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Supplementary Table 1 and Supplementary Figures 1-5

This thesis is intended to contribute to the field of biomechanics of growth and remodeling of arteries. The work focuses particularly on growth and remodeling caused by sustained hypertension, increased blood flow, and ageing. A structure-based constitutive law is employed, which accounts for the elastic and structural properties of the components of the vascular tissue. Analysis of the biomechanical properties of the arterial wall allows for quantification of the developed wall stresses and strains. The dynamics of arterial growth and remodeling is described by appropriate remodeling rate equations. The corner-stone of this theoretical project is, of course, the development of physiologically relevant evolution laws describing the shear stress- and wall stress-induced growth and remodeling of the arterial wall. The model predictions are presented in the form of an introduction, four chapters (four papers) and a conclusion. The introduction begins with the motivation for this project. The link between mechanical load and remodeling in blood vessels follows. The state of the art on theoretical models of arterial remodeling in response to hypertension, changed flow, and ageing is also presented. The first paper presents a novel theoretical model of hypertension-induced arterial remodeling using a structure-based constitutive law. Arterial remodeling in response to sustained hypertension has been previously modeled using a phenomenological strain energy function (SEF), the parameters of which do not bear a clear physiological meaning. Here, we extend the work of Rachev et al. by applying similar evolution laws to a constituent-based SEF, which includes a statistical description for collagen recruitment in load bearing. Remodeling affects the material properties only through changes in the probability density function of collagen engagement. The model simulates the remodeling of a rabbit thoracic aorta and predicts that, at the final adapted hypertensive state, the wall thickness is increased to conserve the baseline value of hoop stress and the lumen radius remains unchanged to preserve the normotensive levels of intimal shear stress. Furthermore, the remodeling of material properties serves to restore the arterial compliance to control levels. The material at the final adapted state is softer than its normotensive counterpart as indicated by the average circumferential stress-strain curves. Model predictions are in good qualitative agreement with experimental data. The novelty in our findings is that biomechanical adaptation leading to maintenance of compliance at the hypertensive state can be perfectly achieved by appropriate readjustment of the collagen engagement profile alone. The second paper addresses a predictive model of arterial remodeling in response to increased flow using a constituent-based SEF. Prior theoretical models of arterial remodeling in response to changes in blood flow were based on the assumption that material properties of the vascular tissue remain unchanged during the remodeling process. Experimental findings show, however, that increased flow causes structural alterations in the elastin resulting in a decrease in its effective elastic stiffness. To account for these effects, we propose a predictive model of arterial remodeling in response to increased flow hypothesizing that the deviation of the intimal shear stress from its baseline value initiates and drives the variation in the mechanical properties of elastin. The mismatch in wall stresses with respect to baseline values drives the changes in the geometrical parameters of the stress-free configuration. A constrained mixture approach is followed and the artery is modeled as a thick-walled cylindrical tube made of nonlinear, elastic, anisotropic and incompressible material. We make use of literature data for a rabbit thoracic aorta. The model predicts that, at the final adapted state, the arterial compliance depends non-monotonically on the magnitude of the flow, which is in agreement with available experimental data in the literature. The third paper expands the model of the first paper in order to include another major aspect of remodeling in a healthy matured vessel: the new mass that is produced during remodeling results from an increase in the mass of smooth muscle cells and collagen fibers. The model also takes into consideration the effect of the average pulsatile strain on collagen fiber engagement in load bearing. Remodeling of a human thoracic aorta was simulated by the model and the results agree well with published model predictions and experimental data. According to the model, the total arterial mass increases fast in the early stages of remodeling and does not vary thereafter, despite any further geometrical changes as well as structural reorganization of the collagen fibers. Furthermore, the perfect or incomplete restoration of the average pulsatile strain at the end of the remodeling process has an impact on the time course of certain parameters of the model such as the opening angle. Future experimental studies on the time variation of compliance, opening angle and mass fractions will validate and improve the introduced hypotheses of the model. In the fourth paper we perform a theoretical study of aortic remodeling in ageing using a constituent-based modeling approach. The model is based on two major hypotheses. First, mechanical fatigue failure in the elastin structure is caused by the pulsatile wall strain and the number of cardiac cycles. The fragmentation of elastin results in an increase in the inner radius at the zero-load state. Second, the accumulation of advanced glycation end products (AGEs) over time increases the cross-linking of collagen fibers making the recruitment of the fibers occur at lower strains and more abruptly. This raises the stiffness of the collagen fiber network. Furthermore, the geometrical remodeling follows the increase in the lumen radius at the load-free configuration and preserves the baseline level of circumferential stress at the inner and outer surface under mean pressure. Additionally, the geometrical changes lead to an increase in the content of collagen fibers, affecting accordingly the mass fractions of elastin and smooth muscle cells. We employ the constituent-based SEF of Zulliger and Stergiopulos in order to verify the results of their curve-fitting study on the elastic and structural properties of the human thoracic aorta. We further monitor the time variation of certain geometrical characteristics. Model results agree well with published experimental data. According to the model, the fragmentation of elastin only affects the geometrical remodeling, with the total arterial mass being increased with increased damage of elastin. With progressed age, elastin contributes less in bearing load, allowing the stiff collagen to lower the arterial compliance and cause a monotonic decrease in the pulsatile strain. Also, the accumulation of AGEs over time impacts on both the material and the geometrical parameters, with the latter being affected at high ages. The net effect is a decrease in the arterial dimensions and mass at high ages due to an increased accumulation of AGEs. Surprisingly, the time course of the mass fractions of the wall components is not affected by the increase or decrease of AGEs, indicating that the geometrical and structural reorganization of the vascular tissue is done in such a way in order to preserve the relative content of the wall constituents. There is a need for more experimental data to support the conclusions of the parametric analysis. The concluding section summarizes the main results of the thesis, presents the improvements made over previous theoretical investigations, emphasizes the need for more experimental data in order to validate and improve the models, and proposes future extensions of the work.

