Model of an automated biotechnical system for analyzing pulseograms as a kind of edge devices

. The rapid development of computer biometrics over the past 2-3 decades is largely due to the development and widespread introduction into clinical practice of new methods of studying human body health, including pulse methods. It is possible to judge changes in hemodynamic characteristics, heart rate, and blood flow rate in the studied part of the body based on the parameters of the pulse wave signal. At the same time, the physical processes of the formation of the pulse wave shape have not been fully studied, although the number of biophysical models of blood circulation is quite significant. The development of such a model will allow us to effectively apply modern developments in digital signal processing to the pulse wave and increase its diagnostic value. A qualitative model of pulse signal can be entrusted to the development of the base unit of the biotechnical system as a type of edge device. The work is devoted to the improvement of methods of rapid diagnosis of the cardiovascular system based on the analysis of model pulse-grams. An adequate mathematical model of the pulse wave, which corresponds to real pulse signals in different states of the human body and contains mathematical relationships between the main parameters of pulse-grams, has been refined. The algorithm of express diagnostics with the established criteria of the analysis of pulsograms is offered 1 .


Introduction
The rapid development of computer biometrics over the past 2-3 decades is largely due to the development and widespread introduction into clinical practice of new methods of studying human body health, including pulse methods.It is possible to judge changes in hemodynamic characteristics, heart rate, and blood flow rate in the studied part of the body based on the parameters of the pulse wave signal.At the same time, the physical processes of the formation of the pulse wave shape have not been fully studied, although the number of biophysical models of blood circulation is quite significant.However, none of them meets all the requirements for models of the pulse signal in terms of rapid and pulse diagnostics, namely: • match with the real signal in all areas of blood circulation; • not only the form reproduction but also the explanation of the pulse wave genesis; • description of the circulatory system activity in the diastolic phase; • presence of mathematical equations that coordinate the basic parameters of blood flow; • relative simplicity of interpretation with sufficient information value.
The development of such a model will allow us to effectively apply modern developments in digital signal processing to the pulse wave and increase its diagnostic value.A qualitative model of pulse signal can be entrusted to the development of the base unit of the biotechnical system as a type of edge device (figure 1).

Theoretical background
An edge device is a peripheral device capable of forwarding packets between traditional interfaces (e.g.Ethernet, Token Ring, etc.) and ATM based on channel or network layer information.However, it is not involved in any routing protocol on the network.
• Overview : HPC at the Edge for medical imaging merges HPC/AI and medical sensing technology in order to provide precision medicine through the use of real-time advanced monitoring and analysis of a patient's medical data to detect early pathologies while lowering the risk of privacy breaches by keeping the data on site.This granular, yet massive amount of patient data can be analysed at the Edge, transformed, and then only pertinent data is sent to the cloud such as alerts or data stripped of information that could lead to the patient's privacy being compromised.Medical Imaging at the Edge using HPC/AI removes the latency and dependence on Cloud Computing resources, as well as reduces the patient's digital footprint by limiting how many systems have access to data.AI used in medical imaging provides tools that augment the clinician's intelligence in a way where they are able to provide better care at reduced costs [50].Figure 14 illustrates the digital development in healthcare and how Edge Computing is being used in healthcare.Pazienza et al. [10] discribed the eLifeCare platform uses AI on the Edge level (figure 3).They say that the platform acts as an alert system using early warning indicators (some forms of edge devices) [10].
Quy et al. [11] consider the architecture of fog-based applications.They note that such an architecture consists of three layers: Thing Layer, Fog Layer, and Cloud Layer.In particular, the Thing Layer level includes end-user devices (edge devices) (figure 4).Those are Arduino motherboards, IoT devices, sensors, body data collection tools (e.g.blood pressure, heart rate, glucose), and so on [11].
Nikitchuk et al. [9] suggest an architecture for edge devices for diagnostics of students' physical condition.The biotechnical system can then be built based on their research.This article aims to develop a mathematical model of the pulse wave, which will correspond to the real pulse signals for certain types of pulsations in the circulatory system, contain mathematical relationships between basic parameters of pulse-grams and will be the basis of a biotechnical system to improve rapid diagnostics of the cardiovascular system.https://doi.org/10.55056/jec.627

