A coupled chemo-fluidic computational model for thrombogenesis in infarcted left ventricles

Influence of the flow split ratio on the position of the main atrial vortex: Implications for stasis on the left atrial appendage

BACKGROUND

Despite the recent advances in computational fluid dynamics (CFD) techniques applied to blood flow within the left atrium (LA), the relationship between atrial geometry, flow patterns, and blood stasis within the left atrial appendage (LAA) remains unclear. A better understanding of this relationship would have important clinical implications, as thrombi originating in the LAA are a common cause of stroke in patients with atrial fibrillation (AF).

AIM

To identify the most representative atrial flow patterns on a patient-specific basis and study their influence on LAA blood stasis by varying the flow split ratio and some common atrial modeling assumptions.

METHODS

Three recent techniques were applied to nine patient-specific computational fluid dynamics (CFD) models of patients with AF: a kinematic atrial model to isolate the influence of wall motion because of AF, projection on a universal LAA coordinate system, and quantification of stagnant blood volume (SBV).

RESULTS

We identified three different atrial flow patterns based on the position of the center of the main circulatory flow. The results also illustrate how atrial flow patterns are highly affected by the flow split ratio, increasing the SBV within the LAA. As the flow split ratio is determined by the patient's lying position, the results suggest that the most frequent position adopted while sleeping may have implications for the medium- and long-term risks of stroke.

Efficient multi-fidelity computation of blood coagulation under flow

Clot formation is a crucial process that prevents bleeding, but can lead to severe disorders when imbalanced. This process is regulated by the coagulation cascade, a biochemical network that controls the enzyme thrombin, which converts soluble fibrinogen into the fibrin fibers that constitute clots. Coagulation cascade models are typically complex and involve dozens of partial differential equations (PDEs) representing various chemical species' transport, reaction kinetics, and diffusion. Solving these PDE systems computationally is challenging, due to their large size and multi-scale nature. We propose a multi-fidelity strategy to increase the efficiency of coagulation cascade simulations. Leveraging the slower dynamics of molecular diffusion, we transform the governing PDEs into ordinary differential equations (ODEs) representing the evolution of species concentrations versus blood residence time. We then Taylor-expand the ODE solution around the zero-diffusivity limit to obtain spatiotemporal maps of species concentrations in terms of the statistical moments of residence time, [Formula: see text], and provide the governing PDEs for [Formula: see text]. This strategy replaces a high-fidelity system of N PDEs representing the coagulation cascade of N chemical species by N ODEs and p PDEs governing the residence time statistical moments. The multi-fidelity order (p) allows balancing accuracy and computational cost providing a speedup of over N/p compared to high-fidelity models. Moreover, this cost becomes independent of the number of chemical species in the large computational meshes typical of the arterial and cardiac chamber simulations. Using a coagulation network with N = 9 and an idealized aneurysm geometry with a pulsatile flow as a benchmark, we demonstrate favorable accuracy for low-order models of p = 1 and p = 2. The thrombin concentration in these models departs from the high-fidelity solution by under 20% (p = 1) and 2% (p = 2) after 20 cardiac cycles. These multi-fidelity models could enable new coagulation analyses in complex flow scenarios and extensive reaction networks. Furthermore, it could be generalized to advance our understanding of other reacting systems affected by flow.

Critical evaluation of kinetic schemes for coagulation

Two well-established numerical representations of the coagulation cascade either initiated by the intrinsic system (Chatterjee et al., PLOS Computational Biology 2010) or the extrinsic system (Butenas et al., Journal of Biological Chemistry, 2004) were compared with thrombin generation assays under realistic pathological conditions. Biochemical modifications such as the omission of reactions not relevant to the case studied, the modification of reactions related to factor XI activation and auto-activation, the adaptation of initial conditions to the thrombin assay system, and the adjustment of some of the model parameters were necessary to align in vitro and in silico data. The modified models are able to reproduce thrombin generation for a range of factor XII, XI, and VIII deficiencies, with the coagulation cascade initiated either extrinsically or intrinsically. The results emphasize that when existing models are extrapolated to experimental parameters for which they have not been calibrated, careful adjustments are required.

