# Feasibility of Ultra-Short-Term Analysis of Heart Rate and Systolic Arterial Pressure Variability at Rest and during Stress via Time-Domain and Entropy-Based Measures

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Protocol

^{−2}) [40,41]. All participants signed a written informed consent form before taking part in the measurement protocol, also requiring a parental or legal guardian permission to participate in the study when the subject was a minor (i.e., less than 18 years of age). All procedures were approved by the Ethical Committee of the Jessenius Faculty of Medicine, Comenius University, Martin, Slovakia. Subjects were asked not to take substances influencing the autonomic nervous system and cardiovascular system activities [40,41].

- A resting condition (R1) with the subject laying in the supine position for 15 min, in order to stabilize the physiological signals on a baseline level;
- A head-up tilt (T) test aimed at evoking mild orthostatic stress by inclining the motorized table by 45 degrees for 8 min;
- Another resting condition (R2) with the subject laying in the supine position for 10 min, in order to restore the physiological parameters to their baseline values;
- A 6 min long mental arithmetic (M) task aimed to evoke cognitive load (i.e., mental stress), during which subjects were asked to mentally calculate the sum of three digits in the least possible time, indicating whether the result was an even or odd number.

#### 2.2. Time Series Extraction

#### 2.3. Time-Domain Analysis

#### 2.4. Information Domain Analysis

#### 2.5. Statistical Analysis

## 3. Results

#### 3.1. Time-Domain Analysis

#### 3.2. Information Domain Analyses

**≤**180 and N ≤ 120, respectively. The Cohen’s d values obtained for lin estimator are higher than for the knn one (see central subplots in each panel in Figure 4). High effect sizes are reported for CE and DE during T, but medium values instead during M; with regard to the SE index, a medium–high effect size is assessed for both physiological state changes and for both estimators. In any case, d appears almost constant at decreasing N (down to N = 120), while a more marked decrease is observed when going to N = 60. Finally, the squared Pearson correlation coefficient (see bottom subplots in each panel in Figure 4) decreases, shortening the time series length N, and still largely shows a high degree of correlation (above the threshold) down to N = 120.

## 4. Discussion

#### 4.1. Time-Domain Analyses on ST Series

#### 4.2. Information Domain Analyses on ST Series

#### 4.3. Ultra-Short-Term versus Short-Term Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Schematic illustration of the experimental protocol, including baseline resting (R1), orthostatic stress (T), second resting (R2) and mental stress (M). Dashed boxes indicate the windows taken into account with regard to short-term (ST, 300 points) analysis. (

**b**) Representative RR and SAP time series, extracted respectively from ECG and BP recordings, which have been investigated through univariate analysis performed after ST (red arrow) and ultra-short-term (UST, 240 to 60 points, blue arrows) time window segmentation.

**Figure 2.**Boxplot distributions (top subplots) of time-domain indexes, i.e., (

**a**) MEAN, (

**b**) SDNN and (

**c**) RMSSD calculated from RR time series during R1 (light gray) and T (light blue), (

**.1**panels), and during R2 (dark gray) and M (orange) (

**.2**panels) phases. Statistical tests: #, p < 0.05, T vs. R1 or M vs. R2; *, p < 0.05, ST vs. UST. Central subplots: Cohen’s d (in absolute value) evaluated between each stress condition and the previous rest phase (i.e., R1-T and R2-M) for all the considered time series lengths. Bottom subplots: squared Pearson correlation coefficients computed between a given UST distribution and the ST reference, with a threshold of ${\mathrm{r}}^{2}=0.81$ (dotted gray line).

**Figure 3.**Boxplot distributions (top subplots) of time-domain indexes, i.e., (

**a**) MEAN and (

**b**) STD calculated from SAP time series during R1 (light gray) and T (light blue), (

**.1**panels), and during R2 (dark gray) and M (orange) (

**.2**panels) phases. Statistical tests: #, p < 0.05, R1 vs. T and R2 vs. M; *, p < 0.05, ST vs. UST. Statistical tests: #, p < 0.05, T vs. R1 or M vs. R2; *, p < 0.05, ST vs. UST. Central subplots: Cohen’s d (in absolute value) evaluated between each stress condition and the previous rest phase (i.e., R1-T and R2-M) for all the considered time series lengths. Bottom subplots: squared Pearson correlation coefficients computed between a given UST distribution and the ST reference, with a threshold of ${\mathrm{r}}^{2}=0.81$ (dotted gray line).

**Figure 4.**Results of information domain analysis on RR time series. Boxplot distributions (top subplots) of ST and UST indices of (

**a**) SE, (

**b**) DE and (

**c**) CE calculated using both lin (.

**1**and

**.2**) and knn (

**.3**and

**.4**) estimators during R1 (light gray) and T (light blue) (

**.1**and

**.3**), and during R2 (dark gray) and T (orange) (

**.2**and

**.4**) phases. Statistical tests: #, p < 0.05, T vs. R1 or M vs. R2; *, p < 0.05 ST vs. UST. Central subplots: Cohen’s d (in absolute value) evaluated between each stress condition and the previous rest phase (i.e., R1-T and R2-M) for all the considered time series lengths. Bottom subplots: squared Pearson correlation coefficients computed between a given UST distribution and the ST reference, with a threshold of ${\mathrm{r}}^{2}=0.81$ (dotted gray line).

**Figure 5.**Results of information domain analysis on SAP time series. Boxplot distributions (top subplots) of ST and UST indices of (

**a**) SE, (

**b**) DE, and (

**c**) CE calculated using both lin (.

**1**and

**.2**) and knn (

**.3**and

**.4**) estimators during R1 (light gray) and T (light blue) (.

**1**and

**.3**), and during R2 (dark gray) and T (orange) (

**.2**and

**.4**) phases. Statistical tests: #, p < 0.05, T vs. R1 or M vs. R2; *, p < 0.05 ST vs. UST. Central subplots: Cohen’s d (in absolute value) evaluated between each stress condition and the previous rest phase (i.e., R1-T and R2-M) for all the considered time series lengths. Bottom subplots: squared Pearson correlation coefficients computed between a given UST distribution and the ST reference, with a threshold of ${\mathrm{r}}^{2}=0.81$ (dotted gray line).

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## Share and Cite

**MDPI and ACS Style**

Volpes, G.; Barà, C.; Busacca, A.; Stivala, S.; Javorka, M.; Faes, L.; Pernice, R.
Feasibility of Ultra-Short-Term Analysis of Heart Rate and Systolic Arterial Pressure Variability at Rest and during Stress via Time-Domain and Entropy-Based Measures. *Sensors* **2022**, *22*, 9149.
https://doi.org/10.3390/s22239149

**AMA Style**

Volpes G, Barà C, Busacca A, Stivala S, Javorka M, Faes L, Pernice R.
Feasibility of Ultra-Short-Term Analysis of Heart Rate and Systolic Arterial Pressure Variability at Rest and during Stress via Time-Domain and Entropy-Based Measures. *Sensors*. 2022; 22(23):9149.
https://doi.org/10.3390/s22239149

**Chicago/Turabian Style**

Volpes, Gabriele, Chiara Barà, Alessandro Busacca, Salvatore Stivala, Michal Javorka, Luca Faes, and Riccardo Pernice.
2022. "Feasibility of Ultra-Short-Term Analysis of Heart Rate and Systolic Arterial Pressure Variability at Rest and during Stress via Time-Domain and Entropy-Based Measures" *Sensors* 22, no. 23: 9149.
https://doi.org/10.3390/s22239149