Dynamic model cardiovascular system

Regulation of CBF is a complex dynamical process and remains relatively constant over a wide range of perfusion pressure via a variety of feedback control mechanisms, such as metabolic, myogenic, and neurally mediated changes in cerebrovascular impedance respond to changes in perfusion pressure. The contribution to the overall CBF regulation by different areas of the brain is modeled by the statistics of the fractional derivative parameter, which determines the multifractal nature of the time series. The source of the multifractality is over and above that produced by the cardiovascular system. 

Using physical principles and applying engineering techniques, we can model the cardiovascular systems of different mammals. However, the complexity of the beat-to-beat dynamic performance of the heart and its interaction with the vascular systems makes this a major challenge. This complexity can be substantially reduced when we first impose appropriate biological scaling laws and identify relevant invariant features that appear across species in the mammalian class. 

An engineering approach to the cardiovascular system necessitates clearly defined rules as well-as quantification of physiological parameters. A quantitative description of a dynamic three dimensional model of the heart presents a major mathematical problem. It requires a good definition of the various laws of... 

Proc Symp on Appl Comput Methods, pp 477-486 Pao YC, Mayendra KK, Padiyar RR, Ritman EL (1980) Derivation of myocardial fiber stiffness equation based on theory of laminated composite. Trans ASME 103 202-259 Parmley WW, Tyberg JV (1976) Determination of myocardial oxygen demand. Prog Cardiol 5 19-36 Pierce WH (1981) Body forces and pressures in elastic models of the myocardium. Biophys J 34 35-39 Pollack OH, Krueger JW (1978) Myocardial sarcomere mechanics some parallels with skeletal muscle. In Baan Y, Noordegraaf A, Raines J (eds) Cardiovascular System Dynamics, Cambridge, pp 3-10... 

So far, chemical processes have been discussed as well as fermentation reactors. These systems can be characterized by the fact that there are usually no discontinuities in the model equations. In physiological systems, however, there is often a threshold value that has to be succeeded before certain phenomena take place. This causes a threshold non-linearity in the model and therefore these systems can be analyzed well through simulation but theoretically they are difficult to analyze. It is not the purpose of this chapter to discuss different physiological models the two systems that will be selected for illustration of system dynamics are the modeling of glucose-insulin dynamics and cardiovascular modeling approaches. 

Another approach to cardiovascular modeling uses the same dynamic model for the cardiovascular system. In addition, a rather simple model is used for the baroreflex (Akay, 2001 Cavalcanti and Belardinelli, 1996). This latter model is responsible for the spontaneous fluctuations that occur in heart rate and heart pressure. Non-linear relationships are assumed between cardiac period (s) and blood pressure (mmHg). In addition, a non-linear relationship between stoke volume (ml) and blood pressure can be assumed (mmHg). The relationship between cardiac period T and blood pressure P can be given by (Cavalcanti and Belardinelli, 1996) ... 

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