Made available in DSpace on 2014-06-11T19:24:49Z (GMT). No. of bitstreams: 0 Previous issue date: 2003-11-28Bitstream added on 2014-06-13T19:11:35Z : No. of bitstreams: 1 mattiazzocardia_e_me_bauru.pdf: 1559863 bytes, checksum: 08b93981a0965d3a5a307d8738f86ec0 (MD5) / Nos cursos de ciências biológicas, os tópicos de estudo estão subdivididos em conteúdos básicos e conteúdos específicos. Entre os básicos considerados fundamentais estão os conhecimentos matemáticos. A questão que esta pesquisa procurou responder foi: quais conteúdos de matemática são mais adequados para auxiliar no entendimento dos processos e padrões biológicos estudados pelos alunos durante o curso? A pesquisa envolveu análise direta de documentação, nela incluídos questionários aplicados a 171 pessoas envolvidas com o tema, entre professores, alunos e biólogos, e pesquisa documental indireta pela análise de livros de biologia e de projetos de ensino de 5 estabelecimentos que mantêm cursos de ciências biológicas. Complementa a pesquisa o resultado de consulta feita a 256 alunos ingressantes nos referidos cursos a respeito do que julgam conhecer da matemática estudada anteriormente ao ingresso em curso superior. O conjunto dos levantamentos efetuados oferece subsídios para a escolha adequada dos conteúdos de matemática a serem abordados em cursos de ciências biológicas propiciando condições para que a escola possa melhor desempenhar o seu papel mediador na transformação dos conhecimentos do cotidiano em conhecimentos específicos / In biological sciences courses, the teaching topics are divided in basic contents and specific contents. Among the basic ones considered fundamental are the ones related to mathematics knowledge. The issue for this research is: what are the most adequate mathematics contents to help the understanding of biological process and patterns studied in the course? The research involved direct analysis of documentation, including questionnaires applied to 171 people involved with the subject, among teachers, students and biologists, and indirect documental research through the analysis of biology textbooks and teaching plans from 5 colleges that offer biological sciences courses. The research also provides the result of an inquiry to 256 freshmen from those courses in relation to what they suppose do know about mathematics studied before they entered college. The data collected offered subsidies for the adequate choice of mathematics contents to be approached in biological sciences courses, allowing the schools to improve their role as mediators in the transformation of daily knowledge into scientific knowledge

The ability of cells to move through their environment and spread on surfaces is fundamental to a host of biological processes; including wound healing, growth and immune surveillance. Controlling cell motion has wide-ranging potential for medical applications; including prevention of cancer metastasis and improved colonisation of clinical implants. The relevance of the topic coupled with the naturally arising interplay of biomechanical and biochemical mechanisms that control cell motility make it an exciting problem for mathematical modellers. Two-phase flow models have been widely used in the literature to model cell motility; however, little is known about the mathematical properties of this framework. The majority of this thesis is dedicated to improving our understanding of the two-phase flow framework. We first present the simplest biologically plausible two-phase model for a cell crawling on a flat surface. Stability analyses and a numerical study reveal a number of features relevant to modelling cell motility. That these features are present in such a stripped-down two-phase flow model is notable. We then proceed to investigate how these features are altered in a series of generalisations to the minimal model. We consider the effect of membrane-regulated polymerization of the cell's actin network, the effect of describing the network as viscoelastic, and the effect of explicitly modelling myosin, which drives contraction of the actin network. Validation of hydrodynamical models for cell crawling and spreading requires data on cell shape. The latter part of the thesis develops an image processing routine for extracting the three-dimensional shape of cells settling on a flat surface from confocal microscopy data. Models for cell and droplet settling available in the literature are reviewed and we demonstrate how these could be compared to our cell data. Finally, we summarise the key results and highlight directions for future work.

