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Cited by 106Control Systems and IdentificationHeart Rate Variability and Autonomic ControlStatistical and numerical algorithms

A practical approach to parameter estimation applied to model predicting heart rate regulation

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Olufsen, Mette S., Ottesen, Johnny T.·2013·Journal of Mathematical Biology
DOI 10.1007/s00285-012-0535-8PMC PMC3526689
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Abstract

Mathematical models have long been used for prediction of dynamics in biological systems. Recently, several efforts have been made to render these models patient specific. One way to do so is to employ techniques to estimate parameters that enable model based prediction of observed quantities. Knowledge of variation in parameters within and between groups of subjects have potential to provide insight into biological function. Often it is not possible to estimate all parameters in a given model, in particular if the model is complex and the data is sparse. However, it may be possible to estimate a subset of model parameters reducing the complexity of the problem. In this study, we compare three methods that allow identification of parameter subsets that can be estimated given a model and a set of data. These methods will be used to estimate patient specific parameters in a model predicting baroreceptor feedback regulation of heart rate during head-up tilt. The three methods include: structured analysis of the correlation matrix, analysis via singular value decomposition followed by QR factorization, and identification of the subspace closest to the one spanned by eigenvectors of the model Hessian. Results showed that all three methods facilitate identification of a parameter subset. The "best" subset was obtained using the structured correlation method, though this method was also the most computationally intensive. Subsets obtained using the other two methods were easier to compute, but analysis revealed that the final subsets contained correlated parameters. In conclusion, to avoid lengthy computations, these three methods may be combined for efficient identification of parameter subsets.

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  • The model outcome is insensitive to variation in parameters a2, a4 and m, hence none of these are practically identifiable.

    “The model outcome is also insensitive to variation in the parameters a 2, a 4 and m , hence none of these are practically identifiable [37].”

    From Patient specific modeling of the HPA axis related to clinical diagnosis of depression (2017) · cites this paper as [37]

    Section 3.3 (page unavailable) says that all parameters in the paper’s heart-rate model were sensitive against the error bound. The Discussion likewise says the authors included all parameters in the sensitive set. The paper therefore does not report that a2, a4 and m were insensitive or practically unidentifiable. (LLM, conf=0.87)

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Research works printed but not linked: 42

