Session W07: Biological Fluid Dynamics: Physiological Cardiac Flows (10:00am - 10:45am CST)

A Novel Computational Framework for Pulsatile Wall-shear Stress in Image-based Computational Fluid Dynamics

Wall shear stress (WSS), a tangential force per unit area exerted on the inner wall of a vessel by blood flow, plays an important role in the prevention, pathogenesis, and treatment of cardiovascular diseases. Image-based computational fluid dynamics provides a unique tool to quantify the velocity vector field, from which WSS is conventionally calculated via finite difference method. The key is to determine the local normal direction of the wall in image-based flow domains. We present a novel computation method seamlessly integrating the quantifications of the normal vector \textbf{\textit{n}} of the local wall via signed distance field and the en-route viscous stress tensor $\sigma $ using volumetric lattice Boltzmann method. The WSS is calculated by \begin{figure}[htbp] \centerline{\includegraphics[width=1.56in,height=0.18in]{020820201.eps}} \label{fig1} \end{figure} (Einstein index notation). An application study is to quantify WSS of Womersley flow in ducts. The computational efficiency and accuracy are assessed via comparisons with analytical solutions. The effects of Reynolds number, Womersley number, and shape of cross-section on WSS are systematically explored.   

Effect of pulmonary vein inflow on patient-specific CFD prediction of left atrial blood stasis

Atrial fibrillation (AF) disrupts left atrial (LA) blood flow, which can cause increased blood stasis leading to thrombosis in the left atrial appendage (LAA), systemic embolism, transient ischemic attacks (TIAs) and stroke. Patient-specific CFD simulations based on time-resolved, three-dimensional (4D) anatomical images can help predict LAA blood stasis. In these simulations, LA geometry and transmitral flow rate can be inferred from the 4D anatomical images. However, the specific flow rates through the pulmonary vein (PV) inlets need to be modeled and could be a major source of uncertainty. We studied how this PV flow split affects LA blood flow, with emphasis on LAA stasis, by performing simulations with 50-50\% (even) and 40-60\% (physiological) splits between left and right PVs. We ran our in-house immersed boundary CFD solver in six patient anatomies obtained from 4D-CT (Garcia-Villalba et al, bioRxiv, 2020.05.07.083220). Three patients were in sinus rhythm and three had AF. The AF patients also had an LAA clot, that was segmented out before running the simulations, or a history of TIAs.   

Non-newtonian Patient-specific Analysis of Left Atrial Blood Stasis

Atrial fibrillation (AF) is the most common arrhythmia, affecting $\sim 35$M people worldwide. During AF, the atria beat weakly and irregularly creating regions of blood stasis where clots may form, especially in the left atrial appendage (LAA). Some of these clots travel to the brain causing strokes or transient ischemic attacks (TIAs). Blood experiences non-Newtonian rheology when its shear rate falls below 100 s$^{-1}$. Blood inside substantial parts of the LAA sustains shear rates well below this threshold; however, previous CFD analyses considered Newtonian rheology. We explored the influence of non-Newtonian rheology in LAA stasis for six patient-specific anatomies obtained from 4D-CT acquisitions. Three patients had an LAA clot, which was segmented out before running the simulations, or a history of TIAs. We included a semi-implicit Carreau-Yasuda shear-thinning model in our in-house immersed-boundary solver, and tailored the CFL condition to ensure numerical stability in the presence of strong viscosity gradients. These simulations are compared with previously reported Newtonian simulations in the same patients (Garcia-Villalba et al, bioRxiv, 2020.05.07.083220).   

A reduced-order model for flow in a coronary artery with bifurcations

Reduced-order models have been developed to estimate the distributions of the volume flow rate and pressure along a subject- or patient-specific artery with bifurcations. We suggest a reduced-order model by considering the losses due to the geometric parameters of coronary arteries such as tapering, curvature, and bifurcations. In this model, an artery is segmented into finite lengths of straight and curved pipes, and the continuity and one-dimensional energy equations are solved with given boundary conditions. The distributions of the volume flow rate and pressure along seventeen subject-specific coronary arteries at rest and exercise conditions are compared with those from three-dimensional numerical simulation (CFD). The present reduced-order model provides better prediction performance than existing reduced-order models. Also, fractional flow reserves (FFRs), which is defined to be the distal pressure of a stenosis to the inlet pressure, are calculated for fifteen patient-specific coronary arteries by combining the present reduced-order model with our zero-dimensional stenosis model for the pressure drop across a stenosis (Kim et al., 2020). FFRs obtained from the present model agree well with those obtained from CFD.   

