Characterizing Fluctuations of Arterial and Cerebral Tissue Oxygenation in Preterm Neonates by Means of Data Analysis Techniques for Nonlinear Dynamical Systems

The cerebral autoregulatory state as well as fluctuations in arterial (SpO2) and cerebral tissue oxygen saturation (StO2) are potentially new relevant clinical parameters in preterm neonates. The aim of the present study was to test the investigative capabilities of data analysis techniques for nonlinear dynamical systems, looking at fluctuations and their interdependence. StO2, SpO2 and the heart rate (HR) were measured on four preterm neonates for several hours. The fractional tissue oxygenation extraction (FTOE) was calculated. To characterize the fluctuations in StO2, SpO2, FTOE and HR, two methods were employed: (1) phase-space modeling and application of the recurrence quantification analysis (RQA), and (2) maximum entropy spectral analysis (MESA). The correlation between StO2 and SpO2 as well as FTOE and HR was quantified by (1) nonparametric nonlinear regression based on the alternating conditional expectation (ACE) algorithm, and (2) the maximal information-based nonparametric exploration (MINE) technique. We found that (1) each neonate showed individual characteristics, (2) a ~60 min oscillation was observed in all of the signals, (3) the nonlinear correlation strength between StO2 and SpO2 as well as FTOE and HR was specific for each neonate and showed a high value for a neonate with a reduced health status, possibly indicating an impaired cerebral autoregulation. In conclusion, our data analysis framework enabled novel insights into the characteristics of hemodynamic and oxygenation changes in preterm infants. To the best of our knowledge, this is the first application of RQA, MESA, ACE and MINE to human StO2 data measured with near-infrared spectroscopy (NIRS).


Introduction
Preterm infants exhibit an immature regulation of respiration as well as systemic and cerebral blood circulation (i.e. cerebral autoregulation, CO 2 vasoreactivity), leading to an increased incidence of hypoxic and hyperoxic episodes due to (1) large fluctuations in cerebral hemodynamics, and (2) impaired coupling between cerebral blood flow (CBF) and metabolic demand [1]. Episodes of intermittent hypoxemia occur in 74 % of preterm infants, compared to 62 % of term infants [2]. Hyperoxemia or hypoxemia may lead to an increase in mortality and neurological morbidity with long-term effects in later adult life. Greater variability in arterial oxygen saturation (SpO 2 ) [3] correlates with an increased incidence of retinopathy of prematurity (ROP). Thus, the assessment of the dynamics of SpO 2 and cerebral tissue oxygen saturation (StO 2 ) in preterm neonates may be of high clinical relevance. Due to continuous advancement in biomedical optics [4,5], a reliable noninvasive longterm measurement of StO 2 in preterm neonates is in principle feasible [6,7].
The aim of the present study was to analyze long-term measurements of StO 2 (conducted by multi-distance near-infrared spectroscopy, MD-NIRS) and SpO 2 , heart rate (HR) and the fractional tissue extraction (FTOE) in preterm infants by means of data analysis techniques for nonlinear dynamical systems in order to investigate the characteristics of cerebral and systemic hemodynamic fluctuations and their interdependence.

Subjects, Instrumentation and Experimental Protocol
A total of 20 clinically stable preterm neonates were enrolled. The study was approved by the ethics committee, and written informed consent was obtained from the parents before the study. Four neonates were selected for the present analysis, namely those with long continuous signals and the highest signal-to-noise ratio (SNR) (  [9] which ensures a robust and high-precision measurement of absolute StO 2 values [10]. The NIRS optode was positioned over the left prefrontal cortex (PFC).
Measurements were performed continuously during the night (from~10 pm till 6 am), i.e. NIRS measured the resting-state activity of cerebral hemodynamics.

