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This thesis work aimed to provide a better knowledge of inclusion behavior at the steel-slag interface. All results are based on mathematical modeling of liquid and solid inclusion separation to the slag. The model descriptions of the inclusion transfer are based on the equation of motion at the system. It is assumed that the inclusion transfer is governed by four forces acting on the inclusion as it has reached the steel-slag interface. These are the buoyancy force, the added mass force, the drag force and the rebound force. The models assume two cases of inclusion separation depending on the inclusion Reynolds number. In the case where Reynolds number is larger or equal to unity, Re≥1, a steel film is formed between the inclusion and the slag. This steel film must first be drained before the inclusion can separate to the slag. If Reynolds number, Re<1, then no steel film is formed and the inclusion will be in direct contact with the slag. The mathematical models also propose three types of inclusion behavior as the inclusion crosses the steel-slag interface. The inclusion can either, pass and separate to the slag, oscillate at the interface with the possibility of reentering the steel bath with the steel flow or it can remain at the interface not completely separated to the slag. A parameter study for 20 μm inclusions showed that the most important parameters controlling the inclusion behavior at the steel-slag interface are the slag viscosity and the interfacial tensions between the phases. For 100μm inclusions also the inclusion density affects the inclusion behavior. The models were applied to ladle and tundish conditions. Since the slags in the chosen industrial conditions have not been studied experimentally before, estimations of the important physical property parameters were made. Future measurements will therefore be needed in order to make predictions of inclusion transfer behavior at the steel-slag interface which are more relevant for the industry. The main conclusion is that useful plots can be made in order to illustrate the tendency for the inclusion transfer and how to manipulate the physical property parameters in order to increase the inclusion separation in ladles and tundishes. / QC 20101221

The spread of infectious agents has been observed as long as their hosts have existed. The spread of infectious diseases in human populations, however, is more than an academic concern, causing millions of deaths every year, and prompting collective surveillance and intervention efforts worldwide. These surveillance data, used in conjunction with statistical methods and mathematical models, present both challenges and opportunities for advancements in scientific understanding and public health. Early mathematical modeling of infectious diseases in humans began by assuming homogeneous contact among individuals, but has since been extended to account for many sources of non-homogeneity in human contact. Detecting the degree of epidemic mixing between geographically separated populations, in particular, remains a difficult problem. The difficulty occurs because although disease case reports have been collected by many governments for decades, case reporting is imperfect, and transmission events themselves are nearly impossible to observe. The degree to which epidemic coupling can be detected from case reports is the central theme of this thesis. We present a careful, biologically motivated and consistent derivation of the transmission coupling (fully derived in Chapter 4). In Chapter 2 we consider the simple scenario of an epidemic spreading from one population to another, and present both numerical and analytic methodology for estimating epidemic coupling. Chapter 3 considers the problem of estimating epidemic coupling among populations undergoing recurrent epidemics, such as those of childhood diseases which have been widely observed. In Chapter 4 we present a method for estimating coupling among an arbitrary number of populations undergoing an epidemic, and apply it to estimate coupling among the parishes of London, England, during the Great Plague of 1665. / Thesis / Doctor of Philosophy (PhD)

During the production of steel in the LD converter the refractory lining is exposed to high temperature emulsion of steel, slag and gas. It protects the steel body of the vessel to come in contact with the molten steel.The main purpose of this work was to observe the temperature distribution profile in converter refractory lining which is very important to understand the life of the refractory lining of the LD converter.In this study, a three dimensional (3D) heat transfer model for the refractory lining of converter was developed. The lining of the refractory material was considered as magnesite brick for inner lining, dolomite for intermediate lining and steel shell as outer part. In order to do the numerical modeling, the CFD software Ansys Fluent 13.0 was used. After considering the proper dimensions, meshing, properties of the lining material and boundary conditions, the modeling in Ansys was performed in two stages. In the first stage, the modeling was performed by assuming that the converter is already heated and the inside temperature of the furnace is 1923K and the outside temperature of the steel body is 300K. In the second stage, the temperature change of the molten steel, slag and the gas was considered as function of blowing time and slag height based on theories from different references. Firstly, the three dimensional (3D) heat transfer model was used for the refractory lining of the converter to show transient heat flow through the lining at different times. Secondly, 3D modeling results from fluent 13.0 was used to develop temperature distribution profile through the lining at different height for different time steps and at different positions with time and also along the converter height from the bottom to top. It has been noticed that refractories in the lining in contact with steel and slag must be of good quality for the reduction of wear cost and downtime and therefore the reduction of refractory cost per ton of steel production.

