Abstract
Uncertainty and variability in material parameters are fundamental challenges in computational biomechanics. Analyzing and quantifying the resulting uncertainty in computed results with parameter sweeps or Monte Carlo methods has become very computationally demanding. In this paper, we consider a stochastic method named the probabilistic collocation method, and investigate its applicability for uncertainty analysis in computing the passive mechanical behavior of the left ventricle. Specifically, we study the effect of uncertainties in material input parameters upon response properties such as the increase in cavity volume, the elongation of the ventricle, the increase in inner radius, the decrease in wall thickness, and the rotation at apex. The numerical simulations conducted herein indicate that the method is well suited for the problem of consideration, and is far more efficient than the Monte Carlo simulation method for obtaining a detailed uncertainty quantification. The numerical experiments also give interesting indications on which material parameters are most critical for accurately determining various global responses.
References
Feb 1, 1991·Journal of Biomechanical Engineering·J M GuccioneL K Waldman
Aug 1, 1990·Journal of Biomechanical Engineering·J D HumphreyF C Yin
Jan 1, 1987·Journal of Biomechanics·F C YinS L Zeger
Nov 1, 1987·Circulation Research·H R HalperinF C Yin
Jun 1, 1983·The Journal of Physiology·L L Demer, F C Yin
May 1, 1993·Journal of Biomechanical Engineering·M S Sacks, C J Chuong
Oct 1, 1995·Journal of Biomechanics·J M GuccioneA D McCulloch
Oct 24, 1998·Progress in Biophysics and Molecular Biology·P J HunterH E ter Keurs
Oct 4, 2000·Annals of Biomedical Engineering·F J Vetter, A D McCulloch
Nov 13, 2002·American Journal of Physiology. Heart and Circulatory Physiology·Socrates DokosIan J LeGrice
May 22, 2003·Annals of Biomedical Engineering·R C P KerckhoffsT Arts
Jan 6, 2006·Computer Methods in Biomechanics and Biomedical Engineering·Tom ThorvaldsenJoakim Sundnes
Nov 30, 2006·Computer Methods in Biomechanics and Biomedical Engineering·F DorriP P Lunkenheimer
Jul 14, 2009·American Journal of Physiology. Heart and Circulatory Physiology·Peter H M BovendeerdTammo Delhaas
Aug 7, 2009·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Gerhard A Holzapfel, Ray W Ogden
Sep 29, 2011·American Journal of Physiology. Heart and Circulatory Physiology·Hon Fai ChoiPiet Claus
Citations
Oct 18, 2015·International Journal for Numerical Methods in Biomedical Engineering·V G EckWouter Huberts
Dec 28, 2012·IEEE Transactions on Bio-medical Engineering·Christian SchmidtUrsula van Rienen
Feb 19, 2015·Annals of Biomedical Engineering·M SierraJ Grasa
Apr 4, 2015·Journal of the Royal Society, Interface·Øyvind NordbøJon Olav Vik
Jan 12, 2019·International Journal for Numerical Methods in Biomedical Engineering·Rocío Rodríguez-CantanoMarie E Rognes
Mar 2, 2019·Computer Methods in Biomechanics and Biomedical Engineering·S KallhovdS T Wall
Apr 27, 2019·Biomechanics and Modeling in Mechanobiology·Joventino O CamposBernardo M Rocha
May 26, 2020·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·J O CamposB M Rocha
Feb 7, 2021·Journal of Molecular and Cellular Cardiology·Kimberly J McCabe, Padmini Rangamani
Feb 19, 2021·International Journal for Numerical Methods in Biomedical Engineering·Stefano Pagani, Andrea Manzoni
Jul 24, 2021·Biomedical Engineering Online·Ekaterina KovachevaAxel Loewe