Applied Mathematics and Mechanics

, Volume 34, Issue 5, pp 529–540 | Cite as

Influence of random uncertainties of anisotropic fibrous model parameters on arterial pressure estimation

  • A. Eddhahak-Ouni
  • I. Masson
  • F. Mohand-Kaci
  • M. ZidiEmail author


This paper deals with a stochastic approach based on the principle of the maximum entropy to investigate the effect of the parameter random uncertainties on the arterial pressure. Motivated by a hyperelastic, anisotropic, and incompressible constitutive law with fiber families, the uncertain parameters describing the mechanical behavior are considered. Based on the available information, the probability density functions are attributed to every random variable to describe the dispersion of the model parameters. Numerous realizations are carried out, and the corresponding arterial pressure results are compared with the human non-invasive clinical data recorded over a mean cardiac cycle. Furthermore, the Monte Carlo simulations are performed, the convergence of the probabilistic model is proven. The different realizations are useful to define a reliable confidence region, in which the probability to have a realization is equal to 95%. It is shown through the obtained results that the error in the estimation of the arterial pressure can reach 35% when the estimation of the model parameters is subjected to an uncertainty ratio of 5%. Finally, a sensitivity analysis is performed to identify the constitutive law relevant parameters for better understanding and characterization of the arterial wall mechanical behaviors.

Key words

arterial pressure non-invasive clinical data hyperelasticity anisotropy random confidence region 

Chinese Library Classification


2010 Mathematics Subject Classification



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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • A. Eddhahak-Ouni
    • 1
  • I. Masson
    • 2
  • F. Mohand-Kaci
    • 2
  • M. Zidi
    • 2
    Email author
  1. 1.Arts et Métiers ParisTech (ENSAM-ESTP/IRC), Institut de Recherche en ConstructibilitéUniversité Paris-Est CréteilCachanFrance
  2. 2.Centre de Recherches Chirurgicales, Faculté de MédecineUniversité Paris-Est CréteilCréteilFrance

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