# SDNN24 Estimation from Semi-Continuous HR Measures

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Dataset and Feature Engineering

- nsr2db: Normal Sinus Rhythm RR Interval Database PhysioNet dataset [25]. This dataset contains beat annotations of 54 normal sinus rhythm subjects (30 men: 28–76 years; 24 women: 58–73 years) extracted from 23 h long ECG.
- chfdb: Congestive Heart Failure RR Interval Database PhysioNet dataset [26]. This dataset includes beat annotation files for 29 long-term ECG recordings of subjects aged 34 to 79, with congestive heart failure (New York Heart Association classes I, II, and III). Subjects included 8 men and 2 women; gender is not known for the remaining 21 subjects.
- mmash: Multilevel Monitoring of Activity and Sleep in Healthy people (MMASH) dataset [27,28] provides 24 h of continuous beat-to-beat heart data, triaxial accelerometer data, sleep quality, physical activity and psychological characteristics (i.e., anxiety status, stress events and emotions) for 22 healthy participants.

#### 2.2. Data Preprocessing

#### 2.3. PPG Error Estimation

#### 2.4. SDNN24

#### 2.4.1. Time Domain Analysis

- SDNN24: The standard deviation of NN intervals recorded during 24 h (Equation (1)).$$\mathrm{SDNN}24=\sqrt{\frac{{\sum}_{i=1}^{N}{({\mathrm{NN}}_{i}-\overline{\mathrm{NN}})}^{2}}{N}}$$
- SDNNi24: The mean of the standard deviations of the NN intervals calculated on segments with defined duration over 24 h (Equation (2)).$$\mathrm{SDNNi}24=\frac{{\sum}_{j=1}^{{N}_{\mathrm{segments}}}\sqrt{\frac{{\sum}_{i=1}^{{n}_{j}}{({\mathrm{NN}}_{i}-\overline{{\mathrm{NN}}_{j}})}^{2}}{{n}_{j}}}}{{N}_{\mathrm{segments}}}$$
- SDANN24: The standard deviation of the means of NN intervals calculated at segments of a defined duration over 24 h (Equation (3)).$$\mathrm{SDANN}24=\sqrt{\frac{{\sum}_{j=1}^{{N}_{\mathrm{segments}}}{(\overline{{\mathrm{NN}}_{j}}-\frac{{\sum}_{j=1}^{{N}_{\mathrm{segments}}}\overline{{\mathrm{NN}}_{j}}}{{N}_{\mathrm{segments}}})}^{2}}{{N}_{\mathrm{segments}}}}$$
- SDANN${}_{\mathrm{HR}}$24: The standard deviation of the Average NN intervals (ANN) derived from the HR, i.e., $\mathrm{ANN}=\frac{60}{\mathrm{HR}}$, calculated on segments with defined duration over 24 h (Equation (4)).$${\mathrm{SDANN}}_{\mathrm{HR}}24=\sqrt{\frac{{\sum}_{j=1}^{{N}_{\mathrm{segments}}}{(\frac{60}{{\mathrm{HR}}_{j}+{\u03f5}_{j}}-\frac{{\sum}_{j=1}^{{N}_{\mathrm{segments}}}\frac{60}{{\mathrm{HR}}_{j}+{\u03f5}_{j}}}{{N}_{\mathrm{segments}}})}^{2}}{{N}_{\mathrm{segments}}}}$$

#### 2.4.2. Frequency Domain Analysis for SDNN24

- SDANN${}_{\mathrm{HR}}$24${}_{\mathrm{adjMean}}$: The root square of the sum between NN intervals (ANN) variance derived from the average HR, i.e., ANN = $\frac{60}{{\mathrm{HR}}_{segment}}+\u03f5$ ($\u03f5$ is a random Gaussian bias of a specific time window length), calculated on segments with defined duration over 24 h (ANN${}_{\mathrm{HR}}$24) and the mean of $a\phantom{\rule{4pt}{0ex}}priori$ missing frequency variance (Equation (6)).$$\phantom{\rule{-28.45274pt}{0ex}}{\mathrm{SDANN}}_{\mathrm{HR}}{24}_{\mathrm{adjMean}}=\sqrt{\mathrm{VAR}\left({\mathrm{ANN}}_{\mathrm{HR}}24\right)+\frac{1}{\pi}{\int}_{freq}^{\infty}{S}_{xx}\left(\omega \right)d\omega}$$With this approach, we attempt to remove the underestimation of SDNN24 by adding the portion of spectrum lost by using HR measures instead of inter-beats intervals data, simply adding the average power of the HRV spectrum above $freq$ to the measured variance. The corrective factor is fixed for all subjects.
- SDANN${}_{\mathrm{HR}}$24${}_{\mathrm{adjW}}$: The root square of the total power predicted in accordance with $a\phantom{\rule{4pt}{0ex}}priori$ PSD (Equation (7)).$${\mathrm{SDANN}}_{\mathrm{HR}}{24}_{\mathrm{adjW}}=\sqrt{\frac{1}{\pi}\mathrm{VAR}\left({\mathrm{ANN}}_{\mathrm{HR}}24\right)+\frac{1}{\pi}\frac{{\int}_{0}^{freq}{S}_{xx}\left(\omega \right)d{\omega}_{ANN}\ast {\int}_{freq}^{\infty}{S}_{xx}\left(\omega \right)d\omega}{{\int}_{0}^{freq}{S}_{xx}\left(\omega \right)d\omega}}$$With this approach we correct the underestimation by assuming that the missing high frequencies perfectly correlate with the measured low frequencies.

