Homogenization Model for Aberrant Crypt Foci

Several explanations can be found in the literature about the origin of colorectal cancer. There is however some agreement on the fact that the carcinogenic process is a result of several genetic mutations of normal cells. The colon epithelium is characterized by millions of invaginations, very small cavities, called crypts, where most of the cellular activity occurs. It is consensual in the medical community, that a potential first manifestation of the carcinogenic process, observed in conventional colonoscopy images, is the appearance of Aberrant Crypt Foci (ACF). These are clusters of abnormal crypts, morphologically characterized by an atypical behavior of the cells that populate the crypts. In this work an homogenization model is proposed, for representing the cellular dynamics in the colon epithelium. The goal is to simulate and predict, in silico, the spread and evolution of ACF, as it can be observed in colonoscopy images. By assuming that the colon is an heterogeneous media, exhibiting a periodic distribution of crypts, we start this work by describing a periodic model, that represents the ACF cell-dynamics in a two-dimensional setting. Then, homogenization techniques are applied to this periodic model, to find a simpler model, whose solution symbolizes the averaged behavior of ACF at the tissue level. Some theoretical results concerning the existence of solution of the homogenized model are proven, applying a fixed point theorem. Numerical results showing the convergence of the periodic model to the homogenized model are presented.Comment: 26 pages, 4 figure

Colorectal Cancer Through Simulation and Experiment

Colorectal cancer has continued to generate a huge amount of research interest over several decades, forming a canonical example of tumourigenesis since its use in Fearon and Vogelstein’s linear model of genetic mutation. Over time, the field has witnessed a transition from solely experimental work to the inclusion of mathematical biology and computer-based modelling. The fusion of these disciplines has the potential to provide valuable insights into oncologic processes, but also presents the challenge of uniting many diverse perspectives. Furthermore, the cancer cell phenotype defined by the ‘Hallmarks of Cancer’ has been extended in recent times and provides an excellent basis for future research. We present a timely summary of the literature relating to colorectal cancer, addressing the traditional experimental findings, summarising the key mathematical and computational approaches, and emphasising the role of the Hallmarks in current and future developments. We conclude with a discussion of interdisciplinary work, outlining areas of experimental interest which would benefit from the insight that mathematical and computational modelling can provide

Analyzing the effects of scaffold and synthesized material properties in an in vitro colonic epithelial cell model

The epithelial layer of the large intestine displays a unique structural biology known as intestinal crypts, invaginations within the epithelial wall which display spontaneous polarization between stem cells at the base of the crypt and differentiated cells approaching the epithelial lumen. This layer is supported by the lamina propria, a supportive and connective layer of tissue which contains a number of extracellular proteins. This layer of epithelial cells is coated by a two-tiered mucus layer, with a compacted inner layer anchored within the crypt goblet cells and a more porous gel-like outer layer which contains bacteria and other debris. This tissue architecture presents a unique opportunity for studying the effects of physical microenvironment properties on stem cell behavior in vitro. It also provides a useful platform for the synthesis and analysis of intestinal mucus, which in recent years has become an important focus in numerous disease models. This dissertation focuses on the analysis of the effects of altering the physical structure of a cell scaffold on in vitro colonic cell culture, as well as the mechanical and chemical properties of generated in vitro mucus. Chapter Two of this dissertation focuses on the rheological and biochemical analysis of generated in vitro mucus, which was produced by a monolayer of colonic epithelial cells using an air-liquid interface and a type I collagen hydrogel scaffold. This mucus was directly compared to mucus harvested from ex vivo colon tissue resections, and demonstrated that this system produces mucus with similar properties to native mucus, though ex vivo mucus did form larger overall mucus complexes. Chapters Three and Four demonstrate the creation of a gradient of surface properties on a single scaffold template via the use of controlled silane vapor deposition. Using this template to create in vitro crypts with controlled microcurvature in the stem cell niche, it was found that crypts with convex curvature displayed higher levels of proliferative activity than flat or convex crypts. It was also found that crypts with convex curvature displayed a higher level of globular, unorganized actin in their extracellular structure.Doctor of Philosoph

