# CardioRVAR: A New R Package and Shiny Application for the Evaluation of Closed-Loop Cardiovascular Interactions

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## Abstract

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## Simple Summary

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Vector Autoregressive Models

**p**is reached, a limit that corresponds to the order of the VAR model [5,6,8,9,12,13,14,15,17,18,19]. Equation (2), as in Barnett and Seth [15] (pp. 52–53) or Faes et al. [6] (p. 278), describes the general structure of a bivariate

**VAR(p)**model [5,17], modified as in Faes et al. [9] (p. 4) to include

**a**

**(0)**coefficients in the structure:

**x**and

**y**, the first branch of Equation (2) would represent the main process of this system (e.g., how HRV influences BPV) whereas the second would describe a feedback controller for the main process (e.g., the baroreflex interaction between BPV and HRV) [5,8]. One should note that the traditional VAR model only considers lagged interactions; therefore, all direct and instantaneous interactions would be due to the model residuals, and

**a**[8,19]. By applying the Fourier transform on the autoregressive coefficients as described in Equation (3) [5] (p. 35) [9] (p. 4), one can obtain the frequency-domain representation of these coefficients, and, thus, of the whole model, as presented in matrix notation in Equation (4) [5] (p. 35):

_{11}(0) = a_{12}(0) = a_{21}(0) = a_{22}(0) = 0**S**is a matrix representing the frequency-domain cross-spectral matrix of the previous variables

**X**and

**Y**, whereas

**Σ**represents the noise-covariance matrix of the model, and

**H**is a matrix containing the transfer functions that link the activity of the estimated noise sources of the model to the modeled variables [5,8,13,15,19]. In addition, operator

*****applied to matrix

**H**in Equation (7) represents its conjugate transpose [8,13,15,19]. Matrix

**Σ**will therefore contain every direct instantaneous interaction in the model, as the main model is designed so that its coefficients represent the captured lagged interactions [8]. These instantaneous interactions can be isolated and incorporated into the main structure of the model by estimating a matrix of interactions capable of diagonalizing the original matrix Σ [8,9,19]. This process is described in Equation (8) [8] (p. 104):

**D**will be incorporated into matrix

**H**and will be propagated back to the transfer functions previously described in Equations (5) and (6) [8]. This makes either

**a**or

_{12}(0) ≠ 0**a**, depending on which direct transfer path is selected, as these paths are unidirectional, while generating a new noise-covariance matrix [8,9,19]. Not only are the corresponding transfer functions estimated, but also one can evaluate the specific contribution that each noise makes to each variable, which can be indicative of the causal strength in the interactions among the modeled variables [8]. These computations and transformations are applied to the frequency-domain representation of the model, but they could also be performed on the time-domain model [9,19]. The time-domain representation of this type of MVAR model is defined by Faes et al. [9,19] as its extended version and also represents the core of the eMVAR MATLAB toolbox.

_{21}(0) ≠ 0#### 2.2. Causal Coherence and Noise Contribution

#### 2.3. Trend Removal with the Discrete Wavelet Transform

#### 2.4. CardioRVAR Workflow

- Select a data file with CardioRVARapp and upload it into the software structure;
- Resample the uploaded time series after selecting a certain frequency, if needed;
- Manually select from the estimated HR and BP recordings a specific time window of interest;
- Transform the model into the frequency domain;
- Extract instantaneous unidirectional interactions from this frequency-domain representation, given a specific zero-lag-interaction path already chosen by the user, and update the model with such interactions;
- Estimate the most important features of the model and then display and report them;
- Generate and report single-subject indices from the model, allowing the user to choose a method to estimate said indices.