  1. [3]Banks HT Davidian M Samuels JR Sutton KL Chowell G Hayman JM Bettencourt LMA Castillo-Chavez C An inverse problem statistical methodology summary, in Mathematical and statistical estimation approaches in Epidemiology 2009 New York, NY Springer
  2. [5]Batzel J Baselli G Mukkamala R Chon KH KH Modeling and disentangling physiological mechanisms: linear and nonlinear identification techniques for analysis of cardiovascular regulation Philos Transact A Math Phys Eng Sci 2009 367 1377 1391 19324714 PMC3268216
  3. [8]Borella B Lucchi E Nicosia S Valigi P A Kalman filtering approach to estimation of maximum ventricle elastsance Conf Proc IEEE Eng Med Biol Soc 2004 5 3642 3645 17271082
  4. [9]Burnham KP Anderson DR Model selection and multimodel inference: A practical information-theoretic approach 2002 2’nd edition New York, NY Springer
  5. [10]Burth M Verghese GC Valez-Reyes MV Subset selection for improved parameter estimation in on-line identification of a synchronous generator IEEE Trans Power Systems 1999 14 218 225
  6. [11]Carson ER Finkelstein L Cobelli C Mathematical modeling of metabolic and endocrine systems: model formulation, identification, and validation 1985 New York, NY John Wiley & Sons
  7. [13]Cobelli C DiStefano JJ Parameter and structural identifiability concepts and ambiguities: a critical review and analysis Am J Physiol 1980 239 R7 R24 7396041
  8. [14]Daun S Rubin J Vodovotz Y Roy A Parker R Clermont G An ensemble of models of the acute inflammatory response to bacterial lipopolysaccharide in rats: Results from parameter space reduction J Theor Biol 2008 253 843 853 18550083
  9. [16]Ellwein LM Tran HT Zapata C Novak V Olufsen MS Sensitivity analysis and model assessment: Mathematical models for arterial blood flow and blood pressure J Cardiovasc Eng 2008 8 94 108 18080757
  10. [18]Eslami M Theory of sensitivity in dynamic systems: an introduction 1994 Berlin, Germany Springer-Verlag
  11. [19]Fadel PJ Stromstad M Wray DW Smith SA Raven PB Secher NH New insights into differential baroreflex control of heart rate in humnas Am J Physiol 2003 284 H735 H743 12388288
  12. [20]Ferguson DW Abboud FM Mark AL Relative contribution of aortic and carotid baroreflexes to heart rate control in man during steady state and dynamic increases in arterial pressure J Clin Invest 1985 76 2265 2274 4077978 PMC424350
  13. [22]Frank P Introduction to sensitivity theory 1978 New York, NY Academic Press
  14. [23]Golub GH van Loan CF Matrix computations, Johns Hopkins Studies in Mathematical Sciences 1996 3’rd edition Baltimore, MD
  15. [25]Godfrey K Compartmental models and their application 1983 New York, NY Academic Press
  16. [26]Guyton AC Coleman TG Granger HJ Overall regulation Ann Rev Physiol 1972 34 13 44 4334846
  17. [30]Gutenkunst RN Casey FP Waterfall JJ Myers CR Sethna JP Extracting falsifiable predictions from sloppy models Ann NY Acad Sci 2007 1115 203 211 17925353
  18. [31]Hu X Nenov V Bergsneider M Glenn TC Vespa P Martin N Estimation of hidden state variables of the intracranial system using constrained nonlinear Kalman filters IEEE Trans Biomed Eng 2007 54 597 610 17405367
  19. [32]Jacquez JA Compartmental analysis in biology and medicine 1985 2’nd edition Ann Arbor, MI The Univ of Michigan Press
  20. [36]Khoo MC Modeling of autonomic control in sleep-disordered breathing Cardiovasc Eng 2008 8 30 41 18060581 PMC3339254
  21. [37]Kim HJ Vignon-Clementel IE Coogan JS Figueroa CA Jansen KE Taylor CA Patient-specific modeling of blood flow and pressure in human coronary arteries Ann Biomed Eng 2010 38 3195 3209 20559732
  22. [40]Liang H Miao H Wu H Estimation of constant and time-varying dynamic parameters of HIV infection in a nonlinear differential equation model Ann Appl Stat 2010 4 460 483 20556240 PMC2885820
  23. [41]Lo M-T Novak V Peng C-K Liu Y Hu K Nonlinear phase interaction between nonstationary signals: A comparison study of methods based on Hilbert-Huang and Fourier transforms Phys Rev E Stat Nonlin Soft Matter Phys 2009 79 6 Pt 1 061924. PMC2730740 19658541
  24. [42]Ljung L System Identification, theory for the user 1999 2’nd edition Upper Saddle River, NJ Prentice Hall Inc
  25. [44]Miao H Dykes C Demeter LM Cavenaugh J Parka SY Perelson AS Wu H Modeling and estimation of kinetic parameters and replicative fitness of HIV-1 from flow-cytometry-based growth competition experiments Bull Math Biol 2008 70 1749 1771 18648886 PMC4065495
  26. [45]Miao H Xia X Perelson AS Wu H On identifiability of nonlinear ODE models and applications in viral dynamics SIAM Review 2011 53 3 39 21785515 PMC3140286
  27. [46]Olufsen MS Ottesen JT Tran HT Ellwein LM Lipsitz LA Novak V Blood pressure and flow variation during postural change from sitting to standing: model development and validation J Appl Physiol 2005 99 1523 1537 15860687 PMC2094039
  28. [47]Olufsen MS Tran HT Ottesen JT Lipsitz LA Novak V Modeling baroreflex regulation of heart rate during orthostatic stress Am J Physiol 2006 291 R1355 R1368 16793939
  29. [48]Olufsen MS Alston AV Tran HT Ottesen JT Novak V Modeling heart rate regulation, Part I: Sit-to-stand versus head-up tilt J Cardiovasc Eng 2008 8 73 87 PMC2767463 18064571
  30. [49]Ottesen JT Olufsen MS Functionality of the baroreceptor nerves in heart rate regulation Comp Meth Prog Biomed 2011 101 208 219 21167621
  31. [51]Olgac U Poulikakos D Saur SC Alkadhi H Kurtcuoglu V Patient-specific three-dimensional simulation of LDL accumulation in a human left coronary artery in its healthy and atherosclerotic states Am J Physiol 2010 296 H1969 H1982 19329764
  32. [52]Pennati G Socci L Rigano S Boito S Ferrazzi E Computational patient-specific models based on 3-D ultrasound data to quantify uterine arterial flow during pregnancy IEEE Trans Med Imaging 2008 27 1715 1722 19033087
  33. [53]Pope SR Ellwein LM Zapata CL Novak V Kelley CT Olufsen MS Estimation and identification of parameters in a lumped cerebrovascular model Math Biosci Eng 2009 6 93 115 19292510
  34. [54]Pope SR Parameter identification in lumped compartment cardiorespiratory models PhD Thesis 2009 Raleigh, NC North Carolina State University
  35. [62]Taylor CA Figueroa CA Patient-specific modeling of cardiovascular mechanics Ann Rev Biomed Eng 2009 11 109 134 19400706 PMC4581431
  36. [64]Yue H Brown M Knowles J Wang H Broomhead DS Kell DB Insights into the behaviour of systems biology models from dynamic sensitivity and identifiability analysis: a case study of an NF-kB signalling pathway Mol BioSyst 2006 2 640 649 17216045
  37. [65]Valdez-Jasso D Haider MA Banks HT Bia D Zocalo Y Armentano R Olufsen MS Viscoelastic mapping of the arterial ovine system using a Kelvin model IEEE Trans Biomed Eng 2008 56 210 219
  38. [67]Velez-Reyes MV Decomposed algorithms for parameter estimation PhD Thesis 1992 Cambridge, MA Massachusetts Institute of Technology
  39. [68]Vilela M Vinga S Grivet Mattoso Maia MA Voit EO Almeida JS Identification of neutral biochemical network models from time series data BMC Systems Biology 2009 3 47 19416537 PMC2694766
  40. [69]Wan J Steele BN Spicer SA Strohband S Feijoo GR Hughes TJR Taylor CA A one-dimensional finite element method for simulation-based medical planning for cardiovascular disease Comp Meth Biomech Biomed Eng 2002 5 195 206 12186712
  41. [70]Wu H Zhua H Miao H Perelson AS Parameter identifiability and estimation of HIV/AIDS dynamic models Bull Math Biol 2008 70 785 799 18247096
  42. [71]Zenker S Rubin J Clermont G From inverse problems in mathematical physiology to quantitative differential diagnoses PLoS Comp Biol 2009 3 2072 2086 PMC2065888 17997590