Includes bibliographical references (p. 137-146). Number of sources in the bibliography: 178 Thesis (Ph. D.) -- University of Cyprus, Faculty of Engineering, Department of Mechanical and Manufacturing Engineering, 2018. The University of Cyprus Library holds the printed form of the thesis. Οι όγκοι παράγουν μηχανικές δυνάμεις κατά τη διάρκεια της ανάπτυξης και της εξέλιξης τους. Αυτές οι δυνάμεις είναι ικανές να συμπιέζουν αγγεία, μειώνοντας τα ποσοστά αιμάτωσης και οξυγόνου. Τόσο η μειωμένη αιμάτωση όσο και η αυξημένη πίεση του υγρού εμποδίζουν την μεταφορά φαρμακευτικών σκευασμάτων μέσω του αίματος, μειώνοντας την αποτελεσματικότητα της χημειοθεραπείας και νανοθεραπείας. Παρά τη μεγάλη σημασία του μικροπεριβάλλοντος για την παθολογία του καρκίνου, υπάρχουν λιγοστές μελέτες για τη μοντελοποίηση και πειραματική μέτρηση των μηχανικών ιδιοτήτων των όγκων και για το πώς αυτές οι παράμετροι επηρεάζουν την ανάπτυξη του όγκου. Σε αυτή την διδακτορική διατριβή αρχικά χαρακτηρίσαμε τις μηχανικές ιδιότητες καρκινικών όγκων και υπολογίσαμε το εύρος των αναπτυσσόμενων δυνάμεων. Στη συνέχεια, παρουσιάζονται στοιχεία για το πώς η χρήση φαρμάκων τα οποία σκοπό έχουν να μειώσουν τις δυνάμεις αυτές θα μπορούσαν να χρησιμοποιηθούν σε συνδυασμό με την χημειοθεραπεία για τη βελτίωση της αποτελεσματικότητας της θεραπείας. Τέλος, επικεντρωθήκαμε στην μελέτη της μοντελοποίησης των μηχανισμών αγγειογένεσης σε καρκίνους του εγκεφάλου (γλιοβλαστώματα), μέσω των οποίων τα καρκινικά κύτταρα μπορούν να οξυγονόνονται και κατ’επέκταση να διατηρούν την περαιτέρω ανάπτυξη του όγκου. Στο πρώτο κεφάλαιο πραγματοποιήσαμε πειράματα μηχανικής συμπίεσης σε δύο τύπους καρκινικών όγκων και διαπιστώσαμε ότι η πειραματικά απόκριση προσαρμόζεται καλύτερα σε μια καταστατική εξίσωση εκθετικής μορφής. Ακολούθως, ενσωματώσαμε την καταστατική αυτή εξίσωση, καθώς και άλλες κοινές για συνδετικούς ιστούς εξισώσεις σε ένα υφιστάμενο μοντέλο ανάπτυξης καρκινικών όγκων. Παρατηρήθηκε ότι οι αναπτυσσόμενες δυνάμεις καθώς και ο ρυθμός ανάπτυξης του όγκου ήταν ανεξάρτητος από την επιλογή της καταστατικής εξίσωσης, αλλά εξαρτόταν έντονα από τις μηχανικές αλληλεπιδράσεις με τον περιβάλλοντα φυσιολογικό ιστό. Στο δεύτερο κεφάλαιο, μελετήσαμε την δυνατοτητα χρήσης του αντι-ινωτικού φαρμάκου Tranilast (Rizaben®) για την μείωση των μηχανικών δυνάμεων σε δύο μοντέλα όγκων του μαστού. Αποδείξαμε πειραματικά ότι το Tranilast μειώνει τις μηχανικές δυνάμεις, βελτιώνει την αιμάτωση του όγκου και ενισχύει σημαντικά την αποτελεσματικότητα των εγκεκριμμένων φαρμάκων για καρκίνους του μαστού: doxorubicin, Abraxane® και Doxil®. Στο τρίτο κεφάλαιο, σχεδιάσαμε νέα πειράματα, χρησιμοποιώντας τέσσερα μοντέλα καρκινικών όγκων, για να μετρήσουμε την μηχανική τάση που αναπτύσσεται λόγω της διόγκωσης του υαλουρονικού οξέως στο εσωτερικό των όγκων και για να συσχετίσουμε την τάση αυτή με τα δομικά συστατικά των καρκινικών όγκων, καθώς και της αιμάτωση τους. Τα δεδομένα μας αποκάλυψαν μια αντίστροφη σχέση μεταξύ της αιμάτωσης και της τάσης διόγκωσης του όγκου, υποδηλώνοντας ότι η μείωση της τάσης διόγκωσης, που μπορεί να προέλθει με μείωση των επιπέδων υαλουρονικού οξέως. Στο τέταρτο κεφάλαιο, χρησιμοποιώντας πειραματικά δεδομένα από δύο μοντέλα καρκίνου του μαστού και χορηγώντας στους όγκους δύο κλινικά εγκεκριμένα αντι-ινωτικά φάρμακα (tranilast and pirfenidone), διαπιστώσαμε ότι η συσσώρευση των δυνάμεων σε όγκους συσχετίζεται με την περιεκτικότητα τους σε υαλουρονικό οξύ και με το μέτρο ελαστικότητας τους. Τέλος, χρησιμοποιώντας μια σειρά από πειραματικά δεδομένα σε γλοιώματα και μεταστάσεις στον εγκέφαλο από κύτταρα καρκίνου του μαστού, προερχόμενα από το εργαστήριο του καθηγητή Rakesh K. Jain του Γενικού Νοσοκομείου της