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1
AFFILI, ELISA. "EVOLUTION EQUATIONS WITH APPLICATIONS TO POPULATION DYNAMICS." Doctoral thesis, Università degli Studi di Milano, 2021. http://hdl.handle.net/2434/820854.
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The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the role of heterogeneity in equations and interactions in coupled systems. In this direction, we investigate three separate problems, each corresponding to a chapter of this thesis. The first problem addresses the evolution of a single population living in a periodic medium with a fast diffusion line; this corresponds to the study of a reaction-diffusion system with equations in different dimensions. We derive results on asymptotic behaviour through the study of some generalised principal eigenvalues. We find that the road has no impact on the survival chances of the population, despite the deleterious effect expected from fragmentation. The second investigation regards a model describing the competition between two populations in a situation of asymmetrically aggressive interactions; this consists of a system of two ODEs. The evolution progresses through two possible scenarios, where only one population survives. Then, the interpretation of one of the parameters as the aggressiveness of the attacker population naturally raises questions of controllability. We characterise the set of initial conditions leading to the victory of the attacker through a suitable (possibly time-dependant) strategy. The third and last part of this thesis analyses the time decay of some evolution equations with classical and fractional time derivatives. Depending on the type of derivative and some degree of non-degeneracy of the spatial operator, quantitative polynomial or exponential estimates are entailed.
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El-Hachem, Maud. "Mathematical models of biological invasion." Thesis, Queensland University of Technology, 2022. https://eprints.qut.edu.au/232864/1/Maud_El-Hachem_Thesis.pdf.
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This thesis studies mathematical models of a population of cells invading the surrounding environment or another living population. A classical single-species model is reformulated using a moving boundary to track the position of the moving front of the invading population. The moving boundary is also used to separate two populations. Other models studied are coupled partial differential equations to describe the interaction of a population with another one. Different types of interaction are represented: the degradation of healthy skin by cancer and the growth of bone tissue on substrate.
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Hodgkinson, Arran. "Mathematical Methods for Modelling Biological Heterogeneity." Thesis, Montpellier, 2019. http://www.theses.fr/2019MONTS119.
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Les processus biologiques sont des phénomènes complexes, multi-échelles, présentant une hétérogénéité importante à travers l’espace, la structure et la fonction. De plus, ils impliquent des événements fortement corrélés et présentent des boucles de rétroaction à travers les échelles. Dans cette thèse, nous utilisons des représentations spatio-structuro-temporelles en grande dimension pour étudier l'hétérogénéité biologique à travers l'espace, la fonction biologique et le temps, et appliquons cette méthode à divers problèmes importants en biologie et en clinique.Nous commençons par introduire un nouveau cadre spatio-structuro-temporel, basé sur équations aux dérivées partielles, pour le cas d’un système biologique dont la fonction dépend de la dynamique dans le temps et l’espace des récepteurs membranaires, des ligands et du métabolisme. Afin d’étudier les solutions de ces équations, nous utilisons un schéma numérique de différences finies ainsi que divers résultats analytiques. Pour tester la validité de nos approches numériques nous prouvons un théorème sur la stabilité de notre schéma.Le cancer est un problème croissant pour la population mondiale, car ses taux d'incidence et sa résistance aux médicaments augmentent. D’abord nous modélisons l’invasion du cancer du sein agressif via sa capacité à produire des enzymes dégradant la matrice extracellulaire, et nous montrons la génération de structures spatiales anatomo-pathologiques difficiles à enlever par la chirurgie. Ensuite, nous développons des modèles mathématiques de tumeurs résistantes au traitement et appliquons ces modèles à la résistance aux thérapies ciblées (inhibiteurs de BRAF et de MEK) du mélanome cutané. Nous constatons que les tumeurs développent une résistance à la fois à travers des processus d'adaptations génétiques ou par le remodelage de leur métabolisme, mais montrons que seules les tumeurs métaboliquement plastiques manifestent une re-sensibilisation à ces thérapies. Enfin, via une approche basée sur des données d’expression en cellule unique (RNA-seq), nous montrons que la dynamique spatiale contribue à l'hétérogénéité tumorale et à la résistante aux traitements de façon liée au statut prolifératif des cellules cancéreuses.Nous appliquons nos méthodes à deux autres systèmes. Dans le contexte de la réponse immunitaire à l’infection virale, nous étudions la production et la dynamique spatiale de l’interféron (IFN) et l’apparent paradoxe de la conservation de molécules d’IFN avec affinités faibles et fortes. Nous constatons que les molécules IFN de faible affinité sont plus capables de se propager dans l'espace, alors que les molécules de haute affinité sont capables de maintenir le signal localement. L’addition de ligands de faible affinité à un système ne comprenant que des ligands de moyenne ou grande affinité peut entraîner une diminution de la charge virale d’environ 23%. Ensuite, nous explorons le contexte de la sélection sexuelle de l'apparence masculine dans l'évolution darwinienne. Nous constatons que les systèmes biologiques conservent les traits sélectionnés sexuellement, même si cela entraîne une diminution générale de la population.Enfin, nous introduisons deux autres techniques de modélisation: pour augmenter la dimensionnalité de notre approche, nous développons une approche pseudo-spectrale basée sur les polynômes de Chebyshev et l’appliquons au même scénario de résistance aux médicaments phénotypiques que ci-dessus. Ensuite, pour étudier un scénario coopératif dans lequel des cellules cancéreuses prolifératives et invasives sont co-injectées, induisant des comportements invasifs dans les cellules prolifératives, nous développons une nouvelle méthode de simulation combinant des automates cellulaires et systèmes d’agents. Nous trouvons que cette méthode est capable de reproduire les résultats de l'expérience de coinjection et d'autres expériences dans lesquelles des cellules ont été placées dans des micropistes de collagène<br>Biological processes are complex, multi-scale phenomena displaying extensive heterogeneity across space, structure, and function. Moreover, these events are highly correlated and involve feedback loops across scales, with nuclear transcription being effected by protein concentrations and vice versa, presenting a difficulty in representing these through existing mathematical approaches. In this thesis we use higher-dimensional spatio-structuro-temporal representations to study biological heterogeneity through space, biological function, and time and apply this method to various scenarios of significance to the biological and clinical communities.We begin by deriving a novel spatio-structuro-temporal, partial differential equation framework for the general case of a biological system whose function depends upon dynamics in time, space, surface receptors, binding ligands, and metabolism. In order to simulate solutions for this system, we present a numerical finite difference scheme capable of this and various analytic results connected with this system, in order to clarify the validity of our predictions. In addition to this, we introduce a new theorem establishing the stability of the central differences scheme.Despite major recent clinical advances, cancer incidence continues to rise and resistance to newly synthesised drugs represents a major health issue. To tackle this problem, we begin by investigating the invasion of aggressive breast cancer on the basis of its ability to produce extracellular matrix degrading enzymes, finding that the cancer produced a surgically challenging morphology. Next, we produce a novel structure in which models of cancer resistance can be established and apply this computational model to study genetic and phenotypic modes of resistance and re-sensitisation to targeted therapies (BRAF and MEK inhibitors). We find that both genetic and phenotypic heterogeneity drives resistance but that only the metabolically plastic, phenotypically resistant, tumour cells are capable of manifesting re-sensitisation to these therapies. We finally use a data-driven approach for single-cell RNA-seq analysis and show that spatial dynamics fuel tumour heterogeneity, contributing to resistance to treatment accordingly with the proliferative status of cancer cells.In order to expound this method, we look at two further systems: To investigate a case where cell-ligand interaction is particularly important, we take the scenario in which interferon (IFN) is produced upon infection of the cell by a virus and ask why biological systems evolve and retain multiple different affinities of IFN. We find that low affinity IFN molecules are more capable of propagating through space; high affinity molecules are capable of sustaining the signal locally; and that the addition of low affinity ligands to a system with only medium or high affinity ligands can lead to a ~23% decrease in viral load. Next, we explore the non-spatial, structuro-temporal context of male elaboration sexual and natural selection in Darwinian evolution. We find that biological systems will conserve sexually selected traits even in the event where this leads to an overall population decrease, contrary to natural selection.Finally, we introduce two further modelling techniques: To increase the dimensionality of our approach, we develop a pseudo-spectral Chebyshev polynomial-based approach and apply this to the same scenario of phenotypic drug resistance as above. Next, to deal with one scenario in which proliferative and invasive cancer cells are co-injected, inducing invasive behaviours in the proliferative cells, we develop a novel agent-based, cellular automaton method and associated analytic theorems for generating numerical solutions. We find that this method is capable of reproducing the results of the co-injection experiment and further experiments, wherein cells migrate through artificially produced collagen microtracks
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Ohlsson, Henrik. "Mathematical Analysis of a Biological Clock Model." Thesis, Linköping University, Department of Electrical Engineering, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-6750.
