Numerical simulations of the complex flows of complex (viscoelastic) fluids are investigated. The primary fluid investigated in this thesis is human blood, a complex fluid which can be modelled via viscoelastic constitutive models. The most commonly used constitutive models for viscoelastic fluids include the OldroydB, Giesekus, Johnson-Segalman, Finitely Extensible Non-Linear Elastic (FENE), Phan-Thein-Tanner (PTT) models etc. Our Numerical approach is based on the finite volume methods implemented on the OpenFOAM platform. We employ the Giesekus, Oldroyd-B, and Generalized Oldroyd-B viscoelastic constitutive models in this thesis, depending on the underlying context. Numerical validation of our results is conducted via the most used benchmark flow problems for viscoelastic fluid flow. The robust and efficient numerical methodologies are then deployed to investigate the flow characteristics, and hence illustrate various novel behavior, for blood flow in stenosed and bifurcated arteries. The present work took advantage of the availability of a reasonable set of viscoelastic constitutive model solvers within OpenFOAM, specifically the viscoelasticFluidFoam solver which we modified and developed to suit our focused needs for blood flow computations. The modified computational algorithms were successfully validated against well-known benchmark flow problems in the literature. Noting that the Giesekus viscoelastic constitutive model is a generalization of both the Oldroyd-B and Generalized Oldroyd-B models, the validation of results is carried out via the Giesekus model enabling us to develop a general-purpose code capable of simulating several viscoelastic constitutive models. The main results were otherwise presented for the Oldroyd-B and Generalized Oldroyd-B models as these are the most applicable to blood flow modelling. The results demonstrate that the velocity spurt through the stenosis is directly proportional to the constriction caused by the stenosis. The higher the blockage from the constriction, the higher the corresponding velocity spurt through the constriction. This velocity behavior, as the constriction blockage increases, correspondingly increase the wall shear stresses. High wall shear stresses significantly increase the possibility of rupture of the stenosis/blockage. This can lead to catastrophic consequences in the usual case where the stenosis is caused by tumor growth.

Aim: To examine local muscle oxygen kinetics when performing wrist extensions till failure in an occluded versus non-occluded state, to compare the perceived ratings of pain and local muscle exertion, and analysing presence of gender differences. Methods: Twenty-one healthy individuals (mean age 25,6±3.2, 10 females) performed wrist extensions at 30% of peak isometric strength till failure. The order in which the states was performed was randomized. The oxygen kinetics in the m. extensor digitorum was analysed using Near-infrared spectroscopy continuously. Ratings of perceived pain and local muscle exertion were collected before exercise, when reaching failure and post exercise recovery. Result: No difference was identified in tissue oxygen saturation (TOI) at the exercise plateau (-24.0±18.3% vs -23.5±13.9%, p=0.609). TOI at rest was lower for the occluded state (64.2±4.5% vs 57.2±5.9%, p<0.001). During the second minute of recovery, there was a greater increase in TOI for the occluded state (0.01±0.01%/sec vs 0.04±0.03/sec, p<0.001). A higher rating of perceived pain was found for the occluded state during baseline (0.0±0.0 vs 0.7±0.9, p=0.005) and first minute of recovery post exercise (2.3±2.0 vs 3.3±2.1, p=0.011). No clinically relevant gender differences were found. Conclusion: Venous occlusion during low-intensity dynamic wrist extensions affects the local oxygen kinetics in the muscle before and after exercise. The oxygenation kinetics does not differ when exercise plateau is reached when both regimes are performed till failure. This suggests that performing low-load dynamic wrist extensions in a no-relaxation manner, may have the same effects no matter whether occlusion is used or not. / Syfte: Att undersöka den lokala syreomsättningen i muskeln när handledsextensioner utförs till failure i ockluderat tillstånd jämfört med icke-ockluderat tillstånd, samt att jämföra den skattade upplevda smärtan och lokala muskelansträngningen, och eventuella skillnader mellan könen. Metod: Tjugoen friska individer (medelålder 25.6±3.2, 10 kvinnor) utförde handledsextentioner på 30 % av maximal isometrisk styrka till failure. Ordningen av ocklusion och icke-ocklusion var randomiserad. Nära-infraröd spektroskopi användes för att undersöka