Μασσαχουσέτης των ΗΠΑ αναπτύχθηκε ένα μαθηματικό μοντέλο για τους μηχανισμούς αγγιογένεσης στους όγκους αυτούς και προτάθηκαν μεθοδολογίες για την επιτυχή στόχευση των μηχανισμών αυτών που μπορούν να οδηγήσουν σε αποτελεσματικότερες θεραπείες. Cancer mechanopathology deals with the causes, consequences and remedies for the effects of tumor mechanics on the pathology of cancer and focuses on the development of therapeutic strategies to reengineer solid tumors in order to improve therapy. Specifically, solid tumors generate mechanical forces during growth and progression. These forces are able to compress blood and lymphatic vessels, increasing the tumor interstitial fluid pressure, reducing perfusion rates, and creating hypoxia. Both hypo-perfusion and elevated fluid pressure hinder delivery of blood-borne therapeutic agents, lowering the efficacy of chemo- and nanotherapies. Despite the great importance of the mechanical microenvironment to the pathology of cancer, there are limited studies for the constitutive modeling and the mechanical properties of tumors and on how these parameters affect tumor growth. In this thesis, we characterized the tissue-level mechanical stresses found in tumor, namely i) the externally applied stress ii) the swelling stress and iii) the growth-induced or residual stress. Subsequently, we tested the hypothesis that alleviation of these mechanical stresses repurposing clinically approved anti-fibrotic drugs can be used in combination with chemotherapy to improve treatment efficacy. Finally, we developed mathematical models for the study of the mechanisms of angiogenesis in brain tumors, incorporating the effect of co-option of the host vasculature by cancer cells, which is a strategy with which some cancer cells can sustain tumor progression. In the first chapter, we performed unconfined compression experiments in two tumor types and found that the experimentally measured stress-strain response is better fitted to an exponential constitutive equation and we incorporated these constitutive equations into a biomechanical model of tumor growth. We found that the evolution of stress during progression and the growth rate of the tumor are independent from the selection of the constitutive equation, but depend strongly on the mechanical interactions with the surrounding host tissue. In the second chapter, using two orthotopic mammary tumor models, we demonstrate that the clinically approved anti-fibrotic drug Tranilast can be repurposed to reduce intratumoral mechanical stresses, improve tumor perfusion and significantly enhance the efficacy of the common anti-cancer drugs: doxorubicin, Abraxane and Doxil. In the third chapter, we designed an experimental strategy, using four orthotopic tumor models, to measure the stress owing to the swelling of hyaluronan and related swelling to the organization of collagen and hyaluronan in the tumors, as well as to tumor perfusion. In the fourth chapter, using experimental data from two orthotopic breast tumor models and treating tumors with two clinically approved anti-fibrotic drugs (tranilast and pirfenidone), we found that accumulation of residual forces in tumors are associated with hyaluronan content and the elastic modulus of the tumor. Finally, in collaboration with the team of Professor Rakesh K. Jain at Massachusetts General Hospital, we developed a mathematical model for the angiogenic mechanisms of brain tumors, which was validated using a series of experimental data in orthotopic gliomas and brain metastasis from breast cancer cells collected from the group of Professor Jain. The model also proposed strategies for targeting the angiogenic mechanisms in order to improve therapy.