#### 2.5. Data Upload and Preprocessing

> library(CardioRVAR) |

> # Data is a list with elements Time, RR, and SBP: |

> Data <- ResampleData(Data, 4) # Interpolates data |

> IBI <- DetrendWithCutoff(Data$RR) # Detrends IBI signal |

> SBP <- DetrendWithCutoff(Data$SBP) # Detrends SBP signal |

> New_Data <- cbind(SBP = SBP, RR = IBI) |

> CheckStationarity(New_Data) # Checks stationarity of the data |

[1] TRUE |

> # Or alternatively: |

> Check_stationarity <- CheckStationarity(New_Data, verbose = TRUE) |

Time series are stationary |

**d**, a frequency cutoff

**f**would be defined by Equation (11), as the allowed frequency bands’ limits are powers of two and depend on the Nyquist frequency

_{C}**f**[20,22,25]:

_{N}**f**is selected, CardioRVAR will find a decomposition level associated with an interval of possible reference frequencies $\left[\left.{{\mathit{f}}_{\mathit{C}}}_{\mathit{d}},{{\mathit{f}}_{\mathit{C}}}_{\mathit{d}-\mathbf{1}}\right)\right.$ that contains

_{ref}**f**and will use said interval to select frequency ${{\mathit{f}}_{\mathit{C}}}_{\mathit{d}}$ as the cutoff. By reordering Equation (11), and adapting it to include reference frequencies, we can obtain Equation (12), which integrates the described steps and generates the optimal decomposition level according to a reference frequency lower than the Nyquist frequency, with $\u2308\xb7\u2309$ representing the ceiling operator:

_{ref}#### 2.6. Analysis of Cardiovascular Closed-Loop Interactions

**VAR(p)**model of the chosen segments, which will be defined by a specific model order or maximum lag limit and will capture the interactions of interest present at said segments. This model order is usually chosen by applying an information criterion, which, in the case of CardioRVAR is, by default, the Akaike Information Criterion (AIC) [31,32], as suggested by authors such as Faes et al. [9] regarding closed-loop cardiovascular analysis. However, the software allows one to select the model order that users consider more appropriate. It should be noted that very low model orders will decrease the resolution of the frequency-domain results, and too high model orders will produce extra peaks in the variability spectra that may deviate from the true frequency-domain representation of the studied signals [32].

> # Data represents a matrix with two interpolated time series, IBI and SBP. |

> Data[,“IBI”] = DetrendWithCutoff(Data[,“IBI”]) |

> Data[,“SBP”] = DetrendWithCutoff(Data[,“SBP”]) |

> # Both signals have been detrended with these commands. |

> CheckStationarity(Data) |

[1] TRUE |

> # A VAR model is estimated from the stationary time series and then validated: |

> model <- EstimateVAR(Data) |

> Check_residuals <- DiagnoseResiduals(model, verbose = TRUE) |

Model residuals are white noise processes |

> Check_stability <- DiagnoseStability(model, verbose = TRUE) |

The model is stable |

#### 2.7. Analysis in the Frequency Domain

**VAR(p)**models into their frequency-domain representations. To do so, one should use the following command, which will be applied to the previous model object:

