Wave Propagation in a 1d Fluid Dynamics Model Using Pressure-Area Measurements From Ovine Arteries

Abstract

This study considers a 1D fluid dynamics arterial network model with 14 vessels developed to assimilate ex vivo 0D temporal data for pressure-area dynamics in individual vessel segments from 11 male Merino sheep. A 0D model was used to estimate vessel wall parameters in a two-parameter elastic model and a four-parameter Kelvin viscoelastic model. This was done using nonlinear optimization minimizing the least squares error between model predictions and measured cross-sectional areas. Subsequently, estimated values for elastic stiffness and unstressed area were related to construct a nonlinear relationship. This relation was used in the network model. A 1D single vessel model of the aorta was then developed and used to estimate the inflow profile and parameters for total resistance and compliance for the downstream network and to demonstrate effects of incorporating viscoelasticity in the arterial wall. Lastly, the extent to which vessel wall parameters estimated from ex vivo data can be used to realistically simulate pressure and area in a vessel network was evaluated. Elastic wall parameters in the network simulations were found to yield pressure-area relationships across all vessel locations and sheep that were in ranges comparable to those in the ex vivo data.

Uncertainty Quantification in a Patient-Specific One-Dimensional Arterial Network Model: EnKF-Based Inflow Estimator

“…Blood flow, pressure, and area are predicted using a 1D fluid dynamics model derived from the Navier-Stokes equations under the assumptions that the vessels are cylindrical, that the vessel length is significantly greater than the vessel radius, that the blood is incompressible, that the fluid is Newtonian, and that the flow is axisymmetric with a parabolic velocity profile. Under these conditions, conservation of mass and momentum [3,8,77] is given by…”

“…Numerous studies have used one-dimensional (1D) fluid dynamics models coupled with constitutive arterial wall models to predict wave propagation in arterial networks [1][2][3][4][5][6][7][8]. Onedimensional models are useful for understanding pulse wave propagation in arterial networks [4,7,[9][10][11][12] and for coupling with 0D and 3D models to generate multiscale representations of larger parts of the cardiovascular system [13][14][15][16][17][18][19][20].…”

“…The measurements of branching angles and ratios in the small vessels used to specify fractal tree models are typically extracted from studies over several species and therefore are not precise. Numerical methods for estimating Windkessel model parameters (two resistors and a capacitor) exist for elastic models but do not hold for viscoelastic models used in this study [8], giving rise to uncertainty in parameter values. (6) Numerical approximation.…”

“…This study employs a 1D finite element method with specified spatial and time discretization schemes. Previous work studying the convergence of this solver showed that the time discretization significantly affects the accuracy of the numerical solution, while the spatial discretization does not [8]. The numerical error in the time discretization of the solver is used in this study as a means of assessing trust in the model predictions, as described in Sec.…”

“…Typical validation of 1D arterial network models includes comparison of predicted and measured flow obtained in networks with geometry specified from MRI measurements. A majority of these studies have been done with models that predict wall deformation using simple linear elastic wall models [6,8,9,14,23,28]. However, it is known that arterial wall deformation (particularly within the aorta) exhibits both nonlinear and viscoelastic characteristics [42].…”