Immersed boundary-finite element model of fluid-structure interaction in the aortic root

It has long been recognized that aortic root elasticity helps to ensure efficient aortic valve closure, but our understanding of the functional importance of the elasticity and geometry of the aortic root continues to evolve as increasingly detailed in vivo imaging data become available. Herein, we describe fluid-structure interaction models of the aortic root, including the aortic valve leaflets, the sinuses of Valsalva, the aortic annulus, and the sinotubular junction, that employ a version of Peskin's immersed boundary (IB) method with a finite element (FE) description of the structural elasticity. We develop both an idealized model of the root with three-fold symmetry of the aortic sinuses and valve leaflets, and a more realistic model that accounts for the differences in the sizes of the left, right, and noncoronary sinuses and corresponding valve cusps. As in earlier work, we use fiber-based models of the valve leaflets, but this study extends earlier IB models of the aortic root by employing incompressible hyperelastic models of the mechanics of the sinuses and ascending aorta using a constitutive law fit to experimental data from human aortic root tissue. In vivo pressure loading is accounted for by a backwards displacement method that determines the unloaded configurations of the root models. Our models yield realistic cardiac output at physiological pressures, with low transvalvular pressure differences during forward flow, minimal regurgitation during valve closure, and realistic pressure loads when the valve is closed during diastole. Further, results from high-resolution computations demonstrate that IB models of the aortic valve are able to produce essentially grid-converged dynamics at practical grid spacings for the high-Reynolds number flows of the aortic root

Mathematical modeling of local perfusion in large distensible microvascular networks

Microvessels -blood vessels with diameter less than 200 microns- form large, intricate networks organized into arterioles, capillaries and venules. In these networks, the distribution of flow and pressure drop is a highly interlaced function of single vessel resistances and mutual vessel interactions. In this paper we propose a mathematical and computational model to study the behavior of microcirculatory networks subjected to different conditions. The network geometry is composed of a graph of connected straight cylinders, each one representing a vessel. The blood flow and pressure drop across the single vessel, further split into smaller elements, are related through a generalized Ohm's law featuring a conductivity parameter, function of the vessel cross section area and geometry, which undergo deformations under pressure loads. The membrane theory is used to describe the deformation of vessel lumina, tailored to the structure of thick-walled arterioles and thin-walled venules. In addition, since venules can possibly experience negative transmural pressures, a buckling model is also included to represent vessel collapse. The complete model including arterioles, capillaries and venules represents a nonlinear system of PDEs, which is approached numerically by finite element discretization and linearization techniques. We use the model to simulate flow in the microcirculation of the human eye retina, a terminal system with a single inlet and outlet. After a phase of validation against experimental measurements, we simulate the network response to different interstitial pressure values. Such a study is carried out both for global and localized variations of the interstitial pressure. In both cases, significant redistributions of the blood flow in the network arise, highlighting the importance of considering the single vessel behavior along with its position and connectivity in the network

Numerical modelling of the fluid-structure interaction in complex vascular geometries

A complex network of vessels is responsible for the transportation of blood throughout the body and back to the heart. Fluid mechanics and solid mechanics play a fundamental role in this transport phenomenon and are particularly suited for computer simulations. The latter may contribute to a better comprehension of the physiological processes and mechanisms leading to cardiovascular diseases, which are currently the leading cause of death in the western world. In case these computational models include patient-specific geometries and/or the interaction between the blood flow and the arterial wall, they become challenging to develop and to solve, increasing both the operator time and the computational time. This is especially true when the domain of interest involves vascular pathologies such as a local narrowing (stenosis) or a local dilatation (aneurysm) of the arterial wall. To overcome these issues of high operator times and high computational times when addressing the bio(fluid)mechanics of complex geometries, this PhD thesis focuses on the development of computational strategies which improve the generation and the accuracy of image-based, fluid-structure interaction (FSI) models. First, a robust procedure is introduced for the generation of hexahedral grids, which allows for local grid refinements and automation. Secondly, a straightforward algorithm is developed to obtain the prestress which is implicitly present in the arterial wall of a – by the blood pressure – loaded geometry at the moment of medical image acquisition. Both techniques are validated, applied to relevant cases, and finally integrated into a fluid-structure interaction model of an abdominal mouse aorta, based on in vivo measurements