Efficient multi-fidelity computation of blood coagulation under flow

Clot formation is a crucial process that prevents bleeding, but can lead to severe disorders when imbalanced. This process is regulated by the coagulation cascade, a biochemical network that controls the enzyme thrombin, which converts soluble fibrinogen into the fibrin fibers that constitute clots. Coagulation cascade models are typically complex and involve dozens of partial differential equations (PDEs) representing various chemical species' transport, reaction kinetics, and diffusion. Solving these PDE systems computationally is challenging, due to their large size and multi-scale nature. We propose a multi-fidelity strategy to increase the efficiency of coagulation cascade simulations. Leveraging the slower dynamics of molecular diffusion, we transform the governing PDEs into ordinary differential equations (ODEs) representing the evolution of species concentrations versus blood residence time. We then Taylor-expand the ODE solution around the zero-diffusivity limit to obtain spatiotemporal maps of species concentrations in terms of the statistical moments of residence time, , and provide the governing PDEs for . This strategy replaces a high-fidelity system of N PDEs representing the coagulation cascade of N chemical species by N ODEs and p PDEs governing the residence time statistical moments. The multi-fidelity order( p ) allows balancing accuracy and computational cost, providing a speedup of over N/p compared to high-fidelity models. Using a simplified coagulation network and an idealized aneurysm geometry with a pulsatile flow as a benchmark, we demonstrate favorable accuracy for low-order models of p = 1 and p = 2. These models depart from the high-fidelity solution by under 16% ( p = 1) and 5% ( p = 2) after 20 cardiac cycles. The favorable accuracy and low computational cost of multi-fidelity models could enable unprecedented coagulation analyses in complex flow scenarios and extensive reaction networks. Furthermore, it can be generalized to advance our understanding of other systems biology networks affected by blood flow.

Model reduction of coagulation cascade based on genetic algorithm

Fibrin is an important product of the coagulation cascade, and plays an eminent role in platelet stabilization. Since coagulation cascade models typically involve the reaction kinetics of dozens of proteins, which will incur burdensome computational costs when coupled to blood flow in complex geometries, researchers often ignore this process when constructing thrombosis models. However, previous studies have shown that fundamental aspects of coagulation can be reproduced with simpler models, which motivated us to obtain a reduced-order model of fibrin generation through a systematic approach. Therefore, we introduced a semi-automatic framework to perform model-reduction of cascade reactions in this study, which consisted of two processes. Specifically, the retained protein species and cascade reactions were determined based on published studies and simulation results from the full cascade model, while the optimal reaction rates for the new cascade network were determined using a genetic algorithm. The framework has been applied to a 19-species coagulation model that triggers fibrin generation in internal fields via reactive boundaries, and a 10-species reduced-order model was obtained to reproduce the kinetics of fibrinogenesis in the full cascade model at different boundary tissue factor concentrations. This reduced-order model of fibrinogenesis would be valuable for thrombosis modeling that considers both the coagulation cascade and platelet activity. Furthermore, the framework proposed herein can also be applied to the reductions of other cascade reaction models.

Computational Methods for Fluid-Structure Interaction Simulation of Heart Valves in Patient-Specific Left Heart Anatomies

Given the complexity of human left heart anatomy and valvular structures, the fluid–structure interaction (FSI) simulation of native and prosthetic valves poses a significant challenge for numerical methods. In this review, recent numerical advancements for both fluid and structural solvers for heart valves in patient-specific left hearts are systematically considered, emphasizing the numerical treatments of blood flow and valve surfaces, which are the most critical aspects for accurate simulations. Numerical methods for hemodynamics are considered under both the continuum and discrete (particle) approaches. The numerical treatments for the structural dynamics of aortic/mitral valves and FSI coupling methods between the solid Ωs and fluid domain Ωf are also reviewed. Future work toward more advanced patient-specific simulations is also discussed, including the fusion of high-fidelity simulation within vivo measurements and physics-based digital twining based on data analytics and machine learning techniques.

Computational Modeling of Drug Dissolution in the Human Stomach

A computational model of drug dissolution in the human stomach is developed to investigate the interaction between gastric flow and orally administrated drug in the form of a solid tablet. The stomach model is derived from the anatomical imaging data and the motion and dissolution of the drug in the stomach are modeled via fluid-structure interaction combined with mass transport simulations. The effects of gastric motility and the associated fluid dynamics on the dissolution characteristics are investigated. Two different pill densities are considered to study the effects of the gastric flow as well as the gravitational force on the motion of the pill. The average mass transfer coefficient and the spatial distributions of the dissolved drug concentration are analyzed in detail. The results show that the retropulsive jet and recirculating flow in the antrum generated by the antral contraction wave play an important role in the motion of the pill as well as the transport and mixing of the dissolved drug concentration. It is also found that the gastric flow can increase the dissolution mass flux, especially when there is substantial relative motion between the gastric flow and the pill.