Analysis of the coagulation kinetics under prosthetic heart valve flows

Thrombosis is a complex process characterized by a cascade of biochemical reactions during which the zymogens convert into active enzymes, promoting the formation of a blood clot. The two coagulation pathways, extrinsic and intrinsic, activating through the Tissue factor (TF) and the activation of the Hageman factor (FXII), respectively, trigger this chain of reactions. The two pathways converge into a common pathway with the activation of factor X (FX), which leads to the activation of thrombin and the conversion of fibrinogen into fibrin. The fact that the dynamics of coagulation could be affected by the flow conditions, renders the phenomenon difficult to be studied \textit{in-vivo}. In this study, the physics of blood clotting under aortic flow field generated by prosthetic heart valves has been numerically analyzed. The Hockin-Mann based Platelet-plasma model has been employed to investigate the dynamics of the biochemical species while a sharp interface Curvilinear Immersed Boundary Method (CURVIB) has been used to evaluate the cardiac mechanics and hemodynamics of prosthetic heart valves. The numerical results provide insights into the concentration of species which are too low to be detected and have been validated against published data.   

Deducing global mixing information in the heart from sparse particle trajectory data

Ineffective or vigorous mixing in the heart, particularly in the left ventricle (LV), has been associated with several adverse cardiovascular events. Over the years, this poor mixing behavior has largely been quantified using particle residence times, shear stress accumulations and finite-time Lyapunov exponents. Unfortunately, these measures are often impractical to clinicians as they require specialized knowledge as well as relatively high spatiotemporal resolutions and computational costs. In this work, we demonstrate how sparse particle trajectory data can be used to deduce a minimal global description of the mixing behavior in the LV. By inspecting the properties of mathematical braids formed by entangled random particle trajectories, three such descriptive properties can be obtained: 1) whether the mixing process has a preferred rotational direction; 2) how well it engages dispersed material elements (avoiding stagnant regions); 3) its energetic complexity or quality. We illustrate the intuitiveness of the braid approach in understanding the mixing behavior in left ventricular flows (using chronic aortic regurgitation datasets for demonstration) and recommend further investigations for the diagnosis of diseases, monitoring disease progression and evaluating medical devices.   

Monitoring Prosthetic Valve Status via In-Situ Pressure Sensors: Concept Evaluation using Supervised Learning Applied to Computational Hemodynamic Models

Transcatheter heart valves (THV) suffer from clinically silent complications like subclinical leaflet thrombosis which may result in fatal outcomes for the patient. Such malfunction is detected incidentally during post-implant follow-up, and common imaging techniques are either invasive or expose the patient to radiation and are cost prohibitive. This informs a critical need for a novel, non-invasive and non-toxic continuous monitoring modality of THVs. We conduct a data-driven, in-silico investigation into the viability of wireless, remote monitoring of prosthetic aortic valve health using pressure microsensors. The strong coupling between leaflet status and downstream hemodynamics facilitates correlating pressure measurements at strategic locations in the vicinity of the THV with leaflet mobility. We developed reduced-order valve models capable of simulating a wide range of valve conditions. High-fidelity simulations of transvalvular flow in a canonical aorta model, with supervised learning methods determine optimal sensor configuration. Preliminary results demonstrate pressure measurements at as few as two discrete locations per valve leaflet can accurately predict its status (``Healthy''/ ``Reduced mobility'') and quantify its range-of-motion.   

