Multiphysics computational models for cardiac flow and virtual cardiography

A 3D scaling law for supravalvular aortic stenosis suited for stethoscopic auscultations

In this study a frequency scaling law for 3D anatomically representative supravalvular aortic stenosis (SVAS) cases is proposed. The law is uncovered for stethoscopy's preferred auscultation range (70-120 Hz). LES simulations are performed on the CFD solver Fluent, leveraging Simulia's Living Heart Human Model (LHHM), modified to feature hourglass stenoses that range between 30 to 80 percent (mild to severe) in addition to the descending aorta. For physiological hemodynamic boundary conditions the Windkessel model is implemented via a UDF subroutine. The flow-generated acoustic signal is then extracted using the FW-H model and analyzed using FFT. A preferred receiver location that matches clinical practice is confirmed (right intercostal space) and a correlation between the degree of stenosis and a corresponding acoustic frequency is obtained. Five clinical auscultation signals are tested against the scaling law, with the findings interpreted in relation to the NHS classification of stenosis and to the assessments of experienced cardiologists. The scaling law is thus shown to succeed as a potential quantitative decision-support tool for clinicians, enabling them to reliably interpret stethoscopic auscultations for all degrees of stenosis, which is especially useful for moderate degrees of SVAS. Computational investigation of more complex stenotic cases would enhance the clinical relevance of this proposed scaling law, and will be explored in future research.

A CFD-FFT approach to hemoacoustics that enables degree of stenosis prediction from stethoscopic signals

In this paper, we identify a new (acoustic) frequency-stenosis relation whose frequencies lie within the recommended auscultation threshold of stethoscopy (< 120 Hz). We show that this relation can be used to extend the application of phonoangiography (quantifying the degree of stenosis from bruits) to widely accessible stethoscopes. The relation is successfully identified from an analysis restricted to the acoustic signature of the von Karman vortex street, which we automatically single out by means of a metric we propose that is based on an area-weighted average of the Q-criterion for the post-stenotic region. Specifically, we perform CFD simulations on internal flow geometries that represent stenotic blood vessels of different severities. We then extract their emitted acoustic signals using the Ffowcs Williams-Hawkings equation, which we subtract from a clean signal (stenosis free) at the same heart rate. Next, we transform this differential signal to the frequency domain and carefully classify its acoustic signatures per six (stenosis-)invariant flow phases of a cardiac cycle that are newly identified in this paper. We then automatically restrict our acoustic analysis to the sounds emitted by the von Karman vortex street (phase 4) by means of our Q-criterion-based metric. Our analysis of its acoustic signature reveals a strong linear relationship between the degree of stenosis and its dominant frequency, which differs considerably from the break frequency and the heart rate (known dominant frequencies in the literature). Applying our new relation to available stethoscopic data, we find that its predictions are consistent with clinical assessment. Our finding of this linear correlation is also unlike prevalent scaling laws in the literature, which feature a small exponent (i.e., low stenosis percentage sensitivity over much of the clinical range). They hence can only distinguish mild, moderate, and severe cases. Conversely, our linear law can identify variations in the degree of stenosis sensitively and accurately for the full clinical range, thus significantly improving the utility of the relevant scaling laws... Future research will investigate incorporating the vibroacoustic role of adjacent organs to expand the clinical applicability of our findings. Extending our approach to more complex 3D stenotic morphologies and including the vibroacoustic role of surrounding organs will be explored in future research to advance the clinical reach of our findings.

Direct 0D-3D coupling of a lattice Boltzmann methodology for fluid-structure aortic flow simulations

This work introduces a numerical approach and implementation for the direct coupling of arbitrary complex ordinary differential equation- (ODE-)governed zero-dimensional (0D) boundary conditions to three-dimensional (3D) lattice Boltzmann-based fluid-structure systems for hemodynamics studies. In particular, a most complex configuration is treated by considering a dynamic left ventricle- (LV-)elastance heart model which is governed by (and applied as) a nonlinear, non-stationary hybrid ODE-Dirichlet system. Other ODE-based boundary conditions, such as lumped parameter Windkessel models for truncated vasculature, are also considered. Performance studies of the complete 0D-3D solver, including its treatment of the lattice Boltzmann fluid equations and elastodynamics equations as well as their interactions, is conducted through a variety of benchmark and convergence studies that demonstrate the ability of the coupled 0D-3D methodology in generating physiological pressure and flow waveforms-ultimately enabling the exploration of various physical and physiological parameters for hemodynamics studies of the coupled LV-arterial system. The methods proposed in this paper can be easily applied to other ODE-based boundary conditions as well as to other fluid problems that are modeled by 3D lattice Boltzmann equations and that require direct coupling of dynamic 0D boundary conditions.