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<p>Have you thought of why you get tired or why you get hungry? Something in your body keeps track of time. It is almost like you have a clock that tells you all those things.</p><p>And indeed, in the suparachiasmatic region of our hypothalamus reside cells which each act like an oscillator, and together form a coherent circadian rhythm to help our body keep track of time. In fact, such circadian clocks are not limited to mammals but can be found in many organisms including single-cell, reptiles and birds. The study of such rhythms constitutes a field of biology, chronobiology, and forms the background for my research and this thesis.</p><p>Pioneers of chronobiology, Pittendrigh and Aschoff, studied biological clocks from an input-output view, across a range of organisms by observing and analyzing their overt activity in response to stimulus such as light. Their study was made without recourse to knowledge of the biological underpinnings of the circadian pacemaker. The advent of the new biology has now made it possible to "break open the box" and identify biological feedback systems comprised of gene transcription and protein translation as the core mechanism of a biological clock.</p><p>My research has focused on a simple transcription-translation clock model which nevertheless possesses many of the features of a circadian pacemaker including its entrainability by light. This model consists of two nonlinear coupled and delayed differential equations. Light pulses can reset the phase of this clock, whereas constant light of different intensity can speed it up or slow it down. This latter property is a signature property of circadian clocks and is referred to in chronobiology as "Aschoff's rule". The discussion in this thesis focus on develop a connection and also a understanding of how constant light effect this clock model.</p>
5
Magi, Ross. "Dynamic behavior of biological membranes." Thesis, The University of Utah, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3680576.
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<p> Biological membranes are important structural units in the cell. Composed of a lipid bilayer with embedded proteins, most exploration of membranes has focused on the proteins. While proteins play a vital role in membrane function, the lipids themselves can behave in dynamic ways which affect membrane structure and function. Furthermore, the dynamic behavior of the lipids can affect and be affected by membrane geometry. A novel fluid membrane model is developed in which two different types of lipids flow in a deforming membrane, modelled as a two-dimensional Riemannian manifold that resists bending. The two lipids behave like viscous Newtonian fluids whose motion is determined by realistic physical forces. By examining the stability of various shapes, it is shown that instability may result if the two lipids forming the membrane possess biophysical qualities, which cause them to respond differently to membrane curvature. By means of numerical simulation of a simplified model, it is shown that this instability results in curvature induced phase separation. Applying the simplified model to the Golgi apparatus, it is hypothesized that curvature induced phase separation may occur in a Golgi cisterna, aiding in the process of protein sorting. </p><p> In addition to flowing tangentially in the membrane, lipids also flip back and forth between the two leaflets in the bilayer. While traditionally assumed to occur very slowly, recent experiments have indicated that lipid flip-flop may occur rapidly. Two models are developed that explore the effect of rapid flip-flop on membrane geometry and the effect of a pH gradient on the distribution of charged lipids in the leaflets of the bilayer. By means of a stochastic model, it is shown that even the rapid flip-flop rates observed are unlikely to be significant inducers of membrane curvature. By means of a nonlinear Poisson- Boltzmann model, it is shown that pH gradients are unlikely to be significant inducers of bilayer asymmetry under physiological conditions. </p>
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Chindelevitch, Leonid Alexandrovich. "Extracting information from biological networks." Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/64607.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 175-194).<br>Systems biology, the study of biological systems in a holistic manner, has been catalyzed by a dramatic improvement in experimental techniques, coupled with a constantly increasing availability of biological data. The representation and analysis of this heterogeneous data is facilitated by the powerful abstraction of biological networks. This thesis examines several types of these networks and looks in detail at the kind of information their analysis can yield. The first part discusses protein interaction networks. We introduce a new algorithm for the pairwise alignment of these networks. We show that these alignments can provide important clues to the function of proteins as well as insights into the evolutionary history of the species under examination. The second part discusses regulatory networks. We present an approach for validating putative drug targets based on the information contained in these networks. We show how this approach can also be used to discover drug targets. The third part discusses metabolic networks. We provide new insights into the structure of constraint-based models of cell metabolism and describe a methodology for performing a complete analysis of a metabolic network. We also present an implementation of this methodology and discuss its application to a variety of problems related to the metabolism of bacteria. The final part describes an application of our methodology to Mycobacterium tuberculosis, the pathogen responsible for almost 2 million deaths around the world every year. We introduce a method for reconciling metabolic network reconstructions and apply it to merge the two published networks for tuberculosis. We analyze the merged network and show how it can be refined based on available experimental data to improve its predictive power. We conclude with a list of potential drug targets.<br>by Leonid Alexandrovich Chindelevitch.<br>Ph.D.
7
Altschul, Stephen Frank. "Aspects of biological sequence comparison." Thesis, Massachusetts Institute of Technology, 1987. http://hdl.handle.net/1721.1/102708.
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Thesis (Ph. D)--Massachusetts Institute of Technology, Dept. of Mathematics, 1987.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Bibliography: leaves 165-168.<br>by Stephen Frank Altschul.<br>Ph.D
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Basse, Britta. "Case studies in mathematical modelling for biological conservation." Thesis, University of Canterbury. Mathematics & Statistics, 1999. http://hdl.handle.net/10092/4804.
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The use of mathematical modelling as a tool for investigating selected topics in conservation
biology is the focus of this thesis.
A continuous system of partial and ordinary differential equations model the age structured
population dynamics of a cohort of endemic, threatened New Zealand North Island
brown kiwi, Apteryx mantelli. Critical predation and recruitment rates of immature birds are
estimated. Stoats, Mustela erminea, are the main predator of immature kiwi. A refinement
to the model allows the calculation of acceptable stoat densities. In order to reduce stoats
to this critical density, a linear system of ordinary differential equations, representing an
acute secondary poisoning regime, is solved. An optimal secondary poisoning scheme, which
minimises the number of prey poisoned and the amount of poison used, is found. The minimum
area required for pest control is estimated by simulating the dispersal of sub-adult kiwi
using a discrete random walk approach. Simulations and a discrete age structured model are
used to investigate pulsed management strategies for both kiwi and kokako, Callaeas cinerea
wilsoni. Finally, a two dimensional discrete random walk is generalised and a continuous
diffusion equation is derived. A diffusion equation is incorporated into a S1 R (Susceptible,
Infected, Recovered) model representing the natural spread of Rabbit Haemorrhagic Disease
from a point source in rabbit, Oryctolagus cuniculus cuniculus, populations. The speed
for the virus, dependant on certain model parameters, is found and the minimum initial
population density, below which the wave of infection will not travel, is estimated.
All specific models discussed throughout the thesis are generic by nature and can be
applied to a diverse range of subjects.
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Grau, Ribes Alexis. "Mathematical models of transport phenomena in biological tissues." Doctoral thesis, Universite Libre de Bruxelles, 2020. https://dipot.ulb.ac.be/dspace/bitstream/2013/303032/4/contents.pdf.
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Cette thèse est consacrée à l’élaboration et l’étude théorique de modèles de transport décrivant les dynamiques cellulaires et la communication intercellulaire dans les tissus épithéliaux. Nous nous intéressons d’abord à l’influence du transport de microARNs (miRNAs) sur la dynamique spatiotemporelle de réseaux de régulation génétique. Ces courtes séquences d’ARN régulent la synthèse des protéines en bloquant l’activité des ARN messagers et leur sécrétion via des vesicules extracellulaires en font des agents de communication intercellulaire. Différents modèles faisant intervenir des miRNAs extracellulaires ont été construits et étudiés numériquement. Les premiers sont des modèles génériques destinés à mettre en évidence l'effet d'une cellule ayant une production de miRNAs anormale sur l'expression génétique dans les cellules voisines. Nous abordons ensuite des modèles plus complexes et réalistes dans lesquels des oscillations (liées à des rythmes biologiques) et de la bistabilité (liée à une différenciation cellulaire) sont observées. Ces modèles permettent d’étudier des dynamiques de communication complexes observées en biologie, comme la synchronisation de cellules couplées ou la propagation d'un changement de phénotype. Nous mettons également en évidence le rôle de défauts, tels que des mutations génétiques ou encore des variations de densité cellulaire dans les tissus, sur ces phénomènes de propagation. La deuxième partie de la thèse est dédiée à la construction de modèles de réaction-diffusion dans lesquels la dynamique des cellules dépend de leur état interne. Sur base d’études expérimentales montrant l’influence de protéines et de miRNAs sur la mobilité et la prolifération des cellules, nous établissons un modèle multi-échelle dans lequel la dynamique intracellulaire et le mouvement des cellules interagissent. En effet, certaines protéines sont responsables de l’adhésion cellulaire ou régulent la vitesse de prolifération. Dans notre modèle, chaque cellule synthétise ces espèces d’intérêt et les processus cellulaires (migration, prolifération) dépendent de la concentration de ces espèces biochimiques. Ce modèle permet de reproduire des expériences de migration cellulaire et de prédire, notamment, l'influence d'E-cadherin, une protéine clé dans l'adhesion cellulaire, sur la dynamique de régénération d'un tissu.<br>Doctorat en Sciences<br>info:eu-repo/semantics/nonPublished
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Orme, Belinda Abigail Amanda. "Biological mixing and chaos." Thesis, University of Birmingham, 2002. http://etheses.bham.ac.uk//id/eprint/7637/.