On the effect of the electrophysiology fast conduction system in the mitral valve closure

The mitral valve assures the correct direction of the left atrial flow into the ventricle and is made of two leaflets that are fastened to the papillary muscles (PM) through the chordae tendineae. The PM are located in the bottom ventricular myocardium and contract at early systole in order to stretch the chordae tendinae, thus preventing the prolapse~of the mitral valve. Hence, the timely electrical activation of the PM is crucial for the correct closing of the valve and a delayed muscular contraction would yield an incomplete valve closure and an undesired backflow in the atrium. In this work, the effect of the fast conduction system (that is responsible for the electrical activation of the PM) on the mitral valve kinematics and on the cardiac hemodynamics is investigated. In particular, the in-house electrophysiology model comprises (i) the whole network of fast conduction bundles originating at the sino-atrial node, (ii) the branched Purkinje network activating the ventricles and the PA, and (iii) the three-dimensional myocardium. The results are seen to agree with the available clinical data, therefore suggesting that this computational tool could be used to predict the effects of valve disease and to improve the outcome of surgical interventions.   

A Row and Column Scaling Preconditioner for Efficient Fluid-Structure Modeling in Cardiovascular System

Blood flow and tissue mechanics are two fundamental elements in cardiovascular modeling. Biological tissue is mostly treated as incompressible, and its governing equations in a velocity-pressure formulation are very similar to the Navier Stokes equations. This similarity enables one to model blood flow and tissue mechanics using the same mixed finite-element numerical framework, which can be advantageous for fluid-structure-interaction simulations. Taylor-Hood elements is commonly used to solve velocity-pressure formulations as they satisfy the inf-sup condition. The challenge is that these elements can lead to extremely ill-conditioned matrix system. Existing open-source softwares usually overcome this by using direct solvers, which become less economic for large scale problems. In this study, we present a new preconditioning strategy, wherein a row and column scaling (RCS) preconditioner is first used to regulate the matrix before applying common preconditioner/iterative solver combinations. We demonstrate that the proposed RCS can drastically reduce the condition number of the matrix systems, and, in turn, the overall computational time with minimal computational overhead. Its capability will be demonstrated in practical patient-specific cardiac modeling applications.   

Fluid--structure--electrophysiology interaction (FSEI) for the heart: a GPU accelerated computational framework

The reliability of cardiovascular simulations depends on the accurate solution of the hemodynamics, the realistic modeling of the tissues and of the electrical activation of the myocardium. The resulting FSEI thus requires an immense computational power and implies long time to get the results or to rely on external computational resources if multi--CPU processors are used (MPI acceleration). In the recent years, the GPU has emerged as a platform for high performance computing and allows for considerable reductions of the time--to--solution. In order to develop a reliable and efficient computational tool to support medical decision, our multi-physics solver has been ported to GPU clusters and workstations. Indeed, the GPU architecture yields a substantial reduction of the number of host nodes required to reach a target performance level. The porting relies on CUDA Fortran that allows the programmer to define subroutines running on the GPUs as well as CUF kernel directories that automatically run single and nested loops on the GPU device without modifying the original CPU code. The GPU accelerated multi-physics heart model shows good strong scaling characteristics, thus allowing for a timely solution of cardiac simulations and to provide data for medical decision.   

A Novel Echocardiographic Data Fusion Framework for Measuring Intraventricular Flow

Left ventricular (LV) flow patterns contribute to diastolic suction and minimize cardiac work. However, the clinical impact of mapping LV flow is yet to be realized due to the difficulty of measuring flow inside opaque cavities. The noninvasiveness and portability of echocardiography makes it well suited for clinical assessment of intraventricular flows. Several ultrasound-based flow quantification techniques have been developed including Doppler vector flow mapping and echocardiographic particle image velocimetry. Still, there exists key limitations such as assumption of planar flow and dependence on Doppler encoding velocity or the need for a finely tuned contrast infusion and high imaging frame rate. To exploit the strengths and mitigate the limitations, we developed a statistically robust data fusion modality that combines bright-mode contrast-agent and color-Doppler sequences acquired with different encoding velocities to infer intraventricular velocity fields. Our model uses Bayesian estimation to fuse the data from these different sources by enforcing priors based on the physics of the flow: mass conservation, momentum balance, boundary conditions, and temporal and spatial smoothness. We tested this method on human patients and a large animal model.   

