found in the %DET or in the sagittal plane.ConclusionA lower frontal-plane %LAM may reflect more frequent switching between different patterns of neuromuscular control states due to the instabilities associated with CAI. With further study and development, %LAM may have the potential to become a useful biomarker for CAI.

Speech kinematic variability in adults who stutter is influenced by treatment and speaking style

AimWe tested whether completion of the Comprehensive Stuttering Program (CSP) is associated with a reduction in speech kinematic variability relative to pre-treatment when adults who stutter (AWS) use a casual speaking manner or fluency skills. RationalKinematic variability is higher in AWS suggesting a sensorimotor vulnerability; however, it is not clear whether high variability is a trait related to the underlying disorder or reflects the mutable state of stuttering. Speech restructuring intervention such as the CSP could support more consistent articulatory control and stable movement patterns. MethodologyThirteen AWS were tested before and after completing the CSP while 11 adults who do not stutter (AWNS) completed a single session. Participants were instructed to use a casual manner of speaking in the first post-treatment session. In the second post-treatment condition, the AWS employed their fluency skills at a control speaking rate. An optical tracking system captured lower lip movements while participants spoke two English phrases and a complex nonword. Across-utterance kinematic variability was measured using the spatiotemporal index (STI) and within-utterance variability was measured with recurrence quantification analysis (RQA). ResultsThere was a positive treatment outcome based on significant reductions in percentage syllables stuttered (%SS) during speaking and reading, decreases in stuttering severity and improved perceptions of stuttering and communication confidence. The STI of the AWS decreased significantly after treatment for both speaking styles. The RQA variables indicated that AWS used a less stereotyped and more flexible manner of speaking in the casual condition after treatment, but speech movement regularity increased when using fluency skills. ConclusionsThe AWS showed a significant decrease in labial kinematic variability alongside a successful treatment outcome involving speech restructuring and cognitive behavioral techniques. These changes in across-utterance and within-utterance kinematic indices demonstrate that effective stuttering treatment can promote speech motor stability along with fluent speech.

The temporal stability of recurrence quantification analysis attributes from chronic atrial fibrillation electrograms

Abstract Introduction The temporal behavior of atrial electrograms (AEGs) collected during persistent atrial fibrillation (persAF) directly affects ablative treatment outcomes. We investigated different durations of AEGs collected during persAF using recurrence quantification analysis (RQA). Methods 797 bipolar AEGs with different durations (from 0.5 s to 8 s) from 18 patients were investigated. Four RQA-based attributes were evaluated based on AEG durations: determinism (DET); recurrence rate (RR); laminarity (LAM); and diagonal lines’ entropy (ENTR). The Spearman correlation (ρ) between each duration versus 8 s was calculated. AEG classification was performed following the CARTO criteria (Biosense Webster) and receiving operating characteristic (ROC) curves were created for the RQA variables. Results The RQA variables successfully discriminated the AEGs: the area under the ROC curves were as high as 0.70 for AEGs with 3.5 s or greater. Three types of AEGs were found using these variables: normal, fractionated and temporally unstable. The number of unstable AEGs decreased with longer AEG segments. Different AEG durations significantly affected the RQA variables (P<0.0001), with no statistical difference between the durations 6 s, 7 s and 8 s for DET, LAM and ENTR, and no difference between 7 s and 8 s for RR (P<0.0001). AEGs with 3 s or longer have shown ρ ≥ 80% for all variables. Conclusion The RQA variables have been shown effective in the characterization of AEGs collected during persAF with a shorter duration than current recommendations, which motivates their use for the characterization of atrial substrate during persAF ablation.

Characterization of human persistent atrial fibrillation electrograms using recurrence quantification analysis.

Atrial fibrillation (AF) is regarded as a complex arrhythmia, with one or more co-existing mechanisms, resulting in an intricate structure of atrial activations. Fractionated atrial electrograms (AEGs) were thought to represent arrhythmogenic tissue and hence have been suggested as targets for radiofrequency ablation. However, current methods for ablation target identification have resulted in suboptimal outcomes for persistent AF (persAF) treatment, possibly due to the complex spatiotemporal dynamics of these mechanisms. In the present work, we sought to characterize the dynamics of atrial tissue activations from AEGs collected during persAF using recurrence plots (RPs) and recurrence quantification analysis (RQA). 797 bipolar AEGs were collected from 18 persAF patients undergoing pulmonary vein isolation (PVI). Automated AEG classification (normal vs. fractionated) was performed using the CARTO criteria (Biosense Webster). For each AEG, RPs were evaluated in a phase space estimated following Takens' theorem. Seven RQA variables were obtained from the RPs: recurrence rate; determinism; average diagonal line length; Shannon entropy of diagonal length distribution; laminarity; trapping time; and Shannon entropy of vertical length distribution. The results show that the RQA variables were significantly affected by PVI, and that the variables were effective in discriminating normal vs. fractionated AEGs. Additionally, diagonal structures associated with deterministic behavior were still present in the RPs from fractionated AEGs, leading to a high residual determinism, which could be related to unstable periodic orbits and suggesting a possible chaotic behavior. Therefore, these results contribute to a nonlinear perspective of the spatiotemporal dynamics of persAF.

Analysis of electrochemical noise data by use of recurrence quantification analysis and machine learning methods

By use of recurrence quantification analysis (RQA), twelve features were extracted from the electrochemical noise signals generated by three types of corrosion: uniform, pitting and passivation. Machine learning methods, i.e. linear discriminant analysis (LDA) and random forests (RF), were used to identify the different corrosion types from those features. Both models gave satisfactory performance, but the RF model showed better prediction accuracy of 93% than the LDA model (88%). Furthermore, an estimation of the importance of the variables by use of the RF model suggested the RQA variables laminarity (LAM) and determinism (DET) played the most significant role with regard to identification of corrosion types. In addition, the comparison of noise resistance with the resistance obtained from EIS measurement showed that the noise resistance can be used for monitoring corrosion rate variations not only for uniform corrosion and passivation, but also for pitting.

Onset of normal and inverse homoclinic bifurcation in a double plasma system near a plasma fireball

Plasma fireballs are generated due to a localized discharge and appear as a luminous glow with a sharp boundary, which suggests the presence of a localized electric field such as electrical sheath or double layer structure. The present work reports the observation of normal and inverse homoclinic bifurcation phenomena in plasma oscillations that are excited in the presence of fireball in a double plasma device. The controlling parameters for these observations are the ratio of target to source chamber (nT/nS) densities and applied electrode voltage. Homoclinic bifurcation is noticed in the plasma potential fluctuations as the system evolves from narrow to long time period oscillations and vice versa with the change of control parameter. The dynamical transition in plasma fireball is demonstrated by spectral analysis, recurrence quantification analysis (RQA), and statistical measures, viz., skewness and kurtosis. The increasing trend of normalized variance reflects that enhancing nT/nS induces irregularity in plasma dynamics. The exponential growth of the time period is strongly indicative of homoclinic bifurcation in the system. The gradual decrease of skewness and increase of kurtosis with the increase of nT/nS also reflect growing complexity in the system. The visual change of recurrence plot and gradual enhancement of RQA variables DET, Lmax, and ENT reflects the bifurcation behavior in the dynamics. The combination of RQA and spectral analysis is a clear evidence that homoclinic bifurcation occurs due to the presence of plasma fireball with different density ratios. However, inverse bifurcation takes place due to the change of fireball voltage. Some of the features observed in the experiment are consistent with a model that describes the dynamics of ionization instabilities.

Characterization of local complex structures in a recurrence plot to improve nonlinear dynamic discriminant analysis

Structures in recurrence plots (RPs), preserving the rich information of nonlinear invariants and trajectory characteristics, have been increasingly analyzed in dynamic discrimination studies. The conventional analysis of RPs is mainly focused on quantifying the overall diagonal and vertical line structures through a method, called recurrence quantification analysis (RQA). This study extensively explores the information in RPs by quantifying local complex RP structures. To do this, an approach was developed to analyze the combination of three major RQA variables: determinism, laminarity, and recurrence rate (DLR) in a metawindow moving over a RP. It was then evaluated in two experiments discriminating (1) ideal nonlinear dynamic series emulated from the Lorenz system with different control parameters and (2) data sets of human heart rate regulations with normal sinus rhythms (n = 18) and congestive heart failure (n = 29). Finally, the DLR was compared with seven major RQA variables in terms of discriminatory power, measured by standardized mean difference (DSMD). In the two experiments, DLR resulted in the highest discriminatory power with DSMD = 2.53 and 0.98, respectively, which were 7.41 and 2.09 times the best performance from RQA. The study also revealed that the optimal RP structures for the discriminations were neither typical diagonal structures nor vertical structures. These findings indicate that local complex RP structures contain some rich information unexploited by RQA. Therefore, future research to extensively analyze complex RP structures would potentially improve the effectiveness of the RP analysis in dynamic discrimination studies.

Selection of minimal length of line in recurrence quantification analysis

A qualitative analysis along with mathematical description was made on the selection of the optimal minimal length of line, lmin, a crucial parameter in the recurrence quantification analysis (RQA). The optimum minimal length of line is defined as a value that enhances the capability of RQA variables (determinism, in this paper) to distinguish between different dynamic states of a system. It was shown that the determinism of the Lorenz time series has a normal distribution. The results indicated that the lowest possible value of the minimal length of line (i.e., lmin=2) is the best choice. This value provides the highest differentiation for determinism of the time series obtained from different dynamic states of the Lorenz system. The applicability of the results was verified by examining determinism for monitoring the fluidization hydrodynamics.

