Modeling Reactive Hyperemia to Better Understand and Assess Microvascular Function: A Review of Techniques

Reactive hyperemia is a well-established technique for the non-invasive evaluation of the peripheral microcirculatory function, measured as the magnitude of limb re-perfusion after a brief period of ischemia. Despite widespread adoption by researchers and clinicians alike, many uncertainties remain surrounding interpretation, compounded by patient-specific confounding factors (such as blood pressure or the metabolic rate of the ischemic limb). Mathematical modeling can accelerate our understanding of the physiology underlying the reactive hyperemia response and guide in the estimation of quantities which are difficult to measure experimentally. In this work, we aim to provide a comprehensive guide for mathematical modeling techniques that can be used for describing the key phenomena involved in the reactive hyperemia response, alongside their limitations and advantages. The reported methodologies can be used for investigating specific reactive hyperemia aspects alone, or can be combined into a computational framework to be used in (pre-)clinical settings

Multiscale Modeling of Hemodynamics in Human Vessel Network and Its Applications in Cerebral Aneurysms

Three-dimensional (3D) simulation of patient-specific morphological models has been widely used to provide the hemodynamic information of individual patients, such as wall shear stress (WSS), oscillatory shear index (OSI), and flow patterns, etc. Since patient-specific morphological segment was only restricted locally, boundary conditions (BCs) are required to implement the CFD simulation. Direct measurements of the flow and pressure waveforms were often required as input BCs for 3D CFD simulations of patient-specific models. However, as the morphology develops, the feedback from this topological deformation may lead to BCs being altered, and hence without this feedback, the flow characteristics of the morphology are only computed locally. A one-dimensional (1D) numerical model containing the entire human vessel network has been proposed to compute the global hemodynamics. In the meantime, experimental studies of blood flow in the patient-specific modeling of the circle of Willies (CoW) was conducted. The flow and pressure waveforms were quantified to validate the accuracy of the pure 1D model. This 1D model will be coupled with a 3D morphological model to account for the effects of the altered BCs. The proposed 1D-3D multi-scale modeling approach investigates how the global hemodynamic changes can be induced by the local morphological effects, and in consequence, may further result in altering of BCs to interfere with the solution of the 3D simulation. Validation of the proposed multi-scale model has also been made by comparing the solution of the flow rate and pressure waveforms with the experimental data and 3D numerical simulations reported in the literature. Moreover, the multi-scale model is extended to study a patient-specific cerebral aneurysm and a stenosis model. The proposed multi-scale model can be used as an alternative to current approaches to study intracranial vascular diseases such as an aneurysm, stenosis, and combined cases

On the poro-elastic models for microvascular blood flow resistance: An in vitro validation

Nowadays, adequate and accurate representation of the microvascular flow resistance constitutes one of the major challenges in computational haemodynamic studies. In this work, a theoretical, porous media framework, ultimately designed for representing downstream resistance, is presented and compared against an in vitro experimental results. The resistor consists of a poro-elastic tube, with either a constant or variable porosity profile in space. The underlying physics, characterizing the fluid flow through the porous media, is analysed by considering flow variables at different network locations. Backward reflections, originated in the reservoir of the in vitro model, are accounted for through a reflection coefficient imposed as an outflow network condition. The simulation results are in good agreement with the measurements for both the homogenous and heterogeneous porosity conditions. In addition, the comparison allows identification of the range of values representing experimental reservoir reflection coefficients. The pressure drops across the heterogeneous porous media increases with respect to the simpler configuration, whilst flow remains almost unchanged. The effect of some fluid network features, such as tube Young’s modulus and fluid viscosity, on the theoretical results is also elucidated, providing a reference for the and simulation of different microvascular conditions