#### 2.4.3. HR Circadian Rhythm

#### 2.5. Validation

#### 2.6. Healthy vs. Unhealthy Subjects

#### 2.6.1. Statistical Analysis

#### 2.6.2. Machine Learning Approach

- LR: Logistic Regression was performed using: only SDNN24 (${\mathrm{LR}}_{\mathrm{SDNN}}24$); only SDNN${}_{\mathrm{HR}}$24 ($L{R}_{\mathrm{SDNN}}\mathrm{HR}24$); all of the HR features as predictors, i.e., SDNN${}_{\mathrm{HR}}$24, MESOR and Amplitude ($L{R}_{\mathrm{HR}}$);
- RF${}_{\mathrm{HR}}$: Random Forest Classifiers (RF) were also performed using all the HR features as predictors;
- NN: Fully connected feed forward Neural Network, using all the HR features as predictors. We used Keras with the TensorFlow backend by using Python 3.8 programming language. We trained our neural networks on the Azure cloud, using bayesian sampling. The only explored topology was fully connected, with a single hidden layer, leaky relu activation function for the neurons of the hidden layer, a single output neuron with sigmoid activation function, and a dropout layer after the hidden layer. The tuned hyper-parameters were:
- The number of neurons in the hidden layer (between 1 and 8);
- Alpha value for the leaky relu activation function of the neurons in the hidden layer (between 0.0 and 1.0);
- The dropout rate (between 0% and 99%);
- The batch size (between 1 and 32).

The training set was split in train and validation using the train_test_split function from the sklearn python package, using a 80-20% split, ensuring stratification on the predicted class. The validation data were not used during hyper-parameter tuning. A total of 400 combinations of hyper-parameters were tested.

## 3. Results

#### 3.1. SDNN24 Estimation

#### 3.1.1. Time Domain Analysis

#### 3.1.2. Frequency Domain Analysis

#### 3.2. Healthy vs. Unhealthy Subjects

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Power spectrum density plot obtained by Lomb-Scargle Periodogram in both low and high cardiovascular risk subjects.

Time Window | Error |
---|---|

1 min | 0.03 ± 5.91 |

5 min | 0.33 ± 5.09 |

10 min | −0.16 ± 4.71 |

30 min | −0.60 ± 4.01 |

60 min | −0.35 ± 3.95 |

**Table 2.**Descriptive and statistics analysis of SDNN24 estimations. All the values are expressed in milliseconds (ms).

Segment | SDNN24 | SDNNi24 | SDANN24 | SDANN${}_{\mathit{H}\mathit{R}}$24 |
---|---|---|---|---|

1 min | 133.73 ± 45.98 | 56.28 ± 18.51 * | 119.38 ± 49.51 * | 120.96 ± 48.91 * |

5 min | 59.47 ± 21.52 * | 117.33 ± 48.03 * | 118.62 ± 47.00 * | |

10 min | 60.77 ± 23.02 * | 116.72 ± 47.37 * | 117.94 ± 46.30 * | |

30 min | 63.11 ± 26.26 * | 115.75 ± 46.69 * | 117.12 ± 45.96 * | |

60 min | 64.61 ± 28.52 * | 114.87 ± 46.23 * | 116.29 ± 45.85 * |

**Table 3.**Descriptive of power spectrum analysis expressed in ms${}^{2}$ in all the segments length. In this table, the power of frequencies that are lower and higher than the maximal frequency that can be evaluated because of the segment length are reported. The results are reported as the mean ± standard deviation.

Segment | Lower Frequency | Higher Frequency | Total Power |
---|---|---|---|

1 min max frequency = 1.67$\times {10}^{-2}$ | 1.17$\times {10}^{4}$± 8.68$\times {10}^{3}$ (20.44%) | 4.57$\times {10}^{4}$± 2.86$\times {10}^{4}$ (79.56%) | 5.74$\times {10}^{4}$± 3.66$\times {10}^{4}$ |

5 min max frequency = 3.33$\times {10}^{-3}$ Hz | 1.12$\times {10}^{4}$± 8.47$\times {10}^{3}$ (19.41%) | 4.62$\times {10}^{4}$± 2.86$\times {10}^{4}$ (80.59%) | |

10 min max frequency = 1.67$\times {10}^{-3}$ Hz | 1.09$\times {10}^{4}$± 8.35$\times {10}^{3}$ (18.88%) | 4.66$\times {10}^{4}$± 2.87$\times {10}^{4}$ (81.22%) | |

30 min max frequency = 5.55$\times {10}^{-4}$ Hz | 1.03$\times {10}^{4}$± 8.09$\times {10}^{3}$ (17.85%) | 4.72$\times {10}^{4}$± 2.90$\times {10}^{4}$ (82.25%) | |

60 min max frequency = 2.78$\times {10}^{-4}$ Hz | 9.77$\times {10}^{3}$± 7.90$\times {10}^{3}$ (17.01%) | 4.77$\times {10}^{4}$± 2.92$\times {10}^{4}$ (82.98%) |

**Table 4.**Descriptive and statistics analysis of SDNN24 and SDNN24 derived from HR data on $mmash$ dataset. All the values are expressed in milliseconds (ms).

