# The Complexity of the Arterial Blood Pressure Regulation during the Stress Test

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## Abstract

**:**

## 1. Introduction

#### The Model of Integral Evaluation of the Human Cardiovascular System

## 2. Methods

#### 2.1. The Description of the Experimental Setup

#### 2.2. The Algorithm for the Identification of the RR/JT Algebraic Relationship

**Step # 1**. Let us fix the current discrete time moment (denoted as k) and time lag $\delta \in 1,2,\dots {\delta}_{max}$, where ${\delta}_{max}$ is the upper bound for the time lag. The six elements of both time series ${x}_{k-\delta},{x}_{k},{x}_{k+\delta},{y}_{k-\delta},{y}_{k},{y}_{k+\delta}$ (current, backward and forward time lagged measurements) are mapped into a two-dimensional perfect matrix of Lagrange differences [47]. A set of the following requirements is raised for perfect matrices of Lagrange differences [47]: (a) all elements of the matrix must be different; (b) zeroth-order differences are located on the main diagonal; (c) first-order differences are located on the secondary diagonal; (d) the matrix is lexicographically balanced (the number of elements from the first and the second time is the same); (e) the matrix is balanced in respect of time (the sum of all time lags is equal to zero). The number of different perfect matrices of Lagrange differences is 18 [47]. For example, the first perfect matrix of Lagrange differences ${L}_{\delta ,k}^{\left(1\right)}=\left(\right)open="["\; close="]">\begin{array}{cc}{x}_{k}& {x}_{k+\delta}-{y}_{k+\delta}\\ {x}_{k-\delta}-{y}_{k-\delta}& {y}_{k}\end{array}$ is used in [48]. Two time series are mapped into a sequence of trajectory matrices ${L}_{\delta ,k}^{\left(\beta \right)};k=(1+\delta ,2+\delta ,\dots ,n-\delta );\beta \in 1,2,\dots ,18$.

**Step # 2**. The sequence of matrices ${L}_{\delta ,k}^{\left(\beta \right)}$ is transformed into a single scalar time series using a mapping $\mathcal{F}:{\mathbb{R}}^{(2\times 2)}\to {\mathbb{R}}^{1}$. The mapping $\mathcal{F}$ can be defined in different ways. For example, the maximal modulus of the two eigenvalues of the matrix ${L}_{\delta ,k}^{\left(\beta \right)}$ is used in [47]; the norm of the matrix ${L}_{\delta ,k}^{\left(\beta \right)}$ is used in [48]. In this paper, we define the mapping $\mathcal{F}$ as the discriminant of the matrix ${L}_{\delta ,k}^{\left(\beta \right)}:\mathcal{F}\left({L}_{\delta ,k}^{\left(\beta \right)}\right)=disc\left({L}_{\delta ,k}^{\left(\beta \right)}\right)={({\alpha}_{11}-{\alpha}_{22})}^{2}+4{\alpha}_{12}{\alpha}_{21}$, where indexes denote the coordinates of elements in the matrix ${L}_{\delta ,k}^{\left(\beta \right)}$. The discriminant of the matrix is chosen instead of another mappings used in [47,48] because the value of the discriminant of the perfect matrix of Lagrange differences tends to zero when the variability of time series x and y becomes similar [47]. This feature helps to bring the RR/JT algebraic relationship almost down to zero when the collapse of complexity happens at the end of the load phase of the stress test [47].

**Step # 3**. In this step, the internal and external smoothing is applied for the scalar sequence $\mathcal{F}\left({L}_{\delta ,k}^{\left(\beta \right)}\right)$. If the radius of the internal smoothing is denoted by ${R}_{i}$ and the radius of the external smoothing is denoted by ${R}_{e}$, then the smoothed sequence depicting the algebraic relationship between the two time series x and y reads:

**Step # 4**. After establishing the algebraic relationships, the statistical operations are performed for the cohort. First, the algebraic relationship between the RR and JT interval is computed for each person and averaged for each minute during the exercise. Then, the arterial blood pressure data (once per minute) are measured during the exercise. Following that, the dataset is put to the linear regression for each individual person. The Gaussian distribution of the slope coefficients of the linear regression computed for each person in the cohort is then applied to the whole dataset. Finally, the one sigma rule is used to perform statistically meaningful difference between the two cohorts (persons with normal ABP and persons with high ABP) to perform the classification. All these steps are discussed in detail below.

