Gyrodactylus salaris Malmberg, 1957, is a notifiable freshwater ecto-parasite that infects both wild and farmed populations of Atlantic salmon (Salmo salar, L.). It has caused catastrophic damage to wild salmon stocks in Norway since its accidental introduction in 1975, reducing salmon density in some rivers by 98% over a period of five years. It is estimated that G. salaris has cost the Norwegian salmon industry more than 500 million EUR. Currently the UK has G. salaris free status under EU law, however, it is believed that if G. salaris emerged in the UK the impact would be similar to that witnessed in Norway. The aim of this thesis is to develop mathematical models that describe the salmon-G. salaris system in order to gain a greater understanding of the possible long-term impact the parasite may have on wild populations of Atlantic salmon in G. salaris-free territories such as the UK. Mathematical models, including deterministic, Leslie matrix and individual based models, were used to investigate the impact of G. salaris on Atlantic salmon at the individual and population level. It is known that the Atlantic strain of Atlantic salmon, examples of which occur naturally in Norway and the UK, does not have any resistance to G. salaris infections and the parasite population is able to quickly grow to epidemic levels. In contrast, the Baltic strain of Atlantic salmon, examples of which occur naturally in Sweden and Russia, exhibits some form of resistance and the parasite is unable to persist. Thus, baseline models were extended to include immunity to infection, a trade-off on salmon reproductive rate, and finally, to consider interactions between populations of G. salaris and multiple strains of salmon exhibiting varying levels of immunity from fully susceptible to resistant. The models proposed predict that in the absence of host resistance or an immune response infections by G. salaris will result in an epidemic followed by the extinction of the salmon host population. Models also predict that if salmon are able to increase their resistance to G. salaris infections through mutations, salmon population recovery after the epidemic is indeed possible within 10-15 years post introduction with low level parasite coexistence. Finally, models also highlight areas where additional information is needed in order to improve predictions and enable the estimation of important parameter values. Model predictions will ultimately be used to assist in future contingency planning against G. salaris outbreaks in the UK and possibly as a basis for future models describing other fish/ecto-parasite systems.

Colorectal cancer (CRC) is one of the most prevalent and deadly forms of cancer. Its high mortality rate is associated with difficulties in early detection, which is crucial to survival. The onset of CRC is marked by macroscopic changes in intestinal tissue, originating from a deviation in the healthy cell dynamics of glands known as the crypts of Lieberkuhn. It is believed that accumulated genetic alterations confer on mutated cells the ability to persist in the crypts, which can lead to the formation of a benign tumour through localised proliferation. Stress on the crypt walls can lead to buckling, or crypt fission, and the further spread of mutant cells. Elucidating the initial perturbations in crypt dynamics is not possible experimentally, but such investigations could be made using a predictive, computational model. This thesis proposes a new discrete crypt model, which focuses on the interaction between cell- and tissue-level behaviour, while incorporating key subcellular components. The model contains a novel description of the role of the surrounding tissue and musculature, which allows the shape of the crypt to evolve and deform. A two-dimensional (2D) cross-sectional geometry is considered. Simulation results reveal how the shape of the crypt base may contribute mechanically to the asymmetric division events typically associated with the stem cells in this region. The model predicts that epithelial cell migration may arise due to feedback between cell loss at the crypt collar and density-dependent cell division, an hypothesis which can be investigated in a wet lab. Further, in silico experiments illustrate how this framework can be used to investigate the spread of mutations, and conclude that a reduction in cell migration is key to confer persistence on mutant cell populations. A three-dimensional (3D) model is proposed to remove the spatial restrictions imposed on cell migration in 2D, and preliminary simulation results agree with the hypotheses generated in 2D. Computational limitations that currently restrict extension to a realistic 3D geometry are discussed. These models enable investigation of the role that mechanical forces play in regulating tissue homeostasis, and make a significant contribution to the theoretical study of the onset of crypt deformation under pre-cancerous conditions.