Computational simulation of aortic dissection with a comparison with 4D flow MRI

Aortic dissection, typically characterized by an intimal flap separating the aortic flow into two channels referred to as true lumen (TL) and false lumen (FL), is a leading cause of death in cardiovascular diseases. 4-dimensional flow magnetic resonance imaging (4D flow MRI) can provide time-resolved volumetric blood-flow information non-invasively, and hereby shows great potential to improve the diagnosis of aortic dissection. However, the inherent imperfection of the 4D flow MRI measurement (e.g., noise, artifacts, and low temporal-special resolution) limits its precision in quantifying the blood flow. Alternatively, computational fluid dynamic (CFD) simulation can produce high-resolution results based on physical models, whilst suffers from model inadequacy caused by unrealistic assumptions such as uniform viscosity or rigid wall. In this paper, we propose a novel data assimilation method that reconstructs the vascular flow field by leveraging both the physiologic authenticity of clinical 4D flow MRI data and the high resolution of the CFD simulation results. Typical biomarkers regarding aortic dissection such as velocity vector field, pressure distribution, and time-averaged wall shear stress are assessed to evaluate the feasibility and effectiveness of the proposed method.   

Effects of stenotic mitral valve on left ventricle hemodynamics

The mitral valve is a bi-leaflet passive structure that, driven by pressure differences between the left atrium and ventricle of the heart, opens and closes during the heartbeat to ensure the emptying and filling of the chambers and the correct flow direction. In elderly individuals or because of particular pathologies, the valve leaflets can stiffen thus impairing the valve functioning and, in turn, the pumping efficiency of the (left) heart. Using the multi-physics left heart model of Viola et al. (2020) [Eur. J. Mech. B/fluids, 79,212], accounting for the electrophysiology, the active contraction of the myocardium and the hemodynamics, we have investigated the changes in the flow structures and in the cardiac output for different severities of the mitral valve stenosis. We have found that, in addition to the expected increase of the transvalvular pressure drop, and decrease of the pumping efficiency, a stenotic mitral valve alters the large scale recirculation of the left ventricle that is beneficial to prevent hemostasis and clot formation.   

Experimental assessment of the impact of cardiac output and valve orientation on bioprosthetic pulmonary valve performance using magnetic resonance velocimetry

Tetralogy of Fallot (ToF), a congenital heart defect that affects 1 in every 2500 newborns annually, requires surgical repair of the right ventricular outflow tract (RVOT) and subsequent placement of an artificial pulmonary valve. The longevity of bioprosthetic valves is highly variable and there are no standard clinical guidelines regarding their placement or size selection during surgery. This work analyzes the hemodynamics in an RVOT model representative of ToF anatomy using magnetic resonance velocimetry at cardiac outputs of 2 L/min, 3.5 L/min, and 5 L/min and two different valve orientations. We also acquired images of the valve at 1500Hz to observe instantaneous leaflet motion. The velocity fields revealed key differences among all cases in the location of reverse flow regions, systolic jet shape, and flow asymmetry. High-speed camera images showed that effective valve orifice area, leaflet closing dynamics, and the flutter frequency of the leaflet tips also varied with cardiac output and valve orientation. In particular, the 2 L/min case produced more asymmetry, stronger recirculation regions, and a smaller orifice area than the other cases, which could contribute to uneven leaflet fatigue and allow for calcification that may lead to early valve dysfunction.   

A complex-valued Stokes solver for simulation of time-periodic creeping flows

The computational cost of a standard CFD solver is proportional to the number of time steps. This dependence leads to costly solutions for the time-periodic flows, such as blood flow in the circulatory system, where a large number of time steps are required for accurate time integration. To lower this cost, we propose an alternative approach by transforming the incompressible unsteady Stokes equations into spectral domain based on Fourier series, which results in Stokes equations with a complex-valued source term. In comparison with a traditional spatio-temporal solver, this new formulation significantly decreases the computational cost since solving for a few modes rather than thousands of time steps suffices for accurate time-reconstruction of the solution. Additionally, the accuracy of this method is independent of that of the time integration schemes. This new formulation avoids instabilities caused by the time integration scheme when contrasted against a traditional scheme. Due to the orthogonality of solutions associated with each mode, the proposed scheme is embarrassingly parallelizable and thus highly scalable. The accuracy and computational efficiency of the proposed method are demonstrated by comparing it against a traditional spatio-temporal finite element solver.   

