Mathematical Biosciences and Engineering, 2009, 6(1): 93-115. doi: 10.3934/mbe.2009.6.93.

Primary: 92C30, 92C35, 92C50, 65L09; Secondary: 93B40

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Estimation and identification of parameters in a lumped cerebrovascular model

1. Department of Mathematics, North Carolina State University, Campus Box 8205, Raleigh, NC 27695
2. Olin Engineering Center, Marquette University, 1515 West Wisconsin Ave, Room 206, Milwaukee, WI 53233
3. Department of Mathematics, University of Utah, 155 S 1400 E, Salt Lake City, UT 84112
4. Harvard Medical School and Beth Israel Deaconess Medical Center Division of Gerontology, 110 Francis Street LM0B Suite 1b, Boston, MA 02215

This study shows how sensitivity analysis and subset selection can be employed in a cardiovascular model to estimate total systemic resistance, cerebrovascular resistance, arterial compliance, and time for peak systolic ventricular pressure for healthy young and elderly subjects. These quantities are parameters in a simple lumped parameter model that predicts pressure and flow in the systemic circulation. The model is combined with experimental measurements of blood flow velocity from the middle cerebral artery and arterial finger blood pressure. To estimate the model parameters we use nonlinear optimization combined with sensitivity analysis and subset selection. Sensitivity analysis allows us to rank model parameters from the most to the least sensitive with respect to the output states (cerebral blood flow velocity and arterial blood pressure). Subset selection allows us to identify a set of independent candidate parameters that can be estimated given limited data. Analyses of output from both methods allow us to identify five independent sensitive parameters that can be estimated given the data. Results show that with the advance of age total systemic and cerebral resistances increase, that time for peak systolic ventricular pressure is increases, and that arterial compliance is reduced. Thus, the method discussed in this study provides a new methodology to extract clinical markers that cannot easily be assessed noninvasively.
  Figure/Table
  Supplementary
  Article Metrics

Keywords cerebrovascular resistance; subset selection; systemic resistance; parameter estimation; sensitivity analysis; cardiovascular modeling

Citation: Scott R. Pope, Laura M. Ellwein, Cheryl L. Zapata, Vera Novak, C. T. Kelley, Mette S. Olufsen. Estimation and identification of parameters in a lumped cerebrovascular model. Mathematical Biosciences and Engineering, 2009, 6(1): 93-115. doi: 10.3934/mbe.2009.6.93

 

