Inlet boundary conditions for blood flow simulations in truncated arterial networks

In Vivo Intravascular Optical Coherence Tomography (IVOCT) Structural and Blood Flow Imaging Based Mechanical Simulation Analysis of a Blood Vessel

INTRODUCTION

Computer modelling of blood vessels based on biomedical imaging provides important hemodynamic and biomechanical information for vascular disease studies and diagnosis. However due to lacking well-defined physiological blood flow profiles, the accuracy of the simulation results is often not guaranteed. Flow velocity profiles of a specific cross section of a blood vessel were obtained by in vivo Doppler intravascular optical coherence tomography (IVOCT) lately. However due to the influence of the catheter, the velocity profile imaged by IVOCT can't be applied to simulation directly.

METHODS

A simulation-experiment combined method to determine the inlet flow boundary based on in vivo porcine carotid Doppler IVOCT imaging is proposed. A single conduit carotid model was created from the 3D IVOCT structural images using an image processing-computer aided design combined method.

RESULTS

With both high- resolution arterial model and near physiological blood flow profile, stress analysis by fluid-structure interaction and computational fluid dynamics were performed. The influence of the catheter to the wall shear stress, the hemodynamics and the stresses of the carotid wall under the measured inlet flow and various outlet pressure boundary conditions, are analyzed.

CONCLUSION

This study provides a solution to the difficulty of getting inlet flow boundary for numerical simulation of arteries. It paves the way for developing IVOCT based vascular stress analysis and imaging methods for the studies and diagnosis of vascular diseases.

Impact of tapering of arterial vessels on blood pressure, pulse wave velocity, and wave intensity analysis using one-dimensional computational model

The angle of arterial tapering increases with ageing, and the geometrical changes of the aorta may cause an increase in central arterial pressure and stiffness. The impact of tapering has been primarily studied using frequency-domain transmission line theories. In this work, we revisit the problem of tapering and investigate its effect on blood pressure and pulse wave velocity (PWV) using a time-domain analysis with a 1D computational model. First, tapering is modelled as a stepwise reduction in diameter and compared with results from a continuously tapered segment. Next, we studied wave reflections in a combination of stepwise diameter reduction of straight vessels and bifurcations, then repeated the experiments with decreasing the length to physiological values. As the model's segments became shorter in length, wave reflections and re-reflections resulted in waves overlapping in time. We extended our work by examining the effect of increasing the tapering angle on blood pressure and wave intensity in physiological models: a model of the thoracic aorta and a model of upper thoracic and descending aorta connected to the iliac bifurcation. Vessels tapering inherently changed the ratio between the inlet and outlet cross-sectional areas, increasing the vessel resistance and reducing the compliance compared with non-tapered vessels. These variables influence peak and pulse pressure. In addition, it is well established that pulse wave velocity increases in an ageing arterial tree. This work provides confirmation that tapering induces reflections and offers an additional explanation to the observation of increased peak pressure and decreased diastolic pressure distally in the arterial tree.

CardioFAN: open source platform for noninvasive assessment of pulse transit time and pulsatile flow in hyperelastic vascular networks

A profound analysis of pressure and flow wave propagation in cardiovascular systems is the key in noninvasive assessment of hemodynamic parameters. Pulse transit time (PTT), which closely relates to the physical properties of the cardiovascular system, can be linked to variations of blood pressure and stroke volume to provide information for patient-specific clinical diagnostics. In this work, we present mathematical and numerical tools, capable of accurately predicting the PTT, local pulse wave velocity, vessel compliance, and pressure/flow waveforms, in a viscous hyperelastic cardiovascular network. A new one-dimensional framework, entitled cardiovascular flow analysis (CardioFAN), is presented to describe the pulsatile fluid-structure interaction in the hyperelastic arteries, where pertaining hyperbolic equations are solved using a high-resolution total variation diminishing Lax-Wendroff method. The computational algorithm is validated against well-known numerical, in vitro and in vivo data for networks of main human arteries with 55, 37 and 26 segments, respectively. PTT prediction is improved by accounting for hyperelastic nonlinear waves between two arbitrary sections of the arterial tree. Consequently, arterial compliance assignments at each segment are improved in a personalized model of the human aorta and supra-aortic branches with 26 segments, where prior in vivo data were available for comparison. This resulted in a 1.5% improvement in overall predictions of the waveforms, or average relative errors of 5.5% in predicting flow, luminal area and pressure waveforms compared to prior in vivo measurements. The open source software, CardioFAN, can be calibrated for arbitrary patient-specific vascular networks to conduct noninvasive diagnostics.