Three different models, relating to the study of microswimmers immersed in a low Reynolds number fluid, are presented. The underlying, mathematical concepts employed in each are developed using singularity methods of Stokes flow. The first topic concerns the motility of an artificial, three-sphere microswimmer with prescribed, non-reciprocal, internal forces. The swimmer progresses through a low Reynolds number, nonlinear, viscoelastic medium. The model developed illustrates that the presence of the viscoelastic rheology, when compared to a Newtonian environment, increases both the net displacement and swimming efficiency of the microswimmer. The second area concerns biological microswimming, modelling a sperm cell with a hyperactive waveform (vigorous, asymmetric beating), bound to the epithelial walls of the female, reproductive tract. Using resistive-force theory, the model concludes that, for certain regions in parameter space, hyperactivated sperm cells can induce mechanical forces that pull the cell away from the wall binding. This appears to occur via the regulation of the beat amplitude, wavenumber and beat asymmetry. The next topic presents a novel generalisation of slender-body theory that is capable of calculating the approximate flow field around a long, thin, slender body with circular cross sections that vary arbitrarily in radius along a curvilinear centre-line. New, permissible, slender-body shapes include a tapered flagellum and those with ribbed, wave-like structures. Finally, the detailed analytics of the generalised, slender-body theory are exploited to develop a numerical implementation capable of simulating a wider range of slender-body geometries compared to previous studies in the field.

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.

Cardiac motion is a highly complex and integrated process of vital importance as it sustains the primary function of the heart, that is pumping blood. Cardiac tissue microstructure, in particular the alignment of myocytes (also referred to as fibre direction) and their lateral organisation into laminae (or sheets), has been shown by both experimental and computational research to play an important role in the determination of cardiac motion patterns. However, current models of cardiac electromechanics, although already embedding structural information in the models equations, are not yet able to fully reproduce the connection between structural dynamics and cardiac deformation. The aim of this thesis was to develop an electromechanical modelling framework to investigate the impact of tissue structure on cardiac motion, focussing on left ventricular contraction in rat. The computational studies carried out were complemented with a preliminary validation study based on experimental data of tissue structure rearrangement during contraction from diffusion tensor MRI.

Orientador: Mara Sueli Simão Moraes / Banca: Eduardo Pereira Cabral Gomes / Banca: José Roberto Boettger Giardinetto / Resumo: Nos cursos de ciências biológicas, os tópicos de estudo estão subdivididos em conteúdos básicos e conteúdos específicos. Entre os básicos considerados fundamentais estão os conhecimentos matemáticos. A questão que esta pesquisa procurou responder foi: quais conteúdos de matemática são mais adequados para auxiliar no entendimento dos processos e padrões biológicos estudados pelos alunos durante o curso? A pesquisa envolveu análise direta de documentação, nela incluídos questionários aplicados a 171 pessoas envolvidas com o tema, entre professores, alunos e biólogos, e pesquisa documental indireta pela análise de livros de biologia e de projetos de ensino de 5 estabelecimentos que mantêm cursos de ciências biológicas. Complementa a pesquisa o resultado de consulta feita a 256 alunos ingressantes nos referidos cursos a respeito do que julgam conhecer da matemática estudada anteriormente ao ingresso em curso superior. O conjunto dos levantamentos efetuados oferece subsídios para a escolha adequada dos conteúdos de matemática a serem abordados em cursos de ciências biológicas propiciando condições para que a escola possa melhor desempenhar o seu papel mediador na transformação dos conhecimentos do cotidiano em conhecimentos específicos / Abstract: In biological sciences courses, the teaching topics are divided in basic contents and specific contents. Among the basic ones considered fundamental are the ones related to mathematics knowledge. The issue for this research is: what are the most adequate mathematics contents to help the understanding of biological process and patterns studied in the course? The research involved direct analysis of documentation, including questionnaires applied to 171 people involved with the subject, among teachers, students and biologists, and indirect documental research through the analysis of biology textbooks and teaching plans from 5 colleges that offer biological sciences courses. The research also provides the result of an inquiry to 256 freshmen from those courses in relation to what they suppose do know about mathematics studied before they entered college. The data collected offered subsidies for the adequate choice of mathematics contents to be approached in biological sciences courses, allowing the schools to improve their role as mediators in the transformation of daily knowledge into scientific knowledge / Mestre

