A brief introduction to cancer biology and treatment is presented with a focus on current clinical advances in the delivery of chemotherapy and antiangiogenic therapies. Mathematical oncology is then surveyed with summaries of various models of tumor growth, tumor angiogenesis and other relevant biological entities such as angiogenic growth factors. Both strictly time-dependent ordinary differential equation (ODE)-based and spatial partial differential equation (PDE)-based models are considered. These biological models are first developed into an ODE model where various treatment options can be compared including different combinations of drugs and dosage schedules. This model gives way to a PDE model that includes the spatially heterogeneous blood vessel distribution found in tumors, as well as angiogenic growth factor imbalances. This model is similarly analyzed and implications are summarized. Finally, including the effects of interstitial fluid pressure into an angiogenic activity model is performed. This model displays the importance of factor convection on the angiogenic behaviour of tumours.

A brief introduction to cancer biology and treatment is presented with a focus on current clinical advances in the delivery of chemotherapy and antiangiogenic therapies. Mathematical oncology is then surveyed with summaries of various models of tumor growth, tumor angiogenesis and other relevant biological entities such as angiogenic growth factors. Both strictly time-dependent ordinary differential equation (ODE)-based and spatial partial differential equation (PDE)-based models are considered. These biological models are first developed into an ODE model where various treatment options can be compared including different combinations of drugs and dosage schedules. This model gives way to a PDE model that includes the spatially heterogeneous blood vessel distribution found in tumors, as well as angiogenic growth factor imbalances. This model is similarly analyzed and implications are summarized. Finally, including the effects of interstitial fluid pressure into an angiogenic activity model is performed. This model displays the importance of factor convection on the angiogenic behaviour of tumours.

The regulation of fluid (water) volume in the body is crucial for tissue homeostasis. The interstitial fluid, which comprises almost 20% of the body fluid, is stored in the loose connective tissue and its volume is actively regulated by components of this tissue. The loose connective tissue provides a path for fluid flow from capillaries to the tissue and lymphatics. This fluid is partially stored in the interstitium and the remainder is directed to the lymphatics. The fibroblasts in the loose connective tissue actively compact the fibrous extracellular matrix (ECM) through mechanotransduction via integrins. This in turn, maintains the interstitial fluid pressure and keeps the ground substance underhydrated. The interstitial fluid pressure is part of the forces that regulate the efflux of fluid from capillaries and keep the ground substance underhydrated. The underhydrated ground substance has a potential to take up fluid 3-fold the plasma volume. Therefore, the active contraction of the ECM via fibroblasts is crucial to prevent the risk of evacuation of fluid from capillaries. During pathologies, such as inflammation and carcinogenesis, the interstitial fluid pressure and hence the interstitial fluid volume is altered. The results presented in this thesis show that the signaling events downstream of αVβ3 integrin, collagen-binding β1 integrins, and platelet-derived growth factor receptor β, that induce cell-mediated matrix contraction, included paired function of PI3K and PLCγ, cofilin activation, actin turnover, and generation of actomyosin forces. Furthermore, the results highlight new potential roles for fibrin and αVβ3 integrins, for instance during clearance of edema. Notably, fibrin extravasation at inflammatory sites induced αVβ3 integrin-dependent matrix contraction, leading to normalization of the altered interstitial fluid volume. It also reprograms the expression of ECM-related genes and hence induces ECM turnover. Taken together, these results provide further insight into the regulatory mechanism through which the loose connective tissue actively regulates the interstitial fluid volume.

Intravenous fluid infusion during surgeries is based on clinical practice guidelines. Many factors impact the fluid distribution in the body, mainly the effect of anesthetic gases and surgical stress. Volume kinetics is a method to simulate the distribution and elimination of infusion fluids by considering the dilution of plasma over time. In this work, two volume kinetic models for fluid therapy are described – the single and two-fluid space model. The goal was to estimate five volume kinetic parameters for implementation in a population kinetic model. The method was based on data from an experiment at the University of Texas Medical Branch where the purpose was to examine the effect of the anesthetic gas isoflurane on fluid distribution after a controlled bleeding. In this project, measured hemoglobin concentrations from the experiment were used to determine the plasma dilution over time. Volume kinetic models were constructed by approximating terms in corresponding differential equations. As opposed to the single-fluid space model, the two-fluid space model gave a closer estimation to the experimental data. The two-fluid space model parameters were considered to be suitable for further population kinetic analysis.

