Session L7: Biofluids: Cardiovascular Fluid Mechanics II

Transition to turbulence in pulsating pipe flow

We report an experimental investigation of the transition to turbulence in a pulsating pipe flow. This flow is a prototype of various pulsating flows in both nature and engineering, such as in the cardiovascular system where the onset of turbulence is often possibly related to various diseases (e.g., the formation of aneurysms). The experiments are carried out in a straight rigid pipe using water with a sinusoidal modulation of the flow rate. The governing parameters, Reynolds number, Womersley number $\alpha $ (dimensionless pulsating frequency) and the pulsating amplitude$_{\mathrm{\thinspace }}A$, cover a wide range $3<\alpha <23$ and $012)$ lifetimes of turbulent spots are entirely unaffected by the pulsation, at lower frequencies they are substantially affected. With decreasing frequency much larger Reynolds numbers are needed to obtain spots of the same characteristic lifetime. Hence at low frequency transition is delayed significantly. In addition the effect of the pulsation amplitude on the transition delay is quantified.   

Quantification of disturbed wall shear stress patterns in complex cardiovascular flows

Wall shear stress (WSS) affects the cardiovascular system in numerous ways, and is thought to play an important role in the pathology of many cardiovascular diseases. The (endothelial) cells lining the inner wall of blood vessels, and perhaps the cells inside the vessel wall, can actively sense WSS and respond both chemically and mechanically. The complexity of WSS in cardiovascular flows extends both spatially and temporally. Furthermore, WSS has magnitude and direction. These facets make simple quantification of WSS in cardiovascular applications difficult. In this study we propose a framework to quantify measures such as WSS angle gradient, WSS magnitude gradient, WSS angle time derivative and WSS magnitude time derivative. We will explain the relation of these parameters to the tensorial WSS gradient and WSS vector time derivative, and propose a new methodology to unify these concepts into a single measure. The correlation between these metrics and more common WSS metrics used in the literature will be demonstrated. For demonstration, these methods will be used for the quantification of complex blood flow inside abdominal aortic aneurysms.   

Uncertainty quantification in virtual surgery predictions for single ventricle palliation

Hemodynamic results from numerical simulations of physiology in patients are invariably presented as deterministic quantities without assessment of associated confidence. Recent advances in cardiovascular simulation and Uncertainty Analysis can be leveraged to challenge this paradigm and to quantify the variability of output quantities of interest, of paramount importance to complement clinical decision making. Physiological variability and errors are responsible for the uncertainty typically associated with measurements in the clinic; starting from a characterization of these quantities in probability, we present applications in the context of estimating the distributions of lumped parameters in 0D models of single-ventricle circulation. We also present results in virtual Fontan palliation surgery, where the variability of both local and systemic hemodynamic indicators is inferred from the uncertainty in pre-operative clinical measurements. Efficient numerical algorithms are required to mitigate the computational cost of propagating the uncertainty through multiscale coupled 0D-3D models of pulsatile flow at the cavopulmonary connection. This work constitutes a first step towards systematic application of robust numerical simulations to virtual surgery predictions.   

The Direct Effect of Flexible Walls on Fontan Connection Fluid Dynamics

The current standard treatment for sufferers of congenital heart defects is the palliative Fontan procedure. The Fontan procedure results in an anastomosis of major veins directly to the branched pulmonary arteries bypassing the dysfunctional ventricle. This total cavopulmonary connection (TCPC) extends life past birth, but Fontan patients still suffer long-term complications like decreased exercise capacity, protein-losing enteropathy, and pulmonary arteriovenous malformations (PAVM). These complications have direct ties to fluid dynamics within the connection. Previous experimental and computation studies of Fontan connection fluid dynamics employed rigid vessel models. More recent studies utilize flexible models, but a direct comparison of the fundamental fluid dynamics between rigid and flexible vessels only exists for a computational model, without a direct experimental validation. Thus, this study was a direct comparison of fluid dynamics within a rigid and two compliant idealized TCPCs. 2D particle image velocimetry measurements were collected at the connection center plane. Results include power loss, hepatic flow distribution, fluid shear stress, and flow structure recognition. The effect of flexible walls on these values and clinical impact will be discussed.   