> freq_model <- ParamFreqModel(model). |

#### 2.8. Assessment of the Transfer Functions

#### 2.9. Assessment of the Noise Source Contribution and Causal Coherence

#### 2.10. Evaluation of the Tool: Data Sources

## 3. Results and Discussion

#### 3.1. Descriptive Study of Two Subjects

#### 3.2. Comparison between Normotensive and Hypertensive Subjects

#### 3.3. EUROBAVAR Analysis Results

#### 3.4. Comparison with Other Works

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Rodríguez-Liñares, L.; Méndez, A.J.; Lado, M.J.; Olivieri, D.N.; Vila, X.A.; Gómez-Conde, I. An Open Source Tool for Heart Rate Variability Spectral Analysis. Comput. Methods Programs Biomed.
**2011**, 103, 39–50. [Google Scholar] [CrossRef] [PubMed] - Martínez, C.A.G.; Quintana, A.O.; Vila, X.A.; Touriño, M.J.L.; Rodríguez-Liñares, L.; Presedo, J.M.R.; Penín, A.J.M. Heart Rate Variability Analysis with the R Package RHRV; Springer International Publishing: Cham, Switzerland, 2017; ISBN 978-3-319-65354-9. [Google Scholar]
- Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology. Heart Rate Variability: Standards of Measurement, Physiological Interpretation and Clinical Use. Circulation
**1996**, 93, 1043–1065. [Google Scholar] [CrossRef] - Swenne, C.A. Baroreflex Sensitivity: Mechanisms and Measurement. Neth. Heart J.
**2013**, 21, 58–60. [Google Scholar] [CrossRef] - Barbieri, R.; Parati, G.; Saul, J.P. Closed- versus Open-Loop Assessment of Heart Rate Baroreflex. IEEE Eng. Med. Biol. Mag.
**2001**, 20, 33–42. [Google Scholar] [CrossRef] - Faes, L.; Porta, A.; Antolini, R.; Nollo, G. Role of Causality in the Evaluation of Coherence and Transfer Function between Heart Period and Systolic Pressure in Humans. In Proceedings of the Computers in Cardiology, Chicago, IL, USA, 19–22 September 2004; IEEE: Piscataway, NJ, USA, 2004; pp. 277–280. [Google Scholar]
- Takalo, R.; Saul, J.P.; Korhonen, I. Comparison of Closed-Loop and Open-Loop Models in the Assessment of Cardiopulmonary and Baroreflex Gains. Methods Inf. Med.
**2004**, 43, 296–301. [Google Scholar] [CrossRef] - Hytti, H.; Takalo, R.; Ihalainen, H. Tutorial on Multivariate Autoregressive Modelling. J. Clin. Monit. Comput.
**2006**, 20, 101–108. [Google Scholar] [CrossRef] - Faes, L.; Erla, S.; Porta, A.; Nollo, G. A Framework for Assessing Frequency Domain Causality in Physiological Time Series with Instantaneous Effects. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
**2013**, 371, 20110618. [Google Scholar] [CrossRef] - Faes, L.; Nollo, G. Measuring Frequency Domain Granger Causality for Multiple Blocks of Interacting Time Series. Biol. Cybern.
**2013**, 107, 217–232. [Google Scholar] [CrossRef] - Faes, L.; Erla, S.; Nollo, G. Block Partial Directed Coherence: A New Tool for the Structural Analysis of Brain Networks. Int. J. Bioelectromagn.
**2012**, 14, 162–166. [Google Scholar] - Faes, L.; Erla, S.; Nollo, G. Measuring Connectivity in Linear Multivariate Processes: Definitions, Interpretation, and Practical Analysis. Comput. Math. Methods Med.
**2012**, 2012, 140513. [Google Scholar] [CrossRef] - Seth, A.K. A MATLAB Toolbox for Granger Causal Connectivity Analysis. J. Neurosci. Methods
**2010**, 186, 262–273. [Google Scholar] [CrossRef] - Seth, A.K. Granger Causal Connectivity Analysis: A MATLAB Toolbox; University of Sussex: Brighton, UK, 2011. [Google Scholar]
- Barnett, L.; Seth, A.K. The MVGC Multivariate Granger Causality Toolbox: A New Approach to Granger-Causal Inference. J. Neurosci. Methods
