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In this work, a mathematical modelling approach is taken to improve and optimize the designs of bioartificial liver (BAL) systems. BALs are an alternative therapy for the extremely serious condition of liver failure where liver transplant is currently the only viable option. As yet, large-scale clinical trials have not been successful enough in order for BALs to gain regulatory approval. Through the work in this report, it is envisaged that BAL design can be improved to the point where they can gain clinical acceptanceOne of the main issues in BAL design is the provision of adequate oxygen to the cell mass. To this end, a mathematical model to describe oxygen mass transport is developed based on the principle of Krogh cylinders. The results of this model are subsequently interpreted and presented in Operating Region charts, an image of a parameter space that corresponds to viable BAL designs. These charts allow several important design trends to be identified, e.g. numerous short and thin hollow fibres are favourable over fewer thicker, longer fibres. In addition, it is shown that a physiologically relevant cell number of more than 10% of the native liver cell mass can be supported in these devices under the right conditions. Subsequently the concept of the Operating Region is expanded to include zonation, a metabolic phenomenon where local oxygen tension is a primary modulator of liver cell function. It is found that zonation profiles can be well controlled and under standard conditions a plasma flow rate of 185 ml/min to the BAL would distribute the three metabolic zones evenly. Finally, the principles of the Operating Region charts and zonation are applied to three existing commercial BAL designs; the HepaMate, BLSS and ELAD systems. In each case it could be seen that the default designs of each system did not present ideal environments for liver cells. Through consideration of zonation profiles, each device design and operating parameters could be optimized to produce in vivo-like environments. In the case of the ELAD, reducing the plasma flow rate from 500 to 90 ml/min resulted in a balanced zonation profile. Overall, the work in this report has developed and detailed a series of tools that will assist a BAL designer in making judicious choices over bioreactor design and operating parameters. As a result, it is hoped that BALs can take a step forward towards clinical practice and ultimately saving lives.

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Expanding cell populations extracted from patients or animals is essential to the process of tissue engineering and is commonly performed in laboratory incubation devices known as bioreactors. Bioreactors provide a means of controlling the chemical and mechanical environment experienced by cells to ensure growth of a functional population. However, maximising this growth requires detailed knowledge of how cell proliferation is affected by bioreactor operating conditions, such as the flow rate of culture medium into the bioreactor, and by the initial cell seeding distribution in the bioreactor. Mathematical modelling can provide insight into the effects of these factors on cell expansion by describing the chemical and physical processes that affect growth and how they interact over different length- and time-scales. In this thesis we develop models to investigate how cell expansion in bioreactors is affected by fluid flow, solute transport and cell seeding. For this purpose, a perfused single-fibre hollow fibre bioreactor is used as a model system. We start by developing a model of the growth of a homogeneous cell layer on the outer surface of the hollow fibre in response to local nutrient and waste product concentrations and fluid shear stress. We use the model to simulate the cell layer growth with different flow configurations and operating conditions for cell types with different nutrient demands and responses to fluid shear stress. We then develop a 2D continuum model to investigate the influence of oxygen delivery, fluid shear stress and cell seeding on cell aggregate growth along the outer surface of the fibre. Using the model we predict operating conditions and initial aggregate distributions that maximise the rate of growth to confluence over the fibre surface for different cell types. A potential limitation of these models is that they do not explicitly consider individual cell interaction, movement and growth. To address this, we conclude the thesis by assessing the suitability of a hybrid framework for modelling bioreactor cell aggregate growth, with a discrete cell model coupled to a continuum nutrient transport model. We consider a simple set-up with a 1D cell aggregate growing along the base of a 2D nutrient bath. Motivated by trying to reduce the high computational cost of simulating large numbers of cells with a cell-based model, and to assess the validity of our previous continuum description of cell aggregate growth, we derive a continuum approximation of the discrete model in the large cell number limit and determine whether it agrees with the discrete model via numerical simulations.