Computational Modeling of Cardiac Biomechanics

The goal of this dissertation was to develop a realistic and patient-specific computational model of the heart that ultimately would help medical scientists to better diagnose and treat heart diseases. In order to achieve this goal, a three dimensional finite element model of the heart was created using magnetic resonance images of the beating pig heart. This model was loaded by the pressure of blood inside the left ventricle which was measured by synchronous catheterization. A recently developed structurally based constitutive model of the myocardium was incorporated in the finite element solver to model passive left ventricular myocardium. Additionally, an unloading algorithm originally designed for arteries was adapted to estimate the stress-free geometry of the heart from its partially-loaded geometry obtained from magnetic resonance imaging. Finally, a regionally varying growth module was added to the computational model to predict eccentric hypertrophy of the heart under various pathological conditions that result in volume overload of the heart. The computational model was validated using experimental data obtained from porcine heart such as in vivo strains measured from magnetic resonance imaging

A modified Holzapfel-Ogden law for a residually stressed finite strain model of the human left ventricle in diastole

In this work, we introduce a modified Holzapfel-Ogden hyperelastic constitutive model for ventricular myocardium that accounts for residual stresses, and we investigate the effects of residual stresses in diastole using a magnetic resonance imaging–derived model of the human left ventricle (LV). We adopt an invariant-based constitutive modelling approach and treat the left ventricular myocardium as a non-homogeneous, fibre-reinforced, incompressible material. Because in vivo images provide the configuration of the LV in a loaded state even in diastole, an inverse analysis is used to determine the corresponding unloaded reference configuration. The residual stress in this unloaded state is estimated by two different methods. One is based on three-dimensional strain measurements in a local region of the canine LV, and the other uses the opening angle method for a cylindrical tube. We find that including residual stress in the model changes the stress distributions across the myocardium and that whereas both methods yield qualitatively similar changes, there are quantitative differences between the two approaches. Although the effects of residual stresses are relatively small in diastole, the model can be extended to explore the full impact of residual stress on LV mechanical behaviour for the whole cardiac cycle as more experimental data become available. In addition, although not considered here, residual stresses may also play a larger role in models that account for tissue growth and remodelling

Unraveling the complexity of vascular tone regulation: a multiscale computational approach to integrating chemo-mechano-biological pathways with cardiovascular biomechanics

Vascular tone regulation is a crucial aspect of cardiovascular physiology, with significant implications for overall cardiovascular health. However, the precise physiological mechanisms governing smooth muscle cell contraction and relaxation remain uncertain. The complexity of vascular tone regulation stems from its multiscale and multifactorial nature, involving global hemodynamics, local flow conditions, tissue mechanics, and biochemical pathways. Bridging this knowledge gap and translating it into clinical practice presents a challenge. In this paper, a computational model is presented to integrate chemo-mechano-biological pathways with cardiovascular biomechanics, aiming to unravel the intricacies of vascular tone regulation. The computational framework combines an algebraic description of global hemodynamics with detailed finite element analyses at the scale of vascular segments for describing their passive and active mechanical response, as well as the molecular transport problem linked with chemo-biological pathways triggered by wall shear stresses. Their coupling is accounted for by considering a two-way interaction. Specifically, the focus is on the role of nitric oxide-related molecular pathways, which play a critical role in modulating smooth muscle contraction and relaxation to maintain vascular tone. The computational framework is employed to examine the interplay between localized alterations in the biomechanical response of a specific vessel segment—such as those induced by calcifications or endothelial dysfunction–and the broader global hemodynamic conditions—both under basal and altered states. The proposed approach aims to advance our understanding of vascular tone regulation and its impact on cardiovascular health. By incorporating chemo-mechano-biological mechanisms into in silico models, this study allows us to investigate cardiovascular responses to multifactorial stimuli and incorporate the role of adaptive homeostasis in computational biomechanics frameworks