**2014**, 223, 50–68. [Google Scholar] [CrossRef] [PubMed] - Chao-Ecija, A.; Dawid-Milner, M.S. BaroWavelet: An R-Based Tool for Dynamic Baroreflex Evaluation through Wavelet Analysis Techniques. Comput. Methods Programs Biomed.
**2023**, 242, 107758. [Google Scholar] [CrossRef] [PubMed] - Farnè, M.; Montanari, A. A Bootstrap Method to Test Granger-Causality in the Frequency Domain. Comput. Econ.
**2022**, 59, 935–966. [Google Scholar] [CrossRef] - Porta, A.; Furlan, R.; Rimoldi, O.; Pagani, M.; Malliani, A.; van de Borne, P. Quantifying the Strength of the Linear Causal Coupling in Closed Loop Interacting Cardiovascular Variability Signals. Biol. Cybern.
**2002**, 86, 241–251. [Google Scholar] [CrossRef] - Faes, L.; Nollo, G. Multivariate Frequency Domain Analysis of Causal Interactions in Physiological Time Series. In Biomedical Engineering, Trends in Electronics, Communications and Software; InTech: Rijeka, Croatia, 2011; pp. 403–428. [Google Scholar]
- Percival, D.B.; Walden, A.T. The Discrete Wavelet Transform. In Wavelet Methods for Time Series Analysis; Cambridge University Press: Cambridge, UK, 2000; pp. 56–158. [Google Scholar]
- Percival, D.B.; Walden, A.T. The Maximal Overlap Discrete Wavelet Transform. In Wavelet Methods for Time Series Analysis; Cambridge University Press: Cambridge, UK, 2000; pp. 159–205. [Google Scholar]
- Percival, D.B.; Walden, A.T. The Discrete Wavelet Packet Transform. In Wavelet Methods for Time Series Analysis; Cambridge University Press: Cambridge, UK, 2000; pp. 206–254. [Google Scholar]
- Tzabazis, A.; Eisenried, A.; Yeomans, D.C.; Hyatt, M.I. V Wavelet Analysis of Heart Rate Variability: Impact of Wavelet Selection. Biomed. Signal. Process. Control
**2018**, 40, 220–225. [Google Scholar] [CrossRef] - Quandt, V.I.; Pacola, E.R.; Pichorim, S.F.; Sovierzoski, M.A. Border Extension in the Wavelet Analysis of Lung Sounds. In World Congress on Medical Physics and Biomedical Engineering 26–31 May 2012, Beijing, China; Springer: Berlin/Heidelberg, Germany, 2013; pp. 597–600. [Google Scholar]
- Li, L.; Li, K.; Liu, C.; Liu, C. Comparison of Detrending Methods in Spectral Analysis of Heart Rate Variability. Res. J. Appl. Sci. Eng. Technol.
**2011**, 3, 1014–1021. [Google Scholar] - Andrecut, M. Fast Time Series Detrending with Applications to Heart Rate Variability Analysis. Int. J. Mod. Phys. C
**2019**, 30, 1950069. [Google Scholar] [CrossRef] - Yoo, C.S.; Yi, S.H. Effects of Detrending for Analysis of Heart Rate Variability and Applications to the Estimation of Depth of Anesthesia. J. Korean Phys. Soc.
**2004**, 44, 561. [Google Scholar] [CrossRef] - Gebauer, J.E.; Adler, J. Using Shiny Apps for Statistical Analyses and Laboratory Workflows. J. Lab. Med.
**2023**, 47, 149–153. [Google Scholar] [CrossRef] - Ding, M.; Bressler, S.; Yang, W.; Liang, H. Short-Window Spectral Analysis of Cortical Event-Related Potentials by Adaptive Multivariate Autoregressive Modeling: Data Preprocessing, Model Validation, and Variability Assessment. Biol. Cybern.
**2000**, 83, 35–45. [Google Scholar] [CrossRef] [PubMed] - Chen, H.-K.; Hu, Y.-F.; Lin, S.