This thesis develops biophysically-based data-driven mathematical models of intracellular calciumdynamics in ventricularmyocytes for both normal and genetically modified mouse hearts, based on species- and temperature-consistent experimental data. The models were subsequently applied to quantitatively examine the changes in calcium dynamics in mice with cardiomyocyte-specific knockout (KO) of the cardiac sarco/endoplasmic reticulum ATPase (SERCA2) gene, to determine the contributing mechanisms which underlie the ultimate development of heart failure in these animals. In Chapter 1, with emphasis on calcium dynamics and calcium regulation in heart failure, an overview of cardiac electrophysiology, excitation-contraction coupling and mathematical models of cardiac electrophysiology is provided. In Chapter 2, models of calcium dynamics in the ventricular myocytes from the C57BL/6 mouse heart at a physiological temperature is developed and validated based on species- and temperature-consistent measurements. In Chapter 3, the C57BL/6 model framework is re-parameterised to experimental data from the control and SERCA2 KO mice at 4 weeks after gene deletion. The models are then used to quantitatively characterise changes in calcium dynamics in the KO animals and the role of the compensatory mechanisms. In Chapter 4, the model framework is extended to include differential distributions of ion channels in the sarcolemma and the calcium dynamics in the sub-sarcolemmal space, with parameters in these sub-components fitted to experimentally measured calcium dynamics from the control and KO cardiomyocytes at 7-week after gene deletion. Finally in Chapter 5, conclusions are drawn, the limitations of this study are discussed, and the future extensions to this study are described.

An estimated 85% of haemorrhagic strokes are secondary to the rupture of an intracranial aneurysm (IA), a localised, blood-filled dilation of the artery wall. The clinically observed rupture of occluded IAs has led to hypothesise that the presence of thrombus may restrict the transport of nutrients, most notably oxygen, to the aneurysmal wall, thus heightening the risk of rupture through the deleterious effects of hypoxia on cellular functionality. The limited research into O2 transport within IAs demonstrate the need for further exploration into the possible detrimental hypoxic conditions as a result of intrasaccular haemodynamics and thrombusformation in untreated, treated and evolving IAs, with the ultimate goal of further understanding disease evolution and developing prognostic decision support models for clinical intervention. Preliminary computational fluid dynamic simulations conducted on a 2Daxisymmetric model of a thrombosed artery highlighted the relative importance of wall-side versus the fluid-side mass transport of oxygen. A sensitivity analysis demonstrated that variations in thrombus thickness, and arterial wall cellular respiration rates have the greatest influence on the oxygen distribution to the portion of wall in direct contact with the thrombus. The results of the coupled flow-mass transport computational fluid dynamic simulations within patient-specific IA show that a reduction in intrasaccular flow as a consequence of stent deployment affects the rate at which oxygenated blood reaches the entirety of the dome. Nonetheless, the distribution ofO2 to the aneurysmal wall itself does not differ from the observed oxygen distribution across the wall when the same IA is left untreated. Conversely, the low velocity recirculations observed in an IA presenting with a very high aspect ratio (i.e a narrow neck and high sack height) limited the transport of oxygen to such an extent as to completely deprive the delivery of oxygen to the fundus. The presence of thrombus within the IA dome results in a dramatic reduction in oxygen delivery to the wall, the extent of which is dependent on the local thrombus thickness. Finally, a novel fluid-solid-growth-mass transport (FSGT) mathematical model is conceived to explore the biochemical role of thrombus on the evolution of an IA. The shear-regulate propagation of a thrombus layer during membrane expansion leads to the gradual decrease in oxygen tension within the wall. Moreover, as a consequence of coupling this oxygen deficiency to fibroblast functionality, the collagen fibre mass density was shown to increase at an insufficient rate to compensate for the transfer in load from the degrading elastinous consitituents to the collagenous constituents, thus resulting in the increased stretch of collagen fibres in order to maintain mechanical equilibrium. Moreover this over-expansion results in the gradual unstable evolution of the IA. The observed obstruction to oxygen delivery as a result of intrasaccular haemodynamics and thrombosis compounds the need for further development of more comprehensive chemo-mechano-biological models of IAs so as to better ascertain the level of rupture risk posed by a hypoxic environment. Refinement to the models proposed within this work would prove invaluable to creating a fully integrated multi-physics, multi-scale in silico framework in aid to patient diagnostics and individual treatment planning of IAs.

