In the work, the mathematical support of the medical computer system for diagnosing the condition of human vessels is developed, which is based on the method of wavelet processing in the Morlet basis. Algorithmic support was developed on the basis of mathematical support, which made it possible to develop software with a graphical user interface in the Matlab environment for a medical computer system. The developed system provides a study of the structural fluctuation of the pulse signal in the time space of observation of different scales according to diagnostic signs in the form of spectra of wavelet coefficients, which makes it possible to identify timely changes in human vessels.
medical computer system, which is implemented using the photoplethysmographic method [1, 2, 3] for the task of diagnosing the condition of the vessels of the human system, is an urgent task. The system makes it possible to obtain diagnostic signs as indicators of the state of human vessels by registering the pulse signal (PS) and further processing it by means of mathematical, algorithmic and software.
Analysis of well-known medical computer systems for diagnosing the functional state of human vessels (Mobil-O-Graph, BPLab, PulseTrace 2 (USA), rteriograph 24, Oscar 2, BPro and others) found that they are limited in processing the pulse signal in order to obtain in addition to the assortment of diagnostic signs, the number of which is determined by the capabilities of the mathematical and algorithmic-software processing of the PS. Among the existing mathematical support of computer systems for diagnosing the functional state of human vessels, the following methods of PS processing are highlighted: quantitative method (S.V.
Danylevska V.G., Lutsuk O.V., Rybin O.I., Sharpan O.B., Yankovenko O.D., Allen J. Murray, etc.) [9-15], spectral-correlation method (Zudov O.M.) [10], the wavelet method with the Dobeshe basis function (N.V. Muzhitska, V.V. Hnilitskyi) [16], the synphase/component method (L.V. Khvostivska) [17, 18].
The design of computer diagnostic systems in medicine is impossible without sensors, which are very important [19-21], especially considering their stability at the stages of development, testing, and operation [22-25]. At the same time, the design of cyber-physical and computer medical systems for biomedical research [26, 27] with their numerical modeling [28] and the development of appropriate software systems [29] using neural network clustering technology [30] and computing methods [31-41] for medical image and biomedical signal processing is a modern and promising scientific area.
The indicated methods of PS processing in relation to wavelet processing do not provide research of structural fluctuation of PS in the time space of observation of different scales, which is necessary for timely detection of changes in human vessels. When searching for effective methods of PS processing, researchers did not use the full potential of wavelet processing, but limited themselves only to the Dobeshe basis function.
Therefore, the extension of new basis functions to wavelet processing of PS will ensure the development of a new effective algorithmic software for a new medical computer system for calculating new diagnostic information about the state of blood vessels, which will ensure their diagnostic level. 2. Hardware support of the medical computer system for diagnosing the state of human vessels The hardware of the medical computer system for diagnosing the state of human vessels in the form of a computer photoplethysmograph (Fig. 1), which was developed by Liliia Khvostivska and Mykola Khvostivskyi at the Department of Biotechnical Systems of Ternopil Ivan Puluj National Technical University, was used for PS registration. and ensures the matching of the detector 2 output with the ADC 3 input relative to impedance (resistance). ADC 3 performs the process of converting analog PS into digital format for further connecting the output of the previous unit to PC 5 via UART-USB 4. At the software level, PC 5 performs the process of processing data of the PS, including saving, processing, visualization and other operations.
The registered PS with the developed system layout and the implemented system are shown in Fig. 2. (b) Figure 2: Registered PS hardware part of the computer medical system (developers Khvostivska L.V., Khvostivskyi M.O. [42]: a) normal state; b) pathology (change in stiffness). 3. Mathematical support of the medical computer system for diagnosing the state of human vessels Many biological and physical systems demonstrate rhythmic processes, in particular the PS [3, 31, 32]. The rhythmic temporal structure of PS embedded in a sequence of numerical data can be extracted and quantified using the Fourier transform (FT) or other spectral processing methods, including the wavelet transform. Wavelet transform (Wavelet Transform), which has a high resolution in both the frequency and time domains. It not only indicates which frequencies are present in the signal, but also at what time these frequencies occurred. This is achieved by working with different scales in accordance with the expression [43]: W ( a , b )= 1 +∞ t −b
∫ s ( t ) ψ ( ) dt ,
√ a −∞ a
(
a
Most PS data usually consists of periodic bursts of sinusoidal oscillations, it is not surprising that the most common basic wavelet is the Morlet wavelet [44, 45], which consists of a complex plane wave modulated by a Gaussian (Fig. 3) (the Morlet wavelet is defined as a sinusoid, tapered to Gauss).