-F. Methodological Considerations in Calculating Heart Rate Variability Based on Wearable Device Heart Rate Samples. Comput. Biol. Med.
**2018**, 102, 396–401. [Google Scholar] [CrossRef] - Shibata, R. Selection of the Order of an Autoregressive Model by Akaike’s Information Criterion. Biometrika
**1976**, 63, 117. [Google Scholar] [CrossRef] - Boardman, A.; Schlindwein, F.S.; Rocha, A.P.; Leite, A. A Study on the Optimum Order of Autoregressive Models for Heart Rate Variability. Physiol. Meas.
**2002**, 23, 325–336. [Google Scholar] [CrossRef] [PubMed] - Bassani, T.; Bari, V.; Marchi, A.; Wu, M.A.; Baselli, G.; Citerio, G.; Beda, A.; de Abreu, M.G.; Güldner, A.; Guzzetti, S.; et al. Coherence Analysis Overestimates the Role of Baroreflex in Governing the Interactions between Heart Period and Systolic Arterial Pressure Variabilities during General Anesthesia. Auton. Neurosci.
**2013**, 178, 83–88. [Google Scholar] [CrossRef] [PubMed] - Laude, D.; Elghozi, J.-L.; Girard, A.; Bellard, E.; Bouhaddi, M.; Castiglioni, P.; Cerutti, C.; Cividjian, A.; Rienzo, M.D.; Fortrat, J.-O.; et al. Comparison of Various Techniques Used to Estimate Spontaneous Baroreflex Sensitivity (the EuroBaVar Study). Am. J. Physiol.-Regul. Integr. Comp. Physiol.
**2004**, 286, R226–R231. [Google Scholar] [CrossRef] - McLoone, V.; Ringwood, J.V. A System Identification Approach to Baroreflex Sensitivity Estimation. In Proceedings of the IET Irish Signals and Systems Conference (ISSC 2012), Maynooth, Ireland, 28–29 June 2012; Institution of Engineering and Technology: Stevenage, UK, 2012; pp. 301–306. [Google Scholar]
- Bari, V.; Vaini, E.; De Maria, B.; Cairo, B.; Pistuddi, V.; Ranucci, M.; Porta, A. Comparison of Different Strategies to Assess Cardiac Baroreflex Sensitivity Based on Transfer Function Technique in Patients Undergoing General Anesthesia. Annu. Int. Conf. IEEE Eng. Med. Biol. Soc.
**2018**, 2018, 2780–2783. [Google Scholar] [CrossRef] - Dani, M.; Dirksen, A.; Taraborrelli, P.; Torocastro, M.; Panagopoulos, D.; Sutton, R.; Lim, P.B. Autonomic Dysfunction in “Long COVID”: Rationale, Physiology and Management Strategies. Clin. Med.
**2021**, 21, e63–e67. [Google Scholar] [CrossRef] - Westerhof, B.E.; Gisolf, J.; Stok, W.J.; Wesseling, K.H.; Karemaker, J.M. Time-Domain Cross-Correlation Baroreflex Sensitivity: Performance on the EUROBAVAR Data Set. J. Hypertens.
**2004**, 22, 1371–1380. [Google Scholar] [CrossRef] - Choi, Y.; Ko, S.; Sun, Y. Effect of Postural Changes on Baroreflex Sensitivity: A Study on the Eurobavar Data Set. In Proceedings of the 2006 Canadian Conference on Electrical and Computer Engineering, Ottawa, ON, Canada, 7–10 May 2006; IEEE: Piscataway, NJ, USA, July, 2006; pp. 110–114. [Google Scholar]
- Parati, G.; Castiglioni, P.; Faini, A.; Di Rienzo, M.; Mancia, G.; Barbieri, R.; Saul, J.P. Closed-Loop Cardiovascular Interactions and the Baroreflex Cardiac Arm: Modulations Over the 24 h and the Effect of Hypertension. Front. Physiol.
**2019**, 10, 477. [Google Scholar] [CrossRef] - Chao-Écija, Á.; Carrasco-Gómez, D.; Dawid-Milner, M.S. Effectiveness of an R-Based Software to Detect Closed-Loop Cardio- Vascular Interactions and Baroreflex Impairment in Human subjects from the EUROBAVAR Data Set. J. Physiol. Biochem.
**2022**, 78, S34. [Google Scholar] [CrossRef]

