Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Supervisors info:
Ιωάννης Στρατής Καθηγ. (Επιβλέπων), Βασίλειος Δουγαλής Καθηγ., Μιχαήλ Ξένος Επίκ. Καθηγ.
Original Title:
Ένα μονοδιάστατο δυναμικό μοντέλο για τη μελέτη της ροής του αίματος στο ανθρώπινο αρτηριακό σύστημα
Translated title:
An one-dimensional model for the study of the blood flow in the human circulatory system
Summary:
The main objective of the thesis is the development of a dynamic
one-dimensional mathematical model for description of the interaction of blood
with the surrounding tissue in human arterial system. This mathematical model
can predict the blood flow and the pressure distributions in human arterial
system to any location along the major arteries. Blood flow in large arteries
is modelled using one-dimensional equations derived from one particular form of
the Navier-Stokes. An approach based on the linear form of the equations
governing the flow can be used for the extraction of the basic system of
equations. The conservation equations of mass and momentum of the blood as well
as the interaction of blood with each artery can be summarized into the
following three equations: The equation for momentum. The model uses a
simplified momentum equation based on specific simplifications. Distensibility
of the artery. The vascular system consists of arteries, arterioles and
capillaries with varying degrees of distensibility. The interaction of blood
with each artery (arterial distensibility of vascular system) is integrated in
the model. The equation of continuity. This equation ensures that the blood
keeps the mass of the system i.e. the quantity of blood that enters the artery
equals the quantity of blood that exits plus the amount of blood that stagnates
in the artery. The arterial tree of major arteries (from the aorta to the
carotid, femoral and subclavian arteries) is then cut off in parts of constant
reference cross-section. The equations that govern the physics of the problem
discretized with the use of finite volumes method and the final system is
solved numerically using a non-linear iterative technique. The blood flow and
pressure in large vessels are calculated as functions of time. The proposed
mathematical model of arterial system will be able to provide us with
information about the flow and pressure in healthy and pathological conditions,
such as an aneurysm of the abdominal aorta. A secondary objective of the model
is to use the extracted information to three-dimensional arterial structures,
for the simulation of blood flow in physiological and pathological cases. It is
thus able to provide the appropriate dynamic conditions (e.g. boundary
conditions) at any point along the tree of major arteries of general
circulation and could be used as a starting point for more advanced
three-dimensional simulations that are based on the principles of computational
fluid dynamics.
Keywords:
One-dimensional model, Blood flow, Momentum equation, Continuity equation, Distensibility
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