Session L06: Biofluids: Cardiac Flows I

A Hypertension Blood Flow Model in Arteries

Higher blood pressure, known as hypertension, refers to a condition where the normal force of blood against the artery walls is above the standard range. Elevated blood pressure levels increase the likelihood of experiencing several health issues, including cardiac disease, heart attack, and stroke. This study presents a mathematical model that captures the blood pressure waveform and characterizes the motion of blood flow within the arterial network. The proposed approach combines the conventional Windkessel modeling of aortic flow with the solution of Womersley pulsatile flow equations to achieve greater accuracy. The derivation setup comprises two compartments, namely proximal and distal, designed in a Windkessel-type fashion. These compartments are interconnected by a tube, simulating the aorta. The blood flow within the aorta is characterized using the Womersley solution, an approach to the simplified Navier-Stokes equations. The model results show the ability to: (i) describe the arterial input impedance; (ii) to mimic changes in the aortic root pressure profile and wave reflections in large arteries; and (iii) to predict physiological frictional and inertial pressure drops in large arteries is presented. The results have been verified using in-vivo data on aortic pressure and flow rate from patients diagnosed with hypertension.   

Systems hemodynamics approach for evaluating myocardial risk zone from carotid pressure waveforms in coronary occlusion /reperfusion rat models

Evaluation of the left ventricle (LV) myocardial risk zone (MRZ) after episodes of coronary occlusion and myocardial infarction, has recently gained significant interest. This evaluation can determine the extent of myocardial salvage and assess the effectiveness of therapeutic interventions. This study presents a hybrid intrinsic frequency (IF)-machine learning (ML) methodology for evaluation of MRZ from carotid pressure waveforms. We used standard occlusion/reperfusion rat models (female Sprague Dawley) where the proximal left coronary artery was occluded for 30 minutes, followed by 3 hours of reperfusion. The coronary artery was then reoccluded and 1 ml of a 50% solution of Unisperse Blue Dye was injected. Post-operation, the LV was transversely sliced and photographed. The risk area, visualized as tissue not stained by the blue dye, was traced manually for each LV slice. Subsequently, the overall risk zone was obtained via computerized planimetry. MRZ was quantified as mass percentage of the risk area over the left ventricle (LV) area. IF parameters were computed from carotid pressure waveforms 2 hours after reperfusion and fed into Random Forest classifiers. The cut-off value for mild and severe MRZ classification was set to 50%. The final model was externally tested on additional rats. Our results showed high accuracies for evaluating the true class of MRZ via an IF-ML method. This method has potential clinical impact in management and treatment of patients under risk especially post-MI patients.   

Efficient, Multi-Fidelity Modelling of the Coagulation Cascade in Patient-Specific Left Atrial Flow

The left atrium (LA) is the most common site of cardiac thrombosis, associated with up to 30% of ischemic strokes. The coagulation cascade regulates thrombosis via a large biochemical network. Under flow, this cascade is governed by a system of dozens of 3D advection-reaction-diffusion partial differential equations (PDE). Solving these PDEs is computationally challenging due to their high dimensionality and multi-scale nature. Here, we leverage a recently developed Multi-Fidelity (MuFi) coagulation model that  reduces the 3D PDE system into an equivalent ordinary differential equation (ODE) system. The MuFi model represents species concentration u_i(x,t) as a function of the statistical moments of blood residence time, which are the only PDEs we need to solve. We apply a 9-species MuFi model to a database of LA flows (N=6 patients, 3 thrombus negative and 3 thrombus/TIA positive) to quantify patient-specific thrombin production. Residence time moments are obtained from the LA velocity fields calculated by LA with CFD analysis of 4D CT patient-specific images. Taking advantage of the MuFi model's low computational cost, we also present a sensitivity analysis of the effect of reaction kinetic constants.   