**Figure 1.**Trend isolation process through a six-level decomposition with the MODWT. The coefficients shown belong to the original signal and its smoothed representation through approximation coefficients (black), as well as to each decomposition level from D1 to D6, which hold the detail coefficients obtained from the analysis (red).

**Figure 2.**Trend isolation process through the MODWT with an additional border handling strategy applied to the transform. The handling strategy extends the original IBI signal and creates an additional number of coefficients (blue).

**Figure 3.**Interface to upload and window cardiovascular data. A csv file containing the necessary data is uploaded and interpolated up to a sample frequency of 4 Hz. A time window is selected, and mean HR and SBP values from this window are reported. The data were obtained from a subject during a head-up tilt session.

**Figure 4.**Time-domain and frequency-domain changes in HRV due to the preprocessing algorithms available in CardioRVAR. (

**A**) Non-detrended signal, with a sample frequency of 4 Hz, and its frequency-domain non-parametric and parametric spectra, with a significant very-low-frequency component. (

**B**) Detrended signal after selecting a reference frequency of 0.04 Hz (cutoff: 0.03125 Hz, blue mark), accompanied by its non-parametric and parametric spectra, showing a mitigated very-low-frequency component. (

**C**) Detrended signal after selecting a reference frequency of 0.07 Hz (cutoff: 0.0625 Hz, blue mark), with spectral densities showing a more mitigated very-low-frequency component, while also affecting part of the LF component. Yellow areas indicate ranges of possible reference frequencies associated with the last decomposition level, used to identify the cutoff frequency (blue marks) in each case. Green marks indicate cutoff frequencies (0.0625 Hz, 0.125 Hz) associated with the previous decomposition level. Red areas indicate frequency components below 0.04 Hz.

**Figure 5.**Relative errors computed for each frequency between the frequency-domain non-parametric spectra of a raw IBI signal and its detrended version using the MODWT-based detrending algorithm with (

**A**) the Haar wavelet and (

**B**) the Daubechies 8 wavelet. Vertical lines indicate frequencies 0.04 Hz and 0.15 Hz.

**Figure 6.**Transfer functions reported by the software from patient during (

**A**) head-up tilt and (

**B**) post-tilt recovery. From left to right: closed-loop transfer function without zero-lagged interactions, closed-loop transfer function with zero-lagged interactions, and open-loop transfer function. Color code: LF band (green), HF band (yellow).

**Figure 7.**Percentage of noise source contribution computed from a patient to the variability of (

**A**) IBI before head-up tilt, (

**B**) SBP before head-up tilt, (

**C**) IBI during head-up tilt, and (

**D**) SBP during head-up tilt. Color code: IBI noise (white), SBP noise (blue).

**Figure 8.**Heart rate (red) and systolic blood pressure (blue) recordings obtained from (

**A**) subject A, a healthy patient who exhibited a weak response during head-up tilt, and (

**B**) subject B, who suffered from Postural Orthostatic Tachycardia Syndrome induced by long-COVID.

**Figure 9.**Individual closed-loop BRS estimates computed through CardioRVARapp from the EUROBAVAR A series of subjects, and their distributions, obtained in (

**A**) supine position, through the maximum coherence strategy; (

**B**) supine position, through the coherence-thresholding strategy; (

**C**) standing position, through the maximum coherence strategy; and (

**D**) standing position, through the coherence-thresholding strategy. Blue arrows indicate subjects with missing estimates due to the coherence-thresholding strategy. Color code: HF band (black), LF band (white).

**Figure 10.**Individual closed-loop BRS estimates computed through CardioRVARapp from the EUROBAVAR B series of subjects, and their distributions, obtained in (

**A**) supine position, through the maximum coherence strategy; (

**B**) supine position, through the coherence-thresholding strategy; (

**C**) standing position, through the maximum coherence strategy; and (

**D**) standing position, through the coherence-thresholding strategy. Red arrows indicate baroreflex-impaired subjects. Blue arrows indicate non-impaired subjects with missing estimates due to the coherence-thresholding strategy. Purple arrows indicate baroreflex-impaired subjects with missing estimates due to the coherence-thresholding strategy. Color code: HF band (black), LF band (white).

