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Development of Patient Specific Cardiovascular Models Predicting Dynamics in Response to Orthostatic Stress Challenges

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Mathematical Modeling and Validation in Physiology

Part of the book series: Lecture Notes in Mathematics ((LNMBIOS,volume 2064))

Abstract

Physiological realistic models of the controlled cardiovascular system are constructed and validated against clinical data. Special attention is paid to the control of blood pressure, cerebral blood flow velocity, and heart rate during postural challenges, including sit-to-stand and head-up tilt. This study describes development of patient specific models, and how sensitivity analysis and nonlinear optimization methods can be used to predict patient specific characteristics when analyzed using experimental data. Finally, we discuss how a given model can be used to understand physiological changes between groups of individuals and how to use modeling to identify biomarkers.

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Notes

  1. 1.

    We note, that depending on the QR factorization algorithm used a different permutation vector may be obtained. The importance of this step is to obtain a parameter set that gives rise to a well-conditioned Jacobian, that can be inverted allowing unique estimation of the selected model parameters. The exact parameter set obtained should include parameters that make sense to estimate in terms of the physiological system studied. In other words, the sub-set of parameters may not be unique, thus care must be taken in analyzing the exact parameter values chosen. Subset selection is further discussed in Chaps. 2, 3 and 11.

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Acknowledgements

The authors wish to thank graduate students involved with this project including Laura Ellwein, Department of Biomedical Engineering, Marquette University, Scott Pope, SAS Corp, Raleigh, NC, April Alston, Department of Mathematics, NCSU, and numerous undergraduate students participating in research and REU program at NCSU. Furthermore, authors would like to thank Hien Tran and Tim Kelley, Department of Mathematics, NCSU. The work by Mette Olufsen was supported in part by NSF-DMS grant # 0616597 and NSF-OISE grant # 0437037. V. Novak, director of the SAFE Laboratory at BIMDC was supported by NIH-NIA Harvard Older American Independence Center 2P60 AG08812-11A1, Core B.

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Authors and Affiliations

  1. Department of Science, Systems, and Models, Roskilde University, 4000, Roskilde, Denmark

    Johnny T. Ottesen

  2. Division of Gerontology, Beth Israel Deaconess Medical Center and Harvard University, Boston, MA, 02215, USA

    Vera Novak

  3. Center for Research in Scientific Computing and Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA

    Mette S. Olufsen

Authors
  1. Johnny T. Ottesen
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  2. Vera Novak
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  3. Mette S. Olufsen
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Corresponding author

Correspondence to Johnny T. Ottesen .

Editor information

Editors and Affiliations

  1. Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, Graz, 8010, Austria

    Jerry J. Batzel

  2. College of Sciences, Department of Mathematics, King Saud University, King Khalid Road, Diriyah Campus, Riyadh, 11451, Saudi Arabia

    Mostafa Bachar

  3. Institute for Mathematics, and Scientific Computing, University of Graz, Heinrichstrasse 36, Graz, 8010, Austria

    Franz Kappel

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Ottesen, J.T., Novak, V., Olufsen, M.S. (2013). Development of Patient Specific Cardiovascular Models Predicting Dynamics in Response to Orthostatic Stress Challenges. In: Batzel, J., Bachar, M., Kappel, F. (eds) Mathematical Modeling and Validation in Physiology. Lecture Notes in Mathematics(), vol 2064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32882-4_10

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