Numerical Study of the Blood Flow in a Deformable Human Aorta

In this work, we present a numerical investigation of blood flow in a portion of the human vascular system. More precisely, the present work analyzed the blood flow in the upper portion of the aorta. The aorta and its ramified blood vessels are surrounded by the cardiac muscle. The blood flow generates pressure on the internal surfaces of the artery and its ramifications, thereby causing deformation of the cardiac muscle. The numerical analysis used the Navier–Stokes equations as the governing equations of blood flow for the calculation of the velocity field and pressure distribution in the blood. The neo-Hookean hyperelastic model was used for the description of the behavior of the vessel walls. The velocity and pressure distributions were analyzed. The deformation of the vessel was also investigated. The numerical results could be used to better understand and predict the factors that trigger cardiovascular diseases and distortions of the aorta and as a diagnostic tool in clinical applications.

Assessment of boundary conditions for CFD simulation in human carotid artery

Computational fluid dynamics (CFD) is an increasingly used method for investigation of hemodynamic parameters and their alterations under pathological conditions, which are important indicators for diagnosis of cardiovascular disease. In hemodynamic simulation models, the employment of appropriate boundary conditions (BCs) determines the computational accuracy of the CFD simulation in comparison with pressure and velocity measurements. In this study, we have first assessed the influence of inlet boundary conditions on hemodynamic CFD simulations. We selected two typical patients suspected of carotid artery disease, with mild stenosis and severe stenosis. Both patients underwent digital subtraction angiography (DSA), magnetic resonance angiography, and the invasive pressure guide wire measured pressure profile. We have performed computational experiments to (1) study the hemodynamic simulation outcomes of distributions of wall shear stress, pressure, pressure gradient and (2) determine the differences in hemodynamic performances caused by inlet BCs derived from DSA and Womersley analytical solution. Our study has found that the difference is related to the severity of the stenosis; the greater the stenosis, the more the difference ensues. Further, in our study, the two typical subjects with invasively measured pressure profile and thirty subjects with ultrasound Doppler velocimeter (UDV) measurement served as the criteria to evaluate the hemodynamic outcomes of wall shear stress, pressure, pressure gradient and velocity due to different outlet BCs based on the Windkessel model, structured-tree model, and fully developed flow model. According to the pressure profiles, the fully developed model appeared to have more fluctuations compared with the other two models. The Windkessel model had more singularities before convergence. The three outlet BCs models also showed good correlation with the UDV measurement, while the Windkessel model appeared to be slightly better ([Formula: see text]). The structured-tree model was seen to have the best performance in terms of available computational cost and accuracy. The results of our numerical simulation and the good correlation with the computed pressure and velocity with their measurements have highlighted the effectiveness of CFD simulation in patient-specific human carotid artery with suspected stenosis.