**Figure 11.**Baroreflex sensitivity changes in closed-loop estimates computed by CardioRVARapp from EUROBAVAR during supine and standing positions in HF and LF bands, excluding the two impaired ones (n = 19), through (

**A**) Gaussian-weighting strategy and (

**B**) maximum coherence strategy. Significance: p < 0.01 (**), p < 0.001 (***).

**Figure 12.**Causal coherence flows from (

**A**) HF band from IBI to SBP (dark green) and vice versa (light green) at both supine (left) and standing (right) positions, and (

**B**) HF band from IBI to SBP (dark green) and vice versa (light green) at both supine (left) and standing (right) positions. The two impaired subjects were excluded from the analysis (n = 19). Significance: p < 0.001 (***).

**Table 1.**Estimates from subjects A and B during the different periods of the head-up tilt test returned by CardioRVAR, using its graphical interface. The displayed results were obtained through the following estimation methods and criteria: coherence threshold (CT), weighted average (WA), and maximum coherence (MC).

Subject A | Subject B | |||||
---|---|---|---|---|---|---|

Variable | Pre-Tilt Interval | Tilt Interval | Post-Tilt Interval | Pre-Tilt Interval | Tilt Interval | Post-Tilt Interval |

HR (bpm) | 48.27 | 54.03 | 49.42 | 78.42 | 109.74 | 69.75 |

SBP (mmHg) | 102.12 | 109.15 | 111.65 | 125.84 | 121.62 | 120.95 |

CT-HF α_{c} (ms/mmHg) | 26.54 | 11.57 | 35.90 | 13.30 | N/A ^{†} | 13.60 |

WA-HF α_{c}(ms/mmHg) | 24.13 | 9.05 | 31.56 | 9.54 | 1.76 | 12.81 |

MC-HF α_{c}(ms/mmHg) | 27.34 | 12.50 | 36.33 | 13.10 | 1.78 | 16.33 |

CT-LF α_{c}(ms/mmHg) | 6.95 | 1.74 | N/A ^{†} | 11.78 | 3.98 | 17.88 |

WA-LF α_{c} (ms/mmHg) | 7.33 | 4.59 | 17.41 | 11.28 | 3.81 | 17.78 |

MC-LF α_{c} (ms/mmHg) | 7.02 | 1.73 | 1.63 | 12.25 | 4.11 | 16.77 |

^{†}Squared coherence was below 0.5 n.u.

**Table 2.**Comparison of estimates obtained from the tool between normotensive and hypertensive subjects using two strategies for the computation of the BRS.

Position | Band | Estimate Type | Normotensive (n = 5) | Hypertensive (n = 7) | p Value |
---|---|---|---|---|---|

Supine rest | HF | Weighted-averaged | 9.02 ± 3.88 | 2.03 ± 0.45 | p < 0.01 |

Estimate at maximum coherence | 10.99 ± 4.14 | 3.10 ± 0.75 | p < 0.05 | ||

LF | Weighted-averaged | 5.94 ± 1.38 | 2.25 ± 0.39 | p = 0.054 | |

Estimate at maximum coherence | 6.19 ± 1.32 | 1.69 ± 0.37 | p < 0.05 | ||

Tilt | HF | Weighted-averaged | 4.34 ± 1.39 | 1.27 ± 0.29 | p = 0.091 |

Estimate at maximum coherence | 5.01 ± 1.95 | 1.46 ± 0.21 | p = 0.143 | ||

LF | Weighted-averaged | 4.90 ± 0.64 | 2.06 ± 0.22 | p < 0.01 | |

Estimate at maximum coherence | 4.69 ± 0.96 | 1.66 ± 0.23 | p < 0.05 |

**Table 3.**Supine and standing position BRS estimates computed by CardioRVARapp through Gaussian-weighting and maximum coherence strategies from EUROBAVAR subjects, excluding the two impaired ones (n = 19).

