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

Toward a physiological model of vascular wall vibrations in the arteriovenous fistula

The mechanism behind hemodialysis arteriovenous fistula (AVF) failure remains poorly understood, despite previous efforts to correlate altered hemodynamics with vascular remodeling. We have recently demonstrated that transitional flow induces high-frequency vibrations in the AVF wall, albeit with a simplified model. This study addresses the key limitations of our original fluid-structure interaction (FSI) approach, aiming to evaluate the vibration response using a more realistic model. A 3D AVF geometry was generated from contrast-free MRI and high-fidelity FSI simulations were performed. Patient-specific inflow and pressure were incorporated, and a three-term Mooney-Rivlin model was fitted using experimental data. The viscoelastic effect of perivascular tissue was modeled with Robin boundary conditions. Prescribing pulsatile inflow and pressure resulted in a substantial increase in vein displacement ( + 400 %) and strain ( + 317 %), with a higher maximum spectral frequency becoming visible above -42 dB (from 200 to 500 Hz). Transitioning from Saint Venant-Kirchhoff to Mooney-Rivlin model led to displacement amplitudes exceeding 10 micrometers and had a substantial impact on strain ( + 116 %). Robin boundary conditions significantly damped high-frequency displacement ( - 60 %). Incorporating venous tissue properties increased vibrations by 91%, extending up to 700 Hz, with a maximum strain of 0.158. Notably, our results show localized, high levels of vibration at the inner curvature of the vein, a site known for experiencing pronounced remodeling. Our findings, consistent with experimental and clinical reports of bruits and thrills, underscore the significance of incorporating physiologically plausible modeling approaches to investigate the role of wall vibrations in AVF remodeling and failure.

Coupled thermal-hemodynamics computational modeling of cryoballoon ablation for pulmonary vein isolation

Cryoballoon ablation (CBA) is a cryo-energy based minimally invasive treatment procedure for patients suffering from left atrial (LA) fibrillation. Although this technique has proved to be effective, it is prone to reoccurrences and some serious thermal complications. Also, the factors affecting thermal distribution at the pulmonary vein-antrum junction that are critical to the treatment success is poorly understood. Computer modeling of CBA can resolve this issue and help understand the factors affecting this treatment. To do so, however, numerical challenges associated with the simulation of advection-dominant transport process must be resolved. Here, we describe the development of a thermal-hemodynamics computational framework to simulate incomplete occlusion in a patient-specific LA geometry during CBA. The modeling framework uses the finite element method to predict hemodynamics, thermal distribution, and lesion formation during CBA. An incremental pressure correction scheme is used to decouple velocity and pressure in the Navier-Stokes equation, whereas several stabilization techniques are also applied to overcome numerical instabilities. The framework was implemented using an open-source FE library (FEniCS). We show that model predictions of the hemodynamics in a realistic human LA geometry match well with measurements. The effects of cryoballoon position, pulmonary vein blood velocity and mitral regurgitation on lesion formation during CBA was investigated. For a -70⁰C cryoballoon temperature, the model predicts lesion formation for gaps less than 2.5 mm and increasing efficiency of CBA for higher balloon tissue contact areas. The simulations also predict that lesion formation is not sensitive to variation in pulmonary vein blood velocity and mitral regurgitation. The framework can be applied to optimize CBA in patients for future clinical studies.

Effects of non-Newtonian viscosity on arterial and venous flow and transport

It is well known that blood exhibits non-Newtonian viscosity, but it is generally modeled as a Newtonian fluid. However, in situations of low shear rate, the validity of the Newtonian assumption is questionable. In this study, we investigated differences between Newtonian and non-Newtonian hemodynamic metrics such as velocity, vorticity, and wall shear stress. In addition, we investigated cardiovascular transport using two different approaches, Eulerian mass transport and Lagrangian particle tracking. Non-Newtonian solutions revealed important differences in both hemodynamic and transport metrics relative to the Newtonian model. Most notably for the hemodynamic metrics, in-plane velocity and vorticity were consistently larger in the Newtonian approximation for both arterial and venous flows. Conversely, wall shear stresses were larger for the non-Newtonian case for both the arterial and venous models. Our results also indicate that for the Lagrangian metrics, the history of accumulated shear was consistently larger for both arterial and venous flows in the Newtonian approximation. Lastly, our results also suggest that the Newtonian model produces larger near wall and luminal mass transport values compared to the non-Newtonian model, likely due to the increased vorticity and recirculation. These findings demonstrate the importance of accounting for non-Newtonian behavior in cardiovascular flows exhibiting significant regions of low shear rate and recirculation.