In this thesis we study three different modelling frameworks for biological systems of dispersal and combinations thereof. The three frameworks involved are individual-based models, group-level models in the form of partial differential equations (PDEs) and robot swarms. In the first two chapters of the thesis, we present ways of coupling individual based models with PDEs in so-called hybrid models, with the aim of achieving improved performance of simulations. Two classes of such hybrid models are discussed that allow an efficient simulation of multi-species systems of dispersal with reactions, but involve individual resolution for certain species and in certain parts of a computational domain if desired. We generally consider two types of example systems: bacterial chemotaxis and reaction-diffusion systems, and present results in the respective application area as well as general methods. The third chapter of this thesis introduces swarm robotic experiments as an additional tool to study systems of dispersal. In general, those experiments can be used to mimic animal behaviour and to study the impact of local interactions on the group-level dynamics. We concentrate on a target finding problem for groups of robots. We present how PDE descriptions can be adjusted to incorporate the finite turning times observed in the robotic system and that the adjusted models match well with experimental data. In the fourth and last chapter, we consider interactions between robots in the form of hard-sphere collisions and again derive adjusted PDE descriptions. We show that collisions have a significant impact on the speed with which the group spreads across a domain. Throughout these two chapters, we apply a combination of experiments, individual-based simulations and PDE descriptions to improve our understanding of interactions in systems of dispersal.

An increasingly important research area within the field of cardiac modelling is the development and study of methods of model-based parameter estimation from clinical measurements of cardiac function. This provides a powerful approach for the quantification of cardiac function, with the potential to ultimately lead to the improved stratification and treatment of individuals with pathological myocardial mechanics. In particular, the diastolic function (i.e., blood filling) of left ventricle (LV) is affected by its capacity for relaxation, or the decay in residual active tension (AT) whose inhibition limits the relaxation of the LV chamber, which in turn affects its compliance (or its reciprocal, stiffness). The clinical determination of these two factors, corresponding to the diastolic residual AT and passive constitutive parameters (stiffness) in the cardiac mechanical model, is thus essential for assessing LV diastolic function. However these parameters are difficult to be assessed in vivo, and the traditional criterion to diagnose diastolic dysfunction is subject to many limitations and controversies. In this context, the objective of this study is to develop model-based applicable methodologies to estimate in vivo, from 4D imaging measurements and LV cavity pressure recordings, these clinically relevant parameters (passive stiffness and active diastolic residual tension) in computational cardiac mechanical models, which enable the quantification of key clinical indices characterising cardiac diastolic dysfunction. Firstly, a sequential data assimilation framework has been developed, covering various types of existing Kalman filters, outlined in chapter 3. Based on these developments, chapter 4 demonstrates that the novel reduced-order unscented Kalman filter can accurately retrieve the homogeneous and regionally varying constitutive parameters from the synthetic noisy motion measurements. This work has been published in Xi et al. 2011a. Secondly, this thesis has investigated the development of methods that can be applied to clinical practise, which has, in turn, introduced additional difficulties and opportunities. This thesis has presented the first study, to our best knowledge, in literature estimating human constitutive parameters using clinical data, and demonstrated, for the first time, that while an end-diastolic MR measurement does not constrain the mechanical parameters uniquely, it does provide a potentially robust indicator of myocardial stiffness. This work has been published in Xi et al. 2011b. However, an unresolved issue in patients with diastolic dysfunction is that the estimation of myocardial stiffness cannot be decoupled from diastolic residual AT because of the impaired ventricular relaxation during diastole. To further address this problem, chapter 6 presents the first study to estimate diastolic parameters of the left ventricle (LV) from cine and tagged MRI measurements and LV cavity pressure recordings, separating the passive myocardial constitutive properties and diastolic residual AT. We apply this framework to three clinical cases, and the results show that the estimated constitutive parameters and residual active tension appear to be a promising candidate to delineate healthy and pathological cases. This work has been published in Xi et al. 2012a. Nevertheless, the need to invasively acquire LV pressure measurement limits the wide application of this approach. Chapter 7 addresses this issue by analysing the feasibility of using two kinds of non-invasively available pressure measurements for the purpose of inverse parameter estimation. The work has been submitted for publication in Xi et al. 2012b.

