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- Aplicações da matemáticaPublication . Azenha, Acilina; Jerónimo, Maria Amélia; Rodrigues, José AlbertoEncontram-se aqui reunidos os artigos apresentados nas Jornadas de Aplicações da Matemática, que tiveram lugar nos dias 14, 15 e 16 de outubro de 1998, no Instituto Superior de Engenharia de Lisboa. A popularidade da Modelação Matemática tem levado ao aparecimento de novos e mais perfeitos modelos, paralelamente com o incremento das técnicas de simulação de problemas quer académicos quer industriais. Contudo, a proliferação da utilização destas técnicas exige um aumento de robustez de eficiência nos programas de aplicação. Neste contexto é essencial a colaboração entre peritos com várias formações. Os artigos apresentados incidem sobre os mais recentes desenvolvimentos efetuados em Modelação Matemática e as suas aplicações realizadas a nível nacional.
- Isogeometric analysis for fluid shear stress in cancer cellsPublication . Rodrigues, José AlbertoThe microenvironment of the tumor is a key factor regulating tumor cell invasion and metastasis. The effects of physical factors in tumorigenesis is unclear. Shear stress, induced by liquid flow, plays a key role in proliferation, apoptosis, invasion, and metastasis of tumor cells. The mathematical models have the potential to elucidate the metastatic behavior of the cells’ membrane exposed to these microenvironment forces. Due to the shape configuration of the cancer cells, Non-uniform Rational B-splines (NURBS) lines are very adequate to define its geometric model. The Isogeometric Analysis allows a simplified transition of exact CAD models into the analysis avoiding the geometrical discontinuities of the traditional Galerkin traditional techniques. In this work, we use an isogeometric analysis to model the fluid-generated forces that tumor cells are exposed to in the vascular and tumor microenvironments, in the metastatic process. Using information provided by experimental tests in vitro, we present a suite of numerical experiments which indicate, for standard configurations, the metastatic behavior of cells exposed to such forces. The focus of this paper is strictly on geometrical sensitivities to the shear stress’ exhibition for the cell membrane, this being its innovation.
- Interpretation of medical images: end of subjectivity?Publication . Almeida, Ana; Vieira, Lina; Figueiredo, Sérgio; Rodrigues, José AlbertoIn medicine, images are often used in order to obtain a diagnosis. Among the innumerable images those from optical microscopy, such as the blood smears, and the computational ones such as renal scintigraphy. Blood smears allow identification and categorization of conditions that affect blood cells, as well as identification of microorganisms. An incorrect interpretation of images can have implications in the diagnosis and evaluation of therapeutic efficacy. Renal scintigraphy is an imaging method of Nuclear Medicine that allows the study of renal dimension and location, evaluation of the renal cortex, and the presence of renal cortical scarring as a consequence of irreversible kidney damage after a urinary infection. The importance in the analysis and interpretation of these studies is related with diagnosis and follow-up of renal pathologies, as well as to the therapeutic decision. However, it is known that there are currently some limitations in the detection of renal scars, which are caused by factors such as: physical, instrumental, and patient-related. The interpretation of either blood smears or renal scintigraphy is associated with training and expertise. These are allied to the subjectivity of the observer, being a limitation in the quality and reproducibility of the results.
- Models on variational methods for image processingPublication . Rodrigues, José AlbertoVariational image-processing models offer high-quality processing capabilities for imaging. They have been widely developed and used in the last two decades, enriching the fields of mathematics as well as information science. Mathematically, several tools are needed: energy optimization, regularization, partial differential equations, level set functions, and numerical algorithms. With this work we analyze some variational imageprocessing models.
- On the growth and mechanical properties of nanostructured cobalt foams by dynamic hydrogen bubble template electrodepositionPublication . Arévalo-Cid, Pablo; Adan-Mas, Alberto; Moura E Silva, Teresa; Rodrigues, José Alberto; Maçôas, Ermelinda Maria Sengo; Vaz; Montemor, M.F.The growth mechanism of nanostructured cobalt foams prepared by hydrogen bubble template electrodeposition has been studied. To that end, cobalt foams have been synthesized under different electrodeposition times and studied with various characterization techniques, namely scanning electron microscopy (SEM) and confocal microscopy in reflection mode. In addition, the mechanical properties of the resulting foams have been tested by bending and tensile tests. To study the influence of chemical additives in the growth mechanism and final properties of the foams, agar-agar has been added to the electrolytic bath during foam preparation. Results evidence that the addition of agar has successfully modified the microstructure of the final foams, creating a denser porous structure with smaller pore area and reduced growth rate that translates into better mechanical properties. By studying the evolution of the microstructure under different deposition conditions, a growth model of cobalt metallic foams by dynamic hydrogen bubble template is proposed. This easy and scalable route paves the way to produce tailored foams for numerous applications that include, for instance, energy storage and energy conversion.