Unlike thin tissues (e.g., skin) which has been successfully grown, growing thick tissues (e.g., bone and muscle) still exhibit certain limitations due to lack of nutrients (e.g., glucose and oxygen) feeding on cells in extracapillary space (ECS) region, or also known as scaffold in an in vitro static culture. The transport of glucose and oxygen into the cells is depended solely on diffusion process which results in a condition where the cells are deprived of adequate glucose and oxygen supply. This condition is termed as hypoxia and leads to premature cell death. Hollow fibre membrane bioreactors (HFMBs) which operate under perfusive cell culture conditions, have been attempted to reduce the diffusion limitation problem. However, direct sampling of glucose and oxygen is almost impossible; hence noninvasive methods (e.g., mathematical models) have been developed in the past. These models have defined that the glucose diffusivity in cell culture medium (CCM) is similar to the diffusivity in water; thus, they do not represent precisely the nutrient transport processes occurring inside the HFMB. In this research, we define glucose as our nutrient specie due to its limited published information with regard to its diffusivity values, especially one that corresponds to cell/tissue engineering (TE) experiments. A series of well-defined diffusion experiments are carried out with TE materials of varying pore size and shapes imbibed in water and CCM, namely, cellulose nitrate (CN) membrane, polyvinylidene fluoride (PVDF) membrane, poly(L-lactide) (PLLA) scaffold, poly(caprolactone) (PCL) scaffold and collagen scaffold. A diffusion cell is constructed to study the diffusion of glucose across these materials. The glucose diffusion across cell-free membranes and scaffolds is investigated first where pore size distribution, porosity and tortuosity are determined and correlated to the effective diffusivity. As expected, the effective diffusivity increases correspondingly with the pore size of the materials. We also observe that the effective glucose diffusivity through the pores of these materials in CCM is smaller than in water. Next, we seeded human osteoblast cells (HOSTE85) on the scaffolds for a culture period of up to 3 weeks. Similar to the first series of the diffusion experiments, we have attempted to determine the effective glucose diffusivity through the pores of the scaffolds where cells have grown at 37°C. The results show that cell growth changes the morphological structure of the scaffolds, reducing the effective pore space which leads to reduced effective diffusivity. In addition, the self-diffusion of glucose in CCM and water has also been determined using a diaphragm cell method (DCM). The results have shown that the glucose diffusivity in CCM has significantly reduced in comparison to the water diffusivity which is due to the larger dynamic viscosity of CCM. The presence of other components and difference in fluid properties of CCM may also contribute to the decrease. We finally employ our experimentally deduced effective diffusivity and self-diffusivity values into a mathematical model based on the Krogh cylinder assumption. The glucose concentration is predicted to be the lowest near the bioreactor outlet, or in the scaffold region, hence this region becomes a location of interest. The governing transport equations are non-dimensionalised and solved numerically. The results shown offer an insight into pointing out the important parameters that should be considered when one wishes to develop and optimise the HFMB design.

An intracranial aneurysm (IA) is a balloon-like focal lesion on the cerebral arterial wall. IAs are poorly understood, but are commonly considered to be a disease caused by multiple factors. Current interventional treatments are accompanied with risks. Given the low incidence of rupture, it would be ideal to only treat aneurysms identified with rupture risk. Numerical models of aneurysm development may provide insight into the disease mechanisms, and contribute to the prediction of disease progression. Better understanding of the disease aetiology will also guide clinical decision making. Different hypotheses have been proposed on the influence of haemodynamic stimuli on IA inception. We investigate this influence by examining the haemodynamic stimuli of the 'pre-aneurysmal' vasculature in the locations of IA formation in 22 clinical cases. The 'pre aneurysmal' geometries are obtained by applying a novel numerical vessel reconstruction method on the aneurysmal geometries. This automated reconstruction method propagates a closed curve along the vessel skeleton using the local Frenet frames to smoothly morph the upstream boundary into the downstream boundary. We observe that locally elevated wall shear stress (WSS) and gradient oscillatory number (GON) are highly correlated with regions susceptible to sidewall IA formation, whilst haemodynamic indices associated with the oscillation of the WSS vectors have much lower correlations. A common assumption made in the literature on arterial growth and remodelling (G&R) is that the 'state of stretch' (denoted as the attachment stretch) at which collagen fibres are configured in the extracellular matrix (ECM) is assumed to be constant. This will lead to an unrealistically thickened arterial wall in modelling aneurysm evolution. We propose a novel 1D mathematical model of collagen microstructural adaption during IA evolution. We assume new collagen fibres are configured into the ECM in a state of attachment stretch distribution which can be temporally adaptive. We explicitly define the functional form of this distribution and model its temporal adaption during IA evolution. This model is then implemented into two 3D models of IA evolution: a solid structural model and Fluid-Solid-Growth (FSG) model. In the solid structural model, the artery is modelled as a two-layer, nonlinear elastic cylindrical membrane using a physiologically realistic constitutive model. The development of the aneurysm is considered as a consequence of the growth and remodelling of its material constituents: elastinous constituents are prescribed to degrade in a localised circular patch; collagen concentration and recruitment variables enable the growth and remodelling of collagen fabric to be simulated; adaption of the attachment stretch distribution is confined locally within the region of aneurysm evolution. The sophisticated solid model predicts stabilised saccular IAs with realistic sizes and wall thicknesses. The FSG model simulates the IA development on patient-specific vasculature: the updated 3D solid structural model is integrated into a patient-specific geometry of the vasculature and the growth and remodelling of the constituents is now linked to the local haemodynamic stimuli obtained from a rigid-wall computational fluid dynamics analysis. Adaption of the attachment stretch distribution is also confined locally in the region where the constituents degrade. An illustrative case of IA development on patient specific geometry is provided. Based on our study, we conclude that incorporating the adaption of attachment stretch distribution is necessary to simulate IA evolution with physiological evolving wall thicknesses. However, how vascular cells confine this adaption heterogeneously needs further investigation. Improved understanding and modelling of the biology of the arterial wall is needed for more sophisticated models of aneurysm evolution. It will in turn assist in understanding the aetiology of IA formation. Ultimately we hope to have a patient-specific growth model that could have the potential be used to assist diagnostic decisions.