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We consider a problem from the field of biological fluid mechanics which considers the flow associated with the motion of a flagellum on a sessile micro-organism. Motivation is taken from the movement of fluid around a species of choanoflagellate, \(Salpingoeca\) \(Amphoridium\). Choanoflagellates are a class of organism in the phylum Protozoa. Because the length scales and velocities are very low, the flow is one dominated by viscous forces and the environment is characterised by a low Reynolds number. The flow caused by the flagellum is initially modelled via a point force. These microorganisms operate in more than one location and the motion they create is modelled in a qualitative sense by using two stokeslets (appropriate to Stokes' flow) whose orientation and position is varied with time. The sessile micro-organism resides above a boundary which is modelled, most generally, as an interface between two fluids possessing different properties. Efficiency of feeding currents generated by the flagellum motion is studied. The resulting dynamics are investigated using chaotic measures, which examine the stretching and consequent mixing of elements within the fluid. Different point force locations lead to various eddy structures such that their superposition results in chaotic advection. The model is developed to examine the flow of particles around a three-dimensional realisation of a micro-organism which involves a flagellum and a cell body attached to a substrate. Green's functions are used to satisfy a number of boundary conditions simultaneously. Particle paths of a tracer introduced into the fully three-dimensional model are investigated. Comparisons with experimental data illustrate good agreement between theoretical and experimental results. Further extensions to the model are suggested.
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O'Keeffe, Stephen George. "The mechanics of growth and residual stress in biological cylinders." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:493473f6-b952-4ce3-a2e5-1a79e97afb7f.
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Biological tissue differs from other materials in many ways. Perhaps the most crucial difference is its ability to grow. Growth processes may give rise to stresses that exist in a body in the absence of applied loads and these are known as residual stresses. Residual stress is present in many biological systems and can have important consequences on the mechanical response of a body. Mathematical models of biological structures must therefore be able to capture accurately the effects of differential growth and residual stress, since greater understanding of the roles of these phenomena may have applications in many fields. In addition to residual stresses, biological structures often have a complex morphology. The theory of 3-D elasticity is analytically tractable in modelling mechanical properties in simple geometries such as a cylinder. On the other hand, rod theory is well-suited for geometrically-complex deformations, but is unable to account for residual stress. In this thesis, we aim to develop a map between the two frameworks. Firstly, we use 3-D elasticity to determine effective mechanical properties of a growing cylinder and map them into an effective rod. Secondly, we consider a growing filament embedded in an elastic foundation. Here, we estimate the degree of transverse reinforcement the foundation confers on the filament in terms of its material properties. Finally, to gain a greater understanding of the role of residual stress in biological structures, we consider a case study: the chameleon's tongue. In particular we consider the role of residual stress and anisotropy in aiding the rapid projection of the tongue during prey capture. We construct a mechanical model of the tongue and use it to investigate a proposed mechanism of projection by means of an energy balance argument.
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Tucker, George Jay. "Statistical methods to infer biological interactions." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/89874.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>169<br>Cataloged from student-submitted PDF version of thesis.<br>Includes bibliographical references (pages 153-170).<br>Biological systems are extremely complex, and our ability to experimentally measure interactions in these systems is limited by inherent noise. Technological advances have allowed us to collect unprecedented amounts of raw data, increasing the need for computational methods to disentangle true interactions from noise. In this thesis, we focus on statistical methods to infer two classes of important biological interactions: protein-protein interactions and the link between genotypes and phenotypes. In the first part of the thesis, we introduce methods to infer protein-protein interactions from affinity purification mass spectrometry (AP-MS) and from luminescence-based mammalian interactome mapping (LUMIER). Our work reveals novel context dependent interactions in the MAPK signaling pathway and insights into the protein homeostasis machinery. In the second part, we focus on methods to understand the link between genotypes and phenotypes. First, we characterize the effects of related individuals on standard association statistics for genome-wide association studies (GWAS) and introduce a new statistic that corrects for relatedness. Then, we introduce a statistically powerful association testing framework that corrects for confounding from population structure in large scale GWAS. Lastly, we investigate regularized regression for phenotype prediction from genetic data.<br>by George Jay Tucker.<br>Ph. D.
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Iyaniwura, Sarafa Adewale. "Mathematical modelling of partially absorbing boundaries in biological systems." Thesis, University of British Columbia, 2016. http://hdl.handle.net/2429/58907.
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This project presents a mathematical framework for identifying partially permeable biological boundaries, and estimating the rate of absorption of diffusing objects at such a boundary based on limited experimental data. We used partial differential equations (PDEs) to derive probability distribution functions for finding a particle performing Brownian motion in a region. These distribution functions can be fit to data to infer the existence of a boundary. We also used the probability distribution functions together with maximum likelihood estimation to estimate the rate of absorption of objects at the boundaries, based on simulated data. Furthermore, we consider a switching boundary and provide a technique for approximating the boundary with a partially permeable boundary.<br>Science, Faculty of<br>Graduate
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Lamb, Angharad. "Mathematical Modelling of the Biological Stress Response to Chronium." Thesis, University of Nottingham, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.517846.
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Turner, Stephen. "Mathematical modelling of cancer invasion and biological cell movement." Thesis, Heriot-Watt University, 2002. http://hdl.handle.net/10399/438.
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Lewis, Miranda Claire. "Mathematical modelling of the growth of soft biological tissues." Thesis, University of Southampton, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.436982.
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Chung, Andy Heung Wing. "Novel mathematical and computational approaches for modelling biological systems." Thesis, University of Sussex, 2016. http://sro.sussex.ac.uk/id/eprint/60405/.
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This work presents the development, analysis and subsequent simulations of mathematical models aimed at providing a basis for modelling atherosclerosis. This cardiovascular disease is characterized by the growth of plaque in artery walls, forming lesions that protrude into the lumen. The rupture of these lesions contributes greatly to the number of cases of stroke and myocardial infarction. These are two of the main causes of death in the UK. Any work to understand the processes by which the disease initiates and progresses has the ultimate aim of limiting the disease through either its prevention or medical treatment and thus contributes a relevant addition to the growing body of research. The literature supports the view that the cause of atherosclerotic lesions is an in inflammatory process-succinctly put, excess amounts of certain biochemical species fed into the artery wall via the bloodstream spur the focal accumulation of extraneous cells. Therefore, suitable components of a mathematical model would include descriptions of the interactions of the various biochemical species and their movement in space and time. The models considered here are in the form of partial differential equations. Specifically, the following models are examined: first, a system of reaction-diffusion equations with coupling between surface and bulk species; second, a problem of optimisation to identify an unknown boundary; and finally, a system of advection-reaction-diffusion equations to model the assembly of keratin networks inside cells. These equations are approximated and solved computationally using the finite element method. The methods and algorithms shown aim to provide more accurate and efficient means to obtain solutions to such equations. Each model in this work is extensible and with elements from each model combined, they have scope to be a platform to give a fuller model of atherosclerosis.
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Njagarah, Hatson John Boscoh. "Modelling water-borne infections : the impact of hygiene, metapopulation movements and the biological control of cholera." Thesis, Stellenbosch : Stellenbosch University, 2014. http://hdl.handle.net/10019.1/95972.
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Thesis (PhD)--Stellenbosch University, 2014.<br>ENGLISH ABSTRACT: Water-borne infections have been a menace in many countries around the globe, claiming
millions of lives. Cholera in particular has spread to all continents and now on its seventh
epidemic. Although control measures have been continually developed through sanitation,
vaccination and rehydration, the infection still devastates populations whenever there is an
outbreak. In this research work, mathematical models for cholera transmission dynamics
with focus on the impact of sanitation and hygiene, metapopulation spread, optimal control
and biological control using a bacteriophage specific for pathogenic Vibrio cholerae are
constructed and analysed. Vital analyses for the models are precisely given as well as numerical
results depicting long term behaviour and the evolution of populations over time.
The results of our analysis indicate that; improved sanitation and hand-hygiene are vital in
reducing cholera infections; the spread of disease across metapopulations characterised by
exchange of individuals and no cross community infection is associated with synchronous
fluctuation of populations in both adjacent communities; during control of cholera, the control
measures/efforts ought to be optimal especially at the beginning of the epidemic where
the outbreak is often explosive in nature; and biological control if well implemented would
avert many potential infections by lowering the concentration of pathogenic vibrios in the
aquatic environment to values lower than the infectious dose.<br>AFRIKAANSE OPSOMMING: Water-infeksies is ’n bedreiging in baie lande regoor die wêreld en eis miljoene lewens.
