Image based computational modeling of intracardiac flows

With continuous advancements in four-dimensional medical imaging technologies, increasing computational speeds, and widespread availability of high performance computing facilities, computational modeling of intracardiac flows is becoming increasingly viable and has the potential to become a powerful non-invasive diagnostic tool for the diagnosis and treatment of cardiovascular disease. The motive of the current study is to develop a modeling framework that facilitates image-based analysis of intracardiac flows in health as well as disease and to use this framework to gain fundamental insights into intracardiac hemodynamics. A procedure is developed for constructing computational fluid dynamics (CFD) – ready models from in vivo imaging data. The key components of this procedure are the registration and segmentation of the 4D data for several (~20) key frames, template based mapping to ensure surface grid conformality and high-fidelity simulations using a sharp-interface immersed boundary solver. A physiologically representative, kinematic model of the mitral valve is also developed for use in these simulations. As a precursor, a comprehensive quantitative validation of the flow solver is performed using experimental data in a simple model of the left ventricle. A quantitative comparison of the phase-averaged velocity and vorticity fields between the simulation and the experiment shows a reasonable agreement. The detailed assessment of this comparison is used to identify and discuss the key challenges and uncertainties associated in conducting such a validation study. The vast majority of computational investigations of intracardiac flows have focused either on the left or the right ventricles while the corresponding atria were modeled in highly simplistic ways. However, the impact of this simplification on the hemodynamics of the ventricular filling has not been clearly understood. Additionally, the surface of the ventricle has been assumed to be smooth although it is well known that the left ventricle is highly corrugated with surface protrusions or trabeculae and papillary muscles extending deep into the ventricular cavity. Hence, separate studies were conducted to understand the effect of complex atrial flows on the intraventricular flow development and also to understand and quantify the impact of the trabeculae and papillary muscles on ventricular hemodynamics Results indicate that the trabeculae and papillary muscles significantly impact ventricular flow resulting in a deeper penetration of the mitral jet into the ventricle during filling. These anatomical features are also found to produce a “squeezing” effect that enhances apical washout. It is also demonstrated that the complex flow dynamics developed inside the left atrium have minimal influence on the flow inside the left ventricle, which is primarily governed by the mitral valve leaflets configuration. The complex vortical structures inside the left atrium are rapidly dissipated due to the complex interaction of multiple vortex rings leading to breakup, annihilation and enhanced viscous dissipation so that the flow is smoothly streamlined as it enters the mitral orifice and produces a near-uniform velocity profile at the level of the mitral annulus. The implications of these findings on the modeling of the intra-ventricular flows are also discussed

A Modular Framework for Implicit 3D-0D Coupling in Cardiac Mechanics

In numerical simulations of cardiac mechanics, coupling the heart to a model of the circulatory system is essential for capturing physiological cardiac behavior. A popular and efficient technique is to use an electrical circuit analogy, known as a lumped parameter network or zero-dimensional (0D) fluid model, to represent blood flow throughout the cardiovascular system. Due to the strong physical interaction between the heart and the blood circulation, developing accurate and efficient numerical coupling methods remains an active area of research. In this work, we present a modular framework for implicitly coupling three-dimensional (3D) finite element simulations of cardiac mechanics to 0D models of blood circulation. The framework is modular in that the circulation model can be modified independently of the 3D finite element solver, and vice versa. The numerical scheme builds upon a previous work that combines 3D blood flow models with 0D circulation models (3D fluid - 0D fluid). Here, we extend it to couple 3D cardiac tissue mechanics models with 0D circulation models (3D structure - 0D fluid), showing that both mathematical problems can be solved within a unified coupling scheme. The effectiveness, temporal convergence, and computational cost of the algorithm are assessed through multiple examples relevant to the cardiovascular modeling community. Importantly, in an idealized left ventricle example, we show that the coupled model yields physiological pressure-volume loops and naturally recapitulates the isovolumic contraction and relaxation phases of the cardiac cycle without any additional numerical techniques. Furthermore, we provide a new derivation of the scheme inspired by the Approximate Newton Method of Chan (1985), explaining how the proposed numerical scheme combines the stability of monolithic approaches with the modularity and flexibility of partitioned approaches

Simulating Developmental Cardiac Morphology in Virtual Reality Using a Deformable Image Registration Approach

