Stochastic sensitivity analysis for timing and amplitude of pressure waves in the arterial system

Abstract

In the field of computational hemodynamics, sensitivity quantification of pressure and flow wave dynamics has received little attention. This work presents a novel study of the sensitivity of pressure-wave timing and amplitude in the arterial system with respect to arterial stiffness. Arterial pressure and flow waves were simulated with a one-dimensional distributed wave propagation model for compliant arterial networks. Sensitivity analysis of this model was based on a generalized polynomial chaos expansion evaluated by a stochastic collocation method. First-order statistical sensitivity indices were formulated to assess the effect of arterial stiffening on timing and amplitude of the pressure wave and backward-propagating pressure wave in the ascending aorta, at the maximum pressure and inflection point in the systolic phase. Only the stiffness of aortic arteries was found to significantly influence timing and amplitude of the backward-propagating pressure wave, whereas other large arteries in the systemic tree showed marginal impact. Furthermore, the ascending aorta, aortic arch, thoracic aorta, and infrarenal abdominal aorta had the largest influence on amplitude, whereas only the thoracic aorta influenced timing. Our results showed that the non-intrusive polynomial chaos expansion is an efficient method to compute statistical sensitivity measures for wave propagation models. These sensitivities provide new knowledge in the relative importance of arterial stiffness at various locations in the arterial network. Moreover, they will significantly influence clinical data collection and effective composition of the arterial tree for in-silico clinical studies.

A benchmark study of numerical schemes for one‐dimensional arterial blood flow modelling

“…Results have shown a good agreement among all numerical schemes and their ability to solve the nonlinear 1D equations accurately and to capture the main features of pulse wave propagation in single arterial segments as well as in larger networks. This is consistent with the outcome of previous studies …”

Analysis of Uncertainty and Variability in Finite Element Computational Models for Biomedical Engineering: Characterization and Propagation

“…PC expansion can be also employed together with surrogate models, previously introduced as response surface method, to reduce the computational cost, for instance, creating the surrogate model in the form of the Hermite polynomials (Isukapalli et al, 1998). Thus, the solution can be computed by fast-converging polynomial approximation based on least-squares linear regression (Du and Chen, 2000; Berveiller et al, 2006; Baroth et al, 2007; Eck et al, 2015). …”

“…These non-intrusive approaches have been employed also in the biomedical engineering fields, mainly in topics such as drug infusion (Preston et al, 2009), hemodynamics (Xiu and Sherwin, 2007; Sankaran and Marsden, 2011), or cardiovascular simulations (Eck et al, 2015, 2016). Both Sankaran and Marsden (2011) and Eck et al (2015) employed the approach of stochastic collocation to carry out sensitivity analysis on blood flow simulations.…”

“…Both Sankaran and Marsden (2011) and Eck et al (2015) employed the approach of stochastic collocation to carry out sensitivity analysis on blood flow simulations.…”

“…Concretely, Eck et al (2015) evaluated how arterial stiffness influenced on backward-propagating pressure waves, using a previously developed model that employs PC expansion in order to set the parameters of the model to create a patient-specific predictive model (Huberts et al, 2015). Later, Eck et al (2016) provided a guideline for the uncertainty analysis in cardiovascular applications.…”