Numerical modeling of 1D arterial networks coupled with a lumped parameters description of the heart

Abstract

The investigations on the pressure wave propagation along the arterial network and its relationships with vascular physiopathologies can be supported nowadays by numerical simulations. One dimensional (1D) mathematical models, based on systems of two partial differential equations for each arterial segment suitably matched at bifurcations, can be simulated with low computational costs and provide useful insights into the role of wave reflections. Some recent works have indeed moved in this direction. The specific contribution of the present paper is to illustrate a 1D numerical model numerically coupled with a model for the heart action. Typically, the action of the heart on the arterial system is modelled as a boundary condition at the entrance of the aorta. However, the left ventricle (LV) and the vascular network are a strongly coupled single mechanical system. This coupling can be relevant in the numerical description of pressure waves propagation, particularly when dealing with pathological situations. In this work, we propose a simple lumped parameter model for the heart and show how it can be coupled numerically with a 1D model for the arteries. Numerical results actually confirm the relevant impact of the heart-arteries coupling in realistic simulations.

Geometric multiscale modeling of the cardiovascular system, between theory and practice

“…In clinical practice a lumped parameter model of this coupling may help clarifying these mutual interactions [61]. An empirical and simple description of the heart leading to lumped parameter models is given for instance in [92] where each ventricle is represented as a deformable chamber whose compliance is time-dependent.…”

“…A distinctive feature of the paper is the inclusion of the heart dynamics represented by a 0D model as well. A similar procedure was carried out in [61] with a 1D-0D coupling to cover the 55 largest arteries represented by 1D models dynamically interfaced with the left ventricle (0D). In particular, the nature of the boundary conditions for the 3D model at the interface with the heart are selected differently over the heart beat, 1. pressure conditions with the coupled multidomain method are prescribed when the valve is open;…”

“…In this case, the role of the lumped parameter model is to calculate the pressure wave reflections generated by peripheral districts and by the microcirculation [63]. In a different context, 0D models have been coupled with a 1D description of the circulatory network in [61] to include the action of the heart. Coherently with the previous assumptions in the present section, we consider here the case when a single arterial cylindrical segment is described by a 1D model, proximally in a region Ω 1 , and by a 0D model in a region Ω 2 located distally.…”

Non-Invasive Hemodynamic Assessment of Aortic Coarctation: Validation with In Vivo Measurements

“…Depending on the availability of in-vivo measurements and the underlying assumptions of the model, researches typically use one of the following inlet boundary condition: (i) time-varying velocity (or flow rate) profile 11,14 , or (ii) a lumped model of the heart coupled at the inlet 4,3 . The former can be easily determined in a clinical setting, and is often part of the diagnostic workflow (2D/3D Phasecontrast MRI, Doppler ultrasound).…”

On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations

“…These models are described by hyperbolic systems of partial differential equations and, despite having a lower level of accuracy compared to the fully 3D model, they capture effectively the pulse waves at a much lower computational cost. This allows one to properly simulate pressure waves propagation in large regions of the arterial tree by a network of these models coupled together [16][17][18]36].…”