While virtual reality (VR) has potential in enhancing cardiovascular diagnosis and treatment, prerequisite labor-intensive image segmentation remains an obstacle for seamlessly simulating 4-dimensional (4-D, 3-D + time) imaging data in an immersive, physiological VR environment. We applied deformable image registration (DIR) in conjunction with 3-D reconstruction and VR implementation to recapitulate developmental cardiac contractile function from light-sheet fluorescence microscopy (LSFM). This method addressed inconsistencies that would arise from independent segmentations of time-dependent data, thereby enabling the creation of a VR environment that fluently simulates cardiac morphological changes. By analyzing myocardial deformation at high spatiotemporal resolution, we interfaced quantitative computations with 4-D VR. We demonstrated that our LSFM-captured images, followed by DIR, yielded average dice similarity coefficients of 0.92 ± 0.05 (n = 510) and 0.93 ± 0.06 (n = 240) when compared to ground truth images obtained from Otsu thresholding and manual segmentation, respectively. The resulting VR environment simulates a wide-angle zoomed-in view of motion in live embryonic zebrafish hearts, in which the cardiac chambers are undergoing structural deformation throughout the cardiac cycle. Thus, this technique allows for an interactive micro-scale VR visualization of developmental cardiac morphology to enable high resolution simulation for both basic and clinical science

Spatial and temporal variations in hemodynamic forces initiate cardiac trabeculation

Hemodynamic shear force has been implicated as modulating Notch signaling-mediated cardiac trabeculation. Whether the spatiotemporal variations in wall shear stress (WSS) coordinate the initiation of trabeculation to influence ventricular contractile function remains unknown. Using light-sheet fluorescent microscopy, we reconstructed the 4D moving domain and applied computational fluid dynamics to quantify 4D WSS along the trabecular ridges and in the groves. In WT zebrafish, pulsatile shear stress developed along the trabecular ridges, with prominent endocardial Notch activity at 3 days after fertilization (dpf), and oscillatory shear stress developed in the trabecular grooves, with epicardial Notch activity at 4 dpf. Genetic manipulations were performed to reduce hematopoiesis and inhibit atrial contraction to lower WSS in synchrony with attenuation of oscillatory shear index (OSI) during ventricular development. γ-Secretase inhibitor of Notch intracellular domain (NICD) abrogated endocardial and epicardial Notch activity. Rescue with NICD mRNA restored Notch activity sequentially from the endocardium to trabecular grooves, which was corroborated by observed Notch-mediated cardiomyocyte proliferations on WT zebrafish trabeculae. We also demonstrated in vitro that a high OSI value correlated with upregulated endothelial Notch-related mRNA expression. In silico computation of energy dissipation further supports the role of trabeculation to preserve ventricular structure and contractile function. Thus, spatiotemporal variations in WSS coordinate trabecular organization for ventricular contractile function

Spatial and temporal variations in hemodynamic forces initiate cardiac trabeculation

Hemodynamic shear force has been implicated as modulating Notch signaling-mediated cardiac trabeculation. Whether the spatiotemporal variations in wall shear stress (WSS) coordinate the initiation of trabeculation to influence ventricular contractile function remains unknown. Using light-sheet fluorescent microscopy, we reconstructed the 4D moving domain and applied computational fluid dynamics to quantify 4D WSS along the trabecular ridges and in the groves. In WT zebrafish, pulsatile shear stress developed along the trabecular ridges, with prominent endocardial Notch activity at 3 days after fertilization (dpf), and oscillatory shear stress developed in the trabecular grooves, with epicardial Notch activity at 4 dpf. Genetic manipulations were performed to reduce hematopoiesis and inhibit atrial contraction to lower WSS in synchrony with attenuation of oscillatory shear index (OSI) during ventricular development. γ-Secretase inhibitor of Notch intracellular domain (NICD) abrogated endocardial and epicardial Notch activity. Rescue with NICD mRNA restored Notch activity sequentially from the endocardium to trabecular grooves, which was corroborated by observed Notch-mediated cardiomyocyte proliferations on WT zebrafish trabeculae. We also demonstrated in vitro that a high OSI value correlated with upregulated endothelial Notch-related mRNA expression. In silico computation of energy dissipation further supports the role of trabeculation to preserve ventricular structure and contractile function. Thus, spatiotemporal variations in WSS coordinate trabecular organization for ventricular contractile function

Fluid-structure interaction simulation of tissue degradation and its effects on intra-aneurysm hemodynamics