Multi-constituent simulation of thrombus formation at LVAD inlet cannula connection: Importance of Virchow's triad

As pump thrombosis is reduced in current-generation ventricular assist devices (VAD), adverse events such as bleeding or stroke remain at unacceptable rates. Thrombosis around the VAD inlet cannula (IC) has been highlighted as a possible source of stroke events. Recent computational fluid dynamics (CFD) studies have attempted to characterize the thrombosis risk of different IC-ventricle configurations. However, purely CFD simulations relate thrombosis risk to ad hoc criteria based on flow characteristics, with little consideration of biochemical factors. This study investigates the genesis of IC thrombosis including two elements of the Virchow's triad: endothelial injury and hypercoagulability. To this end a multi-scale thrombosis simulation that includes platelet activity and coagulation reactions was performed. Our results show significant thrombin formation in stagnation regions (|u| < 0.005 m/s) close to the IC wall. In addition, high shear-mediated platelet activation was observed over the leading-edge tip of the cannula. The current study reveals the importance of biochemical factors to the genesis of thrombosis at the ventricular-cannula junction in a perioperative state. This study is a first step toward the long-term objective of including clinically relevant pharmacological kinetics such as heparin or aspirin in simulations of inflow cannula thrombosis.

Demonstration of Patient-Specific Simulations to Assess Left Atrial Appendage Thrombogenesis Risk

Atrial fibrillation (AF) alters left atrial (LA) hemodynamics, which can lead to thrombosis in the left atrial appendage (LAA), systemic embolism and stroke. A personalized risk-stratification of AF patients for stroke would permit improved balancing of preventive anticoagulation therapies against bleeding risk. We investigated how LA anatomy and function impact LA and LAA hemodynamics, and explored whether patient-specific analysis by computational fluid dynamics (CFD) can predict the risk of LAA thrombosis. We analyzed 4D-CT acquisitions of LA wall motion with an in-house immersed-boundary CFD solver. We considered six patients with diverse atrial function, three with either a LAA thrombus (removed digitally before running the simulations) or a history of transient ischemic attacks (LAAT/TIA-pos), and three without a LAA thrombus or TIA (LAAT/TIA-neg). We found that blood inside the left atrial appendage of LAAT/TIA-pos patients had marked alterations in residence time and kinetic energy when compared with LAAT/TIA-neg patients. In addition, we showed how the LA conduit, reservoir and booster functions distinctly affect LA and LAA hemodynamics. Finally, fixed-wall and moving-wall simulations produced different LA hemodynamics and residence time predictions for each patient. Consequently, fixed-wall simulations risk-stratified our small cohort for LAA thrombosis worse than moving-wall simulations, particularly patients with intermediate LAA residence time. Overall, these results suggest that both wall kinetics and LAA morphology contribute to LAA blood stasis and thrombosis.

An Introductory Overview of Image-Based Computational Modeling in Personalized Cardiovascular Medicine

Cardiovascular diseases account for the number one cause of deaths in the world. Part of the reason for such grim statistics is our limited understanding of the underlying mechanisms causing these devastating pathologies, which is made difficult by the invasiveness of the procedures associated with their diagnosis (e.g., inserting catheters into the coronal artery to measure blood flow to the heart). Likewise, it is also difficult to design and test assistive devices without implanting them in vivo. However, with the recent advancements made in biomedical scanning technologies and computer simulations, image-based modeling (IBM) has arisen as the next logical step in the evolution of non-invasive patient-specific cardiovascular medicine. Yet, due to its novelty, it is still relatively unknown outside of the niche field. Therefore, the goal of this manuscript is to review the current state-of-the-art and the limitations of the methods used in this area of research, as well as their applications to personalized cardiovascular investigations and treatments. Specifically, the modeling of three different physics – electrophysiology, biomechanics and hemodynamics – used in the cardiovascular IBM is discussed in the context of the physiology that each one of them describes and the mechanisms of the underlying cardiac diseases that they can provide insight into. Only the “bare-bones” of the modeling approaches are discussed in order to make this introductory material more accessible to an outside observer. Additionally, the imaging methods, the aspects of the unique cardiac anatomy derived from them, and their relation to the modeling algorithms are reviewed. Finally, conclusions are drawn about the future evolution of these methods and their potential toward revolutionizing the non-invasive diagnosis, virtual design of treatments/assistive devices, and increasing our understanding of these lethal cardiovascular diseases.