Creation of an In-Vitro Generated Colonic Stem-Cell Niche Using Gradient-Generating Microdevices

The limitations of existing cell culture and animal studies have provided an impetus for the development of alternative cell based in vitro models that better mimic the complex structures and functions of living organs. This thesis lays the groundwork for the development of an in vitro model of the colonic epithelium by focusing on the development of microdevices to recreating the colonic stem-cell niche. New advances enable long-term organotypic culture of colonic epithelial stem cells that develop into structures known as colonoids. Colonoids represent a primary tissue source acting as a potential starting material for development of an in vitro model of the colon. However for that to be possible, there needs to an improved crypt isolation and 3-D colonoid protocols. In the first chapter, an incubation buffer and time are outlined, along with the finding that 50% Matrigel resulted in the highest colonoid formation efficiency. In the second chapter, threshold concentrations of the key Wnt-signaling factors are discovered. While critically important to homeostatic renewal, the threshold concentrations of factors such as Wnt-3a and R-spondin1 that promote stem cell renewal are unknown. A simple, linear gradient-generating device was used to screen a wide range of Wnt-3a and R-spondin1 concentrations for their impact on a large number of colonoids. A Wnt-3a concentration of 60 ng/mL and R-spondin1 concentration of 88 ng/mL were identified as the critical concentrations required for stem-cell renewal and colonoid expansion. The lower factor concentrations yielded the added benefit of a more morphologically appropriate colonoid possessing columnar cells surrounding a central lumen with active crypt-like bud formation. In the final chapter, a gradient-generating device was used to introduce variable concentrations of the two key Wnt-signaling proteins along the length of a single colonoid. After 5 days in culture under a combination of Wnt-3a and R-spondin gradients, novel image analysis techniques leveraged the intrinsic fluorescence of the mouse model to quantify the levels of stem cell polarity across a colonoid. The microenvironment able to create a stem cell niche within a colonoid by applying external growth factors in a graded fashion across the colonoid.Doctor of Philosoph

Microphysiological system with continuous control and sensing of oxygen elucidates hypoxic intestinal epithelial stem cell fates

Providing primary human stem cells with the optimal environmental factors required to promote expansion and differentiation is no trivial task in biomedical research. Many diseases and pathologies are caused by deficiencies in oxygen supply or regulation. Here, intestinal ischemia/reperfusion injury is presented as an example to highlight the detrimental impact of loss of oxygen, i.e. hypoxia, on the intestinal epithelium. This dissertation focuses on oxygen as one key environmental factor that must be monitored to mediate cell death and facilitate cell expansion. Typical tissue culture platforms, such as polystyrene well plates or flasks, cannot supply adequate oxygen to cells nor measure oxygen concentrations at the cell-media or cell-tissue interface. A microphysiological system (MPS) provides an advantageous platform to design and fabricate more physiologically relevant cell culture microenvironments that can be continuously monitored in real-time. Oxygen can also be controlled in MPS using the appropriate materials, and, furthermore, oxygen can be monitored with many integrated sensors. Here, two MPS are designed and built to investigate the role of severe tissue hypoxia on (i) tumorigenesis in breast epithelial tissue and (ii) on stem cell function, i.e. proliferation and pluripotency, in the intestinal epithelium. Oxygen monitoring is performed in each MPS using embedded micro-hydrogel oxygen sensors via phosphorescence detection. For the study of hypoxia on intestinal epithelial stem cell function using the developed MPS, significant molecular biology, including bulk and single cell RNA sequencing, data is also presented.Doctor of Philosoph

Improving the Accessibility of Chemical Cytometry Assays for the Investigation of Sphingosine Kinase Activity in Single Cells