The importance of coronary microcirculatory perfusion is highlighted by the severe impact of microvascular diseases such as diabetes and hypertension on heart function. Recently, highly-detailed three-dimensional (3D) data on ex vivo coronary microvascular structure have become available. However, hemodynamic information in individual myocardial capillaries cannot yet be obtained using current in vivo imaging techniques. In this thesis, a novel data-driven modelling framework is developed to predict tissue-scale flow properties from discrete anatomical data, which can in future be used to aid interpretation of coarse-scale perfusion imaging data in healthy and diseased states. Mathematical models are parametrised by the 3D anatomical data set of Lee (2009) from the rat myocardium, and tested using flow measurements in two-dimensional rat mesentery networks. Firstly, algorithmic and statistical tools are developed to separate branching arterioles and venules from mesh-like capillaries, and then to extract geometrical properties of the 3D capillary network. The multi-scale asymptotic homogenisation approach of Shipley and Chapman (2010) is adapted to derive a continuum model of coronary capillary fluid transport incorporating a non-Newtonian viscosity term. Tissue-scale flow is captured by Darcy's Law whose coefficient, the permeability tensor, transmits the volume-averaged capillary-scale flow variations to the tissue-scale equation. This anisotropic permeability tensor is explicitly calculated by solving the capillary-scale fluid mechanics problem on synthetic, stochastically-generated periodic networks parametrised by the geometrical data statistics, and a thorough sensitivity analysis is conducted. Permeability variations across the myocardium are computed by parametrising synthetic networks with transmurally-dependent data statistics, enabling the hypothesis that subendocardial permeability is much higher in diastole to compensate for severely-reduced systolic blood flow to be tested. The continuum Darcy flow model is parametrised by purely structural information to provide tissue-scale perfusion metrics, with the hypothesis that this model is less sensitive and more reliably parametrised than an alternative, estimated discrete network flow solution.

Marine populations worldwide are in decline due to anthropogenic effects. Spatial management via marine reserves may be an effective conservation method for many species, but the requisite theory is still underdeveloped. Integrodifference equation (IDE) models can be used to determine the critical domain size required for persistence and provide a modelling framework suitable for many marine populations. Here, we develop a novel spatially implicit approximation for the proportion of individuals lost outside the reserve areas which consistently outperforms the most common approximation. We examine how results using this approximation compare to the existing IDE results on the critical domain size for populations in a single reserve, in a network of reserves, in the presence of alongshore currents, and in structured populations. We find that the approximation consistently provides results which are in close agreement with those of an IDE model with the advantage of being simpler to convey to a biological audience while providing insights into the significance of certain model components. We also design a stochastic individual based model (IBM) to explore the probability of extinction for a population within a reserve area. We use our spatially implicit approximation to estimate the proportion of individuals which disperse outside the reserve area. We then use this approximation to obtain results on extinction using two different approaches, which we can compare to the baseline IBM; the first approach is based on the Central Limit Theorem and provides efficient simulation results, and the second modifies a simple Galton-Watson branching process to include loss outside the reserve area. We find that this spatially implicit approximation is also effective in obtaining results similar to those produced by the IBM in the presence of both demographic and environmental variability. Overall, this provides a set of complimentary methods for predicting the reserve area required to sustain a population in the presence of strong fishing pressure in the surrounding waters.