Cholera in die besonder, het op sy sewende epidemie na alle kontinente versprei. Hoewel
beheermaatreëls voortdurend ontwikkel word deur middel van higiëne, inentings en rehidrasie,
vernietig die infeksie steeds bevolkings wanneer daar ’n uitbraak voorkom. In
hierdie navorsingswerk, word wiskundige modelle vir cholera-oordrag dinamika met die
fokus op die impak van higiëne, metabevolking verspreiding, optimale beheer en biologiese
beheer met behulp van ’n bakteriofaag spesifiek vir patogene Vibrio cholerae gebou en
ontleed. Noodsaaklike ontledings vir die modelle is gegee sowel as numeriese resultate wat
die langtermyn gedrag uitbeeld en die ontwikkeling van die bevolking oor tyd. Die resultate
van ons ontleding dui daarop dat; verbeterde higiëne is noodsaaklik in die vermindering
van cholera infeksies; die verspreiding van die siekte oor metapopulaties gekenmerk deur
die uitruil van individue en geen kruis gemeenskap infeksie wat verband houmet sinchrone
skommeling van bevolkings in beide aangrensende gemeenskappe; tydens die beheer van
cholera,behoort die beheermaatreëls/pogings optimaal te wees veral aan die begin van die
epidemie waar die uitbreking dikwels plofbaar in die natuur is; en biologiese beheer, indien
dit goed geïmplementeer word, kan baie potensiële infeksies voorkom deur ’n vermindering
in die konsentrasie van patogene vibrio in die water tot waardes laer as die aansteeklike
dosis.
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Breitsch, Nathan W. "Techniques for the Study of Biological Coupled Oscillator Systems." Ohio University Honors Tutorial College / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ouhonors1399892563.
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Waniewski, Jacek. "Mathematical modeling of fluid and solute transport in peritoneal dialysis /." Stockholm, 2001. http://diss.kib.ki.se/2001/91-628-4610-8/.
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Gill, Mandeep Singh. "Application of software engineering methodologies to the development of mathematical biological models." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:35178f3a-7951-4f1c-aeab-390cdd622b05.
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Mathematical models have been used to capture the behaviour of biological systems, from low-level biochemical reactions to multi-scale whole-organ models. Models are typically based on experimentally-derived data, attempting to reproduce the observed behaviour through mathematical constructs, e.g. using Ordinary Differential Equations (ODEs) for spatially-homogeneous systems. These models are developed and published as mathematical equations, yet are of such complexity that they necessitate computational simulation. This computational model development is often performed in an ad hoc fashion by modellers who lack extensive software engineering experience, resulting in brittle, inefficient model code that is hard to extend and reuse. Several Domain Specific Languages (DSLs) exist to aid capturing such biological models, including CellML and SBML; however these DSLs are designed to facilitate model curation rather than simplify model development. We present research into the application of techniques from software engineering to this domain; starting with the design, development and implementation of a DSL, termed Ode, to aid the creation of ODE-based biological models. This introduces features beneficial to model development, such as model verification and reproducible results. We compare and contrast model development to large-scale software development, focussing on extensibility and reuse. This work results in a module system that enables the independent construction and combination of model components. We further investigate the use of software engineering processes and patterns to develop complex modular cardiac models. Model simulation is increasingly computationally demanding, thus models are often created in complex low-level languages such as C/C++. We introduce a highly-efficient, optimising native-code compiler for Ode that generates custom, model-specific simulation code and allows use of our structured modelling features without degrading performance. Finally, in certain contexts the stochastic nature of biological systems becomes relevant. We introduce stochastic constructs to the Ode DSL that enable models to use Stochastic Differential Equations (SDEs), the Stochastic Simulation Algorithm (SSA), and hybrid methods. These use our native-code implementation and demonstrate highly-efficient stochastic simulation, beneficial as stochastic simulation is highly computationally intensive. We introduce a further DSL to model ion channels declaratively, demonstrating the benefits of DSLs in the biological domain. This thesis demonstrates the application of software engineering methodologies, and in particular DSLs, to facilitate the development of both deterministic and stochastic biological models. We demonstrate their benefits with several features that enable the construction of large-scale, reusable and extensible models. This is accomplished whilst providing efficient simulation, creating new opportunities for biological model development, investigation and experimentation.
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Montenegro-Johnson, Thomas D. "Microscopic swimming in biological fluids." Thesis, University of Birmingham, 2013. http://etheses.bham.ac.uk//id/eprint/4220/.
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Fluid interactions are ubiquitous in the natural world; all organisms must find strategies to generate, utilise or resist flow in order to be successful. A process fundamental to all life on earth is reproduction, which in many cases entails the swimming of sperm cells. Cell swimming arises from coupled interactions between physical and biological processes. We will focus on the effects of changing fluid rheology on microscopic swimmers, with a particular application to the study of internal mammalian fertilisation. To reach the egg, mammalian sperm must navigate the convoluted geometry of the female reproductive tract, actively bending their flagella in order to propel themselves through cervical mucus: a suspension of polymer chains that twist, tangle and align with flow, giving it complex properties. Whilst recent work has examined the effects of fluid viscoelasticity on sperm-like swimmers, relatively less attention has been given to the shear-thinning property. We develop a new finite element technique to simulate free swimmers with prescribed beat kinematics in shear-thinning fluids with nonlinear governing equations. This technique is then applied to three qualitatively different viscous swimmers in order to examine the different phenomena that arise from swimmer interactions with of shear-thinning fluid.
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Nelson, Carl John. "Mathematical morphology for quantification in biological & medical image analysis." Thesis, Durham University, 2017. http://etheses.dur.ac.uk/12169/.
Full textAbstract:
Mathematical morphology is an established field of image processing first introduced as an application of set and lattice theories. Originally used to characterise particle distributions, mathematical morphology has gone on to be a core tool required for such important analysis methods as skeletonisation and the watershed transform. In this thesis, I introduce a selection of new image analysis techniques based on mathematical morphology. Utilising assumptions of shape, I propose a new approach for the enhancement of vessel-like objects in images: the bowler-hat transform. Built upon morphological operations, this approach is successful at challenges such as junctions and robust against noise. The bowler-hat transform is shown to give better results than competitor methods on challenging data such as retinal/fundus imagery. Building further on morphological operations, I introduce two novel methods for particle and blob detection. The first of which is developed in the context of colocalisation, a standard biological assay, and the second, which is based on Hilbert-Edge Detection And Ranging (HEDAR), with regard to nuclei detection and counting in fluorescent microscopy. These methods are shown to produce accurate and informative results for sub-pixel and supra-pixel object counting in complex and noisy biological scenarios. I propose a new approach for the automated extraction and measurement of object thickness for intricate and complicated vessels, such as brain vascular in medical images. This pipeline depends on two key technologies: semi-automated segmentation by advanced level-set methods and automatic thickness calculation based on morphological operations. This approach is validated and results demonstrating the broad range of challenges posed by these images and the possible limitations of this pipeline are shown. This thesis represents a significant contribution to the field of image processing using mathematical morphology and the methods within are transferable to a range of complex challenges present across biomedical image analysis.
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Seier, Edith, and Karl H. Joplin. "Introduction to STATISTICS in a Biological Context." Digital Commons @ East Tennessee State University, 2011. http://amzn.com/1463613377.
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Schmidberger, Markus. "Parallel Computing for Biological Data." Diss., lmu, 2009. http://nbn-resolving.de/urn:nbn:de:bvb:19-104921.
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Armond, Jonathan William. "Forces in a biological context." Thesis, University of Warwick, 2010. http://wrap.warwick.ac.uk/4480/.
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Theoretical modelling of the microtubule-Dam1-ring force generation mechanism and the pulling of tubes from surface-supported lipid bilayers are presented and discussed. Atomic force microscopy (AFM) force data of tube pulling experiments is analysed and compared with theoretical predictions. Featurescommonto recent computational models are simplified and examined independently where possible. In particular, the steric confinement of the Dam1 ring on a microtubule (MT) by protofilaments (PFs), the powerstroke produced by curling PFs, the depolymerisation of the MT, and the binding attraction between Dam1 and the MT are modelled. Model parameters are fitted to data. Functional force generation is equally demonstrated when attachment is maintained by steric confinement alone (protofilament model) or by a binding attraction alone (binding model). Moreover, parameters amenable to experimental modification are shown to induce differences between the protofilament model and the binding model. Changing the depolymerisation rate of MTs, the diffusion coefficient of the Dam1 ring, or applying an oscillating load force will allow discrimination of these two different mechanisms of force generation and kinetochore attachment. A previously described theoretical model of pulling lipid bilayer tubes from vesicles is modified for the case of pulling tubes from surface-supported lipid bilayers. A shape equation for axisymmetric membranes is derived variationally and solved numerically for zero pressure. Free energy profiles and force curves are calculated for various AFM probe sizes and compared to experimental data where a ground flat AFM probe is used to pull tubes from surface-supported lipid bilayers. The predicted force curves partially fit the experimental data, although not at short distances, and estimates of the bilayer surface tension are given. Pressure and volume profiles are calculated for the extension of the model to the nonzero pressure case.