The complex form of the Morlet basis is represented as a complex exponent modulated by a Gaussian function: ψ ( t , a , b )=e iω t−ab e−21 ( t−ab )2 (2) where ω– base frequency; a – scale factor; b – time shift.
The choice of wavelet width is a combination of PS processing considerations and theoretical/speculative considerations of the system with which the PS is registered. This parameter is therefore important for the analysis of time-frequency data, and yet is often chosen and reported in a way that obscures the assumptions underlying the processing of the PS data. 4. Algorithmic support of the medical computer system for diagnosing the state of human vessels On the basis of wavelet processing in the Morlet basis, the algorithmic support for PS processing is implemented, which is shown in Fig. 4.
According to the implemented algorithm, which is shown in Fig. 4, the following stages are carried out: entering the values of the scale coefficients, time shift, interval time as a sequence, calculation of the frequency of the base ω and f-th of the base Morlet, wavelet coefficients C(a,b) depending on a, b, t when applying cycle, and then switching to the frequency representation using the Fourier transform function W(f,a,b).
The implemented algorithm provides processing of the PS signal as part of the computer system when using wavelets, which allows you to study the time-frequency fluctuations of the signal in a three-dimensional projection. This provides an opportunity to monitor all variations in the structural units of vessels, indicating min or max disturbances in their functioning.
Algorithmic support of the computer system for diagnosing the state of human vessels is shown in Fig. 5. 5. Software of the medical computer system for diagnosing the condition of human vessels and the results of its work The Matlab environment was used to develop the wavelet processing software based on the developed algorithm (Fig. 5). The result of the software is shown in Fig. 6 in the form of a 3D representation as a "time-scale-spectrum" dependence.
Spectral data (Fig. 6), which are presented in 3D, are visually identical, that is, full invariance is preserved, but numerically evaluating the level of deviations between them is a complicated process. Therefore, the well-known works of the scientist of the Department of Biotechnical Signals, in particular Khvostivskyi M.O., the criterion for averaging spectra by time shifts in accordance with the expression:
Y^ ( a , b )= M b {W ( a , b ) }. (3)
The result is developed software that allows the user (doctor) to automate the process for studying the state of blood vessels. The displayed results clearly reflect the changes between different states, particularly normal and pathological. Similarity of the structure (invariance) is inherent to both states, but a change in the level of the spectra is noted. Such a change indicates the manifestation of a pathological state of blood vessels.
Therefore, the proposed diagnostic parameters make it possible to monitor timely changes in the functioning of blood vessels and thereby expand the diagnostic level (+1 diagnostic feature) of medical computer systems for diagnosing the state of human blood vessels.
Mathematical support, algorithmic support and software for processing the pulse signal in the core with the method of wavelet processing in the Morlet basis were developed for the calculation of new diagnostic information in the form of a spectral representation of wavelet coefficients, which ensured the development of a medical computer system for diagnosing the state of human vessels and expanding the diagnostic level of existing systems Matlab tools and its Guide module were used in the development of the system software.
The operation of the medical computer system was investigated and it was established that the system functions correctly and clearly reflects changes in the state of human vessels by 3D and 2D (3D averaging) realizations of wavelet coefficient spectra (new diagnostic parameters). Neural Networks for Accurate Measurement of Cardiac Stroke Volume. Applied Sciences. 10. 4612. doi: 10.3390/app10134612. [2] Kim K.B.; Baek H.J. Photoplethysmography in Wearable Devices: A Comprehensive Review of Technological Advances, Current Challenges, and Future Directions.