Analysis of mitral valve regurgitation by computational fluid dynamics

The clinical syndrome of mitral insufficiency is a common consequence of mitral valve (MV) prolapse, when the MV leaflets do not seal the closed orifice and blood regurgitates back to the atrium during ventricular contraction. There are different types of MV prolapse that may influence the degree of regurgitation also in relation to the left ventricle (LV) geometry. This study aims to provide some insight into the fluid dynamics of MV insufficiency in view of improving the different measurements available in the clinical setting. The analysis is performed by a computational fluid dynamics model coupled with an asymptotic model of the MV motion. The computational fluid dynamics solution uses the immersed boundary method that is efficiently integrated with clinical imaging technologies. Healthy and dilated LVs obtained by multislice cardiac MRI are combined with simplified models of healthy and pathological MVs deduced from computed tomography and 4D-transesophageal echocardiography. The results demonstrated the properties of false regurgitation, blood that did not cross the open MV orifice and returns into the atrium during the backward motion of the MV leaflets, whose entity should be accounted when evaluating small regurgitation. The regurgitating volume is found to be proportional to the effective orifice area, with the limited dependence of the LV geometry and type of prolapse. These affect the percentage of old blood returning to the atrium which may be associated with thrombogenic risk.

Flow Dynamics in the Aortic Arch and Its Effect on the Arterial Input Function in Cardiac Computed Tomography

The arterial input function (AIF)-time-density curve (TDC) of contrast at the coronary ostia-plays a central role in contrast enhanced computed tomography angiography (CTA). This study employs computational modeling in a patient-specific aorta to investigate mixing and dispersion of contrast in the aortic arch (AA) and to compare the TDCs in the coronary ostium and the descending aorta. Here, we examine the validity of the use of TDC in the descending aorta as a surrogate for the AIF. Computational fluid dynamics was used to study hemodynamics and contrast dispersion in a CTA-based patient model of the aorta. Variations in TDC between the aortic root, through the AA and at the descending aorta and the effect of flow patterns on contrast dispersion was studied via post-processing of the results. Simulations showed complex unsteady patterns of contrast mixing and dispersion in the AA that are driven by the pulsatile flow. However, despite the relatively long intra-aortic distance between the coronary ostia and the descending aorta, the TDCs at these two locations were similar in terms of rise-time and up-slope, and the time lag between the two TDCs was 0.19 seconds. TDC in the descending aorta is an accurate analog of the AIF. Methods that use quantitative metrics such as rise-time and slope of the AIF to estimate coronary flowrate and myocardial ischemia can continue with the current practice of using the TDC at the descending aorta as a surrogate for the AIF.

Finite element modeling of near-wall mass transport in cardiovascular flows

Many cardiovascular processes involve mass transport between blood and the vessel wall. Finite element methods are commonly used to numerically simulate these processes. Cardiovascular mass transport problems are typically characterized by high Péclet numbers, requiring fine near-wall mesh resolution as well as the use of stabilization techniques to avoid numerical instabilities. In this work, we develop a set of guidelines for solving high-Péclet-number near-wall mass transport problems using the finite element method. We use a steady, idealized test case to investigate the required mesh resolution and finite element basis order to accurately capture near-wall concentration boundary layers, as well as the performance of several commonly used stabilization techniques. Linear tetrahedral meshes were found to outperform quadratic tetrahedral meshes of equivalent degrees of freedom, and the commonly used discontinuity-capturing stabilization technique was found to be overly diffusive for these types of problems. Best practices derived from the idealized test case were then applied to a typical patient-specific vascular blood flow modeling application, where it was found that the commonly applied technique of avoiding numerical difficulties by artificially increasing mass diffusivity provides qualitatively similar but quantitatively erroneous results.