- Interpretation of medical image: end of subjectivity?Publication . Almeida, Ana; Vieira, Lina; Figueiredo, Sérgio; Rodrigues, José AlbertoIn medicine, images are often used in order to obtain a diagnosis. Among the innumerable images those from optical microscopy, such as the blood smears, and the computational ones such as renal scintigraphy. Blood smears allow identification and categorization of conditions that affect blood cells, as well as identification of microorganisms. An incorrect interpretation of images can have implications in the diagnosis and evaluation of therapeutic efficacy. Renal scintigraphy is an imaging method of Nuclear Medicine that allows the study of renal dimension and location, evaluation of the renal cortex, and the presence of renal cortical scarring as a consequence of irreversible kidney damage after a urinary infection. The importance in the analysis and interpretation of these studies is related with diagnosis and follow-up of renal pathologies, as well as to the therapeutic decision. However, it is known that there are currently some limitations in the detection of renal scars, which are caused by factors such as: physical, instrumental, and patient-related. The interpretation of either blood smears or renal scintigraphy is associated with training and expertise. These are allied to the subjectivity of the observer, being a limitation in the quality and reproducibility of the results.
- Multiscale stress analysis in CFRC using microscope image data of carbon fibresPublication . Graça, R. J. R.; Rodrigues, José Alberto; Loja, Amélia; Jorge, PedroComposite materials, are known as strong candidates to improve different kinds of structures. The micromechanical study of these materials is very important, because it may define the best composite characteristics to be used and/or predict more accurately its response. In the present work a multi-stage procedure comprising different fibre contour modelling strategies and a sequent hierarchic multiscale analysis is performed. With this study it is intended to achieve a more realistic characterization of the stresses maximum values for a set of case studies, through the use of fibre geometry data obtained from microscope images of carbon fibre laminated composites. The theoretical circular cross-section is also considered to enable a comparative study among the different situations.
- Using the finite element method to understand calculusPublication . Rodrigues, José Alberto; Loja, Amélia; Barbosa, JoaquimThis paper presents a complementary, alternative teaching and learning methodology based on the use of the finite element method to illustrate mathematical models and to explore their (numerical) solutions in the context of vector calculus properties understanding. This methodology is illustrated via a set of examples focused on specific engineering problems, but its scope can also be widened to other scientific areas. The examples presented on this paper allow concluding that this approach may be an interesting way to re-think and complement the perspective usually considered in the transmission of mathematical concepts. The use of a freeware finite element method computational package, FreeFEM++ may also be an important issue to stimulate the dissemination of this phenomena modelling and comprehension approach.
- Porous functionally graded plates: na assessment of the influence of shear correction factor on static behaviorPublication . Mota, Ana F.; Loja, Amélia; Barbosa, Joaquim; Rodrigues, José AlbertoThe known multifunctional characteristic of porous graded materials makes them very attractive in a number of diversified application fields, which simultaneously poses the need to deepen research efforts in this broad field. The study of functionally graded porous materials is a research topic of interest, particularly concerning the modeling of porosity distributions and th ecorresponding estimations of their material properties—in both real situations and from a material modeling perspective. This work aims to assess the influence of different porosity distribution approaches on the shear correction factor, used in the context of the first-order shear deformation theory, which in turn may introduce significant effects in a structure’s behavior. To this purpose, we evaluated porous functionally graded plates with varying composition through their thickness. The bending behavior of these plates was studied using the finite element method with two quadrilateral plate element models. Verification studies were performed to assess the representativeness of the developed and implemented models, namely, considering an alternative higher-order model also employed for this specific purpose. Comparative analyses were developed to assess how porosity distributions influence the shear correction factor, and ultimately the static behavior, of the plates.
- Numerical modeling of cardiomyocytes using Finite Element MethodPublication . Oliveira, Joana; Rodrigues, José AlbertoIn recent years, the use of mathematical and geometrical models has been enabling the simulation of biological complex systems. Models of cardiac cells provide the possibility to understand the biochemistry and biomechanics of cardiac cells and cardiovascular diseases. The main objective of this work is to simulate the calcium flux and contractile activity of the cardiomyocyte, resorting on the Finite Element Method, and to develop a modelling tool with which we can simulate the key physiological aspects of the cardiac myocytes: Calcium concentration and contraction potential (% of shortening). To test our model's performance several tests were applied varying the local active cellular tension driven by the intracellular calcium concentration (Tu), and the position of T-tubules in the cell, from left to right and up to bottom. Our results show that the behaviour of our model is faithful to what is known to be true with the cell's physiology and pathological conditions.