Tissue degradation plays a crucial role in vascular diseases such as atherosclerosis and aneurysms. Computational modeling of vascular hemodynamics incorporating both arterial wall mechanics and tissue degradation has been a challenging task. In this study, we propose a novel finite element method-based approach to model the microscopic degradation of arterial walls and its interaction with blood flow. The model is applied to study the combined effects of pulsatile flow and tissue degradation on the deformation and intra-aneurysm hemodynamics. Our computational analysis reveals that tissue degradation leads to a weakening of the aneurysmal wall, which manifests itself in a larger deformation and a smaller von Mises stress. Moreover, simulation results for different heart rates, blood pressures and aneurysm geometries indicate consistently that, upon tissue degradation, wall shear stress increases near the flow-impingement region and decreases away from it. These findings are discussed in the context of recent reports regarding the role of both high and low wall shear stress for the progression and rupture of aneurysms

On the potential self-amplification of aneurysms due to tissue degradation and blood flow revealed from FSI simulations

Tissue degradation plays a crucial role in the formation and rupture of aneurysms. Using numerical computer simulations, we study the combined effects of blood flow and tissue degradation on intra-aneurysm hemodynamics. Our computational analysis reveals that the degradation-induced changes of the time-averaged wall shear stress (TAWSS) and oscillatory shear index (OSI) within the aneurysm dome are inversely correlated. Importantly, their correlation is enhanced in the process of tissue degradation. Regions with a low TAWSS and a high OSI experience still lower TAWSS and higher OSI during degradation. Furthermore, we observed that degradation leads to an increase of the endothelial cell activation potential index, in particular, at places experiencing low wall shear stress. These findings are robust and occur for different geometries, degradation intensities, heart rates and pressures. We interpret these findings in the context of recent literature and argue that the degradation-induced hemodynamic changes may lead to a self-amplification of the flow-induced progressive damage of the aneurysmal wall

A method to quantify mechanobiologic forces during zebrafish cardiac development using 4-D light sheet imaging and computational modeling

<div><p>Blood flow and mechanical forces in the ventricle are implicated in cardiac development and trabeculation. However, the mechanisms of mechanotransduction remain elusive. This is due in part to the challenges associated with accurately quantifying mechanical forces in the developing heart. We present a novel computational framework to simulate cardiac hemodynamics in developing zebrafish embryos by coupling 4-D light sheet imaging with a stabilized finite element flow solver, and extract time-dependent mechanical stimuli data. We employ deformable image registration methods to segment the motion of the ventricle from high resolution 4-D light sheet image data. This results in a robust and efficient workflow, as segmentation need only be performed at one cardiac phase, while wall position in the other cardiac phases is found by image registration. Ventricular hemodynamics are then quantified by numerically solving the Navier-Stokes equations in the moving wall domain with our validated flow solver. We demonstrate the applicability of the workflow in wild type zebrafish and three treated fish types that disrupt trabeculation: (a) chemical treatment using AG1478, an <i>ErbB2</i> signaling inhibitor that inhibits proliferation and differentiation of cardiac trabeculation; (b) injection of <i>gata1a morpholino oligomer</i> (<i>gata1aMO</i>) suppressing hematopoiesis and resulting in attenuated trabeculation; (c) <i>weak-atrium</i>^<i>m</i>58 mutant (<i>wea</i>) with inhibited atrial contraction leading to a highly undeveloped ventricle and poor cardiac function. Our simulations reveal elevated wall shear stress (WSS) in wild type and AG1478 compared to <i>gata1aMO</i> and <i>wea</i>. High oscillatory shear index (OSI) in the grooves between trabeculae, compared to lower values on the ridges, in the wild type suggest oscillatory forces as a possible regulatory mechanism of cardiac trabeculation development. The framework has broad applicability for future cardiac developmental studies focused on quantitatively investigating the role of hemodynamic forces and mechanotransduction during morphogenesis.</p></div

Comparison of (a) area-averaged WSS (AAWSS) as a function of non-dimensional time, (b) time-averaged wall shear stress (AWSS), between the wild type zebrafish and in response to chemical (AG1478) and genetic (<i>gata1aMO</i>, <i>wea</i>) treatments.

<p>We also include an additional case for genetically treated <i>gata1aMO</i> with blood viscosity reduced by a factor of 4 (<i>gata1aMO</i>_<i>μ</i>1/4) to account for inhibited hematopoiesis.</p