Validation and Application of a Physically Nonlinear ID Computational Model for Bifurcated Arterial Networks

Reduced fluid-structure interaction models are the key component of hemodynamic simulation. In this work, a multi-purpose computational model applicable to specific physiological components such as arterial, venous and cerebrospinal fluid circulatory systems has been developed based on the Hamilton's variational principle. This model encompasses a viscous Newtonian fluid structure interaction (FSI) framework for the large compliant bifurcated arterial networks and its subsystems. This approach provides the groundworks for a correct formulation of reduced FSI models with an account for arbitrary non-linear viscoelastic properties of a compliant vascular tree. The hyperbolic properties of the derived mathematical model are analyzed and used to construct the Lax-Wendroff finite volume numerical scheme, with second order accuracy in time and space. The computational algorithm is validated against well-known numerical and in vitro experimental data reported in the literature for the case of human arterial trees, comprising 55 and 37 main arterial vessels. Utilizing the physics based nonlinear constitutive framework, this model can be adequately tested, calibrated and applied for patient-specific clinical diagnosis and prediction.

Non-Newtonian Blood Flow Simulation of Diastolic Phase in Bileaflet Mechanical Heart Valve Implanted in a Realistic Aortic Root Containing Coronary Arteries

Coronary arteries, which are branched from the sinuses, have tangible effects on the hemodynamic performance of the bileaflet mechanical heart valve (BMHV), especially in the diastolic phase. To better understand this issue, a computer model of ascending aorta including realistic sinus shapes and coronary arteries has been generated in this study in order to investigate the BMHV performance during diastole. Three-dimensional transient numerical analysis is conducted to simulate the diastolic blood flow through the hinges and in coronary arteries under the assumption of non-Newtonian behavior. Results indicate that as blood flows to the coronary arteries mainly during diastole, leakage flow from the hinge and other gaps will change considering the influence of coronary arteries. In addition, BMHV in the case of aortic replacement will increase blood flow rate into the coronary arteries about 100% as the mechanical valve resistance is higher than a native heart valve. Also, it will change the wall shear stress (WSS) distribution and increase coronary artery disease (CAD) potential. It is found out that although less leakage flow reduces the velocity magnitudes through the gaps, the shear stress acting on blood elements with non-Newtonian assumption will be detrimental in the hinge corner at the ventricular side. High WSS of 1800 Pa is observed at beginning of diastole at this region.

Patient-specific structural effects on hemodynamics in the ischemic lower limb artery

Lower limb peripheral artery disease is a prevalent chronic non-communicable disease without obvious symptoms. However, the effect of ischemic lower limb peripheral arteries on hemodynamics remains unclear. In this study, we investigated the variation of the hemodynamics caused by patient-specific structural artery characteristics. Computational fluid dynamic simulations were performed on seven lower limb (including superficial femoral, deep femoral and popliteal) artery models that were reconstructed from magnetic resonance imaging. We found that increased wall shear stress (WSS) was mainly caused by the increasing severity of stenosis, bending, and branching. Our results showed that the increase in the WSS value at a stenosis at the bifurcation was 2.7 Pa. In contrast, the isolated stenosis and branch caused a WSS increase of 0.7 Pa and 0.5 Pa, respectively. The WSS in the narrow popliteal artery was more sensitive to a reduction in radius. Our results also demonstrate that the distribution of the velocity and pressure gradient are highly structurally related. At last, Ultrasound Doppler velocimeter measured result was presented as a validation. In conclusion, the distribution of hemodynamics may serve as a supplement for clinical decision-making to prevent the occurrence of a morbid or mortal ischemic event.

Measurement and modeling of coronary blood flow

Ischemic heart disease that comprises both coronary artery disease and microvascular disease is the single greatest cause of death globally. In this context, enhancing our understanding of the interaction of coronary structure and function is not only fundamental for advancing basic physiology but also crucial for identifying new targets for treating these diseases. A central challenge for understanding coronary blood flow is that coronary structure and function exhibit different behaviors across a range of spatial and temporal scales. While experimental studies have sought to understand this feature by isolating specific mechanisms, in tandem, computational modeling is increasingly also providing a unique framework to integrate mechanistic behaviors across different scales. In addition, clinical methods for assessing coronary disease severity are continuously being informed and updated by findings in basic physiology. Coupling these technologies, computational modeling of the coronary circulation is emerging as a bridge between the experimental and clinical domains, providing a framework to integrate imaging and measurements from multiple sources with mathematical descriptions of governing physical laws. State-of-the-art computational modeling is being used to combine mechanistic models with data to provide new insight into coronary physiology, optimization of medical technologies, and new applications to guide clinical practice.