#### 2.3. The Structure of Machine Learning Algorithms for the Classification

#### 2.3.1. The Averaged RR/JT Algebraic Relationship and ABP Data in a Phase Plane

#### 2.3.2. Data Fitting into the Gaussian Distribution

#### 2.3.3. Classification Using the One Sigma Rule

## 3. Results and Discussions

#### 3.1. The Implementation of the Classification Model

#### 3.2. Classification of New Candidates

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

CNS | central nervous system |

ABP | arterial blood pressure |

HR | heart rate |

MET | metabolic equivalent |

SV | stroke volume |

ABP (sys) | systolic arterial blood pressure |

ABP (dis) | diastolic arterial blood pressure |

JTa | amplitude of the JT interval |

JTd | the duration of the JT interval |

ECG | electrocardiogram |

AHA | American Heart Association |

## References

- Clermont, G.; Angus, D. Towards understanding pathophysiology in critical care: The human body as a complex system. In Yearbook of Intensive Care and Emergency Medicine 2001; Springer: Berlin/Heidelberg, Germany, 2001; pp. 13–22. [Google Scholar]
- Pocock, G.; Richards, C.D.; Richards, D.A. Human Physiology; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2013. [Google Scholar]
- Žemaitytė, M. Širdies Ritmo Autonominis Reguliavimas: Mechanizmai, Vertinimas, Klinikinė Reikšmė; KMA Leidykla: Kaunas, Lithuania, 1997. [Google Scholar]
- Kevelaitis, E.N.N.; Menasché, P. Coronary endothelial dysfunction of isolated hearts subjected to prolonged cold storage: Patterns and contributing factors. J. Heart Lung Transplant.
**1999**, 18, 239–247. [Google Scholar] [CrossRef] - Rowell, L. Neural control of muscle blood flow: Importance during dynamic exercise. Clin. Exp. Pharmacol. Physiol.
**1997**, 24, 117–125. [Google Scholar] [CrossRef] - Hollander, A.; Bouman, L. Cardiac acceleration in man elicited by a muscle-heart reflex. J. Appl. Physiol.
**1975**, 38, 272–278. [Google Scholar] [CrossRef][Green Version] - Faria, E.; Faria, I. Cardiorespiratory responses to exercises of equal relative intensity distributed between the upper and lower body. J. Sport. Sci.
**1998**, 16, 309–315. [Google Scholar] [CrossRef] [PubMed] - O’Sullivan, S.; Bell, C. The effects of exercise and training on human cardiovascular reflex control. J. Auton. Nerv. Syst.
**2000**, 81, 16–24. [Google Scholar] [CrossRef] - Savin, W.M.; Davidson, D.M.; Haskell, W.L. Autonomic contribution to heart rate recovery from exercise in humans. J. Appl. Physiol.
**1982**, 53, 1572–1575. [Google Scholar] [CrossRef] [PubMed] - Chapman, J.; Elliott, P. Cardiovascular effects of static and dynamic exercise. Eur. J. Appl. Physiol. Occup. Physiol.
**1988**, 58, 152–157. [Google Scholar] [CrossRef] [PubMed] - Eriksen, M.O.; Waaler, B.A.; Walløe, L.; Wesche, J. Dynamics and dimensions of cardiac output changes in humans at the onset and at the end of moderate rhythmic exercise. J. Physiol.
**1990**, 426, 423–437. [Google Scholar] [CrossRef][Green Version] - Secher, N.H.; Clausen, J.P.; Klausen, K.; Noer, I.; Trap-Jensen, J. Central and regional circulatory effects of adding arm exercise to leg exercise. Acta Physiol. Scand.