[ES] La comprensión de los aspectos de la funcionalidad de las células que cuentan para los mecanismos de las enfermedades es el mayor reto de la medicina personalizada. A pesar de la disponibilidad creciente de los datos de genómica y transcriptómica, sigue existiendo una notable brecha entre la detección de las perturbaciones en la expresión de genes y la comprensión de su contribución en los mecanismos moleculares que últimamente tienen relación importante con el fenotipo estudiado. A lo largo de la última década, distintos modelos computacionales y matemáticos se han propuesto para el análisis de las rutas. Sin embargo, estos modelos no toman en cuenta los mecanismos dinámicos de las rutas como la estructura y las interacciones entre genes y proteínas. En esta tesis doctoral, presento dos modelos matemáticos ligeramente distintos, para integrar los datos transcriptómicos masivos de humano con un conocimiento previo de de las rutas de señalización y metabólicas para estimar las actividades mecánicas que están detrás de esas rutas (MPAs). Las MPAs son variables continuas con valores de nivel individual que pueden ser usadas con los modelos de aprendizaje de máquinas y métodos estadísticos para determinar los biomarcadores que podemos usar para los diagnósticos tempranos y la clasificación de subtipos de enfermedades, además de poder sugerir las dianas terapéuticas potenciales para las intervenciones individualizadas. El objetivo global es desarrollar nuevos y avanzados enfoques de la biología de sistemas para proponer unas hipótesis funcionales que nos ayuden a entender e interpretar los mecanismos complejos de las enfermedades. Estos mecanismos son cruciales para mejorar los tratamientos personalizados y predecir los resultados clínicos. En primer lugar, contribuí al desarrollo de un método que está diseñado para extraer las subrutas elementales desde la ruta de señalización con sus actividades estimadas. Posteriormente, este algoritmo se ha adaptado a los módulos metabólicos y se ha implementado como una herramienta web. Finalmente , el método ha revelado un panorama metabólico para una lista completa de diferentes tipos de cánceres. En este estudio, analicé el perfil metabólico de 25 tipos de cáncer distintos y se validó el método usando varios enfoques computacionales y experimentales. Cada método desarrollado en esta tesis ha sido enfrentado a otros métodos similares existentes, evaluados por sus sensibilidades y especificidades, experimentalmente validados cuando fue posible y usados para predecir resultados clínicos de varios tipos de cánceres. La investigación descrita en esta tesis y los resultados obtenidos fueron publicados en distintas revistas arbitradas que están relacionadas con el cáncer y biología de sistemas, y también en los periódicos nacionales. / [CA] La comprensió dels aspectes de la funcionalitat de les cèl·lules que compten per als mecanismes de les malalties és el major repte de la medicina personalitzada. Malgrat la disponibilitat creixent de les dades de genòmica i transcriptómica, continua existint una notable bretxa entre la detecció de les pertorbacions en l'expressió de gens i la comprensió de la seua contribució en els mecanismes moleculars que últimament tenen relació important amb el fenotip estudiat. Al llarg de l'última dècada, diferents models computacionals i matemàtics s'han proposat per a l'anàlisi de les rutes. No obstant això, aquests models no tenen en compte els mecanismes dinàmics de les rutes com l'estructura i les interaccions entre gens i proteïnes. En aquesta tesi doctoral, presente dos models matemàtics lleugerament diferents, per a integrar les dades transcriptómicos massius d'humà amb un coneixement previ de de les rutes de senyalització i metabòliques per a estimar les activitats mecàniques que estan darrere d'aqueixes rutes (MPAs). Les MPAs són variables contínues amb valors de nivell individual que poden ser usades amb els models d'aprenentatge de màquines i mètodes estadístics per a determinar els biomarcadores que podem usar per als diagnòstics primerencs i la classificació de subtipus de malalties, a més de poder suggerir les dianes terapèutiques potencials per a les intervencions individualitzades. L'objectiu global és desenvolupar nous i avançats enfocaments de la biologia de sistemes per a proposar unes hipòtesis funcionals que ens ajuden a entendre i interpretar els mecanismes complexos de les malalties. Aquests mecanismes són crucials per a millorar els tractaments personalitzats i predir els resultats clínics. En primer lloc, vaig contribuir al desenvolupament d'un mètode que està dissenyat per a extraure les subrutas elementals des de la ruta de senyalització amb les seues activitats estimades. Posteriorment, aquest algorisme s'ha adaptat als mòduls