The human brain is a complex organ that is responsible for regulating all the physiological processes in the body, ranging from memory to movement. As humans age, the brain goes through a variety of changes including a reduction in glymphatic waste clearance and increase in glial reactivity. Two neurological conditions that affect individuals over the age of 65 include glioblastoma (GBM) and Alzheimer's disease (AD). Interestingly, patients with GBM do not present with AD and vice versa. Both conditions are characterized by a disruption in interstitial fluid flow (IFF) and an increase in neuroinflammation. Throughout the following dissertation, we examined the role of IFF in AD and GBM progression using a three-sided approach (in vivo, in vitro, and in silico). Increased IFF underlies glioma invasion into the surrounding tumor microenvironment (TME) in GBM. We used a 3D hydrogel model of the GBM TME to examine potential pathways by which astrocytes and microglia contribute to glioma invasion. A reduction in IFF contributes to accumulation of the toxic protein amyloid beta (Aβ) in AD. We sought to create a novel, patient-inspired model of the AD hippocampus for examination of the relationship between IFF and Aβ clearance. Human AD and unaffected control hippocampal brain samples were stained for markers of neurons, astrocytes, microglia and Aβ. The percentage of each cell population in the CA1 region of the hippocampus was calculated. We also analyzed the amount and characteristics of the Aβ aggregates present in this hippocampal region. Pearson correlation analysis was completed to assess the relationships between the various cell populations, Aβ load, and patient descriptors. The cell ratios gleaned from the patient samples were incorporated into a novel, 3D hydrogel model of the AD hippocampus. This model features a hydrogel mixture like the native brain extracellular matrix (ECM) and allows for the application of IFF and Aβ. To our knowledge, we are the first group to create a patient-specific triculture model of the AD hippocampus, which is the main site of Aβ aggregation in the AD brain. We used this model to examine the relationship between IFF-mediated Aβ clearance and glial reactivity. The last aim of this dissertation was to create a computational model for examining Aβ binding within the ECM and the effects of IFF on Aβ clearance. In vitro experiments were conducted to generate 3D renderings of glial cells and to determine relevant parameters for our model. Throughout this work, we discuss the relationship between disruption in IFF and glial reactivity in the context of GBM and AD. / Doctor of Philosophy / The human brain is a complex organ that is responsible for regulating all the physiological processes in the body, ranging from memory to movement. As humans age, the brain goes through a variety of changes including a reduction in brain waste removal and an increase in inflammation. Two neurological conditions that affect individuals over the age of 65 include glioblastoma (GBM) and Alzheimer's disease (AD). Interestingly, patients with GBM do not present with AD and vice versa. Both conditions are characterized by a disruption in brain interstitial fluid flow (IFF) and an increase in neuroinflammation. Throughout the following dissertation, we examined the role of IFF in AD and GBM progression using a three-sided approach including analysis of mouse and human tissues, engineered cell models, and computational methods. Specific interactions between brain cell types and their relationships with glioma invasion were examined using a 3D cell model that mimics the brain. Through the work presented here, we also sought to create a novel cell model of the hippocampus region located in the AD brain. We quantified the various cell types in the hippocampus of AD patient samples and incorporated this information into our hydrogel model. The resulting model features three brain cell types (astrocytes, microglia, and neurons) that are added at patient relevant ratios, a matrix that mimics the native brain scaffold, and allows for the application of IFF. In the AD brain there is a reduction in brain waste removal that leads to accumulation of the toxic protein amyloid beta (Aβ). We were successfully able to incorporate this protein within our model so we could assess the relationship between IFF and Aβ removal from the brain. We further studied this relationship using a new computational model of Aβ accumulation in the brain. Throughout this work, we discuss the connection between disrupted IFF and neuroinflammation in the context of GBM and AD.