Reducing the number of parameters in 1D arterial blood flow modeling: less is more for patient-specific simulations

Patient-specific one-dimensional (1D) blood flow modeling requires estimating model parameters from available clinical data, ideally acquired noninvasively. The larger the number of arterial segments in a distributed 1D model, the greater the number of input parameters that need to be estimated. We investigated the effect of a reduction in the number of arterial segments in a given distributed 1D model on the shape of the simulated pressure and flow waveforms. This is achieved by systematically lumping peripheral 1D model branches into windkessel models that preserve the net resistance and total compliance of the original model. We applied our methodology to a model of the 55 larger systemic arteries in the human and to an extended 67-artery model that contains the digital arteries that perfuse the fingers. Results show good agreement in the shape of the aortic and digital waveforms between the original 55-artery (67-artery) and reduced 21-artery (37-artery) models. Reducing the number of segments also enables us to investigate the effect of arterial network topology (and hence reflection sites) on the shape of waveforms. Results show that wave reflections in the thoracic aorta and renal arteries play an important role in shaping the aortic pressure and flow waves and in generating the second peak of the digital pressure and flow waves. Our novel methodology is important to simplify the computational domain while maintaining the precision of the numerical predictions and to assess the effect of wave reflections.

Hemodynamic Shear Stress and Endothelial Dysfunction in Hemodialysis Access

Surgically-created blood conduits used for chronic hemodialysis, including native arteriovenous fistulas (AVFs) and synthetic AV grafts (AVGs), are the lifeline for kidney failure patients. Unfortunately, each has its own limitations: AVFs often fail to mature to become useful for dialysis and AVGs often fail due to stenosis as a result of neointimal hyperplasia, which preferentially forms at the graft-venous anastomosis. No clinical therapies are currently available to significantly promote AVF maturation or prevent neointimal hyperplasia in AVGs. Central to devising strategies to solve these problems is a complete mechanistic understanding of the pathophysiological processes. The pathology of arteriovenous access problems is likely multi-factorial. This review focuses on the roles of fluid-wall shear stress (WSS) and endothelial cells (ECs). In arteriovenous access, shunting of arterial blood flow directly into the vein drastically alters the hemodynamics in the vein. These hemodynamic changes are likely major contributors to non-maturation of an AVF vein and/or formation of neointimal hyperplasia at the venous anastomosis of an AVG. ECs separate blood from other vascular wall cells and also influence the phenotype of these other cells. In arteriovenous access, the responses of ECs to aberrant WSS may subsequently lead to AVF non-maturation and/or AVG stenosis. This review provides an overview of the methods for characterizing blood flow and calculating WSS in arteriovenous access and discusses EC responses to arteriovenous hemodynamics. This review also discusses the role of WSS in the pathology of arteriovenous access, as well as confounding factors that modulate the impact of WSS.

Graphics processing unit accelerated one-dimensional blood flow computation in the human arterial tree

One-dimensional blood flow models have been used extensively for computing pressure and flow waveforms in the human arterial circulation. We propose an improved numerical implementation based on a graphics processing unit (GPU) for the acceleration of the execution time of one-dimensional model. A novel parallel hybrid CPU-GPU algorithm with compact copy operations (PHCGCC) and a parallel GPU only (PGO) algorithm are developed, which are compared against previously introduced PHCG versions, a single-threaded CPU only algorithm and a multi-threaded CPU only algorithm. Different second-order numerical schemes (Lax-Wendroff and Taylor series) are evaluated for the numerical solution of one-dimensional model, and the computational setups include physiologically motivated non-periodic (Windkessel) and periodic boundary conditions (BC) (structured tree) and elastic and viscoelastic wall laws. Both the PHCGCC and the PGO implementations improved the execution time significantly. The speed-up values over the single-threaded CPU only implementation range from 5.26 to 8.10 × , whereas the speed-up values over the multi-threaded CPU only implementation range from 1.84 to 4.02 × . The PHCGCC algorithm performs best for an elastic wall law with non-periodic BC and for viscoelastic wall laws, whereas the PGO algorithm performs best for an elastic wall law with periodic BC.