syreomsättningen lokalt i m. extensor digitorum. Skattning av upplevd smärta och lokal muskelansträngning samlades in före träning, vid failure och vid återhämtning efter träning. Resultat: Ingen skillnad identifierades i vävnadssyremättnad (TOI) vid uppnådd träningsplatå (-24.0±18.3% vs -23.5±13.9%, p=0.609). TOI i vila var lägre för det ockluderade tillståndet (64.2±4.5% vs 57.2±5.9%, p <0.001). Under den andra återhämtningsminuten var det en större ökning av TOI för det ockluderade tillståndet (0.01±0.01%/sek vs 0.04±0.03/sek, p <0.001). En högre skattning av upplevd smärta sågs för det ockluderade tillståndet under den första vilominuten (0.0±0.0 vs 0.7±0.9, p=0.005) och första minuten av återhämtning (2.3±2.0 vs 3.3±2.1, p=0.011). Inga kliniskt relevanta skillnader mellan könen hittades. Slutsats: Ocklusion under lågintensiva dynamiska handledsextensioner påverkar den lokala syreomsättningen i muskeln före och efter träning. Den muskulära syreomsättningen skiljer sig däremot inte när träningsplatå uppnås när båda regimerna utförs till failure. Detta tyder på att utförande av dynamiska handledsextensioner på låg belastning utan att muskeln tillåts att slappna av, kan ge samma effekter oberoende av om ocklusion appliceras eller inte.

The objective of this study was to assess low to high levels of Cognitive Workload by measuring heart rate and cortical blood flow in real-time. Four conditions were implemented into a within-subjects experimental design. Two conditions of difficulty and two conditions of trial order were used to illicit different levels of workload which will be analyzed with psychophysiological equipment. Functional Near-Infrared Spectroscopy (fNIRS) has become more prominent for measuring the blood oxygenation levels in the prefrontal cortex of individuals operating in hazardous work environments, students with learning disabilities, and in research for military training. This is due to the fNIR device being highly mobile, inexpensive, and able to produce a high-spatial resolution of the dorsolateral prefrontal cortex during executive functioning. Heart Rate will be measured by an Electrocardiogram, which will be used in concordance with fNIR oxygenation levels to predict if an individual is in a condition that produces low or high mental workload. Successfully utilizing heart rate and blood oxygenation data as predictors of cognitive workload may validate implementing multiple physiological devices together in real-time and may be a more accurate solution for preventing excessive workload.

[pt] Doenças cardiovasculares são responsáveis por um elevado número de óbitos em seres humanos. Muitas dessas patologias são dependentes do ciclo cardíaco e estão localizadas na aorta, a maior e principal artéria do nosso corpo. O conhecimento dos padrões de escoamento e distribuições de tensões nas paredes da aorta podem auxiliar no diagnóstico e prevenção de algumas dessas doenças. Dessa forma, estudou-se numericamente o escoamento do sangue, durante o ciclo cardíaco, em um modelo 3D da aorta de um paciente específico, após a implantação de TAVI (Transcatheter Aortic Valve Implantation). O ciclo cardíaco é formado por dois períodos chamados de sístole e diástole. Durante a sístole, sangue é bombeado do coração para a aorta, apresentado altos valores de vazão, resultando em escoamento turbulento. Por outro lado, na diástole, com o fechamento da válvula aórtica, o sangue escoa com baixas velocidades em regime laminar. Até hoje, cientistas enfrentam um desafio na modelagem da turbulência, pois não existe uma única modelagem que forneça previsibilidade para todas as situações envolvendo o regime turbulento, com esforço computacional razoável. Para seleção do modelo de turbulência mais adequado para análise do escoamento no interior da aorta, na presença da transição de regimes de escoamento durante o ciclo cardíaco, com um custo razoável, selecionou-se a metodologia baseada na Média de Reynolds. Diferentes modelos foram comparados com dados experimentais extraídos do mesmo modelo aórtico em escala real, porém em regime permanente, com vazão correspondente ao pico da sístole. Por fim, avaliou-se o impacto das condições de contorno e dos modelos de turbulência durante o ciclo cardíaco na distribuição e valores de tensões e grandezas turbulentas no endotélio vascular. Mostrou-se que a distribuição espacial das médias temporais de tensão foram qualitativamente e quantitativamente similares, para os dois ciclos cardíacos representativos de diferentes pacientes, porém com pequenas mudanças locais para cada caso. Em termos dos modelos de turbulência, observou-se que o modelo SAS (Scale Adaptive Simulation) foi capaz de