GPU-accelerated Lattice Boltzmann method for anatomical extraction in patient-specific computational hemodynamics

Existing research of patient-specific computational hemodynamics (PSCH) heavily relies on software for anatomical extraction of blood arteries. Data reconstruction and mesh generation have to be done using existing commercial software due to the gap between medical image processing and CFD, which increases computation burden and introduces inaccuracy during data transformation thus limits the medical applications of PSCH. We use lattice Boltzmann method (LBM) to solve the level-set equation over an Eulerian distance field and implicitly and dynamically segment the artery surfaces from radiological CT/MRI imaging data. The segments seamlessly feed to the LBM based CFD computation of PSCH thus explicit mesh construction and extra data management are avoided. The LBM is ideally suited for GPU (graphic processing unit)-based parallel computing. The parallel acceleration over GPU achieves excellent performance in PSCH computation. An application study will be presented which segments an aortic artery from a chest CT dataset and models PSCH of the segmented artery.   

One dimensional modeling of blood flow in large networks

A fast and valid simulation of blood flow in large networks of vessels can be achieved with a one-dimensional viscoelastic model. In this paper, we developed a parallel code with this model and computed several networks: a circle of arteries, a human systemic network with 55 arteries and a vascular network of mouse kidney with more than one thousand segments. The numerical results were verified and the speedup of parallel computing was tested on multi-core computers. The evolution of pressure distributions in all the networks were visualized and we can see clearly the propagation patterns of the waves. This provides us a convenient tool to simulate blood flow in networks.   

Quantitative Assessment of Wall Shear Stress in an Aortic Coarctation -- Impact of Virtual Interventions

Turbulent and wall impinging blood flow causes abnormal shear forces onto the lumen and may play an important role in the pathogenesis of numerous cardiovascular diseases. In the present study, wall shear stress (WSS) and related flow parameters were studied in a pre-treated aortic coarctation (CoA) as well as after several virtual interventions using computational fluid dynamics (CFD). Patient-specific geometry and flow conditions were derived from magnetic resonance imaging (MRI) data. Finite element analysis was performed to acquire six different dilated CoAs. The unsteady pulsatile flow was resolved by large eddy simulation (LES) including non-Newtonian blood rheology. Pre-intervention, the presence of jet flow wall impingement caused an elevated WSS zone, with a distal region of low and oscillatory WSS. After intervention, cases with a more favorable centralized jet showed reduced high WSS values at the opposed wall. Despite significant turbulence reduction post-treatment, enhanced regions of low and oscillatory WSS were observed for all cases. This numerical method has demonstrated the morphological impact on WSS distribution in an CoA. With the predictability and validation capabilities of a combined CFD/MRI approach, a step towards patient-specific intervention planning is taken.   

An effective fractal-tree closure model for simulating blood flow in large arterial networks

The aim of the present work is to address the closure problem for hemodynamics simulations by developing a flexible and effective model that accurately distributes flow in the downstream vasculature and can stably provide a physiological pressure outflow boundary condition. We model blood flow in the sub-pixel vasculature by using a nonlinear 1D model in self-similar networks of compliant arteries that mimic the structure and hierarchy of vessels in the meso-vascular regime. The proposed model accounts for wall viscoelasticity and non-Newtonian flow effects in arterioles, overcomes cut-off radius sensitivity issues by introducing a monotonically decreasing artery length to radius ratio across different generations of the fractal tree, and convergences to a periodic state in just two cardiac cycles. The resulting fractal trees typically consist of thousands to millions of arteries, posing the need for efficient parallel algorithms. To this end, we have developed a scalable hybrid MPI/OpenMP solver that is capable of computing near real-time solutions. The proposed model is tested on a large patient-specific cranial network returning physiological flow and pressure wave predictions without requiring any parameter estimation or calibration procedures.   