Loading equine oocytes with cryoprotective agents captured with a finite element method model

Cryopreservation can be used to store equine oocytes for extended periods so that they can be used in artificial reproduction technologies at a desired time point. It requires use of cryoprotective agents (CPAs) to protect the oocytes against freezing injury. The intracellular introduction of CPAs, however, may cause irreversible osmotic damage. The response of cells exposed to CPA solutions is governed by the permeability of the cellular membrane towards water and the CPAs. In this study, a mathematical mass transport model describing the permeation of water and CPAs across an oocyte membrane was used to simulate oocyte volume responses and concomitant intracellular CPA concentrations during the exposure of oocytes to CPA solutions. The results of the analytical simulations were subsequently used to develop a phenomenological finite element method (FEM) continuum model to capture the response of oocytes exposed to CPA solutions with spatial information. FEM simulations were used to depict spatial differences in CPA concentration during CPA permeation, namely at locations near the membrane surface and towards the middle of the cell, and to capture corresponding changes in deformation and hydrostatic pressure. FEM simulations of the multiple processes occurring during CPA loading of oocytes are a valuable tool to increase our understanding of the mechanisms underlying cryopreservation outcome.

The Story of Wall Shear Stress in Coronary Artery Atherosclerosis: Biochemical Transport and Mechanotransduction

Coronary artery atherosclerosis is a local, multifactorial, complex disease, and the leading cause of death in the US. Complex interactions between biochemical transport and biomechanical forces influence disease growth. Wall shear stress (WSS) affects coronary artery atherosclerosis by inducing endothelial cell mechanotransduction and by controlling the near-wall transport processes involved in atherosclerosis. Each of these processes is controlled by WSS differently and therefore has complicated the interpretation of WSS in atherosclerosis. In this paper, we present a comprehensive theory for WSS in atherosclerosis. First, a short review of shear stress-mediated mechanotransduction in atherosclerosis was presented. Next, subject-specific computational fluid dynamics (CFD) simulations were performed in ten coronary artery models of diseased and healthy subjects. Biochemical-specific mass transport models were developed to study low-density lipoprotein, nitric oxide, adenosine triphosphate, oxygen, monocyte chemoattractant protein-1, and monocyte transport. The transport results were compared with WSS vectors and WSS Lagrangian coherent structures (WSS LCS). High WSS magnitude protected against atherosclerosis by increasing the production or flux of atheroprotective biochemicals and decreasing the near-wall localization of atherogenic biochemicals. Low WSS magnitude promoted atherosclerosis by increasing atherogenic biochemical localization. Finally, the attracting WSS LCS's role was more complex where it promoted or prevented atherosclerosis based on different biochemicals. We present a summary of the different pathways by which WSS influences coronary artery atherosclerosis and compare different mechanotransduction and biotransport mechanisms.

Experimental validation of computational fluid dynamics for solving isothermal and incompressible viscous fluid flow

In order to validate a computational method for solving viscous fluid flows, experiments are carried out in an eccentric cylindrical cavity showing various flow formations over a range of Reynolds numbers. Especially, in numerical solution approaches for isothermal and incompressible flows, we search for simple experimental data for evaluating accuracy as well as performance of the computational method. Verification of different computational methods is arduous, and analytic solutions are only obtained for simple geometries like a channel flow. Clearly, a method is expected to predict different flow patterns within a cavity. Thus, we propose a configuration generating different flow formations depending on the Reynolds number and make the experimental results freely available in order to be used as an assessment criterion to demonstrate the reliability of a new computational approach.

Coronary artery plaque growth: A two-way coupled shear stress-driven model

Atherosclerosis in coronary arteries can lead to plaque growth, stenosis formation, and blockage of the blood flow supplying the heart tissue. Several studies have shown that hemodynamics play an important role in the growth of coronary artery plaques. Specifically, low wall shear stress (WSS) appears to be the leading hemodynamic parameter promoting atherosclerotic plaque growth, which in turn influences the blood flow and WSS distribution. Therefore, a two-way coupled interaction exists between WSS and atherosclerosis growth. In this work, a computational framework was developed to study the coupling between WSS and plaque growth in coronary arteries. Computational fluid dynamics (CFD) was used to quantify WSS distribution. Surface mesh nodes were moved in the inward normal direction according to a growth model based on WSS. After each growth stage, the geometry was updated and the CFD simulation repeated to find updated WSS values for the next growth stage. One hundred twenty growth stages were simulated in an idealized tube and an image-based left anterior descending artery. An automated framework was developed using open-source software to couple CFD simulations with growth. Changes in plaque morphology and hemodynamic patterns during different growth stages are presented. The results show larger plaque growth towards the downstream segment of the plaque, agreeing with the reported clinical observations. The developed framework could be used to establish hemodynamic-driven growth models and study the interaction between these processes.