On 1-D PDE-Based Cardiovascular Flow Bottleneck Modeling and Analysis: A Vehicular Traffic Flow-Inspired Approach

TL;DR

This paper explores a novel PDE-based approach for modeling and analyzing blood flow in arteries with stenosis by drawing an analogy with vehicular traffic flow, enabling new insights into flow dynamics and control.

Contribution

It introduces a traffic flow-inspired PDE modeling framework for cardiovascular flow analysis, highlighting the correspondence between blood flow and traffic bottleneck dynamics.

Findings

Established a formal analogy between blood flow and traffic flow dynamics.

Derived boundary conditions and regimes characterization for stenosis modeling.

Demonstrated potential for improved cardiovascular flow monitoring and control.

Abstract

We illustrate the potential of PDE-based traffic flow control in cardiovascular flow analysis, monitoring, and control, presenting a PDE-based control-oriented formulation, for 1-D blood flow dynamics in the presence of stenosis. This is achieved adopting an approach for modeling and analysis that relies on the potential correspondence of 1-D blood flow dynamics in the presence of stenosis, with 1-D traffic flow dynamics in the presence of bottleneck. We reveal such correspondence in relation to the respective (for the two flow types), speed dynamics and a (consistent with them) fundamental diagram-based reduction; bottleneck dynamic effects description and resulting boundary conditions; and free-flow/congested regimes characterization.