Made available in DSpace on 2014-06-11T19:23:03Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-03-01Bitstream added on 2014-06-13T19:08:50Z : No. of bitstreams: 1 avila_rp_me_botib.pdf: 756948 bytes, checksum: 1b6fa59ffd51fb229b44fcfa0d2e4ed5 (MD5) / O caranguejo-uçá, Ucides cordatus, tem fundamental importância para os manguezais, seu ambiente natural, realizando a decomposição de matéria orgânica, e também sendo um importante biomonitor de áreas críticas. Sua comercialização é considerada a atividade econômica mais importante relacionada a manguezais, e essencial para o sustento das comunidades ribeirinhas. Desde 1997, têm sido observados eventos de mortandade das populações dessa espécie, com redução de até 85% das coletas. Em tais eventos, os caranguejos doentes apresentavam sintomas comuns, entre eles, uma considerável dificuldade de locomoção, e consequentemente, dificuldade de retornar às suas tocas. Por essa razão, esta enfermidade foi chamada de Doença a do Caranguejo Letárgico (DCL). Em 2005, comprovou-se que o agente causador da DCL é o fungo patogênico Exophiala cf psycrophila, um fungo do Filo Ascomycota... / The mangrove crab, Ucides cordatus, plays a crucial role in a variety of ecosystem processes in its environment, such as nutrient cycling, and it is a biomonitor of critical areas. Moreover, it is an important component in the economy of several underprivileged communities that depend on it for their subsistence. Beginning in 1997, massive mortalities of U. cordatus have been report by crabcollectors, such as 85% reduction in collection rates in some regions. Crabs in areas of high mortality share several common symptoms, such as lethargy, poor motor control and inability to return to the upright position when turned upside down. Hence, this pathology is called Lethargic Crab Disease (LCD). Finally, in 2005, there were several evidences showing that LCD is caused by a fungus of Phylum Ascomycota, Exophiala cf psycrophila. The DCL fungus is not easily found among the periods in which the mortalities occur, been detected only into the mangrove crab U. cordatus, all asymptomatic. There is also no evidence of the presence of this fungus in the soil or plant samples of the mangrove. As a result, the initial hypothesis is that the disease spreads among the estuaries through dispersal of the fungus by the sea. Based on the epidemiology of the LCDdisease,we construct amathematical model using a system of partial differential equations, considering diffusion and advection processes, to describe the dispersion of the disease through the mangrove complexes. The aim of this work is to find travelling waves solutions for the developed model, that connect two equilibrium points. For this, we analyse the characteristic polynomial fromthe jacobianmatrix evaluated at one of equilibrium points, the disease-free equilibrium, and present results about the necessary conditions for the existence of travelling wave solution, numerical simulations and finally, estimate the minimum value... (Complete abstract click electronic access below)

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Colorectal cancer has the third highest mortality and incidence rates of all cancers worldwide, but the prognosis for long-term survival is good if diagnosed early. It is a well-characterised disease, and is initiated in colonic crypts which line the colon wall. The aim of this thesis is to use mathematical modelling to describe the heavily regulated cell renewal cycle in the crypt to determine the key features of the system kinetics, and help to explain the initiation of tumourigenesis. The dynamics of a single colorectal crypt is considered using a compartmental approach, which accounts for populations of stem, transit-amplifying and fullydifferentiated cells. A number of different model formulations are derived, and their validity and suitability are discussed. Two mechanisms are presented that could regulate the growth of cell numbers and maintain homeostasis (equilibrium), and it is illustrated how a model can describe both regulated and unregulated growth, with cancer-driving cells deriving from stem and/or transit cells. This model is used to explain the long lag phases observed in carcinogenesis, which occur between periods of rapid tumour expansion, before unlimited growth in cell numbers ensues. Significantly, it is found that, contrary to general belief, the proportion of cancer-driving cells in the exponential growth phase of a tumour may vary depending on tumour type. The process of cells accumulating mutations is also examined by considering both a stochastic individual cell-based model and an analytic approach. Finally, an ordinary differential equation model is shown to be valid by considering a simplified description of a one-dimensional spatial model, and the latter is used to consider the effect of changing the crypt shape. The suitability of this modelling approach to tracking stem cells in a niche, as well as mutant cell clones as they propagate in the crypt, is also discussed.

The development of a vaccine against some strains of the human papillomavirus (HPV) has led to many interesting public health questions [1]. We address some of these questions in the following work. We develop a compartmental mathematical model and examine the effect of waning immunity, vaccinating individuals prior to their becoming sexually active and the current government policy of vaccinating only females [2]. We calculate parameters based on data. We consider both time-dependent and age dependent ODE models and an age- and time-dependent PDE model and compare the results. We find the “effective” R0 value, Re0, for the time-dependent models. We introduce optimal control to both the time-dependent and age-dependent ODE models to assess the most cost-effective method for introducing the vaccine into a population. We find that the duration of protection offered by the vaccine can influence whether it is possible to eradicate infection from the population. We find the critical proportion to vaccinate to eradicate the disease. We see that introducing male vaccination would lead to a greater proportion of individuals to be vaccinated if the disease is to be eradicated. The PDE model shows that the proportion of females vaccinated has a large impact on the proportion of females infected. We show that it is cost-effective to vaccinate males and females. Our results support current government policy for age of vaccination [2]. We conclude that potential waning immunity will impact the success of the vaccine. We broadly support government policy for vaccination but recommend including male vaccination to most cost-effectively eradicate the disease.