**1977**, 100, 288–297. [Google Scholar] [CrossRef] - Takahara, K.; Miura, Y.; Kouzuma, R.; Yasumasu, T.; Nakamura, T.; Nakashima, Y. Physical training augments plasma catecholamines and natural killer cell activity. J. UOEH
**1999**, 21, 277–287. [Google Scholar] [CrossRef][Green Version] - O’Brien, E.; Pickering, T.; Asmar, R.; Myers, M.; Parati, G.; Staessen, J.; Mengden, T.; Imai, Y.; Waeber, B.; Palatini, P.; et al. Working Group on Blood Pressure Monitoring of the European Society of Hypertension International Protocol for validation of blood pressure measuring devices in adults. Blood Press. Monit.
**2002**, 7, 3–17. [Google Scholar] [CrossRef] - Yamaguchi, M.; Shimizu, M.; Ino, H.; Okeie, K.; Yasuda, T.; Fujino, N.; Fujii, H.; Mabuchi, T.; Mabuchi, H. Diagnostic usefulness of the post-exercise systolic blood pressure response for the detection of coronary artery disease in patients with diabetes mellitus. Jpn. Circ. J.
**2000**, 64, 949–952. [Google Scholar] [CrossRef] [PubMed][Green Version] - Mansia, G.; De Backer, G.; Dominiczak, A.; Cifkova, R.; Fagard, R.; Germano, G.; Grassi, G.; Heagerty, A.M.; Kjeldsen, S.E.; Laurent, S.; et al. 2007 Guidelines for the management of arterial hypertension: The Task Force for the Management of Arterial Hypertension of the European Society of Hypertension (ESH) and of the European Society of Cardiology (ESC). Eur. Heart J.
**2007**, 28, 1462–1536. [Google Scholar] [CrossRef] - Mancia, G.; Laurent, S.; Agabiti-Rosei, E.; Ambrosioni, E.; Burnier, M.; Caulfield, M.J.; Cifkova, R.; Clément, D.; Coca, A.; Dominiczak, A.; et al. Reappraisal of European guidelines on hypertension management: A European Society of Hypertension Task Force document. Blood Press.
**2009**, 18, 308–347. [Google Scholar] [CrossRef] - McHam, S.A.; Marwick, T.H.; Pashkow, F.J.; Lauer, M.S. Delayed systolic blood pressure recovery after graded exercise: An independent correlate of angiographic coronary disease. J. Am. Coll. Cardiol.
**1999**, 34, 754–759. [Google Scholar] [CrossRef][Green Version] - Skirius, J. Sportininkų širdies ir kraujagyslių sistemos funkcinės būklės tyrimas ir vertinimas. In Proceedings of the Sporto Mokslo Dabartis ir Naujosios Idejos, Kaunas, Lithuania, 10–12 September 2002; pp. 46–48. [Google Scholar]
- Fletcher, G.F.; Balady, G.J.; Amsterdam, E.A.; Chaitman, B.; Eckel, R.; Fleg, J.; Froelicher, V.F.; Leon, A.S.; Piña, I.L.; Rodney, R.; et al. Exercise standards for testing and training: A statement for healthcare professionals from the American Heart Association. Circulation
**2001**, 104, 1694–1740. [Google Scholar] [CrossRef][Green Version] - Bar-Yam, Y. About Complex Systems. In Reading; Addison-Wesley: Boston, MA, USA, 1997. [Google Scholar]
- Fonseca, C.G.; Backhaus, M.; Bluemke, D.A.; Britten, R.D.; Chung, J.D.; Cowan, B.R.; Dinov, I.D.; Finn, J.P.; Hunter, P.J.; Kadish, A.H.; et al. The Cardiac Atlas Project—An imaging database for computational modeling and statistical atlases of the heart. Bioinformatics
