Multiscale Fluid-Structure Interaction Models Development and Applications to the 3D Elements of a Human Cardiovascular System

Cardiovascular diseases (CVD) are the number one cause of death of humans in the United States and worldwide. Accurate, non-invasive, and cheaper diagnosis methods have always been on demand as cardiovascular monitoring increase in prevalence. The primary causes of the various forms of these CVDs are atherosclerosis and aneurysms in the blood vessels. Current noninvasive methods (i.e., statistical/medical) permit fairly accurate detection of the disease once clinical symptoms are suggestive of the existence of hemodynamic disorders. Therefore, the recent surge of hemodynamics models facilitated the prediction of cardiovascular conditions. The hemodynamic modeling of a human circulatory system involves varying levels of complexity which must be accounted for and resolved. Pulse-wave propagation effects and high aspect-ratio segments of the vasculature are represented using a quasi-one-dimensional (1D), non-steady, averaged over the cross-section models. However, these reduced 1D models do not account for the blood flow patterns (recirculation zones), vessel wall shear stresses and quantification of repetitive mechanical stresses which helps to predict a vessel life. Even a whole three-dimensional (3D) modeling of the vasculature is computationally intensive and do not fit the timeline of practical use. Thus the intertwining of a quasi 1D global vasculature model with a specific/risk-prone 3D local vessel ones is imperative. This research forms part of a multiphysics project that aims to improve the detailed understanding of the hemodynamics by investigating a computational model of fluid-structure interaction (FSI) of in vivo blood flow. First idealized computational a 3D FSI artery model is configured and executed in ANSYS Workbench, forming an implicit coupling of the blood flow and vessel walls. Then the thesis focuses on an approach developed to employ commercial tools rather than in-house mathematical models in achieving multiscale simulations. A robust algorithm is constructed to combine stabilization techniques to simultaneously overcome the added-mass effect in 3D FSI simulation and mathematical difficulties such as the assignment of boundary conditions at the interface between the 3D-1D coupling. Applications can be of numerical examples evaluating the change of hemodynamic parameters and diagnosis of an abdominal aneurysm, deep vein thrombosis, and bifurcation areas

Synthesis of fixed-order controllers for control systems with long transmission lines

Doktorska disertacija pod naslovom ―Sinteza regulatora fiksnog reda za sisteme upravljanja sa dugačkim hidrauličkim vodovima‖ odnosi se na problem projektovanja regulatora fiksnog reda kada treba upravljati hidrauličkim izvršnim organima (pogonima) sa dugačkim vodovima, koji su opisani matematičkim modelima visokog reda. Obrađena je kroz sedam poglavlja. Prvo poglavlje ukazuje na potrebu i značaj istraživanja sistema sa zapreminskim upravljanjem zbog niza prednosti u odnosu na sisteme sa prigušnim upravljanjem, a posebno sa aspekta energetske efikasnosti. Pošto su ovi sistemi opisani matematičkim modelima visokog reda, ukazano je na neophodnost pronalaženja metodologije za projektovanje regulatora fiksne strukture i niskog reda za upravljanje ovim sistemima, a u cilju poboljšanja kvaliteta rada hidro i hidroelektričnih izvršnih organa sa dugačkim hidrauličkim vodovima. U drugom poglavlju je dat pregled istraživačkih rezultata iz oblasti hidro i hidroelektričnih sistema upravljanja sa dugačkim hidrauličkim vodovima, kao i rezultata iz oblasti teorije upravljanja. Treće poglavlje prikazuje, kroz sveobuhvatni metodološki prilaz, oblike matematičkih modela stujanja radnog fluida u dugačkim upravljačkim hidrauličkim vodovima, od najjednostavnijih do najsloženijih. Modeli su iskazani kroz matrične zavisnosti i sprege hiperboličkih funkcija i izvršen je njihov tabelarno sređen prikaz. Uz realne vrednosti parametara prikazane su frekventne karakteristike usvojenih modela, kao i njihova analiza u frekventnom domenu.The doctoral dissertation ―Synthesis of Fixed-Order Controllers for Control Systems with Long Transmission Lines‖ refers to the problem of fixed-order controller design when hydraulic executive bodies (drives) with long transmission lines, which are described by mathematical models of high order, should be controlled. It consists of seven chapters. Chapter I points out the need for and significance of research on systems with displacement control because of a lot of advantages in relation to the systems with damping control, especially from the aspect of energy efficiency. As these systems are described by mathematical models of high order, the dissertation indicates the necessity of finding a methodology for design of controllers with fixed structure and low order for control of these systems for the purpose of improving the quality of operation of hydraulic and electro-hydraulic executive bodies with long transmission lines. Chapter II provides an overview of research results in the field of hydraulic and electro-hydraulic control systems with long transmission lines as well as results in the field of control theory Chapter III, through a comprehensive methodological approach, presents forms of mathematical model of flow of working fluid in long transmission lines, from the simplest to the most complex ones. The models are shown through matrix dependences and combination of hyperbolic functions and they are presented in tables. Frequent characteristics of the adopted models as well as their analysis in the frequency domain are presented with real values of parameters. Chapter IV develops the methodology of design of P controllers in the system of pump-controlled motor with a long transmission line. The methodology of P controller design was carried out by the root locus of the closed loop where the performances were also included through the specification of relative stability of the system, which implies an a priori given location of poles of transmission function of the closed loop in a complex plane determined on the basis of known requirements. It was shown that the designed controller gave good performances even during variation of the parameters in the system components (for instance: the viscosity coefficient and the module of compressibility which considerably change with the change of temperature and pressure). By using the possibilities offered by computers and software, a simple graphical method for design of the P controller, which often satisfies practical needs, was developed