Research methodology
In the methodological aspect, the study of such complex systems as physiological is carried out on adequate mathematical models using modern computer technology.Data analysis includes: (a) mathematical description, modeling, and parameterization of data; (b) data classification by diagnostic categories to further automate the conclusion; (c) graphic or other visual presentation of the results for the diagnostician.
In the first stage, the selected and/or improved model is analyzed and calculated on a PC (which is a model computational experiment).It should be kept in mind that modeling is a process of studying a phenomenon with the help of mathematical equations.The model is just a simplified description of real phenomena and processes.Therefore, the results obtained by computer simulation need further confirmation (for example, by conducting a clinical experiment).
The second stage is the calculation of the object's characteristics, the definition of diagnostic criteria, and the creation of an identification box (expert system) to automate the conclusion in further clinical trials.
An analysis of modern methods and tools has established [7] that classification by the characteristics of a single pulse wave and classification at an interval of 3-5 periods are not sufficiently informative, since they do not take into account the variability of cardiovascular system indicators expressed in fluctuations in the characteristics of pulseograms over a long interval, which corresponds to the procedure of recording pulse waves for 3-5 minutes.
Therefore, we propose a classification [7] based on the variability of pulseogram characteristics throughout the diagnostic procedure.
To study the dynamics of the cardiovascular system and obtain a set of diagnostic criteria for the analysis of pulse waves over long time intervals, it is recommended to use the methods and techniques of fractal analysis as those that allow to identify the self-similarity and regularity of time sequences.In particular, the phase plane method can be used to quantitatively describe pulse waveforms over a long time interval.The effectiveness of this method lies primarily in the fact that with various changes in the heart rhythm, in case of cardiovascular system dysfunctions, not only the sequence of periods changes but also the rate of their change in time.Therefore, a differentiated pulse signal inevitably contains additional information about the state of the subject's cardiovascular system.
To quantify the obtained trajectories of pulse signals in the phase plane (phase portraits of pulseograms), it is possible to use such indicators as the area of the phase portrait, the degree of portrait chaos, and the fractal dimension of the phase portrait.
At the last stage of computer analysis, the conclusion is performed and the result is displayed in visual form (monitor screen) and/or graphical representation for the diagnostician.
The algorithm for automated inference about the state of a physiological object by creating a classification base (identification box) with the use of model data is shown in figure 5.
Each of the listed stages of data processing and process analysis in a certain period quickly improves, moving to a higher quality level almost abruptly.For example, acquainting a doctor with a diagnosis (conclusion about the state of the biological system), set by the computer automatically, helps to increase the accuracy of the final diagnostic conclusion [7].