**2011**, 27, 2288–2295. [Google Scholar] [CrossRef] [PubMed] - Bharti, R.; Khamparia, A.; Shabaz, M.; Dhiman, G.; Pande, S.; Singh, P. Prediction of heart disease using a combination of machine learning and deep learning. In Computational Intelligence and Neuroscience; Hindawi: London, UK, 2021. [Google Scholar]
- Maurer, M.S.; Burkhoff, D.; Fried, L.P.; Gottdiener, J.; King, D.L.; Kitzman, D.W. Ventricular structure and function in hypertensive participants with heart failure and a normal ejection fraction: The Cardiovascular Health Study. J. Am. Coll. Cardiol.
**2007**, 49, 972–981. [Google Scholar] [CrossRef] [PubMed][Green Version] - Spyropoulos, F.; Vitali, S.H.; Touma, M.; Rose, C.D.; Petty, C.R.; Levy, P.; Kourembanas, S.; Christou, H. Echocardiographic markers of pulmonary hemodynamics and right ventricular hypertrophy in rat models of pulmonary hypertension. Pulm. Circ.
**2020**, 10, 2045894020910976. [Google Scholar] [CrossRef][Green Version] - Rajput, J.S.; Sharma, M.; Tan, R.S.; Acharya, U.R. Automated detection of severity of hypertension ECG signals using an optimal bi-orthogonal wavelet filter bank. Comput. Biol. Med.
**2020**, 123, 103924. [Google Scholar] [CrossRef] - Soh, D.C.K.; Ng, E.; Jahmunah, V.; Oh, S.L.; Tan, R.S.; Acharya, U. Automated diagnostic tool for hypertension using convolutional neural network. Comput. Biol. Med.
**2020**, 126, 103999. [Google Scholar] [CrossRef] [PubMed] - Jain, P.; Gajbhiye, P.; Tripathy, R.; Acharya, U.R. A two-stage deep CNN architecture for the classification of low-risk and high-risk hypertension classes using multi-lead ECG signals. Inform. Med. Unlocked
**2020**, 21, 100479. [Google Scholar] [CrossRef] - Parmar, K.S.; Kumar, A.; Kalita, U. ECG signal based automated hypertension detection using fourier decomposition method and cosine modulated filter banks. Biomed. Signal Process. Control
**2022**, 76, 103629. [Google Scholar] [CrossRef] - Li, H.; Deng, J.; Feng, P.; Pu, C.; Arachchige, D.D.; Cheng, Q. Short-Ter, Nacelle Orientation Forecasting Using Bilinear Transformation and ICEEMDAN Framework. Front. Energy Res
**2021**, 9, 780928. [Google Scholar] [CrossRef] - Li, H.; Deng, J.; Yuan, S.; Feng, P.; Arachchige, D.D. Monitoring and Identifying Wind Turbine Generation Bearing Faults Using Deep Belief Network and EWMA Control Charts. Front. Energy Res.
**2021**, 770, 3–17. [Google Scholar] [CrossRef] - Batzel, J.J.; Kappel, F.; Schneditz, D.; Tran, H.T. Cardiovascular and Respiratory Systems: Modeling, Analysis, and Control; Society for Industrial and Applied Mathematics: Philadelphia, PA, USA, 2007; Volume 29, pp. 129–131. [Google Scholar]
- Šiaučiūnaitė, V.; Ragulskis, M.; Vainoras, A.; Dabiri, B.; Kaniusas, E. Visualization of complex processes in cardiovascular system during electrical auricular vagus nerve stimulation. Diagnostics
**2021**, 11, 2190. [Google Scholar] [CrossRef] - Stock, M.; Ryan, M. Oxygen consumption calculated from the Fick equation has limited utility. Crit. Care Med.
**1996**, 24, 86–90. [Google Scholar] [CrossRef] - Delong, C.; Sharma, S. Physiology, Peripheral Vascular Resistance; StatPearls Publishing: Treasure Island, FL, USA, 2019. [Google Scholar]
- Armstrong, R.B.; Warren, G.L.; Warren, J.A. Mechanisms of exercise-induced muscle fibre injury. Sport. Med.