Mass transfer intervening during the process of immersion influences the final composition of the product. These transfers primarily depend on the size of the immersed products, as well as temperature, the concentration and the nature of the solution of immersion. The main objective of this work is to study the mass transfer phenomena (water loss and solid gain) in solid/liquid system constituted of vegetable product (eggplant) immerged in salt solution. We determined the kinetic studies of eggplant in different salts solutions with two concentrations (saturation and 20%) at 3°C. The physicochemical properties of solution and salt such as molar concentration, molecular weight and ionic type affected the mechanism of water loss and solid gain. Knowledge about interaction ions/vegetable pectin is important for new product formulation. Determination of partition coefficient of ion in equilibrium system showed that the main physicochemical properties of ions and solution are ionic radius, electronegativity, ionic force and molar concentration. Mathematical predictive model was developed to predict the partition coefficient of ions in food/ solution system. Molecular dynamics simulations using a dynamic force field have been carried out to investigate the absorption of ions (K+, Na+, Ca2+, Mg2+, Cl-) in pectin/water/ion/aqueous solution system. Four systems were used. The results showed that the ionic type (cation and anion) influence the type and number of interactions between pectin-ion and water-ion and then offered an explicit description transfer phenomena and distribution of ions in the system solid/liquid / Les transferts de matière intervenant au cours du procédé d’immersion dépendent essentiellement de la taille des produits immergés, la température, la concentration et la nature de la solution d'immersion. L’objectif principal de ce travail porte sur l’étude des transferts dans un système solide/liquide constitué d’un produit végétal (aubergine) et d’une solution saline. Afin de parvenir à une bonne maîtrise de ces paramètres, les études cinétiques ont été conduites à 3°C sur des aubergines immergées dans des solutions salines avec deux concentrations. Les propriétés des solutions et des sels telles que la concentration molaire, la masse molaire et surtout la nature ionique influencent le mécanisme de perte et de gain. Les connaissances sur les interactions ions/pectines végétaux sont importants pour la formulation de nouveaux produits La détermination du coefficient de partage des ions à l’équilibre dans le système aubergine/solution ont montré que les principales propriétés des ions et des solutions influençant le coefficient de partage sont le rayon ionique, l’électronégativité, la force ionique et la concentration molaire. Un modèle mathématique a permis de prédire le coefficient de partage des ions dans ce système. Dans le but d’expliquer l’absorption des ions par la phase solide, une simulation par dynamique moléculaire a été menée sur un système pectine-eau-sels. Quatre systèmes ont été utilisés. Les résultats obtenus ont montré que la nature ionique influencent la nature et le nombre d’interaction entre pectine-ion et eau-ion et donc offrent une description explicite des phénomènes de transferts et distribution des ions dans le système solide/liquide

Brazilian commodities, such as ethanol, are looking for sustainable production to suit the international market demands. An important parameter for assessing sustainability is the carbon (C) footprint calculation of the product. Thus, studies of the variations in soil C stocks on the ethanol production are essential. Studies in relation to land use change are already been developed; however information about parameters of management changes on the sugarcane production is needed. The aim of this research was to evaluate the soil C stock in response to two main management changes in sugarcane production: i) no vinasse to vinasse application (NV-V), ii) burned to unburned harvesting system (B-UB). We also evaluated soil C stock changes in a chronosequence irrigation practices (native vegetation (NV), sugarcane irrigated 4 years (I4) and 6 years (I6), a new management in semi-arid and drought regions in Brazil which also aims high yields. Modelling approaches in order to assess long-term effects were also analysed. The NV-V transition showed higher soil C stock for V regime for topsoil layers 0-40 cm depth mainly due to the addition of organic compounds to the soil. Vinasse can also enhance biomass production and crop yield. The B-UB transition showed higher soil C stock in the UB regime from 20 to 60 cm depth due to