Results
The rapid development of computer biometrics over the past 2-3 decades is largely due to the development and widespread introduction of new, including pulse, methods of studying the state of health of the human body into clinical practice.Based on the parameters of the pulse wave signal, it is possible to judge changes in hemodynamic characteristics, heart rhythm, and blood filling rate in the part of the body under study.At the same time, the physical processes of pulse wave formation are not yet fully understood.
The number of biophysical models of blood circulation is quite significant.At the same time, none of them satisfies all the requirements for pulse signal models in terms of express and pulse diagnostics: • coincidence with the real signal in all parts of the circulation; • reproduction of not only the shape but also explanation of the genesis of the pulse wave; • description of the circulatory system in the diastolic phase; • availability of mathematical equations that coordinate the main parameters of blood flow; • relative ease of interpretation with sufficient information value.https://doi.org/10.55056/jec.627When comparing the vast majority of models and the real signal, discrepancies arise, sometimes significant ones, which cannot be explained by the accompanying factors of pulse wave registration.That is, these are not distortions in the signal caused by the imposition of noise and artifacts, but rather inaccuracies in the representation of blood flow pulsations.Most often, such inaccuracies arise when trying to apply the model to vessels much further away from the heart than the aorta, the so-called peripheral bloodstream.Nevertheless, several models successfully describe individual parts of the circulatory system.However, these models are of theoretical rather than practical value -they attempt to take into account all possible processes in and around the vessel, while the emphasis is not on simple relationships of the main parameters or such relationships are difficult to implement.
Based on the analysis of existing biophysical models of blood circulation [1][2][3]5], it follows that none of the existing models reflects all elements of the pulse wave accurately enough.Therefore, they cannot be used in developing new methods for analyzing pulse signals in particular and the cardiovascular system in general.However, the harmonious model of blood circulation and the model of active diastole can be considered as those that accurately reflect the genesis of pulse waves.They are quite simple and are partially confirmed by practical results [5].
Based on these two models, a mathematical model of blood circulation was developed in [3,5].It was called harmonic three-phase.According to this model, the activity of the circulatory system is considered to be three-phase, i.e. the pulse signal is formed by three components: systolic, dichroic, and presystolic [5]: The systolic component occurs as a result of the release of blood from the left atrium into the aorta.It is described by the harmonic model of circulation as follows When analyzing the pulse waveform locally, you can set local values of blood flow parameters.Considering the brachial artery as the area of sensor overlap, and taking into account the ratio the systolic component in the brachial artery can be represented by the following equation: The dicrotic component, which is part of the total signal, is associated with the active activity of the venous system.From practical clinical results, the general characteristics of the dicrotic component and their approximate correlation with similar parameters of the systolic component are known.Based on these data, the equation of the dicrotic component in the brachial artery was developed: https://doi.org/10.55056/jec.627 where  ′  0 -is the amplitude of the dicrotic wave;  ′ -is the circular frequency of the dicrotic wave;  ′ -the velocity of the dicrotic component of the pulse wave;  ′ -time delay between systolic and dicrotic components.
Since most arteries (except for the aorta and carotid artery) and veins are muscle-type vessels, their pulse wave propagation properties are the same.Consequently, the propagation speed of the dicrotic wave is  = 6.8 m/s for the same category of people.The distance from the heart, is included in the equation as a parameter  = 0.4 m.Since only a positive half-wave is used as a dicrotic component, to ensure synchronization in signal formation, the circular frequency of the dicrotic wave will be half that of the systolic wave frequency,  ′ = 2/ = 3.3 rad/s (the numerical value is valid for the specified category).
Regarding the delay in time of occurrence, the dicrotic wave begins at the moment of the beginning of the systolic wave decline, that is, immediately after its maximum, therefore, for this category of patients it is  ′ = 0.06 − 0.12 s.
The presystolic component occurs due to the release of blood from the left ventricle into the atrium.As in the case of the dicrotic component, the presence of valves leads to the fact that the presystolic component is only a positive half-sine wave.Based on general ideas about the formation of this component, its equation in the brachial artery is as follows: where ′′  0 -is the amplitude of the presystolic wave;  ′′ -is the circular frequency of the presystolic wave;  ′′ -the velocity of the presystolic component of the pulse wave;  ′′ -time delay between systolic and presystolic components.
The relationship between the amplitudes of the presystolic and dicrotic waves . Since only the positive half-wave is involved in the formation of the contour, its frequency will coincide with the frequency of the dicrotic wave  ′′ =  ′ =  2 = 3.30, the propagation speed and distance from the heart for all these components are the same, as evidenced by the uniformity of the contour within a particular area of the blood flow.The phase shift between the systolic and presystolic waves can be found based on the analysis of real pulseograms.According to the results of the analysis presented in [7], the presystolic wave has a maximum at a distance of 0.1 to 0.3 s from the top of the systolic wave, and the presystolic wave appears earlier.The shorter the time delay, the more pronounced the presystolic component.Since no presystolic peak is observed on the brachial plethysmogram, we take  ′′ ≈ 0.3 s.
Taking into account the pressure around the artery to be recorded, the change in pulsations in the brachial artery based on equations ( 5)-( 6) can be written The model is a one-dimensional signal, the position of the extremes and characteristic points of which corresponds to a human pulse wave without pathologies of the cardiovascular system.
The duration is chosen based on several heartbeats.In terms of the data set, this curve is an array of 600 discrete points, which corresponds to a signal with a sampling frequency of 100 Hz (the value of the pressure in the model is calculated at intervals of 0.01 sec.) The model analysis procedure gives an idea of the effectiveness and feasibility of applying appropriate software and algorithms to the real signal.A fragment of the model is graphically shown in figure 6. Assume that the real and mathematically described pulse signals are identical [7].That is, the pulse wave mathematical equation can be developed for the selected 6 types of pulse presented in the classification system based on the variability of the pulsegram characteristics during the diagnostic procedure [7], with the definition of the corresponding dysfunctions of the cardiovascular system.
General view of the mathematical equation of the pulse wave or, considering Taking into account the nominal parameters of blood flow for the category of people with the same type of anthropometric and physiological parameters, without obvious dysfunctions of the heart, the mathematical equation for the pulse signal of "even pulse" According to the equation, computer simulation of the signal "even pulse" was conducted (figure 7).Equation for pulse signal type "uneven pulse": By changing the hemodynamic parameters included in the equation of the pulse wave, a graph of the "uneven" type of pulse was obtained by computer simulation (figure 8).
The equation for pulse signal type "high pulse"  ℎℎ = 60 + 18.The graphic result of the computer simulation of the "high" pulse is shown below (figure 9).The equation for the type of pulse signal "low pulse", is shown in figure 10.The graphic result of the computer simulation of the "fast" pulse is shown in the figure 11.By changing the hemodynamic parameters included in the equation of the pulse wave, the equation and the graph of the "slow" type of pulsations are obtained (figure 12).The obtained mathematical equations of signals for six types of pulse are presented in the phase plane.The numerical indicators of phase portraits of pulse-grams are investigated (PPP) to determine the criteria for rapid diagnosis.
To carry out express diagnostics on pulsegrams, it is necessary to receive indicators on which the conclusion will be automatically received.It is expedient to plow with the phase plane method substantiated in [7].
According to [7], phase portrait can be formed by putting on one axis the signal itself  = (), and on the other one -its derivative () = () (figure 13).To quantify the trajectories in the phase plane in [7] the following indicators are considered: • area of the phase portrait  -the number of occupied cells in the plane; • degree of chaos ℎ; • fractal dimension (maximum length (diameter) of the phase portrait) .
The literature sources show the range of changes in the pulse wave, which allowed to obtain sets of curves according to equations (3) -( 8) for each type of pulse.Pulse signals have been   presented in the phase plane and their phase portraits have been obtained, according to which the values of PPP characteristics have been calculated (tables 1 and 2).