**1991**, 12, 184–207. [Google Scholar] [CrossRef] [PubMed] - Rowel, L. Circulatory responses to upright posture. In Human Cardiovascular Control: Reflex Control During Orthostasis; CRC Press: Boca Raton, FL, USA, 1993; pp. 39–74. [Google Scholar]
- Gargasas, L.; Vainoras, A.; Schwela, H.; Jaruševičius, G.; Ruseckas, R.; Miškinis, V. JT interval changes during bicycle ergometry. In Proceedings of the Kardiologia Polska II Miedzynarodowy Kongres Polskiego Towarzystwa Kardiologieznego, Katowice, Poland, 4–6 September 1998; Volume 49, p. 153. [Google Scholar]
- Shaffer, F.; McCraty, R.; Zerr, C.L. A healthy heart is not a metronome: An integrative review of the heart’s anatomy and heart rate variability. Front. Psychol.
**2014**, 5, 1040. [Google Scholar] [CrossRef][Green Version] - McCraty, R.; Atkinson, M.; Tomasino, D.; Bradley, R.T. The coherent heart heart-brain interactions, psychophysiological coherence, and the emergence of system-wide order. Integral Rev. Transdiscipl. Transcult. J. New Thought Res. Prax.
**2009**, 5, 10–115. [Google Scholar] - Segerstrom, S.; Nes, L. Heart rate variability reflects self-regulatory strength, effort, and fatigue. Psychol. Sci.
**2007**, 18, 275–281. [Google Scholar] [CrossRef] - Woods, K. QT Dispersion in Ischaemic Heart Disease; Oxford University Press: Oxford, UK, 2000; pp. 432–433. [Google Scholar]
- Roukema, G.; Singh, J.P.; Meijs, M.; Carvalho, C.; Hart, G. Effect of exercise-induced ischemia on QT interval dispersion. Am. Heart J.
**1998**, 135, 88–92. [Google Scholar] [CrossRef] - Yoshimura, M.; Yasue, H.; Ogawa, H. Pathophysiological significance and clinical application of ANP and BNP in patients with heart failure. Can. J. Physiol. Pharmacol.
**2001**, 79, 730–735. [Google Scholar] [CrossRef] - Vainoras, A.; Gargasas, L.; Ruseckas, R.; Miškinis, V.; Jurkonienė, R. Computerised exercise electrocardiogram analysis system “Kaunas-Load”. In Proceedings of the 24th International Congress on Electrocardiology and 38th International Symposium on Vectorcardiography: Abstracts Book, Bratislava, Slovak Republic, 24–28 June 1997. [Google Scholar]
- Gargasas, L.; Vainoras, A.; Ruseckas, R.; Jurkoniene, R.; Jurkonis, V.; Miskinis, V. A new software for ECG monitoring system. In Proceedings of the 6th Nordic Conference on eHealth and Telemedicine, Helsinki, Finland, 31 August–1 September 2006. [Google Scholar]
- Ziaukas, P.; Alabdulgader, A.; Vainoras, A.; Navickas, Z.; Ragulskis, M. New approach for visualization of relationships between RR and JT intervals. PLoS ONE
**2017**, 12, e0174279. [Google Scholar] [CrossRef] [PubMed] - Saunoriene, L.; Siauciunaite, V.; Vainoras, A.; Bertasiute, V.; Navickas, Z.; Ragulskis, M. The characterization of the transit through the anaerobic threshold based on relationships between RR and QRS cardiac intervals. PLoS ONE
**2019**, 14, e0216938. [Google Scholar] [CrossRef] [PubMed] - Laio, F. Cramer–von Mises and Anderson-Darling goodness of fit tests for extreme value distributions with unknown parameters. Water Resour. Res.
**2004**, 40. [Google Scholar] [CrossRef]