Inferring left atrial thrombin concentration from 4D CT contrast dynamics by physics-informed neural networks & multi-fidelity coagulation cascade modeling

People with atrial fibrillation (AF), a common arrhythmia with a lifetime risk of 25%, have significantly higher rates of atrial thrombosis and are five times more likely to suffer a stroke than people with a regular heartbeat. Anticoagulant drug prescription to people with AF is based on clinical risk scores based on demographic factors with modest accuracy. These risk scores do not include patient-specific factors affecting thrombosis. Of note, they ignore the dynamics of the coagulation cascade under patient-specific left atrial flow. Here, we present a computational pipeline to predict the concentration of thrombin, a central coagulation enzyme responsible for clot fiber formation and platelet activation, from 4D CT clinical sequences of LAA contrast dynamics. First, a physics-informed neural network predicts blood residence time from contrast agent dynamics. Second, a computationally efficient multi-fidelity model of the coagulation cascade predicts thrombin concentration from residence time. This pipeline is tested on ground-truth data from CFD simulations in idealized, fixed-wall geometries and patient-specific, moving-wall left atrial meshes. Proof-of-principle of clinical application is shown on 4D CT acquisitions from AF patients.   

Investigating Blood Flow Patterns and Hydrodynamics of the Perinatal Single Ventricle Heart: An In Vivo Study

The single ventricle (SV) describes a broad group of congenital heart defects that results in only one functional ventricle to pump blood effectively. Associated anatomical changes and varying loading conditions lead to altered diastolic blood flow patterns and hydrodynamics, which are poorly understood. Early detection of SV conditions through in-vivo echocardiography (echo) during the perinatal period is critical for treatment planning and improving outcomes. However, standard Doppler echo with Color Flow Imaging (CFI) provides a limited analysis of flow pattern changes, which is crucial for understanding SV physiology. Here we employ Doppler Vector Reconstruction (DoVeR), a novel method that resolves the underlying flow velocity vector fields from CFI by iteratively solving the vorticity-streamfunction formulation. DoVeR analysis yields advanced hydrodynamic measurements of abnormal cardiac flow, including energy loss, vortex strength and pressure fields. By comparing both prenatal and postnatal flow patterns in healthy controls and SV patients, we observe that a large free-wall vortex in the diastolic flow of SV that is asymmetric compared to the symmetric vortex in healthy hearts. The disorganized flow pattern in SV hearts results in higher flow energy loss, indicative of lower diastolic efficiency. This pioneering study establishes the significance of intraventricular flow parameters in statistically demarcating healthy versus SV heart diastolic function.   

Enhanced hemodynamics in cerebral aneurysm due to the impact of body movement, an in-vitro study

We aim to understand how human body movement may impact the hemodynamics of cerebral aneurysms due to the physical motion of the vessel wall, beyond typical physiological responses. We first employ a motion collection system to capture the human head movement. We then implement and verify a six-degree-of-freedom motion simulation platform to replay the human head motion. Lastly, and most importantly, we perform an in-vitro hemodynamics measurement in a cerebral aneurysm phantom model, using a high-speed PIV system on this motion simulation platform. Both simplified and patient-specific cerebral aneurysm models are utilized, and different inlet blood flow conditions are tested during this study. In the control group, we measure hemodynamics when the motion simulation platform is at rest. In the treatment group, the hemodynamics measurement and body movement replaying are simultaneously conducted, with identical inlet flow conditions. We evidenced clear differences in hemodynamics in these two groups. This study suggests that, besides physiological response, body movement also physically contributes to the intense hemodynamic changes that need to be considered during any drug or biomedical device design and verification.   