metabòlics i s'ha implementat com una eina web. Finalment, el mètode ha revelat un panorama metabòlic per a una llista completa de diferents tipus de càncers. En aquest estudi, vaig analitzar el perfil metabòlic de 25 tipus de càncer diferents i es va validar el mètode usant diversos enfocaments computacionals i experimentals. Cada mètode desenvolupat en aquesta tesi ha sigut enfrontat a altres mètodes similars existents, avaluats per les seues sensibilitats i especificitats, experimentalment validats quan va ser possible i usats per a predir resultats clínics de diversos tipus de càncers. La investigació descrita en aquesta tesi i els resultats obtinguts van ser publicats en diferents revistes arbitrades que estan relacionades amb el càncer i biologia de sistemes, i també en els periòdics nacionals. / [EN] Understanding the aspects of the cell functionality that account for disease or drug action mechanisms is the main challenge for precision medicine. In spite of the increasing availability of genomic and transcriptomic data, there is still a gap between the detection of perturbations in gene expression and the understanding of their contribution to the molecular mechanisms that ultimately account for the phenotype studied. Over the last decade, different computational and mathematical models have been proposed for pathway analysis. However, they are not taking into account the dynamic mechanisms contained by pathways as represented in their layout and the interactions between genes and proteins. In this thesis, I present two slightly different mathematical models to integrate human transcriptomic data with prior knowledge of signalling and metabolic pathways to estimate the Mechanistic Pathway Activities (MPAs). MPAs are continuous and individual level values that can be used with machine learning and statistical methods to determine biomarkers for the early diagnosis and subtype classification of the diseases, and also to suggest potential therapeutic targets for individualized therapeutic interventions. The overall objective is, developing new and advanced systems biology approaches to propose functional hypotheses that help us to understand and interpret the complex mechanism of the diseases. These mechanisms are crucial for robust personalized drug treatments and predict clinical outcomes. First, I contributed to the development of a method which is designed to extract elementary sub-pathways from a signalling pathway and to estimate their activity. Second, this algorithm adapted to metabolic modules and it is implemented as a webtool. Third, the method used to reveal a pan-cancer metabolic landscape. In this study, I analyzed the metabolic module profile of 25 different cancer types and the method is also validated using different computational and experimental approaches. Each method developed in this thesis was benchmarked against the existing similar methods, evaluated for their sensitivity and specificity, experimentally validated when it is possible and used to predict clinical outcomes of different cancer types. The research described in this thesis and the results obtained were published in different systems biology and cancer-related peer-reviewed journals and also in national newspapers. / Cubuk, C. (2020). Modeling Functional Modules Using Statistical and Machine Learning Methods [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/156175

[EN] Access to the Spanish public university system is a complex process that involved administration, offering a certain number of places in different degrees that offer universities, and students, who must prioritize their preferences in a list. Determine what are the reasons that motivate a student, and their family and personal environment, to choose a particular degree and University to develop his studies, is a complex problem and that we have approached from the point of view of structural analysis. The aim of this work is to propose a partial multivariate model that can give an account of the weight of the different variables and identified factors involved in the decision about the choice of studies and University. The model we propose is specified based on a series of structural relationships involving a set of variables and context data, which we have grouped in the following factors: - Individual factors, associated with aspects related to student and personal interests, some academic and others clearly not. - Social factors, related with aspects that have to do with the social perception of the degree, their employability, the perception that we have of the University prestige, the degree, or the profession that gives access. - Context data, relative to the value of the access mark, the offer of seats or demand that has occurred in a certain degree and