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Caberlin, Martin D. "Stiff ordinary and delay differential equations in biological systems." Thesis, McGill University, 2002. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=29416.
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The Santillan-Mackey model of the tryptophan operon was developed to characterize the anthranilate synthase activity in cultures of Escherichia coli. Similarly, the GABA reaction scheme was formulated to characterize the response of the GABAA receptor at a synapse, and the Hodgkin-Huxley model was developed to characterize the action potential of a squid giant axon. While the Hodgkin-Huxley model has been studied in great detail from a mathematical vantage, much less is known about the preceding two models in this regard. This work examines the stiffness of all three models; a novel perspective for both the Santillan-Mackey model and the GABA reaction. The characterization of the stiffness in these problems gives theoretical biologists insight into the dynamics of the reactions. It also enables them to select more computationally efficient methods for numerical simulations. The discovery of invariant manifolds in the Santillan-Mackey model and the GABA reaction in this work present experimentalists with concrete assays, against which the models can be tested.
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Yu, Yun William. "Compressive algorithms for search and storage in biological data." Thesis, Massachusetts Institute of Technology, 2017. http://hdl.handle.net/1721.1/112879.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2017.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 187-197).<br>Disparate biological datasets often exhibit similar well-defined structure; efficient algorithms can be designed to exploit this structure. In this doctoral thesis, we present a framework for similarity search based on entropy and fractal dimension; here, we prove that a clustered search algorithm scales in time with metric entropy number of covering hyperspheres-if the fractal dimension is low. Using these ideas, entropy-scaling versions of standard bioinformatics search tools can be designed, including for small-molecule, metagenomics, and protein structure search. This 'compressive acceleration' approach taking advantage of redundancy and sparsity in biological data can be leveraged also for next-generation sequencing (NGS) read mapping. By pairing together a clustered grouping over similar reads and a homology table for similarities in the human genome, our CORA framework can accelerate all-mapping by several orders of magnitude. Additionally, we also present work on filtering empirical base-calling quality scores from Next Generation Sequencing data. By using the sparsity of k-mers of sufficient length in the human genome and imposing a human prior through the use of frequent k-mers in a large corpus of human DNA reads, we are able to quickly discard over 90% of the information found in those quality scores while retaining or even improving downstream variant-calling accuracy. This filtering step allows for fast lossy compression of quality scores.<br>by Yun William Yu.<br>Ph. D.
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Tipadis, Grigoris G. "Mathematical models for wastewater treatment by the Rotating Biological Contactor process." Thesis, Imperial College London, 1991. http://hdl.handle.net/10044/1/8514.
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McInerney, Daragh. "Spatio-temporal patterning in biological systems : numerical techniques and mathematical modelling." Thesis, University of Oxford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.393830.
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Gothard, Elizabeth Jane. "Wound healing : a multidisciplinary approach : combining mathematical models and biological experiments." Thesis, University of York, 2016. http://etheses.whiterose.ac.uk/17204/.
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Cutaneous wound repair occurs as a continuous process in both space and time; however, studies of healing mechanisms and outcomes frequently generate spatially and temporally sparse datasets. We propose a range of techniques that allow the size, cellular processes and scar tissue properties of wounds to be measured and predicted at high spatial and temporal resolution. A non-invasive wound imaging system is shown to provide reliable measurements of wound diameter, perimeter and surface area, but is less reliable in producing 3D metrics such as volume and depth. Wound size and time post healing have a combined effect on reliability, with more reliable measurements obtained at earlier timepoints. A semi-automated pipeline is found to be appropriate for determining the cellular composition of the wound space, but cannot be applied to areas of healthy epidermis due to the close packing of keratinocytes. A range of mathematical models are employed to predict cell numbers within the wound space. An extended domain, partial differential equation model with spatial control of cell proliferation and migration is found to best recapitulate the cellular dynamics observed in vivo. However, if epidermal stratification is to be incorporated, an agent-based description may be preferable. Finally, we formulate a model system that can predict the alignment of collagen fibres and fibroblasts over continuous orientation space. Parameter sets that include large shear forces (which may result from elongated wound geometries or interventions such as suturing) can produce skewed distributions of orientation that cannot be established using discontinuous approaches. Together, this suite of computational approaches provides a powerful set of tools with which the mechanisms of cutaneous wound healing can be investigated, quantified and elucidated.
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Musvoto, Eustina Vongai. "Mathematical modelling of integrated chemical, physical and biological treatment of wastewaters." Master's thesis, University of Cape Town, 1998. http://hdl.handle.net/11427/9676.
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Includes bibliographical references.<br>The development of a kinetic-based model to simulate chemical, physical and biological processes in three phase (gaseous-aqueous-solid) mixed weak acid/base systems is described. The chemical processes are expressed in terms of the kinetics of the forward and reverse reactions for the dissociation of the weak acid/bases. In this approach the H⁺ and all the species of the weak acidfbases of interest are included and the pH is calculated directly from H⁺ via pH = -log (H⁺). The advantage of this approach over the alkalinity/equilibrium chemistry approach is that kinetics are used throughout. Also, the approach is general and can be applied to any combination of mixed weak acid/base systems. The kinetic expressions of the carbonate, phosphate, ammonia, acetate and water systems, including the kinetics of the three phase chemical processes viz. precipitation/dissolution of calcium and magnesium phosphates and carbonates and gas stripping/dissolution of O₂, CO₂ and NH₃, were programmed into the AQUASIM shell package to generate simulation results. The chemical processes part of the model was validated by comparing steady state model predictions with those obtained from equilibrium chemistry based models such as STASOFT I and III (Loewenthal et al., 1986, 1991). Virtually identical results were obtained. The kinetic approach allowed integration of the biological kinetic processes of the IAWQ activated sludge model No 1 (Henze et al., 1987), to extend application of the model to situations where precipitation of minerals, stripping of gasses and biological processes take place in an environment where the pH does not remain constant. Where required the interaction between the chemical species and biological processes was included, e.g. CO₂ uptake for autotrophic nitrifier growth and NH₄⁺ uptake for heterotrophic growth and nitrification. Also, literature information on the effect of pH on the maximum specific growth rates of nitrifiers was included.
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Nundloll, Sapna. "Dos and don'ts in augmentative biological control : insights from mathematical modelling." Nice, 2010. http://www.theses.fr/2010NICE4054.
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Les travaux présentés dans cette thèse portent sur des problématiques de modélisation mathématique de lutte biologique augmentative et des recommandations pratiques qui en sont dérivées. La lutte biologique est une méthode de phytoprotection visant à combattre les ravageurs des cultures à l’aide de leurs ennemis naturels ; son développement est crucial en vue de diminuer l’utilisation de pesticides dont les conséquences néfastes sont reconnues, notamment sur la santé des agriculteurs et des consommateurs, mais aussi sur l’environnement. Il est donc nécessaire de proposer et développer des méthodes de lutte biologique efficaces. Dans cette thèse, nous nous intéressons plus particulièrement à la lutte biologique augmentative, qui consiste à lâcher périodiquement des ennemis naturels qui n’ont pas la capacité de s’établir dans l’environnement en l’absence des ravageurs cibles. Nous introduisons une famille générique de modèles représentant d’une part la relation proie / prédateur à la base de la lutte biologique sous forme d’événements discrets. Nous précisons ensuite ce modèle pour diverses situations rencontrées dans le cadre de la lutte biologique et indiquons quelles en sont les conséquences sur les stratégies de déploiements des ennemis naturels : nous étudions notamment l’effet d’interférences entre prédateurs pour l’accès aux proies, l’existence de relations de cannibalisme entre prédateurs et les conséquences que peuvent avoir des récoltes partielles des plantes sur l’efficacité de la lutte biologique. Enfin, nous résumons tous nos résultats sous forme de recommandations pratiques pour la lutte biologique et en présentons une validation expérimentale sur un exemple agronomique d’intérêt, dans lequel les prédateurs entretiennent des relations d’interférence<br>This thesis presents the mathematical analysis of models in augmentative biological control, from which practical guidelines are the derived. Biological control provides a means to fight pest invertebrates that attack crops with their natural predators. It is an essential component in efforts to reduce pesticide usage in agriculture. Pesticides pose a threat to human health, both to the agricultural worker and the consumer, as well as to the environment because of their toxicity : this largely motivates the need for current biological control programs to be improved and new ones developed. In this thesis, we look in particular at augmentative biological control, which involves the periodic release of predators that are not able to establish in an ecosystem in the absence of the pest, their primary prey. We introduce a general class of models that describe the intrinsic predator-prey dynamics by a pair of ordinary differential equations and the periodic releases by a discrete equation. We study the variants of this class of models, that may arise in a biological control set-up and highlight the consequences on the strategy of releases. We analyse the effect of intrapredatory interference occurring when the predator preys the pest, the impact of cannibalism among the predators, and finally the outcome of partial harvests of crops on the biological control program. Finally, we summarise the results of our mathematical analysis into a set of practical guidelines. We also report experiments on an agronomic predator-prey system, in which the predator species exhibits interfering behaviour. The experimental results validates out mathematical predictions
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Lao, Bert Juan. "Diversified approach to the mathematical and computational modeling of biological systems." Diss., Restricted to subscribing institutions, 2008. http://proquest.umi.com/pqdweb?did=1562159981&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.
