Biological Cybernetics

, Volume 113, Issue 1–2, pp 149–159 | Cite as

An optimal control approach for blood pressure regulation during head-up tilt

  • Nakeya D. Williams
  • Jesper Mehlsen
  • Hien T. Tran
  • Mette S. OlufsenEmail author
Original Article


This paper presents an optimal control approach to modeling effects of cardiovascular regulation during head-up tilt (HUT). Many patients who suffer from dizziness or light-headedness are administered a head-up tilt test to explore potential deficits within the autonomic control system, which maintains the cardiovascular system at homeostasis. This system is complex and difficult to study in vivo, and thus we propose to use mathematical modeling to achieve a better understanding of cardiovascular regulation during HUT. In particular, we show the feasibility of using optimal control theory to compute physiological control variables, vascular resistance and cardiac contractility, quantities that cannot be measured directly, but which are useful to assess the state of the cardiovascular system. A non-pulsatile lumped parameter model together with pseudo- and clinical data are utilized in the optimal control problem formulation. Results show that the optimal control approach can predict time-varying quantities regulated by the cardiovascular control system. Our results compare favorable to our previous study using a piecewise linear spline approach, less a priori knowledge is needed, and results were obtained at a significantly lower computational cost.


Cardiovascular dynamics modeling Head-up tilt Non-pulsatile model Orthostatic intolerance Optimal control 


Compliance with ethical standards


Williams and Olufsen were supported in part by the virtual rat physiology project under grant NIH-NIGMS #1P50GM094503. Tran and Olufsen were supported by NSF under the grant NSF/DMS #1022688. Tran was also supported in part by NIAID under grant NIAID 9R01AI071915. Williams was also supported form the Department of Mathematical Sciences of the United States Military Academy at West Point. This research was performed while Williams held an NRC Research Associateship award at the Army Research Lab.

Conflict of interest

The authors declare that they have no conflicts of interest.

Ethical approval

All applicable international, national, and/or institutional guidelines for the care and use of animals were followed. All procedures performed in studies involving animals were in accordance with the ethical standards of the institution at which the studies were conducted.


The datasets generated during and/or analyzed during the current study are available on request from the corresponding author.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Nakeya D. Williams
    • 1
  • Jesper Mehlsen
    • 2
  • Hien T. Tran
    • 3
  • Mette S. Olufsen
    • 3
    Email author
  1. 1.United States Military AcademyNew YorkUSA
  2. 2.Bispebjerg and Frederiksberg HospitalFrederiksbergDenmark
  3. 3.NC State UniversityRaleighUSA

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