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Biological system’s flow from a vehicular traffic viewpoint

Sampani Triantafyllia

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Summary

Nowadays, mathematical models and methods are commonly used in many scientific fields. Therefore, mathematical models such as differential equations can be used in hemodynamics and road traffic dynamics. In order to illustrate and correlate blood flow and traffic flow control, we study one dimensional blood and traffic flow models that are based in partial differential equations.The arterial tree of circulatory system is disassembled into arterial segments in one-dimensional models, which can make accurate predictions in a minimum of time, making them suitable for clinical applications based on specific patient data. Each blood flow model, such as heart model, cerebral circulation, coronary model and others, has its own characteristics and differs significantly from each other in terms of their complexity. 1-D blood flow models can be approached by Navier-Stokes equations as vessels can be assumed as a cylindrical tube.On the other hand, one dimensional traffic flow models, based on partial or ordinary differential equations, represent the behavior of traffic streams. We will introduce the relation between the average traffic density and the average flow of traffic, as it is described with the continuity equation. In this thesis, the 1-D vehicular traffic flow models that are going to be presented are Lighthill-Whitham-Richards models (LWR) and Aw-Rascle-Zhang (ARZ) models. LWR model assumes that all the cars have a steady speed and it can be described by the 1-D continuity equation, as well as the fundamental equation of traffic flow. ARZ model can also be expressed as an extension to LWR model and it provides a more stable behavior from drivers in stop-and-go traffic conditions.After the analysis of traffic and blood flow models, we cite the applications of 1-D blood flow models and how they appear in many medical cases. Last but not least, differences and similarities between blood and traffic flow models are presented and evaluated.

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