Guidewire-mounted thermal sensors to assess coronary hemodynamics

The vessels of the coronary circulation are prone to arteriosclerotic disease, which can lead to the development of obstructions to blood flow. The conventional way to diagnose the severity of this type of disease is by coronary angiography. This method, however, only provides insight into the morphology of the coronary vessels, whereas for an accurate diagnosis a measure for the actual flow impediment is needed. To perform these measurements, sensor-tipped guidewires have been developed to measure intra-coronary pressure and blood flow velocity. Diagnosis of coronary disease based on the time-average of these measurements have been shown to improve the clinical outcome of treatment significantly. However, since the coronary vessels are embedded in the (contracting) cardiac muscle, the interpretation of these indices is complicated and can be improved by simultaneously assessing the dynamics of coronary pressure and flow. The research described in this thesis therefore focusses on the one hand on developing devices for the simultaneous assessment of coronary pressure and flow dynamics and on the other hand on modeling the heart and coronary vessels to support the interpretation of these dynamic measurements. In the development of a device which can measure both coronary pressure and flow, two different strategies have been chosen. In the first strategy, a method has been developed to operate an already clinically used pressure sensor-tipped guidewire (pressure wire) as a thermal anemometer to also measure flow. In an in-vitro model it has been demonstrated that the power required to electrically heat the sensor is a measure for the shear rate at the sensor surface and that the method can be used to assess coronary flow reserve (CFR). By slightly adapting the method and combining it with a continuous thermodilution method, it has also been shown that the dynamics of both pressure and volumetric flow can be measured simultaneously in physiological representative in-vitro and ex-vivo experiments. The main drawbacks of this thermal method with a pressure wire are the relatively high sensor temperature required and the inability to detect flow reversal. In the second strategy, a new flow sensor, embedded in a flexible polyimide chip, has been specially designed to be mounted on a guidewire. The flow sensing element consists of a heater, operated at constant power, and thermocouples measuring the temperature difference up- and downstream from the heater. To gain insight into the working principle and the importance of the different design parameters, an analytical model has been developed. Experiments where upscaled sensors have been subjected to steady and pulsatile flow, indicate that the model is able to reproduce the experimental results fairly well but that the sensitivity to shear rate is rather limited in the physiological range. This sensitivity to shear rate can possibly be improved by operating the heater at constant temperature, which has been investigated with invitro experiments with upscaled sensors and a finite element analysis of the real, small size sensor. These studies have demonstrated that constant temperature operation of the heater is beneficial over constant power operation and that the dynamics of physiological coronary shear rate, including retrograde flow, can be assessed at an overheat temperature of only 5 K. From these characterization studies a new design of the sensor has been proposed, which is currently being manufactured to be tested in both in-vitro and ex-vivo experiments. To support the interpretation of the dynamic pressure and flow measurements, a numerical model of the heart and coronary circulation has been developed. The model is based on the coupling of four interacting parts: A model for the left ventricle which is based on the mechanics of a single myofiber, a 1D wave propagation model for the large epicardial coronary arteries, a stenosis element, and a Windkessel representation of the coronary micro-vessels. Comparison of the results obtained with the model with experimental observations described in literature has shown that the model is able to simulate the effect of different types of disease on coronary hemodynamics. After further validation, the model can be used as a tool to study the effect of combinations of epicardial and/or microcirculatory disease on pressure- and flow-based indices. To model the relation between the pressure and flow waves in the coronary arteries correctly, as well as to assist in the decision-making regarding the mechanical treatment of coronary stenoses, the mechanical behaviour of the coronary arterial wall is required. Therefore, a mixed numerical-experimental method has been employed to fit a micro-structurally based constitutive model to in-situ extensioninflation experiments on porcine coronary arteries. It has been demonstrated that the model can accurately describe the experimental data and, additionally, it has been found that the most influential parameter, describing the collagen fiber orientation, can be considered constant at physiological loading. In further research, this can be used to tackle over-parameterization issues inherent to fitting similar constitutive models to data obtained in a clinical setting. In this thesis, a computational model of the coronary circulation is presented and methods for simultaneous pressure and flow assessment are introduced. By operating an already clinically used pressure wire as a thermal anemometer, a methodology was developed which is close to clinical application, while a new sensor was designed to be more accurate in different flow conditions

Non-invasive in silico determination of ventricular wall pre-straining and characteristic cavity pressures

The clinical application of patient-specific modelling of the heart can provide valuable insights in supplementing and advancing methods of diagnosis as well as helping to devise the best possible therapeutic approach for each individual pathological heart condition. The potential of computational cardiac mechanics, however, has not yet been fully leveraged due to the heart's complex physiology and limitations in the non-invasive in vivo characterisation of heart properties necessary required for accurate patient-specific modelling such as the heart anatomy in an unloaded state, ventricular pressure, the elastic constitutive parameters and the myocardial muscle fibre orientation distribution. From a solid mechanics point of view without prior knowledge of the unloaded heart configuration and the cavity pressure-volume evolution, in particular, the constitutive parameters cannot be accurately estimated to describe the highly nonlinear elastic material behaviour of myocardial tissue. Here, knowledge of the volume-normalized end-diastolic pressure relation for larger mammals is exploited in combination with a novel iterative inverse parameter optimisation framework to determine end-systolic and end diastolic pressures, ventricular wall pre-straining and pre-stressing due the residual end-systolic cavity pressure as well as myocardial tissue stiffness parameters for biventricular heart models