Electronics 2023, 12, 2923. doi: 10.3390/electronics12132923. [3] Khvostivska L., Uniyat S., Khvostivskyi M., Yavorskyi I. Mathematical Support Verification of Methods, Algorithms and Software Processing of Pulse Signals under Physical Load in Computer Diagnostic Systems. Proceedings of the XXVIII International Scientific and Practical Conference. Melbourne, Australia. 2023. Pp. 185-190. ISBN 979-889074-574-3. doi: 10.46299/ISG.2023.1.28. [4] Mlynko B.B, Fryz M.Ie. Identyfikatsiia ta otsiniuvannia diahnostychnykh parametriv na osnovi analizu fotopletyzmohramy. Visnyk Ternopilskoho derzhavnoho tekhnichnoho universytetu Ternopil, 2002. T.7, №4. P.81-87. [in Ukrainian]. [5] Kukharchuk, Vasyl V., Sergii V. Pavlov, Volodymyr S. Holodiuk, Valery E. Kryvonosov, Krzysztof Skorupski, Assel Mussabekova, and Gaini Karnakova. 2022. "Information Conversion in Measuring Channels with Optoelectronic Sensors" Sensors 22, no. 1: 271. https://doi.org/10.3390/s22010271. [6] Marchenko B. Mlynko B., Fryz M. Matematychna model fotopletyzmosyhnalu − osnova identyfikatsii informatyvnykh oznak. Mizhnarodnyi naukovyi zhurnal «Kompiutynh». 2005. T.5. № 2. P. 73-82. [in Ukrainian]. [7] Mlynko, B.B., Fryz M.Ie. Alhorytm statystychnoi diahnostyky na osnovi reiestratsii ta analizu fotopletyzmosyhnaliv. Visnyk Khmelnytskoho natsionalnoho universytetu.
Tekhnichni nauky. Khmelnytskyi, 2013. № 4. P.176-182. [in Ukrainian]. [8] Mlynko B.B., Pastukh O.A., Fryz M.Ie. Obgruntuvannia vyboru matematychnoi modeli rytmichnoho svitlovoho syhnalu, porodzhenoho tsyklichnymy zminamy pulsovoho krovonapovnennia. Vymiriuvalna ta obchysliuvalna tekhnika v tekhnolohichnykh protsesakh. Khmelnytskyi, 2001. №2(16). P. 100-103. [in Ukrainian]. [9] Danylevska V.H., Lutsuk O.V., Rybin O.I., Sharpan O.B. Osoblyvosti i mozhlyvosti diahnostyky za normalizovanym peretvorenniam Furie pulsovoho syhnalu. Elektronyka y sviaz. 2006. № 2. P. 49-54. [in Ukrainian]. [10] Zudov O.M., Sharpan O.B. Diahnostychni mozhlyvosti spektralnoho analizu syhnaliv pulsovoi khvyli. Visnyk ZhITI. Tekhnichni nauky. 2001. № 16. P. 82-85. [in Ukrainian]. [11] The developed software of the computer system allows the user (doctor) to automate the process of diagnosing the state of blood vessels.Wójcik W., Pavlov S., Kalimoldayev M. Information Technology in Medical Diagnostics II. London: (2019). Taylor & Francis Group, CRC Press, Balkema book. 336 Pages. [12] Sharpan O.B. Doslidzhennia zalezhnosti amplitudnoho spektra pulsovoho syhnalu vid stanu systemy hemodynamiky. Naukovi visti NTUU “KPI”. 2004. №1. P.110-117. [in Ukrainian]. [13] Yankovenko O.D. Eksperymentalne doslidzhennia funktsionalnoho stanu liudyny na osnovi amplitudnoho spektralnoho analizu pulsovoi khvyli. Visnyk Natsionalnoho tekhnichnoho universytetu Ukrainy «KPI». Seriia: Radiotekhnika.
Radioaparatobuduvannia. 2010. № 40. P. 35-41. [in Ukrainian]. [14] Allen J. Murray. Effects of filtering on multi-site photoplethysmography pulse waveform characteristics. Comuters in Cardiology Proceedins. 2004. P.485-488. doi: 10.1109/CIC.2004.1442980. [15] Gary E. McVeigh. Pulse Waveform Analysis and Arterial Wall Properties. Hypertension.
