Atherogenesis is the leading cause of death in the developed world, and is putting considerable monetary pressure on health systems the world over. Although the risk factors are well understood, unfortunately, the initiation and development of this disease still remains relatively poorly understood, but it is becoming increasingly identifiable as a dysfunction of the endothelial cells that line the walls of arteries. The prevailing haemodynamic environment plays an important role in the focal nature of atherosclerosis to very specific regions of the human vasculature. Disturbed haemodynamics lead to very low wall shear stress, and inhibit the transport of important blood borne chemicals. The present study models, both computationally and mathematically, the transport and hydrolysis of important blood borne adneosine nucleotides in physiologically relevant arterial geometries. In depth analysis into the factors that affect the transport of these low diffusion coefficient species is undertaken. A mathematical model of the complex underlying endothelial cell dynamics is utilised to model production of key intracellular molecules that have been implicated into the complex initiation processes of atherosclerosis; hence regions of the vasculature can be identified as being 'hot spots' for atherogenesis. This model is linked into CFD software allowing for the assessment of how 3D low yields and mass transfer affect the underlying cell signalling. Three studies are undertaken to further understand nucleotide variations at the endothelium and to understand factors involved in determining the underlying cell dynamics. The major focus of the first two studies is geometric variations. This is primarily due to the plethora of evidence implicating the geometry of the human vasculature, hence the haemodynamics, as an influential factor in atherosclerosis initiation. The final model looks at a physiologically realistic geometry to provide a more realistic reproduction of the in vivo environment.

On vessel wall injury the complex process of blood coagulation is set off. It is composed of vasoconstriction, primary hemostasis, secondary hemostasis and fibrinolysis. This work enriches current model of primary hemostasis of Storti. The previous model used ALE formalism for tracing of development of platelet plug. The phase field method is used for tracing of the development of interface blood-thrombus. Storti's primary hemostasis was extended to capture the fact, that the platelets can be activated in the blood flow in the area of reactive surface not only by influence of chemical agents like thromboxane, ADP and thrombin but also by their exposure to elevated values of shear stress. In our first approach we deal the emerging thrombus as a fluid with very high viscosity. In the second approach it was assumed, that platelet plug develops as a viscoelastic material according to constitutive equations of clot introduced by Kempen. In this manner platelet clot matures into blood clot. In both approaches the blood is represented as a non-Newtonian fluid. The framework of the phase field method was applied also to the model of high shear rate thrombosis of Weller. Weller's original model of Weller took advantage of the cylindrical symmetry of computational domains for its computations, hence the...

A mathematical model of blood flow in infants with hypoplastic left heart syndrome (HLHS) was improved by adding cerebral autoregulation. This is the process by which blood vessels constrict or dilate to keep blood flow steady in certain organs during pressure changes. The original lumped parameter model transformed the fluid flow into an electrical circuit. Its behavior is described using a system of thirty-three coupled differential equations that are solved numerically using a fourth-order Runge-Kutta method implemented in MATLAB. A literature review that includes a discussion of autoregulation mechanisms and approaches to modeling them is followed by a description of the model created for this paper. The model is based on the baroreceptor or neurogenic theory of autoregulation. According to this theory, nerves in certain places within the cardiovascular system detect changes in blood pressure. The brain then compensates by sending a signal to blood vessels to constrict or dilate. The model of the control system responded fairly well to a pressure drop with a steady state error of about two percent. Running the model with or without the control system activated had little effect on other parameters, notably cardiac output. A more complete model of blood flow control would include autonomic regulation. This would vary more parameters than local autoregulation, including heart rate and contractility. This is suggested as a topic of further research.

This thesis deals with the mechanics of the Intra-Aortic Balloon Pump (IABP), the most widely used temporary cardiac assist device, whose beneficial action is based on the principle of counterpulsation. The investigation is carried out in vitro in increasingly more realistic setups, including a mock circulatory system with physiological distribution of peripheral resistance and compliance in which IABP counterpulsation was simulated. Pressure and flow measurements show the effect of variables such as intra-luminal pressure, angle and aortic compliance on balloon hemodynamics. These data are complemented by results on the duration of balloon inflation and deflation obtained by means of high-speed camera visualisation. Furthermore, wave intensity analysis is carried out and it is identified as a possible alternative method for the assessment of IABP performance. This work includes two prototypes of intra-aortic balloons of novel shape with the balloon chamber tapering both from and toward the balloon tip. In clinical terms, with reference to the semi-recumbent position in which patients assisted with the IABP are nursed in the intensive care unit, the results presented in this thesis indicate that operating the balloon at an angle compromises the benefit of counterpulsation when assessed in vitro.