higher organic matter accumulation from the maintenance of the straw to the field. The cumulative soil C stock for 1 metre depth had an increase of 1.1 and 0.75 Mg C ha-1 y-1 in the NV-V and B-UB transitions, respectively. From modelling was observed that V and UB sites had an increase of soil C stock by 2150, being a difference of 2.8 and 23 Mg ha-1 in the equilibrium state between NV-V and B-UB regimes, respectively. In the irrigation practices, the I4 showed higher soil C stock than NV in the 20 to 40 cm; while I6 was lower than NV in the 50 to 100 cm depth. Simulated long-term analyses showed increase of topsoil C stock of 12 and 13 Mg ha-1 for I6 and I4 area, respectively, compared to NV on 2100. The results in this study are pioneers in relation to soil C stock studies in the management transitions and irrigation practices. This information may be used as a basis for public policies decision which dealing of the land use and global warming / Commodities brasileiras, como o etanol, estão à procura de uma produção sustentável para atender às exigências do mercado internacional. Um parâmetro importante para avaliar a sustentabilidade é o cálculo da pegada de carbono (C) do produto. Assim, os estudos sobre as variações nos estoques de carbono do solo (ECS) sobre a produção de etanol são essenciais. Estudos em relação à mudança no uso da terra já estão sendo desenvolvidos; no entanto informações sobre parâmetros de mudanças de manejo na produção de cana de açúcar são necessárias. O objetivo desta pesquisa foi avaliar o ECS em resposta a duas principais mudanças de manejo: i) não vinhaça para aplicação de vinhaça (NV-V), ii) sistema queimado para não queimado (B-UB). Mudanças de ECS também foram avaliadas em sistemas de irrigação em cronoseqüência: vegetação nativa (NV), cana de açúcar irrigada por 4 anos (I4) e por 6 anos (I6). Modelagem matemática para avaliar o efeito a longo prazo também foi analisada. A transição NV-V apresentou maior ECS para o regime V em 40 cm de profundidade, devido principalmente à adição de compostos orgânicos ao solo. A vinhaça também pode aumentar a produção de biomassa e rendimento da cultura. A transição B-UB apresentou maior ECS no regime UB em 20-60 cm de profundidade devido ao acúmulo de matéria orgânica a partir da manutenção da palha no campo. O ECS acumulado para 1 metro de profundidade obteve um aumento de 1,1 e 0,75 Mg C ha-1 y-1 nas transições NV-V e B-UB, respectivamente. A partir de modelagem foi observado que os regimes V e UB obteve um aumento de ECS em 2150, sendo uma diferença de 2,8 e 23 Mg ha-1 no estado de equilíbrio para os regimes NV-V e B-UB, respectivamente. Nas práticas de irrigação, o I4 foi superior ao NV nos 20 a 40 cm; enquanto que I6 foi inferior a NV na profundidade de 50 a 100 cm. As análises de simulação a longo prazo mostraram um aumento de ECS de 12 e 13 Mg ha-1 para as áreas I6 e I4, respectivamente, em comparação com NV em 2100. Os resultados deste estudo são pioneiros em relação aos estudos de ECS nas mudanças de manejo e práticas de irrigação. Esta informação pode ser usada como base para a decisão de políticas públicas que lidam com o uso da terra e do aquecimento global

Desde sua criação por Ferranti, cerca de 50 anos atrás, as tecnologias de projeto e de fabricação das Máquinas de Medir a Três Coordenadas evoluíram muito. Entretanto, ainda é possível fabricar equipamentos livres de erros. Para garantir a acuracidade das medições realizadas é necessário que se conheça tais erros e que rotinas de compensação sejam implementadas. O levantamento dos erros de qualquer equipamento é feito através de procedimentos de calibração. Entretanto, devido à complexidade das MM3Cs, ainda não existem procedimentos internacionalmente aceitos, por usuários e fabricantes, para avaliar o desempenho metrológico desses equipamentos. Técnicas normalizadas existentes, a exemplo, JIS B 7440 de 1987, B89.4.1 de 1997, VDI/VDE 2617 de 1986 entre outras, propõem testes de desempenho que na maioria das vezes superestimam os erros da MM3C. Além disso, dificultam a rastreabilidade para quaisquer condições de medição diferente daquelas em que foi realizado o teste. Assim, diante do exposto, este trabalho tem por objetivo principal apresentar um novo modelo de sintetização de erros para MM3Cs, o Modelo Reduzido de Sintetização de erros. Este modelo possui equações de sintetização, para Ex, Ey e Ez, reduzidas, em comparação à outros modelos conhecidos, necessita de pequeno tempo na calibração o que reduz o custo desta atividade, possibilita o diagnóstico das fontes de erros e garante a rastreabilidade dos erros calculados. / Since the