Glioblastoma (GBM) is the most aggressive and malignant glioma. It accounts for 48.6% of all primary, malignant gliomas with a median survival of 15 months. Infiltration into the surrounding parenchyma is a hallmark of GBM. Radiotherapy is used to address the invasion; however, recent studies have implicated that radiation contributes to increased invasiveness of glioma. Although the effect of radiation on cells has been studied extensively, its effect on the transport of fluid is not well characterized. Transport in the brain which has significant roles in physiology, GBM pathophysiology, and GBM treatment. Thus, understanding the effect of radiation on transport within the lesion and surrounding interstitium will be beneficial in characterizing the effects of radiotherapy in GBM patients. This dissertation seeks to explore the relationship between radiation, transport, and movement of glioma cells and includes the following: 1) Characterizing in vitro motility metrics of glioma stem cell lines in and relating them to in vivo invasion. 2) Studying the effect of radiation on motility, flow-mediated invasion, extracellular matrix components, and transport within the lesion and interstitium. 3) Assessing transport in clinical images and relating transport parameters to progression of GBM. 4) Developing a novel pipeline for applying vector field topology to the study of interstitial fluid flow in glioma. Surprisingly, we found that motility metrics in vitro have a negative correlation trend with in vivo invasion. Next, we found that radiation causes a transient increase in advective flow, and a more sustained decrease in diffusivity in a murine glioma model. Tenascin C was found to correlate significantly with invasion and diffusivity, indicating that it might be a link between radiation, transport, and invasion. Furthermore, interstitial fluid flow was calculated and assessed in clinical images. This showed that interstitial fluid flow velocity magnitude in the tumor correlates with overall survival in GBM patients. Lastly, vector field topology was introduced as a novel method of studying transport that provides more detailed information to identify potential drivers of transport within a flow field. Altogether, this work presents novel insight into the effects of radiation on invasion and transport in GBM. Hopefully, this work can provide a foundation to build upon in efforts of improving treatment planning and clinical outcomes for GBM patients. / Doctor of Philosophy / Glioblastoma (GBM) is the most aggressive glioma. It accounts for 48.6% of all primary, malignant gliomas with a median survival of 15 months. The movement of cancer cells into the surrounding tissue is a defining factor of GBM. Radiotherapy is used after surgery to treat the remaining cancer cells in tissue surrounding the tumor; however, recent studies have implicated that radiation contributes to increased movement of glioma into surrounding tissue. Although the effect of radiation on cells has been studied extensively, its effect on transport of fluid is not well characterized. Interstitial fluid flow in the brain has significant roles in healthy bodily functions, GBM disease state, and GBM treatment. Thus, understanding the effect of radiation on transport within the tumor and surrounding tissue is beneficial in better characterizing the effects of radiotherapy. This dissertation seeks to explore the relationship between radiation, transport, and movement of glioma cells and includes the following: 1) Characterizing in vitro motility metrics of glioma cells in and relating them to in vivo movement into healthy tissue. 2) Studying the effect of radiation on motility, flow-mediated infiltration into healthy tissue, tissue matrix components, and fluid flow within the tumor and surrounding tissue. 3) Assessing transport in clinical images and relating transport parameters to progression of GBM. 4) Developing a novel pipeline for applying vector field topology to the study of interstitial fluid flow in glioma. Surprisingly, we found that motility metrics in vitro have a negative correlation trend with in vivo invasion. Next, we found that radiation causes a transient increase in flow velocity magnitude, and a more sustained decrease in diffusivity in a murine glioma model. Tenascin C, a component of the tissue matrix, was found to correlate significantly with invasion and diffusivity. This indicates that Tenascin C might be a link between radiation, transport, and invasion. Furthermore, interstitial fluid flow was calculated and assessed in clinical images which showed that interstitial fluid flow velocity magnitude in the tumor correlates with survival. Lastly, vector field topology was introduced as a novel method of studying fluid flow in glioma that provides more detailed information regarding the flow field. Altogether, this work presents novel insight into the effects of radiation on fluid flow and cellular movement in GBM. Hopefully, this work can provide a foundation to build upon in efforts of improving treatment planning and clinical outcomes for GBM patients.

Kidney failure results in fluid and toxin accumulation within body fluid compartments, contributing to the excess mortality seen in this condition. Such uremic toxins have been measured in plasma, with levels assumed to reflect extraplasmatic concentrations such as in interstitial fluid (ISF). ISF is separated from plasma by nanometre-order microvascular pores; toxins may not circulate “freely” between the two compartments. This work set out to characterise the ISF in uremic subjects, with the hypothesis that there may be differences with plasma. Any such difference may be clinically relevant, owing to the much larger size of the ISF compartment, its proximity to cell metabolic processes, and its expansion in renal impairment.We used a modified microdialysis technique to successfully sample subcorneal ISF of some the uremic toxins (urea, creatinine, urate, phosphate). Reverse iontophoresis (RI) was also used as a non-invasive technique to sample epidermal ISF of urea. Hollow microneedles were developed and their ability to extract ISF tested in CKD patients and controls. The mechanical properties (pressure, volume, permeability) and biochemical composition (proteomic and metabolomic profiles) of the interstitial compartment were also investigated.Microdialysis and RI performed very well as interstitial uremic toxin sampling techniques. Small differences were seen in steady states between ISF and plasma urea, creatinine, phosphate and urate, with slightly lower ISF levels. Dialysis seemed to enhance this difference, with a lag in the clearance of ISF toxins seen in some patients, most remarkable with phosphate. Metabolomic analysis identified several uremic toxins in ISF, whilst proteomics found some significant differences between the two compartments, with toxins like beta-2 microglobulin occurring in ISF only. Microneedle arrays successfully extracted ISF in 68.8% of patients with oedema. Successful extraction of ISF with microneedles occurred mainly in oedematous patients, who were found to have raised interstitial pressures (ISP) and volumes. ISP correlated significantly with body fluid volumes and seemed time-dependent, lower in more chronic oedema. ISP and volumes also correlated with the oedema depitting time (after thumb pressure), a potential novel parameter that probably relates to tissue hydraulic conductivity and hence volume status and fluid mobility within the interstitium.This study demonstrates that interstitial fluid may need to be considered as a separate active compartment in patients with renal dysfunction, with a different “uremic" composition and unique pathophysiological characteristics that cannot be explained by blood compartment based measurements alone. There is a need for more studies, to further characterise this compartment and elucidate its importance.