This article has been cited by

  • 1. I. C. F. Ipsen, C. T. Kelley, S. R. Pope, Rank-Deficient Nonlinear Least Squares Problems and Subset Selection, SIAM Journal on Numerical Analysis, 2011, 49, 3, 1244, 10.1137/090780882
  • 2. Christopher J. Arthurs, Kevin D. Lau, Kaleab N. Asrress, Simon R. Redwood, C. Alberto Figueroa, A mathematical model of coronary blood flow control: simulation of patient-specific three-dimensional hemodynamics during exercise, American Journal of Physiology-Heart and Circulatory Physiology, 2016, 310, 9, H1242, 10.1152/ajpheart.00517.2015
  • 3. R. Gul, C. Schütte, S. Bernhard, Mathematical modeling and sensitivity analysis of arterial anastomosis in the arm, Applied Mathematical Modelling, 2016, 40, 17-18, 7724, 10.1016/j.apm.2016.03.041
  • 4. Sebastián Acosta, Daniel J. Penny, Ken M. Brady, Craig G. Rusin, An effective model of cerebrovascular pressure reactivity and blood flow autoregulation, Microvascular Research, 2018, 115, 34, 10.1016/j.mvr.2017.08.006
  • 5. Fuyou Liang, Koichi Sughimoto, Kozo Matsuo, Hao Liu, Shu Takagi, Patient-specific assessment of cardiovascular function by combination of clinical data and computational model with applications to patients undergoing Fontan operation, International Journal for Numerical Methods in Biomedical Engineering, 2014, 30, 10, 1000, 10.1002/cnm.2641
  • 6. C.A.D. Leguy, E.M.H. Bosboom, A.S.Z. Belloum, A.P.G. Hoeks, F.N. van de Vosse, Global sensitivity analysis of a wave propagation model for arm arteries, Medical Engineering & Physics, 2011, 33, 8, 1008, 10.1016/j.medengphy.2011.04.003
  • 7. Nicole M. Panza, Andrew A. Wright, James F. Selgrade, A delay differential equation model of follicle waves in women, Journal of Biological Dynamics, 2016, 10, 1, 200, 10.1080/17513758.2015.1115564
  • 8. Brett Matzuka, Jesper Mehlsen, Hien Tran, Mette Sofie Olufsen, Using Kalman Filtering to Predict Time-Varying Parameters in a Model Predicting Baroreflex Regulation During Head-Up Tilt, IEEE Transactions on Biomedical Engineering, 2015, 62, 8, 1992, 10.1109/TBME.2015.2409211
  • 9. Nitin A. Krishna, Hannah M. Pennington, Canaan D. Coppola, Marisa C. Eisenberg, Richard C. Schugart, Connecting Local and Global Sensitivities in a Mathematical Model for Wound Healing, Bulletin of Mathematical Biology, 2015, 77, 12, 2294, 10.1007/s11538-015-0123-3
  • 10. Leszek Pstras, Karl Thomaseth, Jacek Waniewski, Italo Balzani, Federico Bellavere, Mathematical modelling of cardiovascular response to the Valsalva manoeuvre, Mathematical Medicine and Biology, 2016, dqw008, 10.1093/imammb/dqw008
  • 11. Panagiotes A. Voltairas, Antonios Charalambopoulos, Dimitrios I. Fotiadis, Lambros K. Michalis, A quasi-lumped model for the peripheral distortion of the arterial pulse, Mathematical Biosciences and Engineering, 2011, 9, 1, 175, 10.3934/mbe.2012.9.175
  • 12. Antoine Pironet, Thomas Desaive, J. Geoffrey Chase, Philippe Morimont, Pierre C. Dauby, Model-Based Computation of Total Stressed Blood Volume from a Preload Reduction Experiment, IFAC Proceedings Volumes, 2014, 47, 3, 5641, 10.3182/20140824-6-ZA-1003.00548
  • 13. Gregory Arbia, Chiara Corsini, Catriona Baker, Giancarlo Pennati, Tain-Yen Hsia, Irene E. Vignon-Clementel, Pulmonary Hemodynamics Simulations Before Stage 2 Single Ventricle Surgery: Patient-Specific Parameter Identification and Clinical Data Assessment, Cardiovascular Engineering and Technology, 2015, 6, 3, 268, 10.1007/s13239-015-0212-3
  • 14. R. Lal, F. Nicoud, E. Le Bars, J. Deverdun, F. Molino, V. Costalat, B. Mohammadi, Non Invasive Blood Flow Features Estimation in Cerebral Arteries from Uncertain Medical Data, Annals of Biomedical Engineering, 2017, 45, 11, 2574, 10.1007/s10439-017-1904-7
  • 15. Adam Mahdi, Jacob Sturdy, Johnny T. Ottesen, Mette S. Olufsen, Julia C. Arciero, Modeling the Afferent Dynamics of the Baroreflex Control System, PLoS Computational Biology, 2013, 9, 12, e1003384, 10.1371/journal.pcbi.1003384
  • 16. Aurelio A. de los Reyes, Eunok Jung, Franz Kappel, Stabilizing Control for a Pulsatile Cardiovascular Mathematical Model, Bulletin of Mathematical Biology, 2014, 76, 6, 1306, 10.1007/s11538-014-9958-2
  • 17. Desmond Dillon-Murphy, Alia Noorani, David Nordsletten, C. Alberto Figueroa, Multi-modality image-based computational analysis of haemodynamics in aortic dissection, Biomechanics and Modeling in Mechanobiology, 2016, 15, 4, 857, 10.1007/s10237-015-0729-2
  • 18. Helen Moore, How to mathematically optimize drug regimens using optimal control, Journal of Pharmacokinetics and Pharmacodynamics, 2018, 45, 1, 127, 10.1007/s10928-018-9568-y
  • 19. G. Mulder, A. Marzo, A. C. B. Bogaerds, S. C. Coley, P. Rongen, D. R. Hose, F. N. van de Vosse, Patient-Specific Modeling of Cerebral Blood Flow: Geometrical Variations in a 1D Model, Cardiovascular Engineering and Technology, 2011, 2, 4, 334, 10.1007/s13239-011-0060-8
  • 20. Maria-Veronica Ciocanel, Steffen S. Docken, Rebecca E. Gasper, Caron Dean, Brian E. Carlson, Mette S. Olufsen, Cardiovascular regulation in response to multiple hemorrhages: analysis and parameter estimation, Biological Cybernetics, 2018, 10.1007/s00422-018-0781-y
  • 21. Christian Haargaard Olsen, Johnny T. Ottesen, Ralph C. Smith, Mette S. Olufsen, Parameter subset selection techniques for problems in mathematical biology, Biological Cybernetics, 2018, 10.1007/s00422-018-0784-8
  • 22. Maxwell Lewis Neal, , Patient-Specific Modeling of the Cardiovascular System, 2010, Chapter 5, 81, 10.1007/978-1-4419-6691-9_5
  • 23. Johnny T. Ottesen, Vera Novak, Mette S. Olufsen, , Mathematical Modeling and Validation in Physiology, 2013, Chapter 10, 177, 10.1007/978-3-642-32882-4_10
  • 24. Nakeya D. Williams, Renee Brady, Steven Gilmore, Pierre Gremaud, Hien T. Tran, Johnny T. Ottesen, Jesper Mehlsen, Mette S. Olufsen, Cardiovascular dynamics during head-up tilt assessed via pulsatile and non-pulsatile models, Journal of Mathematical Biology, 2019, 10.1007/s00285-019-01386-9
  • 25. E. Benjamin Randall, Anna Billeschou, Louise S. Brinth, Jesper Mehlsen, Mette S. Olufsen, A model-based analysis of autonomic nervous function in response to the Valsalva maneuver, Journal of Applied Physiology, 2019, 10.1152/japplphysiol.00015.2019
  • 26. Salwa Mansour, Édouard Canot, Mohamad Muhieddine, Identification of the Thermophysical Properties of the Soil by Inverse Problem, Journal of Heat Transfer, 2016, 138, 9, 10.1115/1.4032947
  • 27. Mitchel J. Colebank, M. Umar Qureshi, Mette S. Olufsen, Sensitivity analysis and uncertainty quantification of 1‐D models of pulmonary hemodynamics in mice under control and hypertensive conditions, International Journal for Numerical Methods in Biomedical Engineering, 2019, 10.1002/cnm.3242
  • 28. Amanda L. Colunga, Karam G. Kim, N. Payton Woodall, Todd F. Dardas, John H. Gennari, Mette S. Olufsen, Brian E. Carlson, Deep phenotyping of cardiac function in heart transplant patients using cardiovascular system models, The Journal of Physiology, 2020, 10.1113/JP279393

Reader Comments

your name: *   your email: *  

Copyright Info: 2009, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved