Phase Space Reconstruction from a Biological Time Series: A Photoplethysmographic Signal Case Study

Classification of BCI-EEG Based on the Augmented Covariance Matrix

OBJECTIVE

Electroencephalography signals are recorded as multidimensional datasets. We propose a new framework based on the augmented covariance that stems from an autoregressive model to improve motor imagery classification.

METHODS

From the autoregressive model can be derived the Yule-Walker equations, which show the emergence of a symmetric positive definite matrix: the augmented covariance matrix. The state-of the art for classifying covariance matrices is based on Riemannian Geometry. A fairly natural idea is therefore to apply this Riemannian Geometry based approach to these augmented covariance matrices. The methodology for creating the augmented covariance matrix shows a natural connection with the delay embedding theorem proposed by Takens for dynamical systems. Such an embedding method is based on the knowledge of two parameters: the delay and the embedding dimension, respectively related to the lag and the order of the autoregressive model. This approach provides new methods to compute the hyper-parameters in addition to standard grid search.

RESULTS

The augmented covariance matrix performed ACMs better than any state-of-the-art methods. We will test our approach on several datasets and several subjects using the MOABB framework, using both within-session and cross-session evaluation.

CONCLUSION

The improvement in results is due to the fact that the augmented covariance matrix incorporates not only spatial but also temporal information. As such, it contains information on the nonlinear components of the signal through the embedding procedure, which allows the leveraging of dynamical systems algorithms.

SIGNIFICANCE

These results extend the concepts and the results of the Riemannian distance based classification algorithm.

Phase space reconstruction for noise-robust respiration rate estimation from PPG signal

Wearable devices that use optical sensing techniques have become increasingly popular in the healthcare industry for detecting diseases at an early stage and monitoring their progression. Multi-parameter monitoring, specifically the extraction of the respiratory signal, is a growing trend due to its simplicity and cost-effectiveness. However, this can result in an inaccurate respiratory rate (RR) due to external noise. To address this, we propose an attractor reconstruction technique with optimized (auto-correlation coefficient) delay 'τopt' and a Retract strategy to improve the RR accuracy. The performance is evaluated using the BIDMC dataset, and a mean absolute error of 2.19 and 1.87 breaths per minute are reported for the 32- and 64sec windowed PPG, respectively. The result indicates that the proposed method's RR accuracy surpassed the state-of-the-art techniques. Further, the result infers that τopt optimization is insignificant for the PPG signal. Hence, the τopt can be selected as 1/3rd of the signal's average cycle length. In addition, the proposed approach is well within an acceptable range for class II medical devices without losing vital signals.

Dynamical Analyses Show That Professional Archers Exhibit Tighter, Finer and More Fluid Dynamical Control Than Neophytes

Quantifying the dynamical features of discrete tasks is essential to understanding athletic performance for many sports that are not repetitive or cyclical. We compared three dynamical features of the (i) bow hand, (ii) drawing hand, and (iii) center of mass during a single bow-draw movement between professional and neophyte archers: dispersion (convex hull volume of their phase portraits), persistence (tendency to continue a trend as per Hurst exponents), and regularity (sample entropy). Although differences in the two groups are expected due to their differences in skill, our results demonstrate we can quantify these differences. The center of mass of professional athletes exhibits tighter movements compared to neophyte archers (6.3 < 11.2 convex hull volume), which are nevertheless less persistent (0.82 < 0.86 Hurst exponent) and less regular (0.035 > 0.025 sample entropy). In particular, the movements of the bow hand and center of mass differed more between groups in Hurst exponent analysis, and the drawing hand and center of mass were more different in sample entropy analysis. This suggests tighter neuromuscular control over the more fluid dynamics of the movement that exhibits more active corrections that are more individualized. Our work, therefore, provides proof of principle of how well-established dynamical analysis techniques can be used to quantify the nature and features of neuromuscular expertise for discrete movements in elite athletes.

Autonomic Regulation of Facial Temperature during Stress: A Cross-Mapping Analysis

Skin temperature reflects the Autonomic Nervous System (ANS)'s response to emotions and mental states and can be remotely measured using InfraRed Thermography. Understanding the physiological mechanisms that affect facial temperature is essential to improve the precision of emotional inference from thermal imaging. To achieve this aim, we recorded thermal images from 30 volunteers, at rest and under acute stress induced by the Stroop test, together with two autonomic correlates, i.e., heart rate variability and electrodermal activity, the former serving as a measure of cardiovascular dynamics, and the latter of the activity of the sweat glands. We used a Cross Mapping (CM) approach to quantify the nonlinear coupling of the temperature from four facial regions with the ANS correlates. CM reveals that facial temperature has a statistically significant correlation with the two autonomic time series, under both conditions, which was not evident in the linear domain. In particular, compared to the other regions, the nose shows a significantly higher link to the electrodermal activity in both conditions, and to the heart rate variability under stress. Moreover, the cardiovascular activity seems to be primarily responsible for the well-known decrease in nose temperature, and its coupling with the thermal signals significantly varies with gender.