Particle Swarm Optimizer for Accurate Modeling of the Arterial Blood Flow in Health and Disease

Cardiovascular diseases includes a restriction to the blood supplying the body and are the leading cause of death in the world. Therefore there is a need to model arterial blood flow accurately. Blood flow is normally described using the Windkessel model, but it requires an accurate estimation of the total arterial compliance, resistance and inertance, these are usually described using the non-linear square fit (NLSF), which can be a complex process if the parameter space is large. The particle swarm optimization (PSO) was used to describe the lumped parameters and compare them using NLSF. A 6-element Windkessel (WK6) model was defined and data from both healthy and diseased subjects were used to validate both methods. Both solutions replicated the experimental dicrotic notch and the pressure waveform throughout the cardiac cycle. Even though both methods predicted the magnitude of the input impedance, the PSO method outperformed the NLSF method in capturing the impedance phase angle. The P-RMS value was smaller for the PSO compared to the NLSF method. The PSO method shows for the first time to better describe the model parameters of blood flow compared to the NLSF method in a WK6 model.   

Aortic Hemodynamics due to Valve Leaflet Asymmetry

Previously, our lab has shown how asymmetric aortic valve leaflets can significantly alter the wall shear stress distribution in the ascending aorta. Primarily, stiffened leaflets (that may arise form valve stenosis or bicuspid valves) can vector the systolic jet and cause it to impinge on the aortic wall with high velocity, especially when directed to impinge on the outer wall of the aortic arch. This year, we will show the effect of valve leaflet asymmetry on the hemodynamics in close proximity to the valve particularly in the residence time of blood next to each leaflet and to flow in the coronary arteries. Increased residence time is an important marker for increased risk of thrombosis and thrombus formation that can lead to coronary blockage and stroke. Furthermore, stiffened leaflets can lead to large areas of recirculation in the sinus bulge which can lead to altered flow into the coronary arteries.   

Automatic classification of pathological left ventricular flows based on modal decomposition

Despite increasing evidence that left ventricular (LV) flow patterns reflect cardiac health, recent advances in non-invasive LV flow imaging have not been translated into improved diagnosis of cardiac dysfunctions. Ad-hoc flow metrics, such as vortex circulation or pressure gradients, are rigorously based on flow physics. However, they often rely on simplifying assumptions about LV flow and may not fully reflect yet-to-be-discovered interdependencies between flow and cardiac physiology. Thus, we investigated whether unbiased analysis of LV flow can be used to classify healthy and diseased LVs. To this end, we performed modal decompositions (POD and DMD) of 2D and 1D flow fields obtained by color-Doppler echocardiography in healthy subjects and patients with hypertrophic (HCM) or dilated cardiomyopathy (DCM). To isolate flow features from those associated with LV wall motion / shape, each patient's flow was represented in a rectangular stationary domain. Subjects were binary-classified as healthy/DCM and healthy/HCM according to their flow's projection onto canonical sets of DMD/POD modes obtained for the three cohorts. The number of modes used for classification was chosen by grid search, and the performance of the classification was tested by k-fold cross-validation. Receiver operating characteristic curves showed excellent performance for both DMD and POD, and both 1D and 2D flow fields, with areas under the curve between 0.81 and 0.96.   

Insights into mitral regurgitation quantification by proximal isovelocity surface area (PISA) and vena contracta area (VCA): A numerical study

Mitral regurgitation (MR) is the most common valvular heart disease, with a prevalence of 9.3{\%} in US population aged 75 and above. Although Doppler echocardiography (Echo) is the primary tool to assess MR severity, MR quantification remains challenging and a true gold standard technique is still lacking. Therefore, the objectives of this study are to evaluate the fundamental assumptions in MR quantification with Echo and identify their pitfalls using computational modeling. The MR models were created from a subject-specific left heart and fluid-structure interaction (FSI) simulation were used to obtain 3D flow field, where simulated Echo acquisition were performed. Regurgitant volume (RVol) was estimated using 2D and 3D proximal isovelocity surface area (PISA) method, and vena contracta area (VCA) method. In addition, the measurement from both peak PISA/VCA and integrated PISA/VCA were reported. By comparing Rvol using different methods with the reference value obtained directly from FSI models, we found that in general, integrated method was more accurate, 3D PISA was much better than 2D PISA, and VCA was more robust than PISA due to its more concrete theoretical basis.