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Authors
Olufsen, M. S., & Ottesen, J. T.
Affiliations
Roskilde University (DK)
Corresponding author
Olufsen, Mette S.
ORCID
Venue
Journal of Mathematical Biology
Publisher
Springer Science and Business Media LLC
Published
2012-05-16
Volume
67
Issue
1
Pages
39-68
ISSN
  • 0303-6812 (ISSN-L)
  • 1432-1416
DOI
10.1007/s00285-012-0535-8
PMC
PMC3526689
OpenAlex
W1977318420
Cited by
106
References
3
Citations by year
2026: 3 · 2025: 5 · 2024: 6 · 2023: 11 · 2022: 6 · 2021: 17 · 2020: 9 · 2019: 10 · 2018: 13 · 2017: 2 · 2016: 2 · 2015: 5 · 2014: 7 · 2013: 8 · 2012: 2
FWCI
10.21
Type
journal article
Language
en
Open access
Licence
www.springer.com/tdm (tdm)
Locations
  • Journal of Mathematical Biology (publishedVersion)
  • PubMed (publishedVersion)
  • Europe PMC (PubMed Central) (acceptedVersion)
  • PubMed Central (acceptedVersion)
  • RUCforsk (Roskilde University) (submittedVersion)
Funders
  • Japan Student Services Organization
  • National Institute of General Medical Sciences (P50GM094503)
Topics
  • Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
  • Health Sciences › Medicine › Cardiology and Cardiovascular Medicine › Heart Rate Variability and Autonomic Control
  • Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
Keywords
parameter estimation, heart rate regulation, head-up tilt, patient-specific modeling, singular value decomposition, QR decomposition, Hessian eigenvectors, data sparsity, cardiovascular dynamics
MeSH terms
Blood Pressure, Heart Rate, Humans, Models, Cardiovascular, Posture, Baroreflex, Nonlinear Dynamics, Feedback, Physiological, Mathematical Concepts

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