Signal Processing and Data Analysis
From the SpO 2 and StO 2 we calculated the fractional tissue oxygenation extraction (FTOE ¼ (SpO 2 -StO 2 )/SpO 2 ) Â 100 [%]. FTOE quantifies the balance between oxygen delivery and oxygen consumption and correlates significantly with the invasively measured oxygen extraction fraction [11]. All signals (SpO 2 , StO 2 , FTOE and HR) were downsampled to 0.05 Hz to increase the SNR and since only low frequencies were of interest. For each of the four datasets, an interval was chosen for the subsequent analysis which contains data without any signal distortion. The lengths of the data are given in Table 64.1. To characterize the fluctuations in StO 2 , SpO 2 , FTOE and HR, two different methods were applied: • Phase-space modeling and application of the recurrence quantification analysis (RQA) [12,13]. Each signal (StO 2 , SpO 2 , FTOE and HR) was embedded into a phase space with the dimension m and time delay τ. The optimal values for m and τ were determined by finding the first minimum of the false nearest neighbors function depending on m, and the autocorrelation function depending on τ, respectively. In a subsequent step, the phase space trajectories were characterized by the RQA. In particular, the determinism (DET, i.e. the predictability of the system), entropy of the diagonal length (ENT, i.e. the complexity of the system's deterministic dynamics), and laminarity (LAM, i.e. the amount of intermittency of the system's dynamics) were calculated. • Maximum entropy spectral analysis (MESA) [14]. This method enables a highprecision spectral analysis based on the principle of maximum entropy. To prevent spurious peaks, the order of the MESA-based periodogram was set at one third of the number of samples [15].
The correlation between StO 2 and SpO 2 as well as FTOE and HR were quantified by two nonparametric methods: • Nonparametric nonlinear regression based on the alternating conditional expectation (ACE) algorithm [16]. This technique finds the optimal transformations for the dependent and independent variables in order to maximize the correlation. The correlation strength is quantified by the maximal correlation coefficient, r ACE . • Maximal information-based nonparametric exploration (MINE) technique [17]. MINE enables the characterization of dependencies between variables. We calculated the maximal information coefficient (MIC) (relationship strength) and maximum asymmetry score (MAS) (departure from monotonicity).
In addition, each signal was characterized by calculating the median, and variability index 1 (VI 1 , quantified as the mean of the modulus of the first derivation). In addition, the relationship of the fluctuation strength of StO 2 vs. SpO 2 was determined by the ratio of their standard deviations (variability index 2, VI 2 ).   To interpret the results it is helpful to discuss the similarities and differences of the signal characteristics with respects to the four neonates:

Results, Discussion, Conclusion and Outlook
• The physiological interpretation of these findings is not straightforward since all patient-specific characteristics have an influence on the analyzed parameters. In particular, the general health state (e.g. PDA, microbleeds, ischemia: yes/no), the type of respiration (ventilatory support: yes/no, type of support), and the GA (at birth/measurement) could potentially have a strong impact on the parameters. The following observations were made based on our analysis: (1) The general inverse correlation observed between StO 2 and Hct was also noticed by other studies (e.g. [18]). (2) Neonate #3 exhibited a large VI 2 , e.g. the fluctuations in StO 2 were much stronger than in SpO 2 (especially the decreases), a pattern that is observed by neonates with a PDA-indeed, neonate #3 had a PDA (which was however classified as not hemodynamically relevant). The low StO 2 /SpO 2 correlation (r ACE , MIC) and the different frequency spectra (StO 2 vs. SpO 2 , HR vs. FTOE) point also to a specific state of the systemic-cerebral hemodynamic coupling. The observation that neonate #3 had the highest median values for StO 2 and SpO 2 as well as the lowest ones for HR and FTOE is surprising since one would expect an increased FTOE and decrease StO 2 in case of a PDA [19]. (3) The oscillations in the data with T % 60 and 30 min could originate from sleep phases. A sleep-wake cycling (with a quiet sleep phase with T % 20 min) is known [20] in term newborns with T % 50-60 min and an increase in total hemoglobin and HR during active sleep (compared to quite sleep) has previously been observed [21,22]. (4) The two neonates with the lowest GA at birth (#2, #4) had the largest variability of StO 2 , SpO 2 and FTOE which could indicate an immature functioning of cerebral hemodynamic regulation.
In conclusion, using four case studies, we demonstrated the possibility of realizing long-term measurements in preterm neonates with MD-NIRS and we presented a novel framework for investigating the characteristics of cerebral and systemic hemodynamic fluctuations and their interdependence. A follow-up study, investigating the signal characteristics in healthy and ill preterm neonates using the same framework would be the next step. Focusing on the fluctuation characteristics of the signals may offer novel insights into systemic and cerebral hemodynamics that are not assessed routinely only using traditional analyses (i.e. based on moments and linear correlations). To the best of our knowledge, this is the first application of RQA, MESA, ACE and MINE to human NIRS data.
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