Segment | SDNN24 | SDNN${}_{\mathbf{HR}}$24 | SDANN${}_{\mathbf{HR}}$24${}_{\mathbf{adjMean}}$ | SDANN${}_{\mathbf{HR}}$24${}_{\mathbf{adjW}}$ |
---|---|---|---|---|

1 min | 173.53 ± 25.76 | 164.00 ± 32.52 | 213.63 ± 20.81 * | 175.65 ± 25.65 |

5 min | 153.02 ± 32.54 * | 209.23 ± 19.79 * | 165.64 ± 31.59 | |

10 min | 149.84 ± 31.00 * | 198.92 ± 23.90 * | 161.51 ± 30.96 | |

30 min | 146.02 ± 32.47 * | 197.60 ± 24.55 * | 164.21 ± 35.98 | |

60 min | 142.11 ± 35.02 * | 198.38 ± 31.10 * | 155.23 ± 40.00 |

**Table 5.**Difference between people with low and high cardiovascular risk in all the segments length.

Segment | Features | High Risk | Low Risk | t-score |
---|---|---|---|---|

— | SDNN24 (ms) | 86.54 ± 43.29 | 142.14 ± 31.05 | 6.66 * |

1 min | SDNN${}_{\mathrm{HR}}$24 (ms) | 67.86 ± 37.23 | 132.61 ± 30.79 | 8.28 * |

5 min | SDNN${}_{\mathrm{HR}}$24 (ms) | 64.46 ± 37.23 | 128.31 ± 30.63 | 8.27 * |

10 min | SDNN${}_{\mathrm{HR}}$24 (ms) | 62.55 ± 36.67 | 126.02 ± 30.52 | 8.29 * |

30 min | SDNN${}_{\mathrm{HR}}$24 (ms) | 58.37 ± 35.45 | 121.96 ± 30.44 | 8.44 * |

60 min | SDNN${}_{\mathrm{HR}}$24 (ms) | 55.75 ± 34.60 | 118.81 ± 30.26 | 8.49 * |

Model | Class | Precision | Recall | F1-score |
---|---|---|---|---|

${\mathrm{LR}}_{\mathrm{SDNN}}24$ | Low | 0.84 | 1.00 | 0.91 |

High | 1.00 | 0.50 | 0.67 | |

${\mathrm{LR}}_{\mathrm{SDNNi}}24$ | Low | 0.76 | 1.00 | 0.86 |

High | 1.00 | 0.17 | 0.29 | |

${\mathrm{LR}}_{\mathrm{SDANN}}24$ | Low | 0.80 | 1.00 | 0.89 |

High | 1.00 | 0.33 | 0.50 | |

${\mathrm{LR}}_{\mathrm{SDANN}}\mathrm{HR}24$ | Low | 0.80 | 1.00 | 0.89 |

High | 1.00 | 0.33 | 0.50 | |

${\mathrm{LR}}_{\mathrm{HR}}$* | Low | 0.94 | 1.00 | 0.97 |

High | 1.00 | 0.83 | 0.91 | |

${\mathrm{RF}}_{\mathrm{HR}}$ | Low | 0.80 | 1.00 | 0.89 |

High | 1.00 | 0.33 | 0.50 | |

NN | Low | 0.94 | 1.00 | 0.97 |

High | 0.80 | 1.00 | 0.89 | |

$B1$ | Low | 0.72 | 0.81 | 0.76 |

High | 0.25 | 0.17 | 0.20 | |

$B2$ | Low | 0.73 | 1.00 | 0.84 |

High | 0.00 | 0.00 | 0.00 |

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**MDPI and ACS Style**

Morelli, D.; Rossi, A.; Bartoloni, L.; Cairo, M.; Clifton, D.A.
SDNN24 Estimation from Semi-Continuous HR Measures. *Sensors* **2021**, *21*, 1463.
https://doi.org/10.3390/s21041463

**AMA Style**

Morelli D, Rossi A, Bartoloni L, Cairo M, Clifton DA.
SDNN24 Estimation from Semi-Continuous HR Measures. *Sensors*. 2021; 21(4):1463.
https://doi.org/10.3390/s21041463

**Chicago/Turabian Style**

Morelli, Davide, Alessio Rossi, Leonardo Bartoloni, Massimo Cairo, and David A. Clifton.
2021. "SDNN24 Estimation from Semi-Continuous HR Measures" *Sensors* 21, no. 4: 1463.
https://doi.org/10.3390/s21041463