University in the years immediately prior to the taking of the decision. For this purpose a structural model and a questionnaire are proposed to evaluate the model, Model validation concludes with an extensive survey and analysis of the model results. / [ES] El acceso al Sistema Universitario Público Español es un proceso complejo en el que interviene la administración, ofreciendo un número determinado de plazas en las distintas titulaciones que ofertan las Universidades, y el estudiante, que debe priorizar en una lista sus preferencias. Determinar cuáles son las razones que mueven a un estudiante, y a su entorno familiar y personal, a elegir una determinada titulación y/o Universidad para cursar sus estudios superiores, es un problema complejo que hemos abordado desde el punto de vista del análisis estructural. El objetivo de este trabajo es proponer un modelo multivariado y parcial que pueda dar cuenta del peso de las distintas variables y factores identificados que influyen en la decisión acerca de la elección de estudios y universidad. El modelo propuesto se especifica en base a una serie de relaciones estructurales en las que intervienen un conjunto de variables y datos de contexto que hemos agrupado en los siguientes factores: - Factores individuales, vinculados a aspectos relacionados con el estudiante y sus intereses personales, algunos de carácter académico y otros claramente no. - Factores sociales, relacionados con aspectos que tienen que ver con la percepción social de la titulación, su empleabilidad, la percepción que se tiene del prestigio de la Universidad, del título, o de la profesión a la que da acceso.. - Datos de contexto, relativos al valor de la nota de corte de una titulación, a la oferta de plazas o a la demanda que se ha producido en una determinada titulación y universidad en los años inmediatamente anteriores al de la toma de la decisión. Para ello se propone un modelo estructural y se propone un cuestionario para evaluar las variables del modelo. La validación de modelo y cuestionario concluye con una amplia encuesta y el análisis de los resultados del modelo. / [CA] L'accés al Sistema Universitari Públic Espanyol és un procés complex en el qual intervé l'administració, oferint un nombre determinat de places en les diferents titulacions que ofereixen les universitats, i l'estudiant, que ha de prioritzar en una llista seves preferències. Determinar quines són les raons que mouen a un estudiant, i al seu entorn familiar i personal, a triar una determinada titulació i/o Universitat per cursar els seus estudis superiors, és un problema complex que hem abordat des del punt de vista de l'anàlisi estructural. L'objectiu d'aquest treball és proposar un model multivariat i parcial que puga donar compte del pes de les diferents variables i factors identificats que influeixen en la decisió sobre l'elecció d'estudis i universitat. El model proposat s'especifica en la base d'una sèrie de relacions estructurals en què intervenen un conjunt de variables i dades de context que hem agrupat en els següents factors: - Factors individuals, vinculats a aspectes relacionats amb l'estudiant i els seus interessos personals, alguns de caràcter acadèmic i altres clarament no. - Factors socials, relacionats amb aspectes que tenen a veure amb la percepció social de la titulació, la seva ocupabilitat, la percepció que es té del prestigi de la Universitat, del títol, o de la professió a la qual dóna accés .. - Dades de context, relatius al valor de la nota de tall d'una titulació, a l'oferta de places o la demanda que s'ha produït en una determinada titulació i universitat en els anys immediatament anteriors al de la presa de la decisió. Per a això es proposa un model estructural, es proposa un qüestionari per avaluar les variables del model. La validació del model conclou amb una àmplia enquesta i l'anàlisi dels resultats del model. / Soriano Jiménez, PP. (2016). Un modelo estructural para el análisis de los factores asociados a la elección de estudios universitarios [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/64076

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