**Figure 1.**A schematic diagram illustrating the interconnectivity of the Executive System, the Supply System, and the Regulatory System.

**Figure 2.**A simplified schematic diagram illustrating the interconnectivity of the Executive System, the Supply System, and the Regulatory System.

**Figure 3.**The readings are presented for the person with normal ABP. (

**a**) Disc (RR/JT) changes up to 14 min during the load and after 14 min during recovery. (

**b**) Variations in Systolic and Diastolic ABP during the stress test. (

**c**) The phase plane for the parameters X = (S − D)/S and Y = Disc (RR/JT) and the linear regression plot, where the data for each parameter are presented as a one-minute mean during the load and (

**d**) during the recovery.

**Figure 4.**The readings are presented for the person with high ABP. (

**a**) Disc (RR/JT) changes up to 15 min during the load and after 15 min during recovery. (

**b**) Variations in Systolic and Diastolic ABP during the stress test. (

**c**) The phase plane for the parameters X = (S − D)/S and Y = Disc (RR/JT) and the linear regression plot, where the data for each parameter are presented as a one-minute mean during the load and (

**d**) during the recovery.

**Figure 5.**Overall comparison of normal distribution graphs for (

**a**) Persons with normal and high ABP during the load and (

**b**) Persons with normal and high ABP during the recovery.

**Figure 6.**The Gaussian distribution graphs for (

**a**) Persons with normal ABP during the load. (

**b**) Persons with high ABP during the load. (

**c**) Persons with normal ABP during the recovery and (

**d**) Persons with high ABP during the recovery.

**Figure 7.**One case for an individual with (

**a**) Discriminant RR/JT vs. time graph and ABP vs. time graph, (

**b**) Linear regression graph and the slope coefficient (−1.9889) during the load phase, (

**c**) Locating the individual within the variation interval of the Gaussian distribution graph, (

**d**) Visualization of the individual inside the triangle system.

**Figure 8.**One case for an individual with (

**a**) Discriminant RR/JT vs. time graph and ABP vs. time graph, (

**b**) Linear regression graph and the slope coefficient (−0.14562) during the load phase, (

**c**) Locating the individual within the variation interval of the Gaussian distribution graph, (

**d**) Visualization of the individual inside the triangle system.

**Table 1.**Slope coefficients for individuals with normal ABP during the load and recovery. The goodness of the linear regression fit (for each individual slope coefficient) is measured by the Spearman’s rank correlation coefficient.

Persons with Normal ABP | |||||
---|---|---|---|---|---|

No. | Names | Slope Coefficients during Load (W·ms),M1 | Spearman’s Rank Correlation Coefficient during Load | Slope Coefficients during Recovery (W·ms),M2 | Spearman’s Rank Correlation Coefficient during Recovery |

1 | BACCHR | −1.6963 | −0.8035 | −0.32249 | −0.8024 |

2 | BARHEL | −0.65793 | −0.9058 | −0.012758 | −0.0486 |

3 | BROSOR | −1.6554 | −0.9333 | −0.30205 | −0.4667 |

4 | ENGBER | −1.0524 | −0.8161 | −0.19906 | −0.8389 |

5 | PETTHO | −1.0029 | −0.8903 | −0.90867 | −0.9244 |

6 | STEMAR | −0.097479 | −0.2168 | −0.25354 | −0.8146 |

7 | HEIRAL | −1.6539 | −0.8908 | −0.94723 | −0.7538 |

8 | FLOPET | −1.1824 | −0.8389 | −0.35497 | −0.8024 |

9 | SCHMAR | −0.88493 | −0.9515 | −0.16869 | −0.8066 |

**Table 2.**Slope coefficients for persons with high ABP during the load and recovery. The goodness of the linear regression fit (for each individual slope coefficient) is measured by the Spearman’s rank correlation coefficient.

Persons with Normal ABP | |||||
---|---|---|---|---|---|

No. | Names | Slope Coefficients during Load (W·ms),M3 | Spearman’s Rank Correlation Coefficient during Load | Slope Coefficients during Recovery (W·ms),M4 | Spearman’s Rank Correlation Coefficient during Recovery |

1 | ADAWOL | −2.3278 | −0.6960 | −0.61569 | −0.9119 |

2 | BRODOR | −2.229 | −0.7972 | −0.66062 | −0.9624 |

3 | ILLBJO | −2.1799 | −0.4745 | −0.43314 | −0.6869 |

4 | NAUTHO | −1.4895 | −0.9701 | −0.48034 | −0.9157 |

5 | STETHO | −1.6843 | −0.9066 | −0.748 | −0.9758 |

6 | PFEAND | −2.3957 | −0.8654 | −0.152 | −0.7833 |

7 | NEUCHR | −0.48277 | −0.6097 | −0.13909 | −0.8257 |

8 | LINUWE | −0.97304 | −0.4954 | −0.14123 | −0.7500 |

9 | KRAHAR | −0.80256 | −0.8742 | −0.38448 | −0.8074 |

10 | KLITOR | −2.071 | −0.9449 | −0.63648 | −0.9222 |

**Table 3.**Mean, standard deviation and significance values for the cohort of persons throughout the load and recovery process during the bicycle stress test.