representar a relaminarização do escoamento sanguíneo no período diastólico. / [en] Cardiovascular diseases are responsible for a high number of deaths in humans. Many of these pathologies are dependent on the cardiac cycle and are located in the aorta, the largest and main artery in our body. Knowledge of flow patterns and stress distributions in the walls of the aorta can help in the diagnosis and prevention of some of these diseases. Thus, the flow of blood during the cardiac cycle was numerically studied in a 3D model of the aorta of a specific patient, after TAVI (Transcatheter Aortic Valve Implantation) implantation. The cardiac cycle consists of two periods called systole and diastole. During the systole, blood is pumped from the heart to the aorta, presenting high flow rates, resulting in a turbulent flow. On the other hand, in diastole, with the closure of the aortic valve, the blood flows with low velocities in laminar regime. Until today, scientists face a challenge in turbulence modeling, as there is no single model that provides predictability for all situations involving the turbulent regime, with reasonable computational effort. In order to select the most suitable turbulence model for the analysis of the flow inside the aorta, in the presence of the transition of flow regimes during the cardiac cycle, with a reasonable cost, the methodology based on the Reynolds Average was selected. Different models were compared with experimental data extracted from the same real-scale aortic model, but a in steady state, with flow corresponding to the systolic peak. Finally, the impact of boundary conditions and turbulence models during the cardiac cycle on the distribution and values of stresses and turbulent quantities in the vascular endothelium were evaluated. It was shown that the spatial distribution of the temporal averages of tension was qualitatively and quantitatively similar, for the two cardiac cycles representative of different patients, but with small local changes for each case. In terms of turbulence models, it was observed that the SAS (Scale Adaptive Simulation) model was able to represent the relaminarization of blood flow in the diastolic period.

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[pt] Estenose é uma constrição ou estreitamento de um duto ou de uma passagem. Este termo é usado freqüentemente em referência a constrições que ocorrem em vasos sangüíneos, especialmente em artérias. Um vaso estenótico geralmente causa estagnação do fluxo sangüíneo e portanto a formação de trombos, os quais podem ser bastante pre- judiciais à saúde humana. Neste trabalho realizam-se experimentos com a técnica de velocimetria por imagens de partículas (PIV) a fim de estudar o escoamento de um líquido que possui uma tensão limite de escoamento (ou líquido viscoplástico) através de um tubo na vizinhança de uma constrição axissimétrica. Escolheu-se a reologia do líquido de modo a se aproximar daquela do sangue de hematócrito igual a 54%. Estudaram-se números de Reynolds e números de escoamento característicos para diferentes artérias. Obtiveram-se também resultados para fluidos Newtonianos, para fins de comparação. Entre outros resultados, observou- se que a reologia não Newtoniana causa mudanças significativas no padrão de escoamento na vizinhança da estenose. Como as condições para formação de trombos estão diretamente relacionadas com o padrão de escoamento, estudos do escoamento do sangue através de artérias com estenose que supõem uma reologia Newtoniana podem levar a conclusões errôneas. / [en] Stenosis is a constriction or narrowing of a duct or passage. This word is often used to refer to constrictions that occur in blood vessels, especially arteries. A stenotic vessel generally causes blood flow stagnation and hence formation of thrombus, which may be rather harmful to the human physiology. In this work we perform particle image velocimetry (PIV) experiments to study the flow of an yield-stress (or highly shear-thinning) liquid through a tube in the neighborhood of an axisymmetric constriction. The rheology of the liquid was chosen to be close to the one of blood with 54% hematocrit. Reynolds and Yield number values characteristic to different arteries have been studied. Results for a Newtonian liquid were also obtained, for comparison purposes. Among other findings, it has been observed that the non-Newtonian rheology causes a significant change in the flow pattern in the neighborhood of the stenosis. Because the conditions for thrombus formation are directly related to the flow pattern, studies of the flow through stenotic vessels that assume a Newtonian rheology may lead to erroneous conclusions.