Coupling strategies for the numerical simulation of blood flow in deformable arteries by 3D and 1D models

The fluid structure interaction mechanism in vascular dynamics can be described by either 3D or 1D models, depending on the level of detail of the flow and pressure patterns needed for analysis. A successful strategy that has been proposed in the past years is the so-called geometrical multiscale approach, which consists of coupling both 3D and 1D models so as to use the former only in those regions where details of the fluid flow are needed and describe the remaining part of the vascular network by the simplified 1D model. In this paper we review recently proposed strategies to couple the 3D and 1D models, and within the 3D model, to couple the fluid and structure sub-problems. The 3D/1D coupling strategy relies on the imposition of the continuity of flow rate and total normal stress at the interface. On the other hand, the fluid–structure coupling strategy employs Robin transmission conditions. We present some numerical results and show the effectiveness of the new approaches

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

Partitioned Solution of Geometrical Multiscale Problems for the Cardiovascular System:Models, Algorithms, and Applications

The aim of this work is the development of a geometrical multiscale framework for the simulation of the human cardiovascular system under either physiological or pathological conditions. More precisely, we devise numerical algorithms for the partitioned solution of geometrical multiscale problems made of different heterogeneous compartments that are implicitly coupled with each others. The driving motivation is the awareness that cardiovascular dynamics are governed by the global interplay between the compartments in the network. Thus, numerical simulations of stand-alone local components of the circulatory system cannot always predict effectively the physiological or pathological states of the patients, since they do not account for the interaction with the missing elements in the network. As a matter of fact, the geometrical multiscale method provides an automatic way to determine the boundary (more precisely, the interface) data for the specific problem of interest in absence of clinical measures and it also offers a platform where to study the interaction between local changes (due, for instance, to pathologies or surgical interventions) and the global systemic dynamics. To set up the framework an abstract setting is devised; the local specific mathematical equations (partial differential equations, differential algebraic equations, etc.) and the numerical approximation (finite elements, finite differences, etc.) of the heterogeneous compartments are hidden behind generic operators. Consequently, the resulting global interface problem is formulated and solved in a completely transparent way. The coupling between models of different dimensional scale (three-dimensional, one-dimensional, etc.) and type (Navier-Stokes, fluid-structure interaction, etc.) is addressed writing the interface equations in terms of scalar quantities, i.e., area, flow rate, and mean (total) normal stress. In the resulting flexible framework the heterogeneous models are treated as black boxes, each one equipped with a specific number of compatible interfaces such that (i) the arrangement of the compartments in the network can be easily manipulated, thus allowing a high level of customization in the design and optimization of the global geometrical multiscale model, (ii) the parallelization of the solution of the different compartments is straightforward, leading to the opportunity to make use of the latest high-performance computing facilities, and (iii) new models can be easily added and connected to the existing ones. The methodology and the algorithms devised throughout the work are tested over several applications, ranging from simple benchmark examples to more complex cardiovascular networks. In addition, two real clinical problems are addressed: the simulation of a patient-specific left ventricle affected by myocardial infarction and the study of the optimal position for the anastomosis of a left ventricle assist device cannula