Mean $\left(\mathit{\mu}\right)$ | Std. Deviation $\left(\mathit{\sigma}\right)$ | Confidence Interval | Sig. Level | Difference in Means | The Statistical Condition | |
---|---|---|---|---|---|---|

Persons with normal ABP during the load | ${\mu}_{L1}=-1.0982$ | ${\sigma}_{L1}=0.5287$ | $[-1.6269;-0.5695]$ | 0.4636 | $|{\mu}_{L2}-{\mu}_{L1}|=|-1.6636-(-1.0982)|=0.5654$ | $|{\mu}_{L2}-{\mu}_{L1}|\ge min({\sigma}_{L1},{\sigma}_{L2})$ Condition is satisfied |

Persons with high ABP during the load | ${\mu}_{L2}=-1.6636$ | ${\sigma}_{L2}=0.6970$ | $[-2.3606;-0.9665]$ | 0.1789 | ||

Persons with normal ABP during the recovery | ${\mu}_{R1}=-0.3855$ | ${\sigma}_{R1}=0.3239$ | $[-0.7094;-0.0616]$ | 0.0190 | $|{\mu}_{R2}-\phantom{\rule{3.33333pt}{0ex}}{\mu}_{R1}|=|-0.4391-(-0.3855)|=0.0536$ | $|{\mu}_{R2}-{\mu}_{R1}|\ge min({\sigma}_{R1},{\sigma}_{R2})$ Condition is not satisfied |

Persons with high ABP during the recovery | ${\mu}_{R1}=-0.4391$ | ${\sigma}_{R1}=0.2311$ | $[-0.6702;-0.2080]$ | 0.2339 |

Coordinate | Corresponds to |
---|---|

−1, 0 | E (the Executive System) |

0, 1 | R (the Regulatory System) |

1, 0 | S (the Supply System) |

**Table 5.**Formalization of the three conditions for the slope coefficient of the new candidate entering into the system triangle.

Condition 1 | Condition 2 | Condition 3 | |
---|---|---|---|

If | $New\le {\mu}_{L2}-{\sigma}_{L2}$ | $New\ge {\mu}_{L1}+{\sigma}_{L1}$ | ${\mu}_{L2}-{\sigma}_{L2}<New>{\mu}_{L1}+{\sigma}_{L2}$ |

The interpolation coefficient | $C=-1$ | $C=1$ | $C=$ in between the variation interval |

The thickness of the left branch in pixels | $C=10-\frac{C+1}{2}\xb79$ | 1 | $C=2\xb7\frac{New-({\mu}_{L2}-{\sigma}_{L2})}{({\mu}_{L1}+{\sigma}_{L1})-({\mu}_{L2}-{\sigma}_{L2})}\xb79$ |

The thickness of the right branch in pixels | 1 | $C=\frac{C+1}{2}\xb79+1$ |

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## Share and Cite

**MDPI and ACS Style**

Qammar, N.W.; Orinaitė, U.; Šiaučiūnaitė, V.; Vainoras, A.; Šakalytė, G.; Ragulskis, M.
The Complexity of the Arterial Blood Pressure Regulation during the Stress Test. *Diagnostics* **2022**, *12*, 1256.
https://doi.org/10.3390/diagnostics12051256

**AMA Style**

Qammar NW, Orinaitė U, Šiaučiūnaitė V, Vainoras A, Šakalytė G, Ragulskis M.
The Complexity of the Arterial Blood Pressure Regulation during the Stress Test. *Diagnostics*. 2022; 12(5):1256.
https://doi.org/10.3390/diagnostics12051256

**Chicago/Turabian Style**

Qammar, Naseha Wafa, Ugnė Orinaitė, Vaiva Šiaučiūnaitė, Alfonsas Vainoras, Gintarė Šakalytė, and Minvydas Ragulskis.
2022. "The Complexity of the Arterial Blood Pressure Regulation during the Stress Test" *Diagnostics* 12, no. 5: 1256.
https://doi.org/10.3390/diagnostics12051256