Cardiovascular system modeling using windkessel segmentation model based on photoplethysmography measurements of fingers and toes

Ervin Masita Dewi, Sugondo Hadiyoso, Tati Latifah Erawati Rajab Mengko, Hasballah Zakaria, Kastam Astami

DOI: 10.4103/jmss.jmss_101_21


Background: Photoplethysmography (PPG) contains information about the health condition of the heart and blood vessels. Cardiovascular system modeling using PPG signal measurements can represent, analyze, and predict the cardiovascular system. Methods: This study aims to make a cardiovascular system model using a Windkessel model by dividing the blood vessels into seven segments. This process involves the PPG signal of the fingertips and toes for further analysis to obtain the condition of the elasticity of the blood vessels as the main parameter. The method is to find the Resistance, Inductance, and Capacitance (RLC) value of each segment of the body through the equivalent equation between the electronic unit and the cardiovascular unit. The modeling made is focused on PPG parameters in the form of stiffness index, the time delay (?t), and augmentation index. Results: The results of the model simulation using PSpice were then compared with the results of measuring the PPG signal to analyze changes in the behavior of the PPG signal taken from ten healthy people with an average age of 46 years, compared to ten cardiac patients with an average age of 48 years. It is found that decreasing 20% of capacitance value and the arterial stiffness parameter will close to cardiac patients' data. Compared with the measurement results, the correlation of the PPG signal in the simulation model is more than 0.9. Conclusions: The proposed model is expected to be used in the early detection of arterial stiffness. It can also be used to study the dynamics of the cardiovascular system, including changes in blood flow velocity and blood pressure.


Cardiovascular system, finger and toe photoplethysmography, photoplethysmography, stiffness index, Windkessel segmentation model

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Gaziano TA. Lifestyle and cardiovascular disease: More work to do. J Am Coll Cardiol 2017;69:1126-8.

Riegel B, Moser DK, Buck HG, Dickson VV, Dunbar SB, Lee CS, et al. Self-care for the prevention and management of cardiovascular disease and stroke: A scientific statement for healthcare professionals from the American Heart Association. J Am Heart Assoc 2017;6:e006997.

Dewi EM, Mengko TL, Zakaria H, Astami K. Increased arterial stiffness in chaterization patient by photoplethysmography analysis. International Conference on Electrical Engineering and Informatics; 2019. Available fom: https://DOI: 10.1109/ICEEI47359.2019.8988783. [Last accessed on 2020 Feb].

Saveljik I, Nikolic D, Milosevic Z, Isailovic V, Nicolic M, Parodi O, et al. 3D modeling of plague progression in the human coronary artery. Proceedings 2018;2:388.

McLaughlin NB, Campbell RW, Murray A. Accuracy of four automatic QT measurement techniques in cardiac patients and healthy subjects. Heart 1996;76:422-6.

Postema PG, De Jong JS, Van der Bilt IA, Wilde AA. Accurate electrocardiographic assessment of the QT interval: Teach the tangent. Heart Rhythm 2008;5:1015-8.

Bolanos M, Nazeran H, Haltiwanger E. Comparison of heart rate variability signal features derived from electrocardiography and photoplethysmography in healthy individuals. Conf Proc IEEE Eng Med Biol Soc 2006;2006:4289-94.

Zhang Z, Pi Z, Liu B. TROIKA: A general framework for heart rate monitoring using wrist-type photoplethysmographic signals during intensive physical exercise. IEEE Trans Biomed Eng 2015;62:522-31.

Millasseau SC, Kelly RP, Ritter JM, Chowienczyk PJ. Determination of age-related increases in large artery stiffness by digital pulse contour analysis. Clin Sci (Lond) 2002;103:371-7.

Elgendi M. On the analysis of fingertip photoplethysmogram signals. Curr Cardiol Rev 2012;8:14-25.

Formaggia L, Lamponi D, Tuveri M, Veneziani A. Numerical modeling of 1D arterial networks coupled with a lumped parameters description of the heart. Comput Methods Biomech Biomed Engin 2006;9:273-88.

Fu Y, Qiao A, Jin L. The influence of hemodynamics on the ulceration plaques of carotid artery stenosis. J Mech Med Biol 2015;15:1-14.

Van de Vosse FN. Mathematical modelling of the cardiovascular system. J Eng Math 2003;47:175-83.

Formaggia L, Quarteroni A, Veneziani A. Cardiovascular mathematics. In: Modeling and Simulation of the Circulatory System. Milan: Springer-Verlag; 2009.

Heldt T, Mukkamala R, Moody GB, Mark RG. CVSim: An open-source cardiovascular simulator for teaching and research. Open Pacing Electrophysiol Ther J 2010;3:45-54.

Shim EB, Sah JY, Youn CH. Mathematical modeling of cardiovascular system dynamics using a lumped parameter method. Jpn J Physiol 2004;54:545-53.

Abdi M, Karimi A, Navidbakhsh M. A lumped parameter mathematical model to analyze the effects of tachycardia and bradycardia on the cardiovascular system. Int J Numer Model Electron Netw Devices Fields 2015;28:346-57.

Wetterer E. Flow and pressure in the arterial system, their hemodynamic relationship, and the principles of their measurement. Minn Med 1954;37:77-86.

Westerhof N, Stergiopulos N, Noble IM. Snapshots of Hemodynamics an Aid for Clinical Research and Graduate Education. 2nd ed. New York: Springer; 2010. Available from: https://DOI:10.1007/978-1-4419-6363-5. [Last accessed on 2020 Dec].

Westerhof N, Bosman F, DeVries CJ, Noorder-Graaf A. Analogue studies of the human systemic arterial tree. J Biomech 1969;2:121-208.