Implementing boundary conditions in simulations of arterial flows

Computational hemodynamic models of the cardiovascular system are often limited to finite segments of the system and therefore need well-controlled inlet and outlet boundary conditions. Classical boundary conditions are measured total pressure or flow rate imposed at the inlet and impedances of RLR, RLC, or LR filters at the outlet. We present a new approach based on an unidirectional propagative approach (UPA) to model the inlet/outlet boundary conditions on the axisymmetric Navier-Stokes equations. This condition is equivalent to a nonreflecting boundary condition in a fluid-structure interaction model of an axisymmetric artery. First we compare the UPA to the best impedance filter (RLC). Second, we apply this approach to a physiological situation, i.e., the presence of a stented segment into a coronary artery. In that case a reflection index is defined which quantifies the amount of pressure waves reflected upon the singularity.

One-dimensional model for propagation of a pressure wave in a model of the human arterial network: comparison of theoretical and experimental results

Pulse wave evaluation is an effective method for arteriosclerosis screening. In a previous study, we verified that pulse waveforms change markedly due to arterial stiffness. However, a pulse wave consists of two components, the incident wave and multireflected waves. Clarification of the complicated propagation of these waves is necessary to gain an understanding of the nature of pulse waves in vivo. In this study, we built a one-dimensional theoretical model of a pressure wave propagating in a flexible tube. To evaluate the applicability of the model, we compared theoretical estimations with measured data obtained from basic tube models and a simple arterial model. We constructed different viscoelastic tube set-ups: two straight tubes; one tube connected to two tubes of different elasticity; a single bifurcation tube; and a simple arterial network with four bifurcations. Soft polyurethane tubes were used and the configuration was based on a realistic human arterial network. The tensile modulus of the material was similar to the elasticity of arteries. A pulsatile flow with ejection time 0.3 s was applied using a controlled pump. Inner pressure waves and flow velocity were then measured using a pressure sensor and an ultrasonic diagnostic system. We formulated a 1D model derived from the Navier-Stokes equations and a continuity equation to characterize pressure propagation in flexible tubes. The theoretical model includes nonlinearity and attenuation terms due to the tube wall, and flow viscosity derived from a steady Hagen-Poiseuille profile. Under the same configuration as for experiments, the governing equations were computed using the MacCormack scheme. The theoretical pressure waves for each case showed a good fit to the experimental waves. The square sum of residuals (difference between theoretical and experimental wave-forms) for each case was <10.0%. A possible explanation for the increase in the square sum of residuals is the approximation error for flow viscosity. However, the comparatively small values prove the validity of the approach and indicate the usefulness of the model for understanding pressure propagation in the human arterial network.

Numerical analysis for the blood flow in a patient-specific ophthalmic artery

In this paper we investigate blood flow in the ophthalmic artery (OA) which is the major artery supplying blood to the eyes. An OA and several other cerebral arteries are digitized from a computed tomography angiography (CTA) image of an aneurysm patient. Utilizing a reduced version (1D) of the governing Navier-Stokes equations we solve the transient flow in these arteries. The flow waveform of the patient-OA is compared with that in a healthy vascular tree, and also with published ultrasonic measurements. We found that hyperemia rather than ischemia occurred in the OA, and we suggest that this was unlikely to be the cause of impaired vision in the patient. A more likely explanation is the compression of the optic nerves caused by the mass of the aneurysm.