Symmetric Projection Attractor Reconstruction Analysis as a Method to Assess Seismocardiogram Quality in a Healthy Population

Signal quality significantly affects the processing, analysis, and interpretation of biomedical signals. There are many procedures for assessing signal quality that use averaged numerical values, thresholding, analysis in the time or frequency domain, or nonlinear approaches. An interesting approach to the assessment of signal quality is using symmetric projection attractor reconstruction (SPAR) analysis, which transforms an entire signal into a two-dimensional plot that reflects the waveform morphology. In this study, we present an application of SPAR to evaluate the quality of seismocardiograms (SCG signals) from the CEBS database, a publicly available seismocardiogram signal database. Visual inspection of symmetric projection attractors suggests that high-quality (clean) seismocardiogram projections resemble six-pointed asterisks (*), and any deviation from this shape suggests the influence of noise and artifacts.Clinical relevance- SPAR analysis enables quick identification of noise and artifacts that can affect the reliability of the diagnosis of cardiovascular diseases based on SCG signals.

Effects of Motor Task Difficulty on Postural Control Complexity during Dual Tasks in Young Adults: A Nonlinear Approach

Few studies have evaluated the effect of a secondary motor task on the standing posture based on nonlinear analysis. However, it is helpful to extract information related to the complexity, stability, and adaptability to the environment of the human postural system. This study aimed to analyze the effect of two motor tasks with different difficulty levels in motor performance complexity on the static standing posture in healthy young adults. Thirty-five healthy participants (23.08 ± 3.92 years) performed a postural single task (ST: keep a quiet standing posture) and two motor dual tasks (DT). i.e., mot-DT(A)—perform the ST while performing simultaneously an easy motor task (taking a smartphone out of a bag, bringing it to the ear, and putting it back in the bag)—and mot-DT(T)—perform the ST while performing a concurrent difficult motor task (typing on the smartphone keyboard). The approximate entropy (ApEn), Lyapunov exponent (LyE), correlation dimension (CoDim), and fractal dimension (detrending fluctuation analysis, DFA) for the mediolateral (ML) and anterior-posterior (AP) center-of-pressure (CoP) displacement were measured with a force plate while performing the tasks. A significant difference was found between the two motor dual tasks in ApEn, DFA, and CoDim-AP (p < 0.05). For the ML CoP direction, all nonlinear variables in the study were significantly different (p < 0.05) between ST and mot-DT(T), showing impairment in postural control during mot-DT(T) compared to ST. Differences were found across ST and mot-DT(A) in ApEn-AP and DFA (p < 0.05). The mot-DT(T) was associated with less effectiveness in postural control, a lower number of degrees of freedom, less complexity and adaptability of the dynamic system than the postural single task and the mot-DT(A).

Evaluation of Geometric Attractor Structure and Recurrence Analysis in Professional Dancers

BACKGROUND

Human motor systems contain nonlinear features. The purpose of this study was to evaluate the geometric structure of attractors and analyze recurrence in two different pirouettes (jazz and classic) performed by 15 professional dancers.

METHODS

The kinematics of the body's center of mass (CoM) and knee of the supporting leg (LKNE) during the pirouette were measured using the Vicon system. A time series of selected points were resampled, normalized, and randomly reordered. Then, every second time series was flipped to be combined with other time series and make a long time series out of the repetitions of a single task. The attractors were reconstructed, and the convex hull volumes (CHV) were counted for the CoM and LKNE for each pirouette in each direction. Recurrence quantification analysis (RQA) was used to extract additional information.

RESULTS

The CHVs calculated for the LKNE were significantly lower for the jazz pirouette. All RQA measures had the highest values for LKNE along the mediolateral axis for the jazz pirouette. This result underscores the high determinism, high motion recurrence, and complexity of this maneuver.

CONCLUSIONS

The findings offer new insight into the evaluation of the approximation of homogeneity in motion control. A high determinism indicates a highly stable and predictive motion trajectory.

Understanding chaos in COVID-19 and its relationship to stringency index: Applications to large-scale and granular level prediction models

Understanding the underlying and unpredictable dynamics of the COVID-19 pandemic is important. We supplemented the findings of Jones and Strigul (2020) and described the chaotic behavior of COVID-19 using state space plots which depicted the changes in asymptotic behavior and trajectory brought about by the increase or decrease in the number of cases which resulted from the easing or tightening of restrictions and other non-pharmaceutical interventions instituted by governments as represented by the country’s stringency index (SI). We used COVID-19 country-wide case count data and analyzed it using convergent cross-mapping (CCM) and found that the SI influence on COVID-19 case counts is high in almost all the countries considered. When we utilized finer granular geographical data (‘barangay’ or village level COVID-19 case counts in the Philippines), the effects of SI were reduced as the population density increased. The authors believe that the knowledge of the chaotic behavior of COVID-19 and the effects of population density as applied to finer granular geographical data has the potential to generate more accurate COVID-19 non-linear prediction models. This could be used at the local government level to guide strategic and highly targeted COVID-19 policies which are favorable to public health systems but with limited impact to the economy.