A Computational Model for Thrombus Formation in Response to Cardiovascular Implantable Devices

Cardiovascular implantable devices elicit complex physiological responses within blood. Notably, alterations in blood flow dynamics and interactions between blood proteins and biomaterial surface chemistry may lead to the formation of thrombus. For some devices, such as stents and heart valves, this is an adverse outcome. For other devices, such as embolic aneurysm treatments, efficient blood clot formation is desired. Thus a method to study how biomedical devices induce thrombosis is paramount to device development and optimization. A multiscale, multiphysics computational model is developed to predict thrombus formation within the vasculature. The model consists of a set of convection-diffusion-reaction partial differential equations for blood protein constituents involved in the progression of the clotting cascades. This model is used to study thrombus production from endovascular devices with the goal of optimizing the device design to generate the desired clotting response. This work was performed in part under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.   

In Vitro MRV-based Hemodynamic Study of Complex Helical Flow in a Patient-specific Jugular Model

Neurointerventional Radiologists are frequently requested to evaluate the venous side of the intracranial circulation for a variety of conditions including: Chronic Cerebrospinal Venous Insufficiency thought to play a role in the development of multiple sclerosis; sigmoid sinus diverticulum which has been linked to the presence of pulsatile tinnitus; and jugular vein distension which is related to cardiac dysfunction. Most approaches to evaluating these conditions rely on structural assessment or two dimensional flow analyses. This study was designed to investigate the highly complex jugular flow conditions using magnetic resonance velocimetry (MRV). A jugular phantom was fabricated based on the geometry of the dominant jugular in a tinnitus patient. Volumetric three-component time-resolved velocity fields were obtained using 4D PC-MRI --with the protocol enabling turbulence acquisition-- and the patient-specific pulsatile waveform. Flow was highly complex exhibiting regions of jet, high swirling strength, and strong helical pattern with the core originating from the focal point of the jugular bulb. Specifically, flow was analyzed for helicity and the level of turbulence kinetic energy elevated in the core of helix and distally, in the post-narrowing region.   

Velocimetry modalities for secondary flows in a curved artery test section

Secondary flow structures arise due to curvature-related centrifugal forces and pressure imbalances. These flow structures influence wall shear stress and alter blood particle residence times. Magnetic resonance velocimetry (MRV) and particle image velocimetry (PIV) techniques were implemented independently, under the same physiological inflow conditions (Womersley number = 4.2). A 180-degree curved artery test section with curvature ratio (1/7) was used as an idealized geometry for curved arteries. Newtonian blood analog fluids were used for both MRV and PIV experiments. The MRV-technique offers the advantage of three-dimensional velocity field acquisition without requiring optical access or flow markers. Phase-averaged, two-dimensional, PIV-data at certain cross-sectional planes and inflow phases were compared to phase-averaged MRV-data to facilitate the characterization of large-scale, Dean-type vortices. Coherent structures detection methods that included a novel wavelet decomposition-based approach to characterize these flow structures was applied to both PIV- and MRV-data. The overarching goal of this study is the detection of motific, three-dimensional shapes of secondary flow structures using MRV techniques with guidance obtained from high fidelity, 2D-PIV measurements.   

Flow Structures in a Healthy and Plaqued Artificial Artery using Fully Index Matched Vascular Flow Facility

Particle Image Velocimetry measurements are made in a closed loop fully index matched flow facility to study the flow structures and flow wall interactions in healthy and diseased model arteries. The test section is 0.63 m long and the facility is capable of emulating both steady and pulsatile flows under physiologically relevant conditions. The model arteries are in-house developed compliant polymer (PDMS) tubes with 1 cm diameter and 1 mm wall thickness. The Reynolds numbers of flows vary up to 20,000. The plaque is simulated by introducing a radially asymmetric bump that can be varied in shape, size and compliancy. The overall compliancy of the model can be also controlled by varying ratio between the elastomer and the curing agent. The tubes are doped with particles allowing the simultaneous measurements of wall deformation and flows over it. The working fluid in the facility is NaI and is refractive index matched to the PDMS model. This allows flow measurement very close to the wall and measurement of wall shear stress. The aim of this study is to characterize the changes in flow as the compliancy and geometry of blood vessels change due to age or disease. These differences can be used to develop a diagnostic tool to detect early onset of vascular diseases.