Uncertainty Analysis of Ventricular Mechanics Using the Probabilistic Collocation Method

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.

Uncertainty in cardiac myofiber orientation and stiffnesses dominate the variability of left ventricle deformation response

“…The findings are largely in agreement with previous results in Osnes and Sundnes, which considered the influence of uncertainty in material parameters in a similar model of ventricular mechanics. However, the study in Osnes and Sundnes considered an even simpler LV model, with idealized and perfectly symmetric geometry, and a perfect match between the results should therefore not be expected.…”

“…First, we consider the material stiffnesses b ff , b xx , b fx , the incompressibility parameter K and the weighting factor C as uncertain (random) variables of prescribed probability distributions. The mean values of these parameters were taken from Usyk et al, with statistical properties chosen as in Osnes and Sundnes . Moreover, we similarly treat randomness in fiber orientations as a direct function of the random input variables α endo , α epi , β endo , and β epi to the LDRB algorithm.…”

Towards causally cohesive genotype–phenotype modelling for characterization of the soft-tissue mechanics of the heart in normal and pathological geometries

“…These two submappings should be considered separately when discussing the low proportion of nonlinearity and interactions in figure 4. Uncertainty and variability [25] and interdependency [38] of material parameters are fundamental challenges in biomechanical modelling. Here, the genotype-parameter map was modelled additively, meaning that all residual variance in rsif.royalsocietypublishing.org J. R. Soc.…”

“…Specifically, we model the passive filling phase (late diastole) of the left ventricle, in which many individual factors have been studied previously [22][23][24][25]. The mechanics in this phase are relatively simple owing to the absence of active contraction, yet the strain and elastic energy stored in diastole gives our conclusions some relevance to the later phases of the heartbeat as well.…”

Adaptive unscented transform for uncertainty quantification in EMC large-scale systems

“…Many papers recently show the application of stochastic collocation methods or polynomial chaos decomposition in order to estimate the output variance due to parameter uncertainty in many fields of science (van Dijk, 2002;Stievano et al, 2012;Dongbin et al, 2005;Moro et al, 2011;Gaignaire et al, 2010Gaignaire et al, , 2012Preston et al, 2009;Beddek et al, 2012;Tartakovsky and Dongbin, 2007;Osnes and Sundnes, 2012;Freitas et al, 2010;Hansen et al, 2009;Hildebrand and Gevers, 2004;Silly-Carette et al, 2009).…”