Closed-Loop | Open-Loop (Type II) | Open-Loop (Type I) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Band | Method | Supine (ms/mmHg) | Standing (ms/mmHg) | p Value | Supine (ms/mmHg) | Standing (ms/mmHg) | p Value | Supine (ms/mmHg) | Standing (ms/mmHg) | p Value |

HF | Weighted average | 11.06 ± 2.46 | 3.54 ± 0.54 | p < 0.001 | 13.82 ± 2.92 | 5.03 ± 0.81 | p < 0.001 | 20.79 ± 3.74 | 7.82 ± 1.27 | p < 0.001 |

Maximum coherence | 13.03 ± 2.47 | 4.84 ± 0.79 | p < 0.001 | 16.07 ± 2.68 | 6.40 ± 1.07 | p < 0.001 | 17.40 ± 2.92 | 7.51 ± 1.38 | p < 0.001 | |

LF | Weighted average | 8.12 ± 1.72 | 4.12 ± 0.55 | p < 0.001 | 9.23 ± 2.25 | 5.12 ± 0.77 | p < 0.001 | 12.72 ± 2.75 | 7.12 ± 0.91 | p < 0.001 |

Maximum coherence | 7.92 ± 1.50 | 4.06 ± 0.54 | p < 0.01 | 10.48 ± 2.04 | 5.42 ± 0.68 | p < 0.01 | 12.43 ± 2.25 | 6.41 ± 0.77 | p < 0.01 |

**Table 4.**Supine and standing position causal coherence estimates computed by CardioRVARapp from EUROBAVAR subjects, excluding the two impaired ones (n = 19).

Position | Band | ${{\mathbf{C}\mathbf{o}\mathbf{h}}^{\mathbf{2}}}_{\mathbf{S}\mathbf{B}\mathbf{P}\to \mathbf{I}\mathbf{B}\mathbf{I}}$ (n.u.) | ${{\mathbf{C}\mathbf{o}\mathbf{h}}^{\mathbf{2}}}_{\mathbf{I}\mathbf{B}\mathbf{I}\to \mathbf{S}\mathbf{B}\mathbf{P}}$ (n.u.) | p Value |
---|---|---|---|---|

Supine | HF | 0.23 ± 0.02 | 0.21 ± 0.02 | p = 0.644 |

LF | 0.19 ± 0.03 | 0.54 ± 0.04 | p < 0.001 | |

Standing | HF | 0.21 ± 0.03 | 0.19 ± 0.02 | p = 0.510 |

LF | 0.29 ± 0.04 | 0.32 ± 0.03 | p = 0.606 |

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**MDPI and ACS Style**

Chao-Écija, A.; López-González, M.V.; Dawid-Milner, M.S.
*CardioRVAR*: A New R Package and Shiny Application for the Evaluation of Closed-Loop Cardiovascular Interactions. *Biology* **2023**, *12*, 1438.
https://doi.org/10.3390/biology12111438

**AMA Style**

Chao-Écija A, López-González MV, Dawid-Milner MS.
*CardioRVAR*: A New R Package and Shiny Application for the Evaluation of Closed-Loop Cardiovascular Interactions. *Biology*. 2023; 12(11):1438.
https://doi.org/10.3390/biology12111438

**Chicago/Turabian Style**

Chao-Écija, Alvaro, Manuel Víctor López-González, and Marc Stefan Dawid-Milner.
2023. "*CardioRVAR*: A New R Package and Shiny Application for the Evaluation of Closed-Loop Cardiovascular Interactions" *Biology* 12, no. 11: 1438.
https://doi.org/10.3390/biology12111438