Characterisation of neonatal cardiac dynamics using ordinal partition network

Characterizing unstructured data with the nearest neighbor permutation entropy

Permutation entropy and its associated frameworks are remarkable examples of physics-inspired techniques adept at processing complex and extensive datasets. Despite substantial progress in developing and applying these tools, their use has been predominantly limited to structured datasets such as time series or images. Here, we introduce the k-nearest neighbor permutation entropy, an innovative extension of the permutation entropy tailored for unstructured data, irrespective of their spatial or temporal configuration and dimensionality. Our approach builds upon nearest neighbor graphs to establish neighborhood relations and uses random walks to extract ordinal patterns and their distribution, thereby defining the k-nearest neighbor permutation entropy. This tool not only adeptly identifies variations in patterns of unstructured data but also does so with a precision that significantly surpasses conventional measures such as spatial autocorrelation. Additionally, it provides a natural approach for incorporating amplitude information and time gaps when analyzing time series or images, thus significantly enhancing its noise resilience and predictive capabilities compared to the usual permutation entropy. Our research substantially expands the applicability of ordinal methods to more general data types, opening promising research avenues for extending the permutation entropy toolkit for unstructured data.

Autonomic nervous activity analysis based on visibility graph complex networks and skin sympathetic nerve activity

Background: Autonomic nerve system (ANS) plays an important role in regulating cardiovascular function and cerebrovascular function. Traditional heart rate variation (HRV) and emerging skin sympathetic nerve activity (SKNA) analyses from ultra-short-time (UST) data cannot fully reveal neural activity, thereby quantitatively reflect ANS intensity.

Methods: Electrocardiogram and SKNA from sixteen patients (seven cerebral hemorrhage (CH) patients and nine control group (CO) patients) were recorded using a portable device. Ten derived HRV (mean, standard deviation and root mean square difference of sinus RR intervals (NNmean, SDNN and RMSSD), ultra-low frequency (<0.003 Hz, uLF), very low frequency ([0.003 Hz, 0.04 Hz), vLF), low frequency ([0.04 Hz, 0.15 Hz), LF) and high frequency power ([0.15 Hz, 0.4 Hz), HF), ratio of LF to HF (LF/HF), the standard deviation of instantaneous beat-to-beat R-R interval variability (SD1), and approximate entropy (ApEn)) and ten visibility graph (VG) features (diameter (Dia), average node degree (aND), average shortest-path length (aSPL), clustering coefficient (CC), average closeness centrality (aCC), transitivity (Trans), average degree centrality (aDC), link density (LD), sMetric (sM) and graph energy (GE) of the constructed complex network) were compared on 5-min and UST segments to verify their validity and robustness in discriminating CH and CO under different data lengths. Besides, their potential for quantifying ANS-Load were also investigated.

Results: The validation results of HRV and VG features in discriminating CH from CO showed that VG features were more clearly distinguishable between the two groups than HRV features. For effectiveness evaluation of analyzing ANS on UST segment, the NNmean, SDNN, RMSSD, LF, HF and LF/HF in HRV features and the CC, Trans, Dia and GE of VG features remained stable in both activated and inactivated segments across all data lengths. The capability of HRV and VG features in quantifying ANS-Load were evaluated and compared under different ANS-Load, the results showed that most HRV features (SDNN, LFHF, RMSSD, vLF, LF and HF) and almost all VG features were correlated to sympathetic nerve activity intensity.

Conclusions: The proposed autonomic nervous activity analysis method based on VG and SKNA offers a new insight into ANS assessment in UST segments and ANS-Load quantification.