Sphingolipids are an integral part of eukaryotic cell membranes and are involved in regulating cell survival, proliferation, and migration. The sphingolipid pathway, and more specifically, sphingosine kinase, has been implicated in many diseases, including Alheimer’s disease, diabetes, multiple sclerosis, COVID-19, leukemia, colorectal cancer, and many other cancers. As such, manipulation of the sphingosine rheostat through inhibition of SK has long been a therapeutic target of great interest. Several assays have been developed for analyzing sphingolipids in cells, including chromatography techniques, microscopy, mass spectrometry, and capillary electrophoresis (CE). CE offers copious advantages over other separation techniques that make it especially amenable for chemical cytometry; CE has high peak capacity, superb resolving power, and excellent limits of detection that enable analysis of individual cells. the use of CE has not been adopted clinically nor has it been widely adopted in research laboratories. This dissertation describes work toward improving accessibility of CE-based chemical cytometry measurements through reducing instrument cost and complexity as well as improving assay throughput. Chapter 2 of this dissertation describes the characterization of silicon photomultipliers (SiPMs) as fluorescence detectors in chemical cytometry. Many chemical cytometry assays have employed photomultiplier tubes (PMTs), but PMTs are relatively expensive and can be easily damaged compared to other fluorescence detectors. Conversely, SiPMs are more rugged and are available at a fraction (< 5%) of the cost and demonstrated comparable performance to PMTs. Chapter 3 describes work toward improving the accuracy and versatility of chemical cytometry assays through rational reporter design. A “fix and click” strategy is developed, where an alkyne-terminated reporter is loaded into cells, the cells are fixed and enzyme activity halted, and the fluorophore necessary for fluorescence detection is added to the alkyne reporter and metabolites through a click chemistry reaction. The alkyne-terminated reporter more closely mimics native sphingosine and is expected to provide a more accurate depiction of signaling in the sphingolipid pathway relative to the more commonly used sphingosine fluorescein. Additionally, the “fix and click” strategy offers the benefits of cell fixation, including the ability to separate in space and time the processes of reporter loading and cell analysis. Chapter 4 describes work toward improving the throughput of chemical cytometry assays through parallelization. This chapter describes the development of a microdevice that not only improves throughput through decreasing separation time, but also by analyzing several cells simultaneously. The innovations described in this dissertation are expected to improve the accuracy and accessibility of CE-based chemical cytometry assays.Doctor of Philosoph

Towards human-relevant preclinical models: fluid-dynamics and three-dimensionality as key elements

The activity of research of this thesis focuses on the relevance that appropriate in vitro fully humanized models replicating physiological microenvironments and cues (e.g., mechanical and fluidic) are essential for improving human biology knowledge and boosting new compound testing. In biomedical research, the high percentage of the low rate of successful translation from bench to bedside failure is often attributed to the inability of preclinical models in generating reliable results. Indeed, it is well known that 2D models are far from being representative of human complexity and, on the other side, although animal tests are currently required by regulatory organizations, they are commonly considered unpredictive. As a matter of fact, there is a growing awareness that 3D human tissue models and fluid-dynamic scenarios are better reproducers of the in vivo context. Therefore, during this PhD, I have worked to model and validate technologically advanced fluidic platforms, where to replicate biological processes in a systemic and dynamic environment to better assess the pharmacokinetics and the pharmacodynamics of drug candidates, by considering different case studies. First, skin absorption assays have been performed accordingly to the OECD Test Guidelines 428 comparing the standard diffusive chamber (Franz Diffusion Cell) to a novel fluidic commercially available organ on chip platform (MIVO), demonstrating the importance of emulating physiological fluid flows beneath the skin to obtain in vivo-like transdermal penetration kinetics. On the other hand, after an extensive research analysis of the currently available intestinal models, which resulted insufficient in reproducing chemicals and food absorption profiles in vivo, a mathematical model of the intestinal epithelium as a novel screening strategy has been developed. Moreover, since less than 8% of new anticancer drugs are successfully translated from preclinical to clinical trials, breast, and ovarian cancer, which are among the 5 most common causes of death in women, and neuroblastoma, which has one of the lowest survival rates of all pediatric cancers, have been considered. For each, I developed and optimized 3D ECM-like tumor models, then cultured them under fluid-dynamic conditions (previously predicted by CFD simulations) by adopting different (customized or commercially available) fluidic platforms that allowed to mimic u stimuli (fluid velocity and the fluid flow-induced shear stress) and investigate their impact on tumor cells viability and drug response. I provided evidence that such an approach is pivotal to clinically reproduce the complexity and dynamics of the cancer phenomenon (onset, progression, and metastasis) as well as to develop and validate traditional (i.e., platin-based drugs, caffein active molecule) or novel treatment strategies (i.e., hydroxyapatite nanoparticles, NK cells-based immunotherapies)

