One-dimensional modeling of concentration propagation in the human circulatory system

One-dimensional modeling of concentration propagation in the human circulatory system

Groen, Stan (TU Delft Applied Sciences; TU Delft Electrical Engineering, Mathematics and Computer Science)

Kenjeres, S. (mentor)
Vuik, Cornelis (mentor)

Delft University of Technology

Applied Mathematics | Applied Physics

2023-06-30

This thesis investigates the behaviour of one-dimensional blood flow in the human arterial tree. It focuses on modeling the change in velocity, cross-sectional area, and concentration. The equations governing this flow are derived using the physical laws of conservation of mass, conservation of momentum, and the
advection-diffusion equation. To solve this set of equations numerically, the Finite Volume Method in combination with a flux difference splitting approach is employed. The study begins with an examination of a single artery, revealing wave-like behavior in pressure and concentration. Pressure propagates along the vessel, while concentration gradually dilutes over time. This
behaviour is also visible when expanding to the 55-artery model of the entire human body. The results of this model were found to be very comparable to the literature. Additionally, the propagation of a chemical
species injected into an artery near the heart is investigated. It takes around 25 seconds to propagate to
the legs but the amount of concentration is greatly reduced. The strength of this wave upon reaching the
legs is investigated for different values of the diffusion coefficient. It is found that when
D = 0.02 cm2/s, the strength is around the 80% of its original value while a value of D = 2 cm2/s reduces
it to 40%. Further research should focus on expanding this model and improving its accuracy. Especially
the exact concentration waves in single arteries are very prone to spurious oscillations. By optimizing the
numerical code, the accuracy can be greatly increased. Moreover, more realistic additions can be made to
this model. Such as expanding to a two-way model enabling to inject at various points around the arterial
tree. Nevertheless, this model provides insight into the propagation of blood and concentration in the
human circulatory system, highlighting the need for refinement.

conentration
Modeling
circulatory system

http://resolver.tudelft.nl/uuid:40cf9fc9-4c0c-41e0-846a-7c5ef19db493

Student theses

bachelor thesis

© 2023 Stan Groen