SYNTHESIS OF STATE SPACE MODEL FOR HUMAN CARDIO VASCULAR SYSTEM USING BOND GRAPH APPROACH

Abstract

Cardio Vascular System (CVS) is a closed circulatory system responsible to provide the oxygenated blood to all the parts of the body and to collect the deoxygenated blood from all the parts of the body. It mainly consists of the heart, the blood vessels and the blood. It is one of the most important systems of the body and the heart being the chief organ; pumping the blood which carry all the vital nutrients to each and every cell of the body. The pumping action of the heart is regulated by a feedback mechanism called the baroreflex mechanism. Cardio Vascular diseases have a major impact worldwide; more than 55% of the total deaths in the world are due to malfunctioning of the CVS. Cardiovascular disease includes conditions that affect the structure or function of the heart, such as, coronary artery disease, heart attack, abnormal heart rhythms arrhythmias, heart failure, heart valve disease, congenital heart disease, heart muscle disease and many others too. Depending on the different malfunction conditions of the heart, artificial pumps and other invasive surgeries are proposed. The heart is a very vital organ and is also not easily accessible as it is located inside the ribcage. Due to this fact, the experimental monitoring of the functioning of the heart assist devices is impossible and is also life threatening. Therefore for proper designing of the required assistive devices, the very first requirement is the availability of proper mathematical model of the system which can clearly portrays the hemodynamic of the heart and can serve as an important test bed against which estimation and identification algorithms can be evaluated and controlled. A significant amount of valuable research work has already been undertaken regarding the mathematical modeling of the CVS and the baroreflex system. All these models cover many of the physiological characteristics but still there is a space for new strategies and improvement. The cardiac activity includes mechanical, hydraulic, chemical and electrical events; the modeling of such a multi domain system requires a unified modeling approach. The other limitations of the existing mathematical models may include the lack of cause effect relationship, complexity due to separate feedback loops, absence of fault diagnosis at element level etc. To overcome the above stated shortcomings in the existing models, a Bond Graph modeling approach to model the CVS and the baroreflex system has been proposed in this dissertation. The Bond Graph has proved to be an effective methodology for modeling the systems having subsystems of different physical nature. The benefit of using the Bond Graph for modeling is the ability to represent the circuits using flow, effort and energy conservation elements providing cause effect relationship. The fault diagnosis at element level also became possible. Consequently, in the Bond Graph technique there is a useful distinction between the reciprocal flow of influence inherent in the dynamics of the system and the feedback that arise by the design of system and therefore eliminates the complexity due to the separate feed back loops. Bond Graph modeling approach for the CVS was also proposed and presented by some researchers and had added remarkable contributions, but none of them analyzed the whole CVS on element basis and no idea was given for finding out the state space representation of the CVS using the cause-effect relation property of the Bond Graph. In this thesis, in addition to the complete Bond Graph model of the CVS and the baroreceptors, the time varying state space is also generated for these systems. The proposed state space model from the Bond Graph provides information about the internal state variables. The internal state variables are the smallest possible subset of the system that can represent the entire state of the system at any given time. Due to the in-depth analysis on element level and the information about the internal state variable the proposed model can provide a better platform for the CVS diagnostics, therapy selection, surgery and interventions.