A Highly Automated Computational Method for Modeling of Intracranial Aneurysm Hemodynamics

Intracranial aneurysms manifest in a vast variety of morphologies and their growth and rupture risk are subject to patient-specific conditions that are coupled with complex, non-linear effects of hemodynamics. Thus, studies that attempt to understand and correlate rupture risk to aneurysm morphology have to incorporate hemodynamics, and at the same time, address a large enough sample size so as to produce reliable statistical correlations. In order to perform accurate hemodynamic simulations for a large number of aneurysm cases, automated methods to convert medical imaging data to simulation-ready configuration with minimal (or no) human intervention are required. In the present study, we develop a highly-automated method based on the immersed boundary method framework to construct computational models from medical imaging data which is the key idea is the direct use of voxelized contrast information from the 3D angiograms to construct a level-set based computational “mask” for the hemodynamic simulation. Appropriate boundary conditions are provided to the mask and the dynamics of blood flow inside the vessels and aneurysm is simulated by solving the Navier-Stokes equations on the Cartesian grid using the sharp-interface immersed boundary method. The present method does not require body conformal surface/volume mesh generation or other intervention for model clean-up. The viability of the proposed method is demonstrated for a number of distinct aneurysms derived from actual, patient-specific data.

Optimized Time-Resolved Echo Particle Image Velocimetry– Particle Tracking Velocimetry Measurements Elucidate Blood Flow in Patients With Left Ventricular Thrombus

Contrast ultrasound is a widely used clinical tool to obtain real-time qualitative blood flow assessments in the heart, liver, etc. Echocardiographic particle image velocimetry (echo-PIV) is a technique for obtaining quantitative velocity maps from contrast ultrasound images. However, unlike optical particle image velocimetry (PIV), routine echo images are prone to nonuniform spatiotemporal variations in tracer distribution, making analysis difficult for standard PIV algorithms. This study introduces optimized procedures that integrate image enhancement, PIV, and particle tracking velocimetry (PTV) to obtain reliable time-resolved two-dimensional (2D) velocity distributions. During initial PIV analysis, multiple results are obtained by varying processing parameters. Optimization involving outlier removal and smoothing is used to select the correct vector. These results are used in a multiparameter PTV procedure. To demonstrate their clinical value, the procedures are implemented to obtain velocity and vorticity distributions over multiple cardiac cycles using images acquired from four left ventricular thrombus (LVT) patients. Phase-averaged data elucidate flow structure evolution over the cycle and are used to calculate penetration depth and strength of left ventricular (LV) vortices, as well as apical velocity induced by them. The present data are consistent with previous time-averaged results for the minimum vortex penetration depth associated with LVT occurrence. However, due to decay and fragmentation of LV vortices, as they migrate away from the mitral annulus, in two cases with high penetration, there is still poor washing near the resolved clot throughout the cycle. Hence, direct examination of entire flow evolution may be useful for assessing risk of LVT relapse before prescribing anticoagulants.

Comprehensive computational assessment of blood flow characteristics of left ventricle based on in-vivo MRI in presence of artificial myocardial infarction

BACKGROUND

Understanding the effects of cardiac diseases on the heart's functionality which is the purpose of many biomedical researches, directly affects the diagnostic and therapeutic methods. Myocardial infarction (MI) is a common complication of cardiac ischemia, however, the impact of MI on the left ventricle (LV) flow patterns has not been widely considered by computational fluid dynamics studies thus far.

METHODS

In this study, we present an insightful numerical method that creates an artificial MI on an image-based fluid-structure interactional model of normal LV to investigate its influence on the flow in comparison with the normal case. Seventeen different models were developed to evaluate the effects of location, percentage, myocardial material properties and dilation size of MI on the LV's performance, area strain, wall displacement, pressure-volume loop, wall shear stress and velocity field.

RESULTS

The results show that MI considerably changes blood flow features which are fully dependent on MI parameters. For the case of constant MI location, the effect of a decrease of infarcted myocardium stiffness, increase of dilation size and increase of MI percentage are mostly similar. Although the location differences of MI under other constant conditions have similar impact on the ejection fraction, they also lead to dissimilar variations in the LV flow pattern and other indicators.

CONCLUSIONS

The presented model showed a capable computational method for investigating various mechanical MI conditions with respect to cardiac flow pattern. The perspective of this model development seems to be an applicable tool for MI clinical diagnosis and prediction of complications related to MI.

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

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 ErbB2 signaling inhibitor that inhibits proliferation and differentiation of cardiac trabeculation; (b) injection of gata1a morpholino oligomer (gata1aMO) suppressing hematopoiesis and resulting in attenuated trabeculation; (c) weak-atriumm58 mutant (wea) 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 gata1aMO and wea. 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.