Parameters of Flow through Paravalvular Leak Channels from Computational Fluid Dynamics Simulations—Data from Real-Life Cases and Comparison with a Simplified Model

Background: Shear forces affecting erythrocytes in PVL channels can be calculated with computational fluid dynamics (CFD). The presence of PVLs is always associated with some degree of hemolysis in a simplified model of the left ventricle (LV); however, data from real-life examples is lacking. Methods: Blood flow through PVL channels was assessed in two variants. Firstly, a PVL channel, extracted from cardiac computed tomography (CCT), was placed in a simplified model of the LV. Secondly, a real-life model of the LV was created based on CCT data from a subject with a PVL. The following variables were assessed: wall shear stress (τ_w) shear stress in fluid (τ), volume of PVL channel with wall shear stress above 300 Pa (V₃₀₀), duration of exposure of erythrocytes to shear stress above 300 Pa (Vt₃₀₀) and compared with lactate dehydrogenase (LDH) activity levels. Results: τ_w and τ were higher in the simplified model. V₃₀₀ and Vt₃₀₀ were almost identical in both models. Conclusions: Parameters that describe blood flow through PVL channels can be reliably assessed in a simplified model. LDH levels in subjects with PVLs may be related to V₃₀₀ and Vt₃₀₀. Length and location of PVL channels may contribute to a risk of hemolysis in mitral PVLs.

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 Fluid Dynamics Simulations of Mitral Paravalvular Leaks in Human Heart

In recent years, computational fluid dynamics (CFD) has been extensively used in biomedical research on heart diseases due to its non-invasiveness and relative ease of use in predicting flow patterns inside the cardiovascular system. In this study, a modeling approach involving CFD simulations was employed to study hemodynamics inside the left ventricle (LV) of a human heart affected by a mitral paravalvular leak (PVL). A simplified LV geometry with four PVL variants that varied in shape and size was studied. Predicted blood flow parameters, mainly velocity and shear stress distributions, were used as indicators of how presence of PVLs correlates with risk and severity of hemolysis. The calculations performed in the study showed a high risk of hemolysis in all analyzed cases, with the maximum shear stress values considerably exceeding the safe level of 300 Pa. Results of our study indicated that there was no simple relationship between PVL geometry and the risk of hemolysis. Two factors that potentially played a role in hemolysis severity, namely erythrocyte exposure time and the volume of fluid in which shear stress exceeded a critical value, were not directly proportional to any of the characteristic geometrical parameters (shape, diameters, circumference, area, volume) of the PVL channel. Potential limitations of the proposed simplified approach of flow analysis are discussed, and possible modifications to increase the accuracy and plausibility of the results are presented.

Multiphysics computational modelling of the cardiac ventricles

Development of cardiac multiphysics models has progressed significantly over the decades and simulations combining multiple physics interactions have become increasingly common. In this review, we summarise the progress in this field focusing on various approaches of integrating ventricular structures. electrophysiological properties, myocardial mechanics, as well as incorporating blood hemodynamics and the circulatory system. Common coupling approaches are discussed and compared, including the advantages and shortcomings of each. Currently used strategies for patient-specific implementations are highlighted and potential future improvements considered.

Elastohydrodynamic Scaling Law for Heart Rates

Animal hearts are soft shells that actively pump blood to oxygenate tissues. Here, we propose an allometric scaling law for the heart rate based on the idea of elastohydrodynamic resonance of a fluid-loaded soft active elastic shell that buckles and contracts axially when twisted periodically. We show that this picture is consistent with numerical simulations of soft cylindrical shells that twist-buckle while pumping a viscous fluid, yielding optimum ejection fractions of 35%-40% when driven resonantly. Our scaling law is consistent with experimental measurements of heart rates over 2 orders of magnitude, and provides a mechanistic basis for how metabolism scales with organism size. In addition to providing a physical rationale for the heart rate and metabolism of an organism, our results suggest a simple design principle for soft fluidic pumps.

Towards a Computational Framework for Modeling the Impact of Aortic Coarctations Upon Left Ventricular Load

Computational fluid dynamics (CFD) models of blood flow in the left ventricle (LV) and aorta are important tools for analyzing the mechanistic links between myocardial deformation and flow patterns. Typically, the use of image-based kinematic CFD models prevails in applications such as predicting the acute response to interventions which alter LV afterload conditions. However, such models are limited in their ability to analyze any impacts upon LV load or key biomarkers known to be implicated in driving remodeling processes as LV function is not accounted for in a mechanistic sense. This study addresses these limitations by reporting on progress made toward a novel electro-mechano-fluidic (EMF) model that represents the entire physics of LV electromechanics (EM) based on first principles. A biophysically detailed finite element (FE) model of LV EM was coupled with a FE-based CFD solver for moving domains using an arbitrary Eulerian-Lagrangian (ALE) formulation. Two clinical cases of patients suffering from aortic coarctations (CoA) were built and parameterized based on clinical data under pre-treatment conditions. For one patient case simulations under post-treatment conditions after geometric repair of CoA by a virtual stenting procedure were compared against pre-treatment results. Numerical stability of the approach was demonstrated by analyzing mesh quality and solver performance under the significantly large deformations of the LV blood pool. Further, computational tractability and compatibility with clinical time scales were investigated by performing strong scaling benchmarks up to 1536 compute cores. The overall cost of the entire workflow for building, fitting and executing EMF simulations was comparable to those reported for image-based kinematic models, suggesting that EMF models show potential of evolving into a viable clinical research tool.