Westerhof N, Elzinga G, Sipkema P. An artificial arterial system for pumping hearts. J Appl Physiol 1971;31:776-81.

Wang JJ, O'Brien AB, Shrive NG, Parker KH, Tyberg JV. Time-domain representation of ventricular-arterial coupling as a windkessel and wave system. Am J Physiol Heart Circ Physiol 2003;284:H1358-68.

Burattini R, Natalucci S. Complex and frequency-dependent compliance of viscoelastic windkessel resolves contradictions in elastic windkessels. Med Eng Phys 1998;20:502-14.

Stergiopulos N, Westerhof BE, Westerhof N. Total arterial inertance as the fourth element of the windkessel model. Am J Physiol 1999;276:H81-8.

Grant BJ, Paradowski LJ. Characterization of pulmonary arterial input impedance with lumped parameter models. Am J Physiol 1987;252:H585-93.

Burattini R, Gnudi G. Computer identification of models for the arterial tree input impedance: Comparison between two new simple models and first experimental results. Med Biol Eng Comput 1982;20:134-44.

Burattini R, Di Salvia PO. Development of systemic arterial mechanical properties from infancy to adulthood interpreted by four-element windkessel models. J Appl Physiol (1985) 2007;103:66-79.

Frasch HF, Kresh JY, Noordergraaf A. Two-port analysis of microcirculation: An extension of windkessel. Am J Physiol 1996;270:H376-85.

Milisic V, Quarteroni A. Analysis of lumped parameter models for blood flow simulations and their relation with 1D models. Math Mod Numer Anal 2004;38:613-32.

Formaggia L, Veneziani A. Reduced and Multiscale Models for the Human CVS. Technical Report, PoliMI, Milan; 2003.

Belarminus P, Florida Boa G. Factors affecting the occurrence of coronary heart disease in the general hospital of Waikabubak, Indonesia. KnE Life Sci 2022;2022:1004-12.

Suryati T, Suyitno S. Prevalence and risk factors of the ischemic heart diseases in Indonesia: A data analysis of Indonesia basic health research (Riskesdas) 2013. Public Health Indonesia 2020;6:138-44.

Castaneda D, Esparza A, Ghamari M, Soltanpur C, Nazeran H. A review on wearable photoplethysmography sensors and their potential future applications in health care. Int J Biosens Bioelectron 2018;4:195-202.

Bramwell JC, Hill A. Velocity of transmission of the pulse-wave. Lancet 1922;199:891-2.

Eliakim M, Sapoznikov D, Weinman J. Pulse wave velocity in healthy subjects and in patients with various disease states. Am Heart J 1971;82:448-57.

Elgendi M, Fletcher R, Liang Y, Howard N, Lovell NH, Abbott D, et al. The use of photoplethysmography for assesing hypertension. NPJ Digit Med 2019;2:60.

Simek J, Wichterle D, Melenovsky V, Malik J, Svacina S, Widimsky J. Second derivative of the finger arterial pressure waveform: An insight into dynamics of the peripheral arterial pressure pulse. Physiol Res 2005;54:505-13.

Millasseau SC, Guigui FG, Prasa J, Cockcroft JR, Ritter JM, Choweienczyk PJ. Non-invasive assessment of the digital volume pulse comparison with the peripheral pressure pulse. Hypertension 2000;36:952-7.

Elgendi M, Norton I, Brearley M, Abbott D, Schuurmans D. Systolic peak detection in acceleration photoplethysmograms measured from emergency responders in tropical conditions. PLoS ONE 2013;8:e76585.

Yousef Q. Assessment of atherosclerosis in erectile dysfunction subjects using second derivative of photoplethysmogram. Sci Res Essays 2012;7:2230-6.

Olufsen MS, Nadim A. On deriving lumped models for blood flow and pressure in the systemic arteries. Math Biosci Eng 2004;1:61-80.

Palladino JL, Ribeiro LC, Noordergraaf A. Human circulatory system model based on Frank's mechanism. Stud Health Technol Inform 2000;71:29-40.

Zahedi E, Chellappan K, Ali MA, Singh H. Analysis of the effect of ageing on rising edge characteristics of the photoplethysmogram using a modified Windkessel model. Cardiovasc Eng 2007;7:172-81.

Allen J, Murray A. Modelling the relationship between peripheral blood pressure and blood volume pulses using linear and neural network system identification techniques. Physiol Meas 1999;20:287-301.

Catanho M, Sinha M, Vijayan V. Model of Aortic Blood Flow Using the Windkessel. Mathematical Methods in Bioengineering Report; 2012. p. 1-15.

Ferreira A, Souza M. Three-section transmission-line arterial model for non-invasive assessment of vascular remodeling in primary hypertension. Biomed Signal Process Control 2009;4:2-6.

Safaei S, Bradley CP, Suresh V, Mithraratne K, Muller A, Ho H, et al. Roadmap for cardiovascular circulation model. J Physiol 2016;594:6909-28.

Shi Y, Lawford P, Hose R. Review of zero-D and 1-D models of blood flow in the cardiovascular system. Biomed Eng Online 2011;10:33.

Deepankaew R, Naiyanetr P. The Simulation of Cardiovascular System for Physiology Study. The 7th Biomedical Engineering International Conference; 2014. Available from: https://DOI: 10.1109/BMEiCON0.2014.7017430. [Last accessed on 2020 Dec].

Avolio AP. Multi-branched model of the human arterial system. Med Biol Eng Comput 1980;18:709-18.

Ghasemalizadeh O, Mirzaee M, Firoozabadi B. Modeling the human cardiovascular system and peristaltic motion of descending arteries using the lumped method. Internet J Bioeng 2012;3:1-11.


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