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Sinfield, James Lister. "Synchronization and causality in biological networks." Thesis, University of Warwick, 2009. http://wrap.warwick.ac.uk/3789/.
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Rackauckas, Christopher Vincent. "Simulation and Control of Biological Stochasticity." Thesis, University of California, Irvine, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10827971.
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<p> Stochastic models of biochemical interactions elucidate essential properties of the network which are not accessible to deterministic modeling. In this thesis it is described how a network motif, the proportional-reversibility interaction with active intermediate states, gives rise to the ability for the variance of biochemical signals to be controlled without changing the mean, a property designated as mean-independent noise control (MINC). This noise control is demonstrated to be essential for macro-scale biological processes via spatial models of the zebrafish hindbrain boundary sharpening. Additionally, the ability to deduce noise origin from the aggregate noise properties is shown. </p><p> However, these large-scale stochastic models of developmental processes required significant advances in the methodology and tooling for solving stochastic differential equations. Two improvements to stochastic integration methods, an efficient method for time stepping adaptivity on high order stochastic Runge-Kutta methods termed Rejection Sampling with Memory (RSwM) and optimal-stability stochastic Runge-Kutta methods, are combined to give over 1000 times speedups on biological models over previously used methodologies. In addition, a new software for solving differential equations in the Julia programming language is detailed. Its unique features for handling complex biological models, along with its high performance (routinely benchmarking as faster than classic C++ and Fortran integrators of similar implementations) and new methods, give rise to an accessible tool for simulation of large-scale stochastic biological models.</p><p>
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Janse, Van Vuuren Adriaan. "Niche Occupation in Biological Species Competition." Thesis, Stellenbosch : University of Stellenbosch, 2008. http://hdl.handle.net/10019.1/2932.
Full textAbstract:
Thesis (MSc (Logistics))--University of Stellenbosch, 2008.<br>The primary question considered in this study is whether a small population of a biological
species introduced into a resource-heterogeneous environment, where it competes for
these resources with an already established native species, will be able to invade successfully.
A two-component autonomous system of reaction-diffusion equations with spatially
inhomogeneous Lotka-Volterra competitive reaction terms and diffusion coefficients is derived
as the governing equations of the competitive scenario. The model parameters for
which the introduced species is able to invade describe the realized niche of that species.
A linear stability analysis is performed for the model in the case where the resource heterogeneity
is represented by, and the diffusion coefficients are, two-toned functions. In the
case where the native species is not directly affected by the resource heterogeneity, necessary
and sufficient conditions for successful invasion are derived. In the case where the
native species is directly affected by the resource heterogeneity only sufficient conditions
for successful invasion are derived.
The reaction-diffusion equations employed in the model are deterministic. However, in
reality biological species are subject to stochastic population perturbations. It is argued
that the ability of the invading species to recover from a population perturbation is
correlated with the persistence of the species in the niche that it occupies. Hence, invasion
time is used as a relative measure to quantify the rate at which a species’ population
distribution recovers from perturbation.
Moreover, finite difference and spectral difference methods are employed to solve the
model scenarios numerically and to corroborate the results of the linear stability analysis.
Finally, a case study is performed. The model is instantiated with parameters that represent
two different cultivars of barley in a hypothetical environment characterized by
spatially varying water availability and the sufficient conditions for successful invasion are
verified for this hypothetical scenario.
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Kirkham, Sharon Kaye. "On the mathematical modelling of cerebral autoregulation." Thesis, University of Southampton, 2001. https://eprints.soton.ac.uk/50623/.
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Cerebral autoregulation is the process by which blood flow to the brain is maintained despite changes in arterial blood pressure. Experiments using transcranial Doppler ultrasonography allow rapid measurements of blood flow velocity in the middle cerebral artery. Measurements of this velocity and a subject's arterial blood pressure are used in the assessment of the dynamic cerebral autoregulatory response. Two mathematical models representing the dynamic cerebral autoregulation response as a feedback mechanism, dependent on pressure and flow respectively, are derived. For each model two parameters are introduced, a rate of restoration and a time delay. Solutions for both flow between fixed plates and flow in a rigid pipe are obtained using Laplace transform methods. In both cases solutions for the velocity are found for a general arterial blood pressure, allowing the model to be applied to any experiment that uses changes in arterial blood pressure to assess dynamic cerebral autoregulation. Velocity profiles are determined for the thigh cuff and vacuum box experiments, modelled as a step change and sinusoidal variation in pressure gradient in the middle cerebral artery respectively. The influence of the underlying heart and breathing cycles on measurements obtained from the vacuum box experiments is assessed, before results derived using the mathematical model with a flow dependent feedback mechanism are compared with data from the two experiments. The comparisons yield similar estimates for the rate of restoration and time delay suggesting that these parameters could be independent of the pressure change stimulus and depend only on the main features of the dynamic cerebral autoregulation process. The modelling also indicates that for imposed oscillatory variations in arterial blood pressure a small phase difference between the pressure and velocity waveforms does not necessarily imply impaired autoregulation. The ratio between the percentage variation in maximum velocity and pressure can be used, along with the phase difference, to indicate more accurately the nature of the autoregulatory response. Finally, the relationship between arterial blood pressure and pressure gradient in the middle cerebral artery is modelled using electrical analogue theory. The influence of this relationship on the autoregulation model for flow in a rigid pipe is investigated.
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Mao, Dong. "Biological time series classification via reproducing kernels and sample entropy." Related electronic resource: Current Research at SU : database of SU dissertations, recent titles available full text, 2008. http://wwwlib.umi.com/cr/syr/main.
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Faraday, David Brian Foster. "The mathematical modelling of the cell cycle of a hybridoma cell line." Thesis, University of Surrey, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341620.
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Wittenberg, Ralf W. "Models of self-organization in biological development." Master's thesis, University of Cape Town, 1993. http://hdl.handle.net/11427/17405.
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Bibliography: p. 297-320.<br>In this thesis we thus wish to consider the concept of self-organization as an overall paradigm within which various theoretical approaches to the study of development may be described and evaluated. In the process, an attempt is made to give a fair and reasonably comprehensive overview of leading modelling approaches in developmental biology, with particular reference to self-organization. The work proceeds from a physical or mathematical perspective, but not unduly so - the major mathematical derivations and results are relegated to appendices - and attempts to fill a perceived gap in the extant review literature, in its breadth and attempted impartiality of scope. A characteristic of the present account is its markedly interdisciplinary approach: it seeks to place self-organization models that have been proposed for biological pattern formation and morphogenesis both within the necessary experimentally-derived biological framework, and in the wider physical context of self-organization and the mathematical techniques that may be employed in its study. Hence the thesis begins with appropriate introductory chapters to provide the necessary background, before proceeding to a discussion of the models themselves. It should be noted that the work is structured so as to be read sequentially, from beginning to end; and that the chapters in the main text were designed to be understood essentially independently of the appendices, although frequent references to the latter are given. In view of the vastness of the available information and literature on developmental biology, a working knowledge of embryological principles must be assumed. Consequently, rather than attempting a comprehensive introduction to experimental embryology, chapter 2 presents just a few biological preliminaries, to 'set the scene', outlining some of the major issues that we are dealing with, and sketching an indication of the current status of knowledge and research on development. The chapter is aimed at furnishing the necessary biological, experimental background, in the light of which the rest of the thesis should be read, and which should indeed underpin and motivate any theoretical discussions. We encounter the different hierarchical levels of description in this chapter, as well as some of the model systems whose experimental study has proved most fruitful, some of the concepts of experimental embryology, and a brief reference to some questions that will not be addressed in this work. With chapter 3, we temporarily move away from developmental biology, and consider the wider physical and mathematical concepts related to the study of self-organization. Here we encounter physical and chemical examples of spontaneous structure formation, thermodynamic considerations, and different approaches to the description of complexity. Mathematical approaches to the dynamical study of self-organization are also introduced, with specific reference to reaction-diffusion equations, and we consider some possible chemical and biochemical realizations of self-organizing kinetics. The chapter may be read in conjunction with appendix A, which gives a somewhat more in-depth study of reaction-diffusion equations, their analysis and properties, as an example of the approach to the analysis of self-organizing dynamical systems and mathematically-formulated models. Appendix B contains a more detailed discussion of the Belousov-Zhabotinskii reaction, which provides a vivid chemical paradigm for the concepts of symmetry-breaking and self-organization. Chapter 3 concludes with a brief discussion of a model biological system, the cellular slime mould, which displays rudimentary development and has thus proved amenable to detailed study and modelling. The following two chapters form the core of the thesis, as they contain discussions of the detailed application of theoretical concepts and models, largely based on self-organization, to various developmental situations. We encounter a diversity of models which has arisen largely in the last quarter century, each of which attempts to account for some aspect of biological pattern formation and morphogenesis; an aim of the discussion is to assess the extent of the underlying unity of these models in terms of the self-organization paradigm. In chapter 4 chemical pre-patterns and positional information are considered, without the overt involvement of cells in the patterning. In chapter 5, on the other hand, cellular interactions and activities are explicitly taken into account; this chapter should be read together with appendix C, which contains a brief introduction to the mathematical formulation and analysis of some of the models discussed. The penultimate chapter, 6, considers two other approaches to the study of development; one of these has faded away, while the other is still apparently in the ascendant. The assumptions underlying catastrophe theory, the value of its applications to developmental biology and the reasons for its decline in popularity, are considered. Lastly, discrete approaches, including the recently fashionable cellular automata, are dealt with, and the possible roles of rule-based interactions, such as of the so-called L-systems, and of fractals and chaos are evaluated. Chapter 7 then concludes the thesis with a brief assessment of the value of the self-organization concept to the study of biological development.
