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Bulletin of Mathematical Biology

, Volume 76, Issue 6, pp 1306–1332 | Cite as

Stabilizing Control for a Pulsatile Cardiovascular Mathematical Model

  • Aurelio A. de los ReyesV
  • Eunok Jung
  • Franz Kappel
Original Article

Abstract

In this paper, we develop a pulsatile model for the cardiovascular system which describes the reaction of this system to a submaximal constant workload imposed on a person at a bicycle ergometer test after a period of rest. Furthermore, the model should allow to use measurements for the pulsatile pressure in fingertips which provide information on the diastolic and the systolic pressure for parameter estimation. Based on the assumption that the baroreceptor loop is the essential control loop in this case, we design a stabilizing feedback control for the pulsatile model which is obtained by solving a linear-quadratic regulator problem for the linearization of a non-pulsatile counterpart of the pulsatile model. We also investigate the behavior of the model with respect to changes in the weight of the term in the cost functional for the linear-quadratic regulator problem which penalizes the deviation of the momentary pressure in the aorta from the pressure at the stationary situation which should be obtained.

Keywords

Cardiovascular model Baroreceptor loop Linear-quadratic regulator problem Stabilizing control 

Mathematics Subject Classification

92C30 49J15 49K15 

Notes

Acknowledgments

Jung’s work was supported by Konkuk University Research Grant in 2012. A. de los Reyes was supported by an ASEA-UNINET PhD-Technology Grant (administered by the Austrian Academic Exchange Service (OeAD)), by the University of the Philippines and by Konkuk University.

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Copyright information

© Society for Mathematical Biology 2014

Authors and Affiliations

  • Aurelio A. de los ReyesV
    • 1
    • 2
    • 3
  • Eunok Jung
    • 1
  • Franz Kappel
    • 4
  1. 1.Department of MathematicsKonkuk UniversitySeoulRepublic of Korea
  2. 2.Institute of MathematicsC.P. Garcia St., U.P. CampusQuezon CityPhilippines
  3. 3.Renal Research InstituteNew YorkUSA
  4. 4.Institute for Mathematics and Scientific ComputingUniversity of GrazGrazAustria

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