2003. 41. P. 1010-1011. doi:10.1161/01.HYP.0000069006.98113.22. [16] Hnilitskyi V.V., Muzhytska N.V. Zadacha vyboru materynskoho veivletu dlia obrobky pulsovoi khvyli v umovakh zavad. Visnyk ZhDTU. №2. 2011. S.64-69. [in Ukrainian]. [17] Khvostivska L.V. Mathematical model and methods of pulse signal analysis to increase the informativeness of photoplethysmographic systems: dysertatsiia na zdobuttia naukovoho stupenia kandydata tekhnichnykh nauk za spetsialnistiu 01.05.02 / Liliia Volodymyrivna Khvostivska. Ternopil: TNTU, 2021. 177 p. [ in Ukrainian]. [18] Khvostivska L.V., Yavorskyi B.I. Aktualnist zastosuvannia synfaznoho ta komponentnoho metodiv shchodo analizu pulsovoho syhnalu sudyn liudyny. Materialy XVII naukovoi konferentsii Ternopilskoho natsionalnoho tekhnichnoho universytetu imeni Ivana Puliuia «Pryrodnychi nauky ta informatsiini tekhnolohii» (20-21 lystopada 2013).
Ternopil, 2013. T.1. P. 45. [in Ukrainian]. [19] Martsenyuk V., Klos-Witkowska A., Dzyadevych S., Sverstiuk A. Nonlinear Analytics for Electrochemical Biosensor Design Using Enzyme Aggregates and Delayed Mass Action.
Sensors 2022, 22(3), 980; https://doi.org/10.3390/s22030980. [20] Martsenyuk, V. P., Andrushchak, I. Ye., Zinko, P. N., & Sverstiuk, A. S. (2018). On Application of Latticed Differential Equations with a Delay for Immunosensor Modeling. In Journal of Automation and Information Sciences (Vol. 50, Issue 6, pp. 55–65). Begell House. https://doi.org/10.1615/jautomatinfscien.v50.i6.50. [21] Martsenyuk, V., Sverstiuk, A., & Gvozdetska, I. S. (2019). Using Differential Equations with Time Delay on a Hexagonal Lattice for Modeling Immunosensors. In Cybernetics and Systems Analysis (Vol. 55, Issue 4, pp. 625–637). Springer Science and Business Media LLC. https://doi.org/10.1007/s10559-019-00171-2. [22] Martsenyuk, V., Soldatkin, O., Klos-Witkowska, A., Sverstiuk, A., & Berketa, K. (2024).
Operational stability study of lactate biosensors: modeling, parameter identification, and
stability analysis. In Frontiers in Bioengineering and Biotechnology (Vol. 12). Frontiers
Media SA. https://doi.org/10.3389/fbioe.2024.1385459.
[23] Martsenyuk V.P., Sverstiuk A.S., Andrushchak I.Ye. Approach to the study of global
asymptotic stability of lattice differential equations with delay for modeling of
immunosensors (2019) Journal of Automation and Information Sciences, 51 (2), pp. 58 –
71. DOI: 10.1615/jautomatinfscien.v51.i2.70.
[24] Martsenyuk, V., Klos-Witkowska, A., & Sverstiuk, A. (2020). Stability Investigation of
Biosensor Model Based on Finite Lattice Difference Equations. In Springer Proceedings in
Mathematics & Statistics (pp. 297–321). Springer International Publishing.
https://doi.org/10.1007/978-3-030-35502-9_13.
[25] Sverstiuk A.S. Research of global attractability of solutions and stability of the
immunosensor model using difference equations on the hexagonal lattice (2019)
Innovative Biosystems and Bioengineering, 3 (
Vector of Diagnostic Features in the Form of Decomposition Coefficients of Statistical Estimates Using a Cyclic Random Process Model of Cardiosignal. 2019 10th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS). IEEE. https://doi.org/10.1109/idaacs.2019.8924398. [36] Trysnyuk V., Zozulia A., Lupenko S., Lytvynenko I., Sverstiuk A. Methods of rhythmcardio signals processing based on a mathematical model in the form of a vector of