The brain accounts for around 2 % of human adult bodyweight but consumes 20 % of the resting oxygen available to the whole body. The brain is dependent on a constant supply of oxygen to tissue, transported from the heart via the vasculature and carried in blood. An interruption to flow can lead to ischaemia (a reduced oxygen supply) and prolonged interruption may result in tissue death, and permanent brain damage. The cerebral vasculature consists of many, densely packed, micro-vessels with a very large total surface area. Oxygen dissolved in blood enters tissue by passive diffusion through the micro-vessel walls. Imaging shows bursts of metabolic activity and flow in localised brain areas coordinated with brain activity (such as raising a hand). An appropriate level of oxygenation, according to physiological demand, is maintained via autoregulation; a set of response pathways in the brain which cause upstream or downstream vessels to expand or contract in diameter as necessary to provide sufficient oxygen to every region of the brain. Further, autoregulation is also evident in the response to pressure changes in the vasculature: the perfusing pressure can vary over a wide range from the basal-state with only a small effect on flow due to the constriction or dilation of vessels. Presented here is a new vasculature model where diameter and length are calculated in order to match the data available for flow velocity and blood pressure in different sized vessels. These vessels are arranged in a network of 6 generations each of bifurcating arterioles and venules, and a set of capillary beds. The input pressure and number of generations are the only specifications required to describe the network. The number of vessels, and therefore vessel geometry, is governed by how many generations are chosen and this can be altered in order to create more simple or complex networks. The flow, geometry and oxygen concentrations are calculated based on the vessel resistance due to flow from geometry based on Kirchoff circuit laws. The passive and active length-tension characteristics of the vasculature are established using an approximation of the network at upper and lower autoregulation limits. An activation model is described with an activation factor which governs the contributions of elastic andmuscle tension to the total vessel tension. This tension balances with the circumferential tension due to pressure and diameter and the change in activation sets the vessel diameter. The mass transport equation for oxygen is used to calculate the concentration of oxygen at every point in the network using data for oxygen saturation to establish a relationship between the permeability of the vessel wall to oxygen and the geometry and flow in individual vessels. A tissue compartment is introduced which enables the modelling of metabolic control. There is evidence for a coordinated response by surrounding vessels to local changes. A signal is proposed based on oxygen demand which can be conducted upstream. This signal decays exponentially with vessel length but also accumulates with the signal added from other vessels. The activation factor is therefore set by weighted signals proportional to changes in tissue concentration, circumferential tension, shear stress and conducted oxygen demand. The model is able to reproduce the autoregulation curve whereby a change in pressure has only a small effect on flow. The model is also able to replicate experimental results of diameter and tissue concentration following an increase in oxygen demand.

Είναι πλέον αποδεκτό ότι οι αγγειακές βιολογικές διαδικασίες επηρεάζονται από την τοπική αιμοδυναμική. Πειράματα in vivo, in vitro και αριθμητικές μελέτες επιβεβαίωσαν ότι τα μοντέλα της ροής στην αρτηριοφλεβική αναστόμωση (ΑΦΑ) είναι αυστηρά εξαρτημένα από τη γεωμετρία της περιοχής. Στην παρούσα εργασία μελετήθηκε το πεδίο ροής του αίματος σε "εικονικές γεωμετρίες" των ΑΦΑ μέσω μεθόδων υπολογιστικής ρευστομηχανικής. Με τον όρο "εικονική γεωμετρία" καλούμε μια γεωμετρία που δεν προσδιορίζεται από μετρήσεις σε πραγματικές αναστομώσεις αλλά προσομοιάζει προσεγγιστικά σ'αυτή. Ως οριακές συνθήκες του προβλήματος ετέθησαν κατανομές ταχύτητας που είχαν μετρηθεί σε συγκεκριμένες θέσεις εισόδου στο επίπεδο αρτηρίας και φλέβας της ΑΦΑ. Η μελέτη του πεδίου ροής περιλαμβάνει την κατανομή ταχυτήτων σε όλη την περιοχή της ΑΦΑ, τον προσδιορισμό και μελέτη των περιοχών ανακυκλοφορίας, κατανομή των πιέσεων και των διατμητικών τάσεων στο τοίχωμα της ΑΦΑ. Η μελέτη του πεδίου ροής περιλαμβάνει τη σύγκριση των υπολογιστικά λαμβανομένων μεγεθών με τα αντίστοιχα αποτελέσματα εκ της βιβλιογραφίας. Σε ένα ξεχωριστό μέρος της εργασίας αναλύονται οι ΑΦΑ και οι τεχνικές τους, οι επιπλοκές τους καθώς και τα εμβιομηχανικά χαρακτηριστικά τους. Επίσης αναλύεται η συσχέτιση των αιμοδυναμικών διαταραχών με την ανάπτυξη ινομυϊκής υπερπλασίας. / It is widely accepted that the vascular biological procedure is influenced by the local hemodynamics. Experiments in vivo, in vitro and numerical studies have confirmed that the flow models in Arteriovenous Anastomosis (AVA) depend strongly on the area geometry. This project goes through the flow distribution in “virtual geometries”of AVA using computational fluid dynamics (CFD). The term “virtual geometry” refers to a type of geometry which is not determined by calculations of real anastomosis but roughly simulates it. The boundary conditions of the problem were the velocity distributions that were calculated in specific entrance points in artery and vein of the AVA. The study of the flow distribution encompasses the velocity distribution in the whole area of the AVA, the specification and investigation of back flow areas, the distribution of pressure and shear stress in the AVA walls. It also encompasses the comparison of computated results to the equivalent measurements accumulated from the international bibliography. A separate chapter of this study refers to different kinds of AVA and their techniques, complications and biomechanical characteristics. Furthermore, it elaborates the correlations of the hemodynamical disorders and intimal hyperplasia.