High interstitial fluid pressure (IFP) in tumours is recognized as a barrier to drug delivery resulting in reduced efficacy. High IFP impedes the normal process of convective fluid flow (CFF) from blood vessels into the interstitium. The aim of this study was to develop an in vitro model that could be used to measure CFF and to study its effects on drug delivery. The model consists of a transwell cell culture insert which supports the growth of multicell layers (MCL) on collagen coated membranes. A graduated tube is inserted into the transwell and a pressure gradient is applied across the membrane by raising the volume of medium in the tube above that of the bottom chamber. CFF is determined by measuring the weight of medium in the bottom chamber as a function of time. CFF was inversely proportional to MCL thickness and 41.1±3.6µm thick MCL has completely stopped CFF. Using a physiologically relevant hydrostatic pressure of 28mmHg, a CFF of 21µL/min was recorded using a DLD-1 MCL that was 12.21±3.2µm thick. Under these conditions, the rates of penetration of doxorubicin, imatinib and gefitinib were respectively 42, 26 and 13 folds greater than when no CFF exists. Reversing the CFF so that it opposed the drug diffusion gradient significantly impairs drug penetration. In conclusion, a novel in vitro model for assessing the impact of CFF on drug delivery has been developed. This model could be used to evaluate strategies designed to increase drug delivery to solid tumours by modifying the CFF.

Ce mémoire de maîtrise porte sur le développement de microaiguilles hydrogels pour la capture et la détection précoce de biomarqueurs protéiques spécifiques du liquide interstitiel cutané. Le diagnostic précoce d’une maladie et le suivi préventif des paramètres biologiques peuvent effectivement améliorer les traitements et auront un rôle plus important dans les années à venir. Cependant, des obstacles considérables à cette approche persistent, en particulier la nature hautement invasive et perturbatrice des analyses biologiques. Se rendre dans une clinique et subir un prélèvement invasif de sang (ou de liquide biologique) sont des défis considérables par rapport aux traitements courants, qui consistent souvent en des médicaments qui peuvent être pris sans douleur à la maison. Une solution à ces problèmes peut être trouvée dans l'invention de méthodes peu invasives pour le diagnostic et l'analyse des soins de santé, idéalement celles qui peuvent être utilisées à domicile sans nécessiter de personnel formé. À cet égard, les micro-aiguilles (MNs) démontrent un énorme potentiel car leur petite taille garantit qu’elles sont relativement simples et presque indolores. De plus, leur nature simple et à usage unique permet potentiellement une administration à domicile par le patient. Les micro-aiguilles d'hydrogel présentent des caractéristiques bénéfiques à des fins de diagnostic compte tenu de leurs propriétés de gonflement qui permettent d'absorber les fluides corporels tels que le liquide interstitiel (ISF) et de capturer les biomarqueurs. Ces caractéristiques remarquables ont poussé les scientifiques à utiliser des micro-aiguilles d'hydrogel pour des applications de diagnostic. Afin de fournir un contexte pour le développement de cette technologie, cette thèse commence par un examen des principes et des avancées récentes dans le domaine des applications diagnostiques des MN (Chapitre 1). Par la suite, des sections expérimentales, de résultats et de discussion seront présentes sur la fonctionnalisation de l'hydrogel avec des anticorps pour la détection de biomarqueurs spécifiques (Chapitre 2). Le dernier chapitre aborde la conclusion générale et les perspectives d'avenir de cette approche (Chapitre 3). / This master’s thesis focuses on the development of hydrogel microneedles (HMNs) for capture and early detection of specific protein biomarkers form the skin interstitial fluid. Early disease diagnosis and preventative monitoring of biological parameters can effectively improve medical results and anticipate playing a more important part in the forthcoming years. However, considerable barriers to this approach persist, specifically the highly invasive and disruptive nature of biological analyses. Visiting clinics and undergoing invasive blood (or biological fluid) sampling are considerable challenges in comparison with common treatments, which often consist of drugs that may be taken painlessly at home. A solution to these concerns can be found in the invention of minimally invasive methods for diagnostics and healthcare analyzing, ideally ones that may be utilized at home without the requirement for trained staff. In this regard, microneedles (MNs) demonstrate tremendous potential as their small size ensures that they are relatively straightforward and almost painless. Also, their simple and single-use nature potentially permits at-home administration by the patient. HMNs demonstrate beneficial features for the diagnosis purposes considering the swelling properties of them which give the chance of absorbing body fluids such as ISF and capture of the biomarkers. These remarkable features have driven scientists to employ HMNs for diagnostic applications. To provide background for the development of this technology, this thesis begins with a review of the principles and recent advances in the field of diagnostic applications of MNs (Chapter 1). Subsequently, experimental, result, and discussion sections will be present about the functionalization of hydrogel with a model antibody for specific biomarkers detection (Chapter 2). The last chapter discusses the general conclusion and future prospects of this approach (Chapter 3).