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Luo, Yang. "Stochastic modelling in biological systems." Thesis, University of Cambridge, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.610145.
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Murrel, Benjamin. "Improved models of biological sequence evolution." Thesis, Stellenbosch : Stellenbosch University, 2012. http://hdl.handle.net/10019.1/71870.
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Thesis (PhD)--Stellenbosch University, 2012.<br>ENGLISH ABSTRACT: Computational molecular evolution is a field that attempts to characterize
how genetic sequences evolve over phylogenetic trees – the branching processes
that describe the patterns of genetic inheritance in living organisms. It has a
long history of developing progressively more sophisticated stochastic models
of evolution. Through a probabilist’s lens, this can be seen as a search for
more appropriate ways to parameterize discrete state continuous time Markov
chains to better encode biological reality, matching the historical processes
that created empirical data sets, and creating useful tools that allow biologists
to test specific hypotheses about the evolution of the organisms or the genes
that interest them. This dissertation is an attempt to fill some of the gaps that
persist in the literature, solving what we see as existing open problems. The
overarching theme of this work is how to better model variation in the action
of natural selection at multiple levels: across genes, between sites, and over
time. Through four published journal articles and a fifth in preparation, we
present amino acid and codon models that improve upon existing approaches,
providing better descriptions of the process of natural selection and better
tools to detect adaptive evolution.<br>AFRIKAANSE OPSOMMING: Komputasionele molekulêre evolusie is ’n navorsingsarea wat poog om die evolusie
van genetiese sekwensies oor filogenetiese bome – die vertakkende prosesse
wat die patrone van genetiese oorerwing in lewende organismes beskryf – te karakteriseer.
Dit het ’n lang geskiedenis waartydens al hoe meer gesofistikeerde
waarskynlikheidsmodelle van evolusie ontwikkel is. Deur die lens van waarskynlikheidsleer
kan hierdie proses gesien word as ’n soektog na meer gepasde
metodes om diskrete-toestand kontinuë-tyd Markov kettings te parametriseer
ten einde biologiese realiteit beter te enkodeer – op so ’n manier dat die historiese
prosesse wat tot die vorming van biologiese sekwensies gelei het nageboots
word, en dat nuttige metodes geskep word wat bioloë toelaat om spesifieke hipotesisse
met betrekking tot die evolusie van belanghebbende organismes of
gene te toets. Hierdie proefskrif is ’n poging om sommige van die gapings
wat in die literatuur bestaan in te vul en bestaande oop probleme op te los.
Die oorkoepelende tema is verbeterde modellering van variasie in die werking
van natuurlike seleksie op verskeie vlakke: variasie van geen tot geen, variasie
tussen posisies in gene en variasie oor tyd. Deur middel van vier gepubliseerde
joernaalartikels en ’n vyfde artikel in voorbereiding, bied ons aminosuur- en
kodon-modelle aan wat verbeter op bestaande benaderings – hierdie modelle
verskaf beter beskrywings van die proses van natuurlike seleksie sowel as beter
metodes om gevalle van aanpassing in evolusie te vind.
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Crawford, David Michael. "Analysis of biological pattern formation models." Thesis, University of Oxford, 1989. http://ora.ox.ac.uk/objects/uuid:aaa19d3b-c930-4cfa-adc6-8ea498fa5695.
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In this thesis we examine mathematical models which have been suggested as possibile mechanisms for forming certain biological patterns. We analyse them in detail attempting to produce the requisite patterns both analytically and numerically. A reaction diffusion system in two spatial dimensions with anisotropic diffusion is examined in detail and the results compared with certain snakeskin patterns. We examine two other variants to the standard reaction diffusion system: a system where the reaction kinetics and the diffusion coefficients depend upon the cell density suggested as a possible model for the segmentation sequence in Drosophila and a system where the model parameters have one dimensional spatial gradients. We also analyse a model derived from known cellular processes used to model the branching behaviour in bryozoans and show that, in one dimension, such a model can, in theory, give all the required solution behaviour. A genetic switch model for pattern elements on butterfly wings is also briefly examined to obtain expressions for the solution behaviour under coldshock.
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Lewis, Mark A. "Analysis of dynamic and stationary biological pattern formation." Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.276976.
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Gilbert, Mark. "Modelling species invasions in heterogeneous landscapes." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:944d15d3-257a-47e5-acb9-9bdfba26985b.
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Biological invasions are devastating ecosystems and economies world-wide, while many native species' survival depends on their ability to track climate change. Characterising the spread of biological populations is therefore of utmost importance, and can be studied with spatially explicit, discrete-time integro-difference equations (IDEs), which reflect numerous species' processes of demography and dispersal. While spatial variation has often been ignored when implementing IDE models, real landscapes are rarely spatially uniform and environmental variation is crucial in determining biological spread. To address this, we use novel methods to characterise population spread in heterogeneous landscapes. Asymptotic analysis is used for highly fragmented landscapes, where habitat patches are isolated and smaller than the dispersal scale, and in landscapes with low environmental variation, where the ecological parameters vary by no more than a small factor from their mean values. We find that the choice of dispersal kernel determines the effect of landscape structure on spreading speed, indicating that accurately fitting a kernel to data is important in accurately predicting speed. For the low-variation case, the spreading speeds in the heterogeneous and homogeneous landscapes differ by ϵ<sup>2</sup>, where ϵ governs the degree of variation, suggesting that in many cases, a simpler homogeneous model gives similar spread rates. For irregular landscapes, analytical methods become intractable and numerical simulation is needed to predict spread. Accurate simulation requires high spatial resolution, which, using existing techniques, requires prohibitive amounts of computational resources (RAM, CPU etc). We overcome this by developing and implementing a novel algorithm that uses adaptive mesh refinement. The approximations and simulation algorithm produce accurate results, with the adaptive algorithm providing large improvements in efficiency without significant losses of accuracy compared to non-adaptive simulations. Hence, the adaptive algorithm enables faster simulation at previously unfeasible scales and resolutions, permitting novel areas of scientific research in species spread modelling.
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Glacken, Michael W. (Michael William). "Development of mathematical descriptions of mammalian cell culture kinetics for the optimization of fed-batch bioreactors." Thesis, Massachusetts Institute of Technology, 1987. http://hdl.handle.net/1721.1/16493.
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Nurtay, Anel. "Mathematical modelling of pathogen specialisation." Doctoral thesis, Universitat Autònoma de Barcelona, 2019. http://hdl.handle.net/10803/667178.