Οι καρδιαγγειακές παθήσεις αποτελούν την κύρια αιτία θανάτου στις αναπτυγμένες χώρες. Η στένωση σε μία αρτηρία, είτε αυτή προκαλείται από μία πάθηση όπως το ανεύρυσμα, είτε προκαλείται από μία περίδεση, όπως στις περιπτώσεις των συγγενών καρδιοπαθειών, μπορεί να μεταβάλλει σε σημαντικό βαθμό τα χαρακτηριστικά της ροής του αίματος. Η μελέτη της φυσιολογικής παλλόμενης ροής μέσα από στένωση είναι ιδιαίτερα σημαντική για τη διάγνωση και αντιμετώπιση των αγγειακών νόσων. Το ιατρικό πρόβλημα το οποίο εξετάζουμε στην παρούσα εργασία, είναι η στένωση της πνευμονικής αρτηρίας από περίδεση. Η περίδεση γίνεται προφανώς για να μειωθεί η υψηλή αρτηριακή πίεση και τελικά η ροή του αίματος προς τους πνεύμονες. Πρόκειται για μία χειρουργική μέθοδο αντιμετώπισης συγγενών καρδιοπαθειών. Η περίδεση της πνευμονικής αρτηρίας (pulmonary artery banding - PAB) είτε με συμβατικό τρόπο, ή με την πλέον σύγχρονη μέθοδο μέσω της συσκευής FloWatchTM προκαλεί τη στένωσή της. Με τον συμβατικό τρόπο η στένωση μπορεί να θεωρηθεί αξονικά συμμετρική, ωστόσο με τη χρήση του FloWatchTM είναι μη αξονικά συμμετρική. Έχει αποδειχθεί ότι τόσο η αξονικά συμμετρική, όσο και η μη συμμετρική περίδεση δημιουργεί διαφόρου βαθμού ίνωση του τοιχώματος της πνευμονικής αρτηρίας. Η αναδόμηση της πνευμονικής αρτηρίας είναι πολύ ηπιότερη στην περίπτωση της περίδεσης με το FloWatchTM. Η διαφοροποίηση αυτή έγκειται κυρίως στο ότι η συμβατική περίδεση προκαλεί για συγκεκριμένη μείωση της διατομής ισχυρότερη μείωση της περιμέτρου της διατομής από εκείνης της περίδεσης με το FloWatchTM. Στην παρούσα εργασία γίνεται αναφορά και ανάλυση των διαφόρων περιπτώσεων ροής σε στενώσεις αρτηριών, των συγγενών καρδιοπαθειών και των τεχνικών περίδεσης της πνευμονικής αρτηρίας. Επιπρόσθετα, μελετήθηκαν και υπολογίστηκαν η μόνιμη και η παλλόμενη ροή σε αξονικά συμμετρική 25% στένωση προκαλούμενη από συμβατική περίδεση, καθώς και η μόνιμη και παλλόμενη ροή σε μη συμμετρική 25% στένωση της πνευμονικής αρτηρίας όπως προκαλείται από το FloWatchTM, μέσω των πακέτων Fluent και Gambit. Η υπολογιστική μελέτη του πεδίου ροής περιλαμβάνει την κατανομή ταχυτήτων, τον προσδιορισμό των περιοχών ανακυκλοφορίας, την κατανομή των πιέσεων και την σύγκριση των παραπάνω μεγεθών με τα αντίστοιχα αποτελέσματα της βιβλιογραφίας. Τέλος, με βάση τα αποτελέσματα γίνεται η σύγκριση των δύο μελετούμενων μεθόδων περίδεσης. Αριθμητικά ρεαλιστικά δεδομένα ελήφθησαν από την καρδιοχειρουργική κλινική του νοσοκομείου Παίδων «Αγία Σοφία». / Cardiovascular diseases are the leading cause of death in developed countries. A stenosis in an artery , caused either by a disease such as an aneurism or by a banding (such as in congenital diseases) can change the characteristics of the blood flow very seriously. The study of the physiological pulsatile flow through a stenosis is very important for the diagnosis and treatment of the arterial diseases. The medical problem which is examined in this study is pulmonary artery stenosis caused by a banding. The banding takes place to reduce the high arterial pressure and finally the blood flow from the heart to the lungs. It is a surgical method used for treatment of congenital heart diseases. The pulmonary artery banding either with the use of the conventional method or the most modern with the use of the FloWatchTM technology causes stenosis of the artery. With the conventional method, stenosis can be considered axially symmetrical while with the use of FloWatchTM it is asymmetrical. It has been proven that both the axially symmetrical and asymmetrical banding cause fibrosis of the pulmonary artery walls of different degrees. The reconstruction of the pulmonary artery is milder where there is banding with FloWatchTM. This differentiation is based mainly on the fact that the conventional banding causes, for a specific decrease of the cross-section, a decrease in the perimeter of the cross-section higher than that of banding with FloWatchTM. In this assignment there is a report of different cases of flow in arterial stenosis, in congenital heart diseases and pulmonary banding techniques. In addition what was studied and appreciated was the steady and pulsatile flow in axially symmetrical 25% stenosis caused by the conventional banding, as well as the steady and pulsatile flow in asymmetrical 25% stenosis of pulmonary artery caused by FloWatchTM with the use of Fluent and Gambit. The numerical study of flow distribution includes velocity distribution, designation of back flow area, distribution of pressure and comparison of these quantities with the results in bibliography. Finally, based on the results, there is a comparison of the two banding methods under study. The numerical realistic data were received from the cardio-surgical clinic of children’s hospital “Aghia Sophia”.