Introduktion: Främre korsbandsskador är väldigt vanligt, cirka 8000/år i Sverige och förekommer främst inom idrott. Ungefär 50% av de som får en skada på sitt främre korsband väljer att operera, det kallas för främre korsbandsrekonstruktion. Rehabiliteringen är väldigt lång och rekommendationen är att inte återgå till sin sport förrän efter 9 månader efter operationen. Den nuvarande rehabiliteringsformen inkluderar högintensiv styrketräning på 70% av repetition max vilket lägger hög belastning på knäleden. Ny forskning visar goda resultat för ocklusionsträning där belastningen ligger på 30% av repetition max med användning av blodtrycksmanschetter. Syfte: Att genom en systematisk litteraturöversikt jämföra effekten av ocklusionsbaserad rehabilitering jämfört sedvanlig rehabilitering efter en främre korsbandsrekonstruktion. Metod: Artikelsökningar gjordes på databaserna Pubmed, Web of Science och Cinahl. Inklusionskriterierna utformades med PICOS-modellen. Samtliga studier var randomiserade kontrollerade studier från 2010-2023. Urvalsprocessen gjordes med hjälp av PRISMA’s flödesdiagram och kvalitetsgranskningen genom SBUs granskningsmall för “Bedömning av randomiserade studier”. Resultat: Totalt nio studier inkluderades efter litteratursökning och relevansbedömning. Studierna hade låg-hög kvalitet. De utfallsmått som bedömdes i studierna var: muskelstyrka, muskelvolym/tvärsnittsarea (Cross Sectional Area), smärta, patientrapporterade utfallsmått. Sammanställningen visade att ocklusionsbaserad rehabilitering hade bättre resultat på samtliga utfallsmått jämfört med sedvanlig rehabilitering. Konklusion: Resultaten antyder att ocklusionsbaserad rehabilitering är en effektiv rehabiliteringsmetod. Ocklusionsbaserad rehabilitering kan därför vara ett alternativ att använda som komplement till sedvanlig rehabilitering av vårdgivare för patienter som genomgått rekonstruktion av främre korsband.

In this Thesis we explore, both theoretically and numerically, splitting strategies for a hyperbolic system of one-dimensional (1D) blood flow equations with a passive scalar transport equation. Our analysis involves a two-step framework that includes splitting at the level of partial differential equations (PDEs) and numerical methods for discretizing the ensuing problems. This study is inspired by the original flux splitting approach of Toro and Vázquez-Cendón (2012) originally developed for the conservative Euler equations of compressible gas dynamics. In this approach the flux vector in the conservative case, and the system matrix in the non-conservative one, are split into advection and pressure terms: in this way, two systems of partial differential equations are obtained, the advection system and the pressure system. From the mathematical as well as numerical point of view, a basic problem to be solved is the special Cauchy problem called the Riemann problem. This latter provides an analytical solution to evaluate the performance of the numerical methods and, in our approach, it is of primary importance to build the presented numerical schemes. In the first part of the Thesis a detailed theoretical analysis is presented, involving the exact solution of the Riemann problem for the 1D blood flow equations, depicted for a general constant momentum correction coefficient and a tube law that allows to describe both arteries and veins with continuous or discontinuous mechanical and geometrical properties and an advection equation for a passive scalar transport. In literature, this topic has been already studied only for a momentum correction coefficient equal to one, that is related to the prescribed velocity profile and in this case corresponds to a flat one, i.e. an inviscid fluid. In the case of discontinuous properties, only the subsonic regime is considered. In addition we propose a procedure to compute the obtained exact solution and finally we validate it numerically, by comparing exact solutions to those obtained with well-known, numerical schemes on a carefully designed set of test problems. Furthermore, an analogous theoretical analysis and resolution algorithm are presented for the advection system and the pressure system arising from the splitting at the level of PDEs of the complete system of 1D blood flow equations. It is worth noting that the pressure system, in case of veins, presents a loss of genuine non-linearity resulting in the formation of rarefactions, shocks and compound waves, these latter being a composition of rarefactions and shocks. In the second part of the Thesis we present novel finite volume-type, flux splitting-based, numerical schemes for the conservative 1D blood flow equations and splitting-based numerical schemes for the non-conservative 1D blood flow equations that incorporate an advection equation for a passive scalar transport, considering tube laws that allow to model blood flow in arteries and veins and take into account a general constant momentum correction coefficient. A detailed efficiency analysis is performed in order to showcase the advantages of the proposed methodologies in comparison to standard approaches.