A Particle Filter Based Framework for the Prognosis of Atherosclerosis via Lumped Cardiovascular Modeling



Karan Jain Arijit Guha Amit Patra


Atherosclerosis refers to the plaque deposition in the arteries that can eventually lead to any of the three cardiovascular diseases, namely, heart attack, stroke, or peripheral vascular disease, depending upon the site of the blockage in the human arterial network. This work attempts to prognose this pathological condition via lumped cardiovascular modeling while utilizing the radial artery blood pressure measurements. To
achieve this, the cardiovascular system has been modeled as a third order non-linear system with explicit emphasis on the systemic circulation. The parameters of the model are estimated using non-linear least squares estimation technique by minimizing the error between the measured and the estimated arterial pressure waveforms. The arterial pressure is found to be sensitive to three of the model parameters, namely, arterial compliance, systemic vascular resistance, and the peak cardiac muscle elastance. Based on the analysis, a growth model of systolic blood pressure is developed as a function of the arterial blockage. A particle filter based mathematical framework is then utilized to predict the time it would take to reach the stage of critical arterial blockage that may cause heart attacks.

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particle filter, Atherosclerosis, lumped cardiovascular model, radial artery blood pressure, vascular resistance, arterial compliance, non-linear least squares estimation

Abdolrazaghi, M., Navidbakhsh, M., & Hassani, K. (2010). Mathematical modelling and electrical analog equivalent of the human cardiovascular system. Cardiovascular Engineering, 10(2), 45–51.
American Heart Association, A. (2014). Understanding blood pressure readings.
Arulampalam, M. S., Maskell, S., Gordon, N., & Clapp, T. (2002). A tutorial on particle filters for online nonlinear/non-gaussian bayesian tracking. IEEE
Transactions on Signal Processing, 50(2), 174–188.
Assante, R., Acampa, W., Zampella, E., Arumugam, P., Nappi, C., Gaudieri, V., . . . Tonge, C. M. (2017). Prognostic value of atherosclerotic burden and coronary vascular function in patients with suspected coronary artery disease. European Journal of Nuclear Medicine and Molecular Imaging, 44(13), 2290–2298.
Batzel, J. J., Bachar, M., & Kappel, F. (2012). Mathematical Modeling and Validation in Physiology: Applications to the Cardiovascular and Respiratory Systems (Vol. 2064). Springer.
Calais, F., O¨ stman, M. E., Hedberg, P., Rosenblad, A., Leppert, J., & Fr¨obert, O. (2018). Incremental prognostic value of coronary and systemic atherosclerosis after myocardial infarction. International Journal of Cardiology, 261, 6–11.
Farrar, C. R., & Lieven, N. A. (2007). Damage prognosis: the future of structural health monitoring. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 365(1851), 623–632.
Guha, A., & Patra, A. (2018). State of health estimation of lithium-ion batteries using capacity fade and internal resistance growth models. IEEE Transactions on Transportation Electrification, 4(1), 135-146.
Hao, W., & Friedman, A. (2014). The LDL-HDL profile determines the risk of atherosclerosis: A mathematical model. PloS One, 9(3), e90497.
He, W., Williard, N., Osterman, M., & Pecht, M. (2011). Prognostics of lithium-ion batteries based on Dempster–Shafer theory and the Bayesian Monte Carlo method. Journal of Power Sources, 196(23), 10314–10321.
Jain, K., Maka, S., & Patra, A. (2018). Modeling of cardiovascular circulation for the early detection of coronary arterial blockage. Mathematical Biosciences, 304, 79–88.
Jain, K., Patra, A., & Maka, S. (2018). Modeling of the human cardiovascular system for detection of atherosclerosis. IFAC-PapersOnLine, 51(15), 545 - 550.
Mussleman, M., Gates, D., & Djurdjanovic, D. (2016). A system-based approach to monitoring the performance of a human neuromusculoskeletal system. International Journal of Prognostics and Health Management, 7, 14.
Saha, B., Goebel, K., & Christophersen, J. (2009). Comparison of prognostic algorithms for estimating remaining useful life of batteries. Transactions of the Institute of Measurement and Control, 31(3-4), 293–308.
Sankararaman, S., Ling, Y., Shantz, C., & Mahadevan, S. (2011). Uncertainty quantification in fatigue crack growth prognosis. International Journal of Prognostics and Health Management, 2(1), 15.
Suga, H., & Sagawa, K. (1974). Instantaneous pressurevolume relationships and their ratio in the excised, supported canine left ventricle. Journal of The American Heart Association, 35, 117-126.
WebMD. (2016). High blood pressure and atherosclerosis. Retrieved 2018-05-20, from https://www.webmd.com/hypertension-high-blood
Westerhof, N., Lankhaar, J.-W., & Westerhof, B. E. (2009). The arterial windkessel. Medical & Biological Engineering & Computing, 47(2), 131–141.
Williams, N. D., Wind-Willassen, O., Wright, A. A., Mehlsen, J., Ottesen, J. T., & Olufsen, M. S. (2014). Patient-specific modelling of head-up tilt. Mathematical Medicine and Biology: A Journal of the IMA, 31(4), 365–392.
Yu, Y. C., Boston, J. R., Simaan, M. A., & Antaki, J. F. (1998). Estimation of systemic vascular bed parameters for artificial heart control. IEEE Transactions on Automatic Control, 43(6), 765–778.
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