Cardiovascular Engineering

, Volume 8, Issue 2, pp 73–87 | Cite as

Modeling Heart Rate Regulation—Part I: Sit-to-stand Versus Head-up Tilt

  • Mette S. Olufsen
  • April V. Alston
  • Hien T. Tran
  • Johnny T. Ottesen
  • Vera Novak
Original Paper


In this study we describe a model predicting heart rate regulation during postural change from sitting to standing and during head-up tilt in five healthy elderly adults. The model uses blood pressure as an input to predict baroreflex firing-rate, which in turn is used to predict efferent parasympathetic and sympathetic outflows. The model also includes the combined effects of vestibular and central command stimulation of muscle sympathetic nerve activity, which is increased at the onset of postural change. Concentrations of acetylcholine and noradrenaline, predicted as functions of sympathetic and parasympathetic outflow, are then used to estimate the heart rate response. Dynamics of the heart rate and the baroreflex firing rate are modeled using a system of coupled ordinary delay differential equations with 17 parameters. We have derived sensitivity equations and ranked sensitivities of all parameters with respect to all state variables in our model. Using this model we show that during head-up tilt, the baseline firing-rate is larger than during sit-to-stand and that the combined effect of vestibular and central command stimulation of muscle sympathetic nerve activity is less pronounced during head-up tilt than during sit-to-stand.


Mathematical modeling Heart rate regulation Sensitivity analysis 



Drs. Olufsen and Tran were supported by the National Science Foundation (OISE) #0437037. In addition Dr. Tran was supported by a grant from the National Institue of Health (NIH) NIH/NIAID #9 RO1 AI071915-05. This work was a response to discussion supported by the American Institute of Mathematics in Palo Alto, CA. Data collection at the SAFE Laboratory, Beth Israel Deaconess Medical Center, Boston, MA was supported by an American Diabetes Association Grant to 1-06-CR-25, an NIH-NINDS 1R01-NS045745-01A21 to V. Novak, an NIH Older American Independence Center Grant 2P60 AG08812 and a General Clinical Research Center Grant MO1-RR01032. Alston, AV was partially supported by NIH-NIA (1 T32 AG023480-01) BIDMC/Harvard Translational research in Aging Training Program traineeship.


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Mette S. Olufsen
    • 1
  • April V. Alston
    • 1
  • Hien T. Tran
    • 1
  • Johnny T. Ottesen
    • 2
  • Vera Novak
    • 3
  1. 1.Department of MathematicsNorth Carolina State UniversityRaleighUSA
  2. 2.Department of Mathematics and PhysicsRoskilde UniversityRoskildeDenmark
  3. 3.Department of Gerontology, Beth Israel Deaconess Medical CenterHarvard Medical SchoolBostonUSA

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