Multiscale Modeling of Cardiovascular Flows

Simulations of blood flow in the cardiovascular system offer investigative and predictive capabilities to augment current clinical tools. Using image-based modeling, the Navier-Stokes equations can be solved to obtain detailed 3-dimensional hemodynamics in patient-specific anatomical models. Relevant parameters such as wall shear stress and particle residence times can then be calculated from the 3D results and correlated with clinical data for treatment planning and device evaluation. Reduced-order models such as open or closed loop 0D lumped-parameter models can simulate the dynamic behavior of the circulatory system using an analogy to electrical circuits. When coupled to 3D simulations as boundary conditions, they produce physiologically realistic pressure and flow conditions in the 3D domain. We describe fundamentals and current state of the art of patient-specific, multi-scale computational modeling approaches applied to cardiovascular disease. These tools enable investigations of hemodynamics reflecting individual patients physiology, and we provide several illustrative case studies. These methods can supplement current clinical measurement and imaging capabilities and provide predictions of patient outcomes for surgical planning and risk stratification

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

Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation

A novel multiscale mathematical and computational model of the pulmonary circulation is presented and used to analyse both arterial and venous pressure and flow. This work is a major advance over previous studies by Olufsen et al. (Ann Biomed Eng 28:1281–1299, 2012) which only considered the arterial circulation. For the first three generations of vessels within the pulmonary circulation, geometry is specified from patient-specific measurements obtained using magnetic resonance imaging (MRI). Blood flow and pressure in the larger arteries and veins are predicted using a nonlinear, cross-sectional-area-averaged system of equations for a Newtonian fluid in an elastic tube. Inflow into the main pulmonary artery is obtained from MRI measurements, while pressure entering the left atrium from the main pulmonary vein is kept constant at the normal mean value of 2 mmHg. Each terminal vessel in the network of ‘large’ arteries is connected to its corresponding terminal vein via a network of vessels representing the vascular bed of smaller arteries and veins. We develop and implement an algorithm to calculate the admittance of each vascular bed, using bifurcating structured trees and recursion. The structured-tree models take into account the geometry and material properties of the ‘smaller’ arteries and veins of radii ≥ 50 μ m. We study the effects on flow and pressure associated with three classes of pulmonary hypertension expressed via stiffening of larger and smaller vessels, and vascular rarefaction. The results of simulating these pathological conditions are in agreement with clinical observations, showing that the model has potential for assisting with diagnosis and treatment for circulatory diseases within the lung

Mathematical methods for modeling the microcirculation

The microcirculation plays a major role in maintaining homeostasis in the body. Alterations or dysfunctions of the microcirculation can lead to several types of serious diseases. It is not surprising, then, that the microcirculation has been an object of intense theoretical and experimental study over the past few decades. Mathematical approaches offer a valuable method for quantifying the relationships between various mechanical, hemodynamic, and regulatory factors of the microcirculation and the pathophysiology of numerous diseases. This work provides an overview of several mathematical models that describe and investigate the many different aspects of the microcirculation, including geometry of the vascular bed, blood flow in the vascular networks, solute transport and delivery to the surrounding tissue, and vessel wall mechanics under passive and active stimuli. Representing relevant phenomena across multiple spatial scales remains a major challenge in modeling the microcirculation. Nevertheless, the depth and breadth of mathematical modeling with applications in the microcirculation is demonstrated in this work. A special emphasis is placed on models of the retinal circulation, including models that predict the influence of ocular hemodynamic alterations with the progression of ocular diseases such as glaucoma

Effects of age-associated regional changes in aortic stiffness on human hemodynamics revealed by computational modeling

Although considered by many as the gold standard clinical measure of arterial stiffness, carotid-to-femoral pulse wave velocity (cf-PWV) averages material and geometric properties over a large portion of the central arterial tree. Given that such properties may evolve differentially as a function of region in cases of hypertension and aging, among other conditions, there is a need to evaluate the potential utility of cf-PWV as an early diagnostic of progressive vascular stiffening. In this paper, we introduce a data-driven fluid-solid-interaction computational model of the human aorta to simulate effects of aging-related changes in regional wall properties (e.g., biaxial material stiffness and wall thickness) and conduit geometry (e.g., vessel caliber, length, and tortuosity) on several metrics of arterial stiffness, including distensibility, augmented pulse pressure, and cyclic changes in stored elastic energy. Using the best available biomechanical data, our results for PWV compare well to findings reported for large population studies while rendering a higher resolution description of evolving local and global metrics of aortic stiffening. Our results reveal similar spatio-temporal trends between stiffness and its surrogate metrics, except PWV, thus indicating a complex dependency of the latter on geometry. Lastly, our analysis highlights the importance of the tethering exerted by external tissues, which was iteratively estimated until hemodynamic simulations recovered typical values of tissue properties, pulse pressure, and PWV for each age group.</p

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

Parameter estimation to study the immediate impact of aortic cross-clamping using reduced order models

Aortic cross-clamping is a common strategy during vascular surgery, however, its instantaneous impact on hemodynamics is unknown. We, therefore, developed two numerical models to estimate the immediate impact of aortic clamping on the vascular properties. To assess the validity of the models, we recorded continuous invasive pressure signals during abdominal aneurysm repair surgery, immediately before and after clamping. The first model is a zero-dimensional (0D) three-element Windkessel model, which we coupled to a gradient-based parameter estimation algorithm to identify patient-specific parameters such as vascular resistance and compliance. We found a 10% increase in the total resistance and a 20% decrease in the total compliance after clamping. The second model is a nine-artery network corresponding to an average human body in which we solved the one-dimensional (1D) blood flow equations. With a similar parameter estimation method and using the results from the 0D model, we identified the resistance boundary conditions of the 1D network. Determining the patient-specific total resistance and the distribution of peripheral resistances through the parameter estimation process was sufficient for the 1D model to accurately reproduce the impact of clamping on the pressure waveform. Both models gave an accurate description of the pressure wave and had a high correlation (R2 >.95) with experimental blood pressure data.Fil: Ventre, Jeanne. Centre National de la Recherche Scientifique; FranciaFil: Politi, Teresa. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Fisiología y Biofísica Bernardo Houssay. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Fisiología y Biofísica Bernardo Houssay; ArgentinaFil: Fernández, Juan M.. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Fisiología y Biofísica Bernardo Houssay. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Fisiología y Biofísica Bernardo Houssay; ArgentinaFil: Ghigo, Arthur R.. Université de Toulouse; FranciaFil: Gaudric, Julien. Centre National de la Recherche Scientifique; Francia. Université de Toulouse; FranciaFil: Wray, Sandra. Universidad Favaloro; ArgentinaFil: Lagaert, Jean Baptiste. Université Paris Sud; FranciaFil: Armentano, Ricardo Luis. Universidad de la República; UruguayFil: Capurro, Claudia Graciela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Fisiología y Biofísica Bernardo Houssay. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Fisiología y Biofísica Bernardo Houssay; ArgentinaFil: Fullana, José Maria. Centre National de la Recherche Scientifique; FranciaFil: Lagrée, Pierre Yves. Centre National de la Recherche Scientifique; Franci