Table 1
Numerical values of PPP indicators ("even", "uneven", "slow").physical relationships between specific indicators of the circulatory system.Substantiation of such relationships and dependencies is contained in biophysical models of blood circulation.In this study, the feasibility of using a refined harmonic model of the pulse wave is substantiated, which is entrusted to the study of the possibility of rapid diagnosis of the cardiovascular system.We also propose a classification of pulseograms based on the variability of pulseogram characteristics throughout the diagnostic procedure.
Based on the study, six functional sets are formed.Each of them contains an array of values from the analysis criteria -numerical characteristics of phase portraits of pulse-grams.These characteristics correspond to a particular pulse type, which will help to detect various pulsegrams, as well as diagnose the cardiovascular system for lack of dysfunction.The algorithm for analyzing pulseograms with automated conclusion is proposed and considered in detail.
The future biotechnical system that will be developed based on this model of pulsograms will be a type of edge device.This system will promote carrying out express organism diagnostics on pulse signals and also will transfer results to the server of the remote diagnostic center.
https://doi.org/10.55056/jec.627Data collection using a signal sensor Signal filtering / useful signal extraction Transfer to PC Mathematical description of physiological process (signal) Modeling of physiological process (signal)

Figure 5 :
Figure 5: Algorithm for conducting research and automatic inference about the state of a physiological object using model data.

Figure 6 :
Figure 6: A fragment of the model signal.

Figure 13 :
Figure 13: Algorithm for forming a phase portrait of a model pulse signal.