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Zbl 0799.92002
Kappel, F.; Peer, R.O.
A mathematical model for fundamental regulation processes in the cardiovascular system. (English)
[J] J. Math. Biol. 31, No.6, 611-631 (1993). ISSN 0303-6812; ISSN 1432-1416/e

The authors present a model for the basic control mechanisms in the cardiovascular system (CVS) under the assumption that the control is optimal with respect to the quadratic criterion. The model is based on the {\it F. S. Grodins} compartmental model [Control theory and biological systems. Columbia Univ./N.Y. (1963)] in which the change of heart rate with respect to time is chosen as a control variable. The authors assume that the basic feedback loop is a baroreceptor loop and that only the pressure in the arterial compartment is observed. They propose to reconstruct the state variables by using a dynamic observer.\par For the obtained nonlinear control problem the authors prove some properties of the solution and its relation to the LQ problem associated with it. The feedback law for the LQ problem is found to stabilize locally the nonlinear control system and is used to approximate the nonlinear solution. The numerical experiments are based on the Grodins' model parameters as well as on one found by identification and have been performed on a number of computer systems. The simulation results show the agreement with the corresponding data and indicate that the overall regulation in response to the activity test can be done through a single control variable.
[A.Šwierniak (Gliwice)]

MSC 2000:: *92C30 Physiology
49N70 Differential games
49N75 Pursuit and evasion games
92C50 Medical appl. of mathematical biology
93C10 Nonlinear control systems
93C95 Appl. of control theory

Keywords: regulation of heart rate; cardiovascular system; quadratic criterion; compartmental model; change of heart rate; feedback loop; baroreceptor loop; pressure; arterial compartment; nonlinear control problem; LQ problem; Grodins' model; simulation results

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Zentralblatt MATH Berlin [Germany]