Computational fluid dynamics indicators to improve cardiovascular pathologies

In recent years, the study of computational hemodynamics within anatomically complex vascular regions has generated great interest among clinicians. The progress in computational fluid dynamics, image processing and high-performance computing haveallowed us to identify the candidate vascular regions for the appearance of cardiovascular diseases and to predict how this disease may evolve. Medicine currently uses a paradigm called diagnosis. In this thesis we attempt to introduce into medicine the predictive paradigm that has been used in engineering for many years. The objective of this thesis is therefore to develop predictive models based on diagnostic indicators for cardiovascular pathologies. We try to predict the evolution of aortic abdominal aneurysm, aortic coarctation and coronary artery disease in a personalized way for each patient. To understand how the cardiovascular pathology will evolve and when it will become a health risk, it is necessary to develop new technologies by merging medical imaging and computational science. We propose diagnostic indicators that can improve the diagnosis and predict the evolution of the disease more efficiently than the methods used until now. In particular, a new methodology for computing diagnostic indicators based on computational hemodynamics and medical imaging is proposed. We have worked with data of anonymous patients to create real predictive technology that will allow us to continue advancing in personalized medicine and generate more sustainable health systems. However, our final aim is to achieve an impact at a clinical level. Several groups have tried to create predictive models for cardiovascular pathologies, but they have not yet begun to use them in clinical practice. Our objective is to go further and obtain predictive variables to be used practically in the clinical field. It is to be hoped that in the future extremely precise databases of all of our anatomy and physiology will be available to doctors. These data can be used for predictive models to improve diagnosis or to improve therapies or personalized treatments.En els últims anys, l'estudi de l'hemodinàmica computacional en regions vasculars anatòmicament complexes ha generat un gran interès entre els clínics. El progrés obtingut en la dinàmica de fluids computacional, en el processament d'imatges i en la computació d'alt rendiment ha permès identificar regions vasculars on poden aparèixer malalties cardiovasculars, així com predir-ne l'evolució. Actualment, la medicina utilitza un paradigma anomenat diagnòstic. En aquesta tesi s'intenta introduir en la medicina el paradigma predictiu utilitzat des de fa molts anys en l'enginyeria. Per tant, aquesta tesi té com a objectiu desenvolupar models predictius basats en indicadors de diagnòstic de patologies cardiovasculars. Tractem de predir l'evolució de l'aneurisma d'aorta abdominal, la coartació aòrtica i la malaltia coronària de forma personalitzada per a cada pacient. Per entendre com la patologia cardiovascular evolucionarà i quan suposarà un risc per a la salut, cal desenvolupar noves tecnologies mitjançant la combinació de les imatges mèdiques i la ciència computacional. Proposem uns indicadors que poden millorar el diagnòstic i predir l'evolució de la malaltia de manera més eficient que els mètodes utilitzats fins ara. En particular, es proposa una nova metodologia per al càlcul dels indicadors de diagnòstic basada en l'hemodinàmica computacional i les imatges mèdiques. Hem treballat amb dades de pacients anònims per crear una tecnologia predictiva real que ens permetrà seguir avançant en la medicina personalitzada i generar sistemes de salut més sostenibles. Però el nostre objectiu final és aconseguir un impacte en l¿àmbit clínic. Diversos grups han tractat de crear models predictius per a les patologies cardiovasculars, però encara no han començat a utilitzar-les en la pràctica clínica. El nostre objectiu és anar més enllà i obtenir variables predictives que es puguin utilitzar de forma pràctica en el camp clínic. Es pot preveure que en el futur tots els metges disposaran de bases de dades molt precises de tota la nostra anatomia i fisiologia. Aquestes dades es poden utilitzar en els models predictius per millorar el diagnòstic o per millorar teràpies o tractaments personalitzats.Postprint (published version

Fluid-structure interaction in blood flow capturing non-zero longitudinal structure displacement

We present a new model and a novel loosely coupled partitioned numerical scheme modeling fluid-structure interaction (FSI) in blood flow allowing non-zero longitudinal displacement. Arterial walls are modeled by a {linearly viscoelastic, cylindrical Koiter shell model capturing both radial and longitudinal displacement}. Fluid flow is modeled by the Navier-Stokes equations for an incompressible, viscous fluid. The two are fully coupled via kinematic and dynamic coupling conditions. Our numerical scheme is based on a new modified Lie operator splitting that decouples the fluid and structure sub-problems in a way that leads to a loosely coupled scheme which is {unconditionally} stable. This was achieved by a clever use of the kinematic coupling condition at the fluid and structure sub-problems, leading to an implicit coupling between the fluid and structure velocities. The proposed scheme is a modification of the recently introduced "kinematically coupled scheme" for which the newly proposed modified Lie splitting significantly increases the accuracy. The performance and accuracy of the scheme were studied on a couple of instructive examples including a comparison with a monolithic scheme. It was shown that the accuracy of our scheme was comparable to that of the monolithic scheme, while our scheme retains all the main advantages of partitioned schemes, such as modularity, simple implementation, and low computational costs