Stroke is one of the leading causes of death and adult disability worldwide. The major therapeutic intervention for acute ischemic stroke is the administration of recombinant tissue plasminogen activator (rtPA) to help to restore blood flow to the brain. This has been shown to increase the survival rate and to reduce the disability of ischemic stroke patients. However, rtPA is associated with intracranial haemorrhage and thus its administration is currently limited to only about 5% of ischemic stroke patients. More advanced imaging techniques can be used to better stratify patients for rtPA treatment. One new imaging technique, chemical exchange saturation transfer (CEST) magnetic resonance imaging, can potentially image intracellular pH and since tissue acidification happens prior to cerebral infarction, CEST has the potential to predict ischemic injury and hence to improve patient selection. Despite this potential, most studies have generated pH-weighted rather than quantitative pH maps; the most widely used metric to quantify the CEST effect is only able to generate qualitative contrast measurements and suffers from many confounds. The greatest clinical benefit of CEST imaging lies in its ability to non-invasively measure quantitative pH values which may be useful to identify salvageable tissue. The quantitative techniques and work presented in this thesis thus provide the necessary analysis to determine whether a threshold for the quantified CEST effect or for pH exists to help to define tissue outcome following stroke; to investigate the potential of CEST for clinical stroke imaging; and subsequently to facilitate clinical translation of CEST for acute stroke management.

The erosion and transport of fertile topsoil is a serious problem in the U.S., Australia, China and throughout Europe. It results in extensive environmental damage, reduces soil fertility and productivity, and causes significant environmental loss. It is as big a threat to the future sustainability of global populations as climate change, but receives far less attention. With both chemicals (fertilizers, pesticides, herbicides) and biological pathogens (bacteria, viruses) preferentially sorbing to silt and clay sized soil particles, estimating contaminant fluxes in eroded soil also requires predicting the transported soils particle size distribution. The Hairsine-Rose (HR) erosion model is considered in this thesis as it is one of the very few that is specifically designed to incorporate the effect of particle size distribution, and differentiates between non-cohesive previously eroded soil compared with cohesive un-eroded soil. This thesis develops a new extended erosion model that couples the HR approach with the one-dimensional St Venant equations, and an Exner bed evolution equation to allow for feedback effects from changes in the local bed slope on surface hydraulics and erosion rates to be included. The resulting system of 2I +3 (where I = number of particle size classes) nonlinear hyperbolic partial differential equations is then solved numerically using a Liska-Wendroff predictor corrector finite difference scheme. Approximate analytical solutions and series expansions are derived to overcome singularities in the numerical solutions arising from either boundary or initial conditions corresponding to a zero flow depth. Three separate practical applications of the extended HR model are then considered in this thesis, (i) flow through vegetative buffer strips, (ii) modelling discharge hysteresis loops and (iii) the growth of antidunes, transportational cyclic steps and travelling wave solutions. It is shown by comparison against published experimental flume data that predictions from the extended model are able to closely match measurements of deposited sediment distribution both upstream and within the vegetative buffer strip. The experiments were conducted with supercritical inflow to the flume which due to the increased drag from the vegetative strip, resulted in a hydraulic jump just upstream of the vegetation. As suspended sediment deposited at the jump, this resulted in the jump slowly migrating upstream. The numerical solutions were also able to predict the position and hydraulic jump and the flow depth throughout the flume, including within the vegetative strip, very well. In the second application, it is found that the extended HR model is the first one that can produce all known types of measured hysteresis loops in sediment discharge outlet data. Five main loop types occur (a) clockwise, (b) counter-clockwise, (c,d) figure 8 of both flow orientations and (e) single curve. It is clearly shown that complicated temporal rainfall patterns or bed geometry are not required to developed complicated hysteresis loops, but it is the spatial distribution of previously eroded sediment that remains for the start of a new erosion event, which primarily governs the form of the hysteresis loop. The role of the evolution of the sediment distribution in the deposited layer therefore controls loop shape and behavior. Erosion models that are based solely on suspended sediment are therefore unable to reproduce these hysteretic loops without a priori imposing a hysteretic relationship on the parameterisations of the erosion source terms. The rather surprising result that the loop shape is also dominated by the suspended concentration of the smallest particle size is shown and discussed. In