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L’aparició de nous virus causants de malalties està estretament lligada a l’especialització de subpoblacions virals cap a nous tipus d’amfitrions. La modelització matemàtica proporciona un marc quantitatiu que pot ajudar amb la predicció de processos a llarg termini com pot ser l’especialització. A causa de la naturalesa complexa que presenten les interaccions intra i interespecífiques en els processos evolutius, cal aplicar eines matemàtiques complexes, com ara l’anàlisi de bifurcacions, al estudiar dinàmiques de població. Aquesta tesi desenvolupa una jerarquia de models de població per poder comprendre l’aparició i les dinàmiques d’especialització, i la seva dependència dels paràmetres del sistema. Utilitzant un model per a un virus de tipus salvatge i un virus mutat que competeixen pel mateix amfitrió, es determinen les condicions per a la supervivència únicament de la subpoblació mutant, juntament amb la seva coexistència amb el cep de tipus salvatge. Els diagrames d’estabilitat que representen regions de dinàmiques diferenciades es construeixen en termes de taxa d’infecció, virulència i taxa de mutació; els diagrames s’expliquen en base a les característiques biològiques de les subpoblacions. Per a paràmetres variables, s’observa i es descriu el fenomen d’intersecció i intercanvi d’estabilitat entre diferents solucions sistemàtiques i periòdiques en l’àmbit dels ceps de tipus salvatge i els ceps mutants en competència directa. En el cas de que diversos tipus d’amfitrions estiguin disponibles per a ser disputats per ceps especialitzats i generalistes existeixen regions de biestabilitat, i les probabilitats d’observar cada estat es calculen com funcions de les taxes d’infecció. S’ha trobat un rar atractor caòtic i s’ha analitzat amb l’ús d’exponents de Lyapunov. Això, combinat amb els diagrames d’estabilitat, mostra que la supervivència del cep generalista en un entorn estable és un fet improbable. A més, s’estudia el cas dels diversos ceps N>>1 que competeixen per diferents tipus de cèl·lules amfitriones. En aquest cas s’ha descobert una dependència no monotònica, contraria al que es preveia, del temps d’especialització sobre la mida inicial i la taxa de mutació, com a conseqüència de la realització d’un anàlisi de regressió sobre dades obtingudes numèricament. En general, aquest treball fa contribucions àmplies a la modelització matemàtica i anàlisi de la dinàmica dels patogens i els processos evolutius.<br>La aparición de nuevos virus causantes de enfermedades está estrechamente ligada a la especialización de las subpoblaciones virales hacia nuevos tipos de anfitriones. La modelizaci ón matemática proporciona un marco cuantitativo que puede ayudar a la predicción de procesos a largo plazo como la especialización. Debido a la naturaleza compleja que presentan las interacciones intra e interespecíficas en los procesos evolutivos, aplicar herramientas matemáticas complejas, tales como el análisis de bifurcación, al estudiar dinámicas de población. Esta tesis desarrolla una jerarquía de modelos de población para poder comprender la aparición y las dinámicas de especialización, y su dependencia de los parámetros del sistema. Utilizando un modelo para un virus de tipo salvaje y un virus mutado que compiten por el mismo anfitrión, se determinan las condiciones para la supervivencia únicamente de la subpoblación mutante, junto con su coexistencia con la cepa de tipo salvaje. Los diagramas de estabilidad que representan regiones de dinámicas diferenciadas se construyen en términos de tasa de infección, virulencia y tasa de mutación; los diagramas se explican en base a las características biológicas de las subpoblaciones. Para parámetros variables, se observa y se describe el fenómeno de intersección e intercambio de estabilidad entre diferentes soluciones sistemáticas y periódicas en el ámbito de las cepas de tipo salvaje y las cepas mutantes en competencia directa. En el caso de que varios tipos de anfitriones estén disponibles para ser disputados por cepas especializadas y generalistas existen regiones de biestabilidad, y las probabilidades de observar cada estado se calculan como funciones de las tasas de infección. Se ha encontrado un raro atractor caótico y se ha analizado con el uso de exponentes de Lyapunov. Esto, combinado con los diagramas de estabilidad, muestra que la supervivencia de la cepa generalista en un entorno estable es un hecho improbable. Además, se estudia el caso de los varias cepas N>> 1 que compiten por diferentes tipos de células anfitrionas. En este caso se ha descubierto una dependencia no monotónica, contraria a lo que se preveía, del tiempo de especialización sobre el tamaño inicial y la tasa de mutación, como consecuencia de la realización de un análisis de regresión sobre datos obtenidos numéricamente. En general, este trabajo hace contribuciones amplias a la modelización matemática y el análisis de la dinámica de los patógenos y los procesos evolutivos.<br>The occurrence of new disease-causing viruses is tightly linked to the specialisation of viral sub-populations towards new host types. Mathematical modelling provides a quantitative framework that can aid with the prediction of long-term processes such as specialisation. Due to the complex nature of intra- and interspecific interactions present in evolutionary processes, elaborate mathematical tools such as bifurcation analysis must be employed while studying population dynamics. In this thesis, a hierarchy of population models is developed to understand the onset and dynamics of specialisation and their dependence on the parameters of the system. Using a model for a wild-type and mutant virus that compete for the same host, conditions for the survival of only the mutant subpopulation, along with its coexistence with the wild-type strain, are determined. Stability diagrams that depict regions of distinct dynamics are constructed in terms of infection rates, virulence and the mutation rate; the diagrams are explained in terms of the biological characteristics of the sub-populations. For varying parameters, the phenomenon of intersection and exchange of stability between different periodic solutions of the system is observed and described in the scope of the competing wild-type and mutant strains. In the case of several types of hosts being available for competing specialist and generalist strains, regions of bistability exist, and the probabilities of observing each state are calculated as functions of the infection rates. A strange chaotic attractor is discovered and analysed with the use of Lyapunov exponents. This, combined with the stability diagrams, shows that the survival of the generalist in a stable environment is an unlikely event. Furthermore, the case of N=1 different strains competing for different types of host cells is studied. For this case, a counterintuitive and non-monotonic dependence of the specialisation time on the burst size and mutation rate is discovered as a result of carrying out a regression analysis on numerically obtained data. Overall, this work makes broad contributions to mathematical modelling and analysis of pathogen dynamics and evolutionary processes.
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Mthombeni, Lestinah. "Mathematical modeling in the sustainable use of natural resources." University of the Western Cape, 2015. http://hdl.handle.net/11394/4346.
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>Magister Scientiae - MSc<br>The sustainable use of natural resources is of utmost importance for every community. In particular, it is important for every given generation to plan in such a way that proper provision is made for future generations. The scientific understanding of resources use and appreciation for its life-supporting capacity is therefore essential. Mathematical modeling has proved useful to inform the planning and management of strategies for sustainable use of natural resources. Some specific topics in resource management has been studied intensively through many decades. In particular, mining, fisheries, forestry and water resources are among these. Instead of presenting a study of the latter topics, this dissertation presents a variety of cases of mathematical modeling in resource management. The aim is to improve the general understanding of the relevant problems. We expand on existing literature, papers of other authors, and add to such studies by focusing on specific items in the work, illuminating it with further explanations and graphs, or by modifying the models through the introduction of stochastic perturbations. In particular this dissertation makes contributions by giving more explanation, on the so-called environmental Fisher information or EFI for brevity (Section 2.4 and Chapter 6), and by introducing stochasticity into a pest control model (Chapter 4) and into a savanna vegetation model (Chapter 5). In Chapter 3 we present a model from the literature pertaining to the problem of shifting cultivation, i.e, the use of forest land when used for subsistence level agricultural purposes, until the land is so degraded that the occupants abandon it and move on to a new stand. The model used to study the shifting period is similar to the forest rotation problem. A model, already in the literature, for biological control of a pest is studied in Chapter 4. Onto the deterministic model we impose a stochastic perturii bation, so that we obtain a stochastic differential equation model. We prove stochastic stability of the disease-free state, when the basic reproduction number of the pest is below unity. We have performed simulations of solutions of the stochastic system. In Chapter 5 we review an existing ordinary differential equation model for the competition between trees and grass in savanna environment. The competition between them is for soil water, fed by annual rainfall. On the other hand, trees and grass are perturbed by fire, and some other environmental forcings such as herbivores. For this ODE model, we introduce stochastic perturbations. The stochastic perturbations are in the form of three mutually independent Brownian motions. Simulations to illustrate the effect of the stochasticity are shown. We present a three-tiered predator-prey model and consider its stability in terms of Fisher information. This appears as Chapter 6. The Fisher information is defined on the basis of the so-called sustainable measures hypotheses. The model is already in the literature and in the dissertation we present several computations to show the influence of carrying capacity of prey and of mortality rate on EFI. Another problem that we consider, in Chapter 7, is that of lake eutrophication caused by excessive phosphorus inflow. The computation illustrates the management of the runoff nutrients into or out of the lake. Necessary and the sufficient conditions for an optimal utility management are obtained using standard optimal control theory. The results of this dissertation demonstrate the modeling techniques in the sustainable use of natural resources. Sustainability is the quest for equal opportunities over all generations. The manner in which this sustainability is quantified in models is being debated and improved all the time. The discourse on sustainability is especially important in view of a growing world population, and with forcings such as climate change. The most important original contribution in this dissertation is the stochastic analysis on the pest control model and the savanna model.
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Abraham, Tara Helen. "Microscopic cybernetics, mathematical logic, automata theory, and the formalization of biological phenomena, 1936-1970." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ53763.pdf.
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