Assessment of methodologies to calculate intraventricular pressure differences in computational models and patients

Intraventricular pressure differences (IVPDs) govern left ventricular (LV) efficient filling and are a significant determinant of LV diastolic function. Our primary aim is to assess the performance of available methods (color M-mode (CMM) and 1D/2D MRI-based methods) to determine IVPDs from intracardiac flow measurements. Performance of three methods to calculate IVPDs was first investigated via an LV computational fluid dynamics (CFD) model. CFD velocity data were derived along a modifiable scan line, mimicking ultrasound/MRI acquisition of 1D (IVPD_CMM/IVPD_{1D MRI}) and 2D (IVPD_{2D MRI}) velocity-based IVPD information. CFD pressure data (IVPD_CFD) was used as a ground truth. Methods were also compared in a small cohort (n = 13) of patients with heart failure with preserved ejection fraction (HFpEF). In silico data showed a better performance of the IVPD_{2D MRI} approach: RMSE values for a well-aligned scan line were 0.2550 mmHg (IVPD_{1D MRI}), 0.0798 mmHg (IVPD_{2D MRI}), and 0.2633 mmHg (IVPD_CMM). In vivo data exhibited moderate correlation between techniques. Considerable differences found may be attributable to different timing of measurements and/or integration path. CFD modeling demonstrated an advantage using 2D velocity information to compute IVPDs, and therefore, a 2D MRI-based method should be favored. However, further studies are needed to support the clinical significance of MRI-based computation of IVPDs over CMM.

Modeling Left Ventricular Blood Flow Using Smoothed Particle Hydrodynamics

This study aims to investigate the capability of smoothed particle hydrodynamics (SPH), a fully Lagrangian mesh-free method, to simulate the bulk blood flow dynamics in two realistic left ventricular (LV) models. Three dimensional geometries and motion of the LV, proximal left atrium and aortic root are extracted from cardiac magnetic resonance imaging and multi-slice computed tomography imaging data. SPH simulation results are analyzed and compared with those obtained using a traditional finite volume-based numerical method, and to in vivo phase contrast magnetic resonance imaging and echocardiography data, in terms of the large-scale blood flow phenomena usually clinically measured. A quantitative comparison of the velocity fields and global flow parameters between the in silico models and the in vivo data shows a reasonable agreement, given the inherent uncertainties and limitations in the modeling and imaging techniques. The results indicate the capability of SPH as a promising tool for predicting clinically relevant large-scale LV flow information.

Flow patterns in the jugular veins of pulsatile tinnitus patients

Pulsatile Tinnitus (PT) is a pulse-synchronous sound heard in the absence of an external source. PT is often related to abnormal flow in vascular structures near the cochlea. One vascular territory implicated in PT is the internal jugular vein (IJV). Using computational fluid dynamics (CFD) based on patient-specific Magnetic Resonance Imaging (MRI), we investigated the flow within the IJV of seven subjects, four symptomatic and three asymptomatic of PT. We found that there were two extreme anatomic types classified by the shape and position of the jugular bulbs: elevated and rounded. PT patients had elevated jugular bulbs that led to a distinctive helical flow pattern within the proximal internal jugular vein. Asymptomatic subjects generally had rounded jugular bulbs that neatly redirected flow from the sigmoid sinus directly into the jugular vein. These two flow patterns were quantified by calculating the length-averaged streamline curvature of the flow within the proximal jugular vein: 130.3±8.1m^-1 for geometries with rounded bulbs, 260.7±29.4m^-1 for those with elevated bulbs (P<0.005). Our results suggest that variations in the jugular bulb geometry lead to distinct flow patterns that are linked to PT, but further investigation is needed to determine if the vortex pattern is causal to sound generation.