Fibrosis effect on left atrial hemodynamics using multi-physics, multi-scale simulations

Atrial fibrillation (AF) is the most frequent arrhythmia, with a prevalence of 0.5% of the world population. During AF, irregular electric impulses cause unsynchronized myocardial motion leading to blood stasis in the left atrial (LA) appendage (LAA), increasing thrombosis and stroke risk. Fibrosis is clinically associated with stroke but the underlying mechanisms are not understood. Fibrotic remodeling modifies myocardial structure impairing LA electrical propagation, myocardium mechanics, and function. To dissect these effects, we perform multi-physics, multi-scale simulations coupling electrophysiology, biomechanics, and hemodynamics. We simulate the LA contraction against a constant ventricular pressure using 4 different models with modified mechanical properties in the fibrotic tissue: no fibrosis effect, 5X increased tissue passive stiffness (iPS), 2X reduced cardiomyocyte peak tension (rPT), and combined effect (iPS+rPT). The results from 4 patient-specific LA anatomies with different fibrotic burdens suggest fibrosis reduces LA kinetic energy (KE) globally, especially in the iPS+rPT model. KE decreases linearly with emptying fraction (LA function impairment measure) in the LA body and in a patient-specific fashion in the LAA.    

A Unified Modular Framework for Implicit 3D-0D Coupling in Cardiovascular Finite Element Simulations

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, also known as a lumped-parameter network or 0-dimensional (0D) fluid model, to represent blood flow throughout the cardiovascular system. In this work, we present a modular framework for implicitly coupling 3-dimensional (3D) finite element simulations of fluid or solid mechanics to 0D fluid models of blood circulation. The coupling 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 couples 3D blood flow models to 0D circulation models (3D fluid - 0D fluid). Here, we extend it to couple 3D cardiac tissue mechanics models to 0D circulation models (3D structure - 0D fluid), showing that both mathematical problems can be solved within a unified coupling scheme. We also provide a new derivation inspired by the Approximate Newton Method, which explains how the proposed numerical scheme combines the stability of monolithic approaches with the modularity and flexibility of partitioned approaches. The effectiveness, temporal convergence, and computational cost of the algorithm are assessed through several examples relevant to the cardiovascular modeling community.   

High Resolution Numerical Simulations of LVAD Outflow graft Haemodynamics

For patients who have reached late stage heart failure, Left Ventricle Assist Device (LVAD) therapy is a life-saving treatment which involves surgical implantation of a battery operated mechanical pump that supplements blood supply to the body. However, this therapy may involve significant risks such as bleeding as well as thrombosis and the causes for these are not very well understood.Some studies have suggested that orientation of the outflow graft attached to the aorta impacts the onset of these events substantially. Hence, this study aims to numerically simulate blood flow from the graft to the aorta and analyze qualitatively and quantitatively the flow metrics that may indicate onset of such adversarial events.This is undertaken using 3-D patient specific geometry as well as solution of Incompressible Navier-Stokes equation using the substantially validated Curvilinear Immersed Boundary(CURVIB) solver, coupled with a Fluid Structure Interaction (FSI) algorithm to simulate aortic wall compliance.   

Super-resolution and denoising of 4D flow MRI data using Physics-Informed Neural Network

This study introduces an innovative and advanced approach to significantly improve the spatial and temporal resolution of 4D Flow MRI data through the application of a physics-informed neural network (PINN). By synergizing physics-based principles with neural networks, the PINN addresses challenges related to variations and noise in MRI measurements, enhancing the reliability of velocity field predictions. Through rigorous evaluations, the PINN showcases exceptional accuracy in predicting velocity fields for both laminar and turbulent flows within a 2D stenosis model. Furthermore, when applied to Fontan 4D flow MRI data, the PINN effectively mitigates resolution and noise issues, underscoring its potential in enhancing the quality of 4D Flow MRI data. Although promising, this study acknowledges the presence of discrepancies in streamline predictions, particularly in complex patient-specific cases. As such, further refinement and investigation are crucial to optimize the PINN's performance and overcome the remaining limitations. This research represents a significant advancement in 4D Flow MRI, offering the prospect of more reliable and precise predictions in various clinical applications. By continually exploring and developing this novel approach, clinicians and researchers can elevate patient care and understanding of hemodynamic phenomena.