the third application, a linear stability analysis shows that instabilities, antidunes, will grow and propagate upstream under supercritical flow conditions. Numerical simulations are carried out that confirm the stability analysis and show the development and movement of antidunes. For various initial parameter configurations a series of travelling antidunes, or transportational cyclic steps, separated by hydraulic jumps are shown to develop and evolve to a steady form and wave speed. Two different forms arise whereby (a) the deposited layer completely shields the underlying original cohesive soil so that the cohesive layer plays no role in the speed or shape of the wave profile or (b) the cohesive soil is exposed along the back of the wave such that both the non-cohesive and cohesive layers affect the wave profile. Under (a) the solutions are obtained up to an additive constant as the actual location of the boundary of the cohesive soil is not required, whereas for (b) this constant must be determined in order to find the location on the antidune from where the cohesive soil becomes accessible. For single size class soils the leading order travelling wave equations are fairly straightforward to obtain for both cases (a) and (b). However for multi-size class soils, this becomes much more demanding as up to 2I + 3 parameters must be found iteratively to define the solution as each size class has its own wave profile in suspension and in the antidune.

Cerebral ischemia is a vascular disorder that is characterized by the reduction of blood supply to the brain, resulting in impaired metabolism and finally death of brain cells. Cerebral ischemia is a major clinical problem associated with global morbidity and mortality rates of about 30%. Clinical management of cerebral ischemia relies heavily on perfusion analysis using dynamic susceptibility contrast MRI (DSC-MRI). DSC-MRI analysis is performed using mathematical models that simulate the underlying vascular physiology of brain. Cerebral perfusion is calculated using perfusion imaging and is used as a marker of tissue health status; low perfusion being an indicator of impaired tissue metabolism. In addition to measurement of cerebral perfusion, it is possible to quantify the blood flow variation within the capillary network referred to as cerebral microvascular hemodynamics. It has been hypothesized that microvascular hemodynamics are closely associated with tissue oxygenation and that hemodynamics might undergo a considerable amount of variation to maintain normal tissue metabolism under conditions of ischemic stress. However with DSC-MRI perfusion imaging, quantification of cerebral hemodynamics still remains a big challenge. Singular Value Decomposition (SVD) is currently a standard methodology for estimation of cerebral perfusion with DSC-MRI in both research and clinical settings. It is a robust technique for quantification of cerebral perfusion, however, the quantification of hemodynamic information cannot be achieved with SVD methods because of the non-physiological behaviour of SVD in microvascular hemodynamic estimation. SVD is sensitive to the noise in the MR signal which appears in the calculated microvascular hemodynamics, thus making it difficult to interpret for pathophysiological significance. Other methods, including model-based approaches or methods based on likelihood estimation, stochastic modeling and Gaussian processes, have been proposed. However, none of these have become established as a means to study tissue hemodynamics in perfusion imaging. Possibly because of the associated constrains in these methodologies that limited their sensitivity to hemodynamic variation in vivo. The objective of the research presented in this thesis is to develop and to evaluate a method to perform a quantitative estimation of cerebral hemodynamics using DSC-MRI. A new Control Point Interpolation (CPI) method has been developed to perform a non-parametric analysis for DSC-MRI. The CPI method was found to be more accurate in estimation of cerebral perfusion than the alternative methods. Capillary hemodynamics were calculated by estimating the transit time distribution of the tissue capillary network using the CPI method. The variations in transit time distribution showed quantitative differences between normal tissue and tissue under ischemic stress. The method has been corrected for the effects of macrovascular bolus dispersion and tested over a larger clinical cohort of patients with atherosclerosis. CPI method is thus a promising method for quantifying cerebral hemodynamics using perfusion imaging. CPI method is an attempt to evaluate the use of quantitative hemodynamic information in diagnostic and prognostic monitoring of patients with ischemia and vascular diseases.