introduction of coordinate measuring machines by Ferranti in late fifties, the CMM design and manufacturing technology have enormously developed. Nevertheless, it is stile impossible to produce mechanical devices that are exempted from errors. In order to ensure measurements accuracy, it becomes necessary to understand such errors and establish compensation routines. The errors survey of any piece of equipment is performed by means of calibration procedures. However, due to the complexity of CMMs, there are not, until the present time, procedures that are internationally accepted by uses and manufactures to evaluate the metrological performance of this sort of equipment. Current standardized techniques, for instance, JIS B 7440 from 1987, B89.4.1. from 1997, VDI/VDE 2617 from 1986, among others, propose performance tests that usually overestimate CMM errors. Furthermore, they obstruct traceability to whatever measurement condition that is different from the ones used to perform the test. This being the case, the aim of this work comprises the presentation of the new error sinthetization model. This model deals with sinthetization equations for Ex, Ey and Ez that are reduced if compared to other known models, requires short calibration periods, reducing its expenses, allow the determination of the sources of errors and ensures traceability of calculated errors.

Estudamos a dinâmica de formação de bolhas em fluidos viscosos. Desenvolvemos novas técnicas experimentais para aprofundar o estudo do sistema de um bico borbulhador no fundo de um cilindro preenchido por uma solução de água e glicerina. Neste sistema, controlamos o fluxo de ar por meio de um fluxímetro de massa e uma válvula solenoide. Medimos simultaneamente: o tempo entre duas bolhas sucessivas usando um laser focalizado em um foto- diodo, cuja luz é espalhada com a passagem das bolhas; as ondas de pressão que o borbulhamento causa no sistema de injeção usando microfones colocados entre a válvula solenoide e o bico; e a geometria das bolhas em formação, através da análise de imagens coletadas por uma câmera de alta velocidade. Motivados pelos resultados deste sistema, construímos um modelo para a dinâmica de formação de bolhas, baseado em primeiros princípios, que descreve a rota de adição de períodos observada no experimento. Investigamos também um novo sistema experimental, que tem dois bicos borbulhadores dentro do mesmo tubo. Usamos as mesmas técnicas experimentais desenvolvidas para o experimento de um bico. Identificamos que os borbulhamentos sincronizam apesar de seus sistemas de injeção de ar serem independentes, concluímos, portanto, que o acoplamento deve-se à circulação que o líquido introduz. Estudamos a sincronização por meio da construção de diagramas de bifurcação e espaços de parâmetros mostrando as regiões de sincronização. Adaptamos também o modelo de um bico para descrever este sistema. Descobrimos que a interação entre as duas dinâmicas de formação de bolhas é maior conforme aumentamos a altura da coluna líquida. / We studied the bubble formation dynamics in viscous fluids. We developed new experimental techniques to provide a better understanding of the system with one bubbling nozzle on the bottom of a cylinder filled with a water and glycerol solution. In this system, we control the air flow with a mass flowme- ter and a solenoid valve. We have measured simultaneously: the time between successive bubbles, using a laser focused in a photo-diode that has his light scattered when one bubble passes between them; the pressure waves that the bubbling causes in the air injecting system using microphones placed between the solenoid valve and the nozzle; and the geometry of the growing bubbles, through the analysis of the images collected by a high speed camera. The re- sults from this system motivated us to make a model for the bubbles formation dynamics that describes the period-adding route observed in the experiment and is based on first principles. We also investigated a new experimental system, that has two bubbling nozzles inside the same cylinder. We used the same experimetal techniques developed to the one nozzle experiment. We identified that the bubbling on the nozzles synchronizes due the coupling introduced by the liquid circulation, as the air injecting systems are independent. We studied the synchronization by constructing bifurcation diagrams and parameter spaces that show the syn- chronized regions. We also adapted the one nozzle bubbling model to decribe this system. We discovered that the interaction between the two bubble forma- tion dynamics is stronger when we increase the liquid height.