Dans ce travail de thèse nous nous sommes intéressés aux phénomènes de transport au sein du réseau lacuno-canaliculaire (RLC) et de l'ostéon dans le tissu osseux cortical. Pour étudier la mécanotransduction ostéocytaire amenant au remodelage osseux, nous avons développé un modèle à trois échelles où sont pris en : l'électrcompte ostatique (modélisée par l'équation de Poisson Boltzmann), l'écoulement du fluide (représenté textit{via} une équation de Stokes modifiée et la conservation de la masse fluide) et le transport ionique (régi par l'équation de Nernst-Planck). L'étude de la distribution du potentiel électrique, a mis en exergue l'importance des double-couches électriques au voisinage des parois chargées des pores. Ces double-couches électriques, ainsi que la composition chimique du fluide donnent lieu à des phénomènes d'osmose et d'électroosmose intervenant dans l'écoulement du fluide interstitiel, et influençant la diffusion efficace des ions dans les pores. L'étude a démarré à l'échelle du pore canaliculaire pour être propagée à l'échelle du canalicule puis de l'ostéon, en utilisant une procédure d'homogénéisation périodique asymptotique. Une étude paramétrique nous a permis de cibler les paramètres agissant sur les phénomènes de transport et pouvant faire réagir les ostéocytes. Il est ressorti de cette étude que les effets électro-chimiques jouent rôle important. Nous avons donc choisi de nous focaliser sur la chimie et plus particulièrement sur les effets des flux ioniques physiologiques sur les ostéocytes dans le RLC. Des expériences, mises en place pour étayer ces aspects ont souligné l'importance des échanges chimiques entre les cellules et le fluide qui les entoure. Finalement, nous avons montré que les phénomènes de transports ayant lieu dans le RLC et dans l'ostéon interagissent les uns les autres, parachevant ainsi la description à trois échelles du tissu cortical / Transport phenomena appearing within the cortical bone lacuno-canalicular network (LCN) and the osteon were the objective of this study. We developped a three-scale model to investigate the osteocyte mechanotranduction which is at the origin of the bone remodeling process. This model took into account three physical phenomena : the electrostatics (through the Poisson-Boltzman equation), the interstitial fluid flow (modeled by a modified Stokes equation) and the ionic transport (governed by a Nernst-Planck equation). Analysis of the electrical potential distribution highlighted the importance of the electrical double layers close to the pore charged surface. These electrical double layers, as well as the interstitial fluid chemical composition, induce osmotic and electroosmotic fluid flows and affect the ionic effective diffusion within the pores. Using a periodic asymptotic homogeneisation procedure, the model at the canalicular pore scale was upscaled at the canalicular scale and then at the osteonal scale. A parametric study pointed out the relevant parameters acting on the transport phenomena and possibly affecting osteocyte mecanosensitivity. Our results emphasized the importance of the electro-chemical effects. We thus focused on the chemistry and more especially on the effects of the physiological ionic fluxes on the osteocyte. In vitro experiments and numrical simulations were performed to elucidate these questions. Our results underlined the importance of the chemical exchanges between the osteocyte and the surrounding fluid. Finally, we showed that fluid flow and chemical transport occuring within the LCN and the osteon interact with each other, thus achieving a three-scale description of the transport phenomena in the osteon