Heart blood flow simulation: a perspective review

Cardiovascular disease (CVD), the leading cause of death today, incorporates a wide range of cardiovascular system malfunctions that affect heart functionality. It is believed that the hemodynamic loads exerted on the cardiovascular system, the left ventricle (LV) in particular, are the leading cause of CVD initiation and propagation. Moreover, it is believed that the diagnosis and prognosis of CVD at an early stage could reduce its high mortality and morbidity rate. Therefore, a set of robust clinical cardiovascular assessment tools has been introduced to compute the cardiovascular hemodynamics in order to provide useful insights to physicians to recognize indicators leading to CVD and also to aid the diagnosis of CVD. Recently, a combination of computational fluid dynamics (CFD) and different medical imaging tools, image-based CFD (IB-CFD), has been widely employed for cardiovascular functional assessment by providing reliable hemodynamic parameters. Even though the capability of CFD to provide reliable flow dynamics in general fluid mechanics problems has been widely demonstrated for many years, up to now, the clinical implications of the IB-CFD patient-specific LVs have not been applicable due to its limitations and complications. In this paper, we review investigations conducted to numerically simulate patient-specific human LV over the past 15 years using IB-CFD methods. Firstly, we divide different studies according to the different LV types (physiological and different pathological conditions) that have been chosen to reconstruct the geometry, and then discuss their contributions, methodologies, limitations, and findings. In this regard, we have studied CFD simulations of intraventricular flows and related cardiology insights, for (i) Physiological patient-specific LV models, (ii) Pathological heart patient-specific models, including myocardial infarction, dilated cardiomyopathy, hypertrophic cardiomyopathy and hypoplastic left heart syndrome. Finally, we discuss the current stage of the IB-CFD LV simulations in order to mimic realistic hemodynamics of patient-specific LVs. We can conclude that heart flow simulation is on the right track for developing into a useful clinical tool for heart function assessment, by (i) incorporating most of heart structures' (such as heart valves) operations, and (ii) providing useful diagnostic indices based hemodynamic parameters, for routine adoption in clinical usage.

Hemodynamics in the Left Atrium and Its Effect on Ventricular Flow Patterns

In the present study, we investigate the hemodynamics inside left atrium (LA) and understand its impact on the development of ventricular flow patterns. We construct the heart model using dynamic-computed tomographic images and perform simulations using an immersed boundary method based flow solver. We show that the atrial hemodynamics is characterized by a circulatory flow generated by the left pulmonary veins (LPVs) and a direct stream from the right pulmonary veins (RPVs). The complex interaction of the vortex rings formed from each of the PVs leads to vortex breakup and annihilation, thereby producing a regularized flow at the mitral annulus. A comparison of the ventricular flow velocities between the physiological and a simplified pipe-based atrium model shows that the overall differences are limited to about 10% of the peak mitral flow velocity. The implications of this finding on the functional morphology of the left heart as well the computational and experimental modeling of ventricular hemodynamics are discussed.

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

A coupled chemo-fluidic computational model for investigating flow-mediated thrombogenesis in infarcted left ventricles (LVs) is proposed. LV thrombus (LVT) formation after the acute myocardial infarction (AMI) may lead to thromboembolic events that are associated with high mortality and morbidity, and reliable stratification of LVT risk is the key to managing the treatment of AMI patients. There have been several studies emphasizing the importance of LV blood flow patterns on thrombus formation; however, given the complex interplay between ventricular flow dynamics and biochemistry of thrombogenesis, current understanding is mostly empirical. In the present model, blood flow in the LV is obtained by solving the incompressible Navier-Stokes equations, and this is coupled to the biochemical modeling of the coagulation cascade, platelet activation, and fibrinogen polymerization. The coupled model is used to examine the effect of ventricular flow patterns on thrombogenesis in modeled ventricles. It is expected that the method developed here will enable in-depth studies of thrombogenesis in patient-derived infarcted LV models.

A New MRI-Based Model of Heart Function with Coupled Hemodynamics and Application to Normal and Diseased Canine Left Ventricles

A methodology for the simulation of heart function that combines an MRI-based model of cardiac electromechanics (CE) with a Navier–Stokes-based hemodynamics model is presented. The CE model consists of two coupled components that simulate the electrical and the mechanical functions of the heart. Accurate representations of ventricular geometry and fiber orientations are constructed from the structural magnetic resonance and the diffusion tensor MR images, respectively. The deformation of the ventricle obtained from the electromechanical model serves as input to the hemodynamics model in this one-way coupled approach via imposed kinematic wall velocity boundary conditions and at the same time, governs the blood flow into and out of the ventricular volume. The time-dependent endocardial surfaces are registered using a diffeomorphic mapping algorithm, while the intraventricular blood flow patterns are simulated using a sharp-interface immersed boundary method-based flow solver. The utility of the combined heart-function model is demonstrated by comparing the hemodynamic characteristics of a normal canine heart beating in sinus rhythm against that of the dyssynchronously beating failing heart. We also discuss the potential of coupled CE and hemodynamics models for various clinical applications.