Structured Equations for Complex Living Systems - Modeling, Asymptotics and Numerics

Complex living systems differ from those systems whose evolution is well described by the laws of Classical Physics. In fact, they are endowed with self-organizing abilities that result from the interactions among their constituent individuals, which behave according to specific functions, strategies or traits. These functions/strategies/traits can evolve over time, as a result of adaptation to the surrounding environment, and are usually heterogeneously distributed over the individuals, so that the global features expressed by the system as a whole cannot be reduced to the superposition of the single functions/strategies/traits. Quoting Aristotle, we can say that, within these systems, "the whole is more than the sum of its parts". As a result, when we study the dynamics of complex living systems, there are new concepts that come into play, such as adaptation, herding and learning, which do not belong to the traditional vocabulary of physical sciences and make the dynamics of these systems hardly to be forecast. Moving from the above considerations, the subject of my PhD was the development and the study of structured equations for population dynamics (partial differential equations and integro-differential equations) applied to modelling the evolution of complex living systems. In particular, I designed models for multicellular systems, living species and socio-economic systems with the aim of inspecting mechanisms underlying the emergence of collective behaviors and self-organization. In the framework of structured equations, individuals belonging to a given system are divided into different populations and heterogeneously distributed characteristics are modelled by suitable independent variables, the so-called structuring variables. For each population, a function describing the distribution of the individuals over the structuring variables is introduced, which evolves through a partial differential equation, or an integro-differential equation, whose parameter functions are defined according to the phenomena under study. I decided to use such mathematical framework since it makes possible to effectively model the afore mentioned complexity aspects of living systems and provides an efficient way to reduce complexity in view of the mathematical formalization. With particular reference to multicellular systems, I focused on the design and the study of mathematical models describing the evolutionary dynamics of cancer cell populations under the selective pressures exerted by therapeutic agents and the immune system. Proliferation, mutation and competition phenomena are included in these models, which rely on the idea that the process leading to the emergence of resistance to anti-cancer therapies and immune action can be considered, at least in principles, as a Darwinian micro-evolution. It is worth noting that most of these models stem from direct collaborations with biologists and clinicians. Besides local and global existence results for the mathematical problems linked to the models, my PhD thesis presents results related to concentration phenomena arising in phenotype-structured equations and opinion-structured equations (i.e., the weak convergence of the solutions to sums of Dirac masses), and with the derivation of macroscopic models from space-velocity structured equations. From the applicative standpoint such concentration phenomena provide a possible mathematical formalization of the selection principle in evolutionary biology and the emergence of opinions; macroscopic models, instead, offer an overall view of the systems at hand. Numerical simulations are performed with the aim of illustrating, and extending, analytical results and verifying the consistency of the model with empirical dat

A Complete Approach to Predict Biodistribution of Nanomaterials Within Animal Species from In-vitro Data

Smart drug-design for antibody and nanomaterial-based therapies allows for optimization of drug efficacy and more efficient early-stage pre-clinical trials. The ideal drug must display maximum efficacy at target tissue sites, but to track and predict distribution to these sites, one must have a mechanistic understanding of the kinetics involved with the individual cells of the tissue itself. This process can be tracked through biological simulations coupled with in-vitro approaches, which result in a rapid and efficient in-depth understanding of drug transport within tissue vasculature and cellular environment. As a result, it becomes possible to predict drug biodistribution within live animal tissue cells without the need for animal studies. Herein, we use in-vitro assays to translate transport kinetics to whole-body animal simulations to predict drug distribution from vasculature into individual tissue cells for the first time. Our approach is based on rate constants obtained from an in-vitro assay that accounts for cell-induced degradation, which are translated to a complete animal simulation to predict nanomedicine biodistribution at the single cell level. This approach delivers predictions for therapies of varying size and type for multiple species of animals solely from in-vitro data. Thus, we expect this work to assist in refining, reducing, and replacing animal testing, while at the same time, giving scientists a new perspective during early stages of drug development