Study on Fractional Order Arterial Windkessel Model Using Optimization Method

Abstract

In biomedical sciences, the identification of cardiovascular diseases is more challenging and it is detected only after they become severe due to the delay in symptoms. On the other hand, experimentation with the cardiovascular system is unsafe and hence it is necessary to develop a cardiovascular system model which helps to predict the abnormalities in the early stage itself. In the existing arterial Windkessel model, the viscoelasticity characteristics are not considered, leading to error in the model and hence false prediction is unavoidable. To incorporate this characteristic, an improved fractional order Windkessel model is proposed. In this paper, fractional order is introduced in the existing 2-element, 3-element and 4-element Windkessel models. Further, a fmincon solver is used to optimize the model parameters and fractionality of the differential equation by minimizing the error between the clinical data and the model output. The simulation results indicate that the fractional order models provide less integral square error than the existing integer order Windkessel models. In specific, the fractional order 4-element Windkessel model provides better closeness to the clinical data than other fractional order models. This model is further used to study the behaviour of abnormalities (i) atherosclerosis and (ii) arterial stiffness.

KEYWORDS:

• Windkessel model
• Fractional order model
• Integer order model
• Fmincon solver

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

V. L. Resmi

V L Resmi received her BTech degree in electrical and electronics engineering from Rajiv Gandhi Institute of Technology, Kottayam, Kerala, in 2013; and MTech degree in control systems from the Department of Avionics, Indian Institute of Space Science and Technology (IIST), Trivandrum in 2016. She worked as a senior project fellow/engineer at IIST and Sree Chitra Tirunal Institute for Medical Sciences and Technology during 2016-2018 handling (i) controller design for micro actuator, and (ii) development of test circuit for hydrocephalus shunt respectively. In 2019, she joined as a research student at IIST and pursuing research in the area of fractional order modeling and control of cardiovascular system. Her area of interest includes control system design, adaptive control, and modeling of biological systems. Email: [email protected]

N. Selvaganesan

N Selvaganesan received his BE in electrical and electronics engineering, ME in control systems and PhD in adaptive control system from Mepco Schlenk Engineering College, Sivakasi; PSG College of Technology, Coimbatore; and MIT Campus, Anna University, Chennai in the year 1997, 2000, and 2005, respectively. He has more than 20 years of research and teaching experience (MIT Campus, Anna University, Chennai, Pondicherry Engineering College and Indian Institute of Space Science and Technology (IIST), Trivandrum). Currently, he is working as a professor and head, Department of Avionics in IIST-Trivandrum. He served many administrative positions at IIST and other institutions/universities which include Head, Department of Avionics, IIST during 2013-16. He has 42 peer reviewed international journal papers and 48 conference papers to his research credit. He has completed three research projects sponsored by ISRO and DSTE in the field of modeling and control. His current research direction is towards health monitoring and disease diagnosis of astronauts in space. He was involved in many editorial activities/reviews in various international journals/conferences, and workshops (Control System Design-CSD). His areas of interest include CSD, biological modeling, fault diagnosis, and fractional order control. He is a senior member of IEEE.