Characterising non-linear dynamics in nocturnal breathing patterns of healthy infants using recurrence quantification analysis

Breathing dynamics vary between infant sleep states, and are likely to exhibit non-linear behaviour. This study applied the non-linear analytical tool recurrence quantification analysis (RQA) to 400 breath interval periods of REM and N-REM sleep, and then using an overlapping moving window. The RQA variables were different between sleep states, with REM radius 150% greater than N-REM radius, and REM laminarity 79% greater than N-REM laminarity. RQA allowed the observation of temporal variations in non-linear breathing dynamics across a night's sleep at 30s resolution, and provides a basis for quantifying changes in complex breathing dynamics with physiology and pathology.

Research on zheng classification fusing pulse parameters in coronary heart disease.

This study was conducted to illustrate that nonlinear dynamic variables of Traditional Chinese Medicine (TCM) pulse can improve the performances of TCM Zheng classification models. Pulse recordings of 334 coronary heart disease (CHD) patients and 117 normal subjects were collected in this study. Recurrence quantification analysis (RQA) was employed to acquire nonlinear dynamic variables of pulse. TCM Zheng models in CHD were constructed, and predictions using a novel multilabel learning algorithm based on different datasets were carried out. Datasets were designed as follows: dataset1, TCM inquiry information including inspection information; dataset2, time-domain variables of pulse and dataset1; dataset3, RQA variables of pulse and dataset1; and dataset4, major principal components of RQA variables and dataset1. The performances of the different models for Zheng differentiation were compared. The model for Zheng differentiation based on RQA variables integrated with inquiry information had the best performance, whereas that based only on inquiry had the worst performance. Meanwhile, the model based on time-domain variables of pulse integrated with inquiry fell between the above two. This result showed that RQA variables of pulse can be used to construct models of TCM Zheng and improve the performance of Zheng differentiation models.

Application of recurrence quantification analysis to automatically estimate infant sleep states using a single channel of respiratory data

Previous work has identified that non-linear variables calculated from respiratory data vary between sleep states, and that variables derived from the non-linear analytical tool recurrence quantification analysis (RQA) are accurate infant sleep state discriminators. This study aims to apply these discriminators to automatically classify 30 s epochs of infant sleep as REM, non-REM and wake. Polysomnograms were obtained from 25 healthy infants at 2 weeks, 3, 6 and 12 months of age, and manually sleep staged as wake, REM and non-REM. Inter-breath interval data were extracted from the respiratory inductive plethysmograph, and RQA applied to calculate radius, determinism and laminarity. Time-series statistic and spectral analysis variables were also calculated. A nested cross-validation method was used to identify the optimal feature subset, and to train and evaluate a linear discriminant analysis-based classifier. The RQA features radius and laminarity and were reliably selected. Mean agreement was 79.7, 84.9, 84.0 and 79.2 % at 2 weeks, 3, 6 and 12 months, and the classifier performed better than a comparison classifier not including RQA variables. The performance of this sleep-staging tool compares favourably with inter-human agreement rates, and improves upon previous systems using only respiratory data. Applications include diagnostic screening and population-based sleep research.

Study of transition velocity from bubbling to turbulent fluidisation by recurrence plots analysis on pressure fluctuations

AbstractRecurrence plot (RP) and recurrence quantification analysis (RQA) have been used for studying the dynamic behaviour of gas–solid fluidised beds. RQA variables (recurrence rate, determinism, laminarity and entropy) were calculated for the bubbling fluidised bed at different superficial gas velocities (ranging 0.1–1.5 m/s) and aspect ratios (1, 1.5 and 2). Patterns within RP changed with these various conditions, and subsequently RQA parameters changed accordingly. These changes can be potentially useful to study the bed hydrodynamic. It was shown that transition from bubbling to turbulent velocity can be determined by the variation of recurrence rate and entropy. © 2011 Canadian Society for Chemical Engineering

Using recurrence plot analysis to distinguish between endogenous and exogenous stock market crashes

Recurrence Plots are graphical tools based on Phase Space Reconstruction. Recurrence Quantification Analysis (RQA) is a statistical quantification of RPs. RP and RQA are good at working with non-stationarity and noisy data, in detecting changes in data behavior, in particular in detecting breaks, like a phase transition and in informing about other dynamic properties of a time series. Endogenous Stock Market Crashes have been modeled as phase changes in recent times. Motivated by this, we have used RP and RQA techniques for detecting critical regimes preceding an endogenous crash seen as a phase transition and hence give an estimation of the initial bubble time. We have used a new method for computing RQA measures with confidence intervals. We have also used the techniques on a known exogenous crash to see if the RP reveals a different story or not. The analysis is made on Nifty, Hong Kong AOI and Dow Jones Industrial Average, taken over a time span of about 3 years for the endogenous crashes. Then the RPs of all time series have been observed, compared and discussed. All the time series have been first transformed into the classical momentum divided by the maximum Xmax of the time series over the time window which is considered in the specific analysis. RPs have been plotted for each time series, and RQA variables have been computed on different epochs. Our studies reveal that, in the case of an endogenous crash, we have been able to identify the bubble, while in the case of exogenous crashes the plots do not show any such pattern, thus helping us in identifying such crashes.

Postural sway in low back pain: Effects of dual tasks

Recurrence quantification analysis (RQA), a nonlinear method of postural analysis, was used to explore the effects of dual-tasking on postural performance in people with nonspecific low back pain (LBP) compared with healthy participants. Postural performance was quantified by RQA % recurrence, % determinism, entropy and trend. People with nonspecific LBP ( n = 22) and unimpaired individuals ( n = 22) randomly performed quiet standing tasks with three levels of difficulty (rigid-surface eyes open, rigid-surface eyes closed and foam-surface eyes closed). These tasks were performed in isolation or concurrently with an easy or difficult cognitive task. Increasing postural difficulty was associated with higher % determinism, higher entropy and lower trend in anteroposterior (AP) and mediolateral (ML) directions in people with LBP and healthy participants. All RQA variables in the ML direction decreased as cognitive conditions became more difficult. Significant interactions between group and cognitive difficulty were shown for % recurrence, % determinism and trend in the AP direction. While healthy participants decreased % recurrence and trend by increasing the level of cognitive difficulty, the LBP patients did not. This preliminary study suggests that LBP may be one factor that modulates the posture–cognition interaction.

Optimization of Euclidean distance threshold in the application of recurrence quantification analysis to heart rate variability studies

An integrated approach is proposed to solve the optimization problem of the Euclidean distance threshold ε in recurrence quantification analysis (RQA), which is increasingly applied in the study of heart rate variability (HRV). In this paper, ε is inversely computed from a given recurrence rate (REC), the percentage of recurrence points. From the inversely computed ε, two other RQA output variables: determinism (DET), the percentage of recurrence points forming diagonal line structures, and laminarity (LAM), the percentage of recurrence points forming vertical and horizontal structures, are computed out as well. The trend of DET, LAM values at different REC levels (DLR trend) is introduced to comprehensively represent the dynamic properties of a time series. Based on the DLR trend, the variation of discrimination power, represented by the average loss (or Bayes risk), of DET and LAM, at different REC values is analyzed. Surrogate techniques are used to generate reliable test data sets for the discrimination evaluation. In particular, the results show that (1) the optimal REC can be much higher than the widely used 1% REC, and (2) after the optimization, the average loss can be reduced compared to 1% REC. It is also demonstrated that the optimal ε depends on the dynamic source and RQA variables, and the DLR trend based ε optimization method can improve RQA discrimination analysis especially for the short term HRV analysis.

Influence of embedding parameters and noise in center of pressure recurrence quantification analysis

Recurrence quantification analysis (RQA) can extract the dynamics of postural control from center of pressure (CoP) data by quantifying the system's repeatability, complexity, and local dynamic stability through several variables. Computation of these variables requires the selection of suitable embedding parameters for state space reconstruction (i.e. time delay and embedding dimension); however, it is unclear how the parameters influence RQA variables when examining noisy CoP data. This study evaluated the sensitivity of RQA variables to embedding parameter values and noise level, and assessed methods of selecting embedding parameters for CoP data. Five healthy male subjects maintained quiet stance for 30 s while the anterior–posterior CoP was measured. The effect of noise was evaluated by adding uniform white noise of increasing amplitude to the raw CoP signal. The magnitude of all RQA variables decreased with increasing noise amplitude for all subjects. A sensitivity analysis was performed by systematically altering the embedding parameters for the raw data with and without a selected level of added noise. The key result was that, for all subjects, the RQA variables were sensitive to the embedding parameter values and the level of noise in the CoP data. Finally, the performance of false nearest neighbors and average displacement algorithms for choosing embedding parameters was evaluated. Both methods gave clear and consistent results for all subjects with either raw or noisy data. The results suggest that careful selection of embedding parameters is essential when using RQA to examine postural control based on noisy CoP data.

Revealing deterministic structures in click-evoked otoacoustic emissions.

Click-evoked otoacoustic emissions (CEOAEs) were studied by means of recurrence quantification analysis (RQA) and were found to be endowed with a relevant amount of deterministic structuring. Such a structure showed highly significant correlation with the clinical evaluation of the signal over a data set including 56 signals. Moreover, 1) one of the RQA variables, Trend, was very sensitive to phase transitions in the dynamical regime of CEOAEs, and 2) appropriate use of principal component analysis proved able to isolate the individual character of the studied signals. These results are of general interest for the study of auditory signal transduction and generation mechanisms.