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The dialysis catheter indwelling in human bodies has a high risk of inducing thrombus and stenosis. Biomechanical research showed that such physiological complications are triggered by the wall shear stress of the vascular vessel. This study aimed to assess the impact of CVC implantation on central venous haemodynamics and the potential alterations in the haemodynamic environment related to thrombus development. The SVC structure was built from the images from computed tomography. The blood flow was calculated using the Carreau model, and the fluid domain was determined by CFD. The vascular wall and the CVC were computed using FEA. The elastic interaction between the vessel wall and the flow field was considered using FSI simulation. With consideration of the effect of coupling, it was shown that the catheter vibrated in the vascular systems due to the periodic variation of blood pressure, with an amplitude of up to 10% of the vessel width. Spiral flow was observed along the catheter after CVC indwelling, and recirculation flow appeared near the catheter tip. High OSI and WSS regions occurred at the catheter tip and the vascular junction. The arterial lumen tip had a larger effect on the WSS and OSI values on the vascular wall. Considering FSI simulation, the movement of the catheter inside the blood flow was simulated in the deformable vessel. After CVC indwelling, spiral flow and recirculation flow were observed near the regions with high WSS and OSI values. [ABSTRACT FROM AUTHOR]

The deformability of blood vessels in one‐dimensional blood flow models is typically described through a pressure‐area relation, known as the tube law. The most used tube laws take into account the elastic and viscous components of the tension of the vessel wall. Accurately parametrizing the tube laws is vital for replicating pressure and flow wave propagation phenomena. Here, we present a novel mathematical‐property‐preserving approach for the estimation of the parameters of the elastic and viscoelastic tube laws. Our goal was to estimate the parameters by using ovine and human in vitro data, while constraining them to meet prescribed mathematical properties. Results show that both elastic and viscoelastic tube laws accurately describe experimental pressure‐area data concerning both quantitative and qualitative aspects. Additionally, the viscoelastic tube law can provide a qualitative explanation for the observed hysteresis cycles. The two models were evaluated using two approaches: (i) allowing all parameters to freely vary within their respective ranges and (ii) fixing some of the parameters. The former approach was found to be the most suitable for reproducing pressure‐area curves. [ABSTRACT FROM AUTHOR]

The reconstruction of blood velocity in a vessel from contrast enhanced x‐ray computed tomography projections is a complex inverse problem. It can be formulated as reconstruction problem with a partial differential equation constraint. A solution can be estimated with the a variational adjoint method and proper orthogonal decomposition (POD) basis. In this work, we investigate new inversion approaches based on PODs coupled with deep learning methods. The effectiveness of the reconstruction methods is shown with simulated realistic stationary blood flows in a vessel. The methods outperform the reduced adjoint method and show large speed‐up at the online stage. [ABSTRACT FROM AUTHOR]

Prediction of blood cell flow is known as the difficult research by reason of the complexity of blood vessel. In this study, considering the complex structure of blood vessels, a mechanical model for red blood cell (RBC) based on unstructured grid has been established to study the flow characteristics of RBCs in complex blood vessels. In the model, the strain‐energy function by Skalak is employed to model the shear elasticity and surface‐area conservation of the membrane, and the hinge spring is used to describe the forces originating from local bending of the membrane. The immersed boundary method is utilized to couple the interphase force. Using the model, the stretching test of RBC is compared with the experiment data, and the good agreement verified the validation of the present model. The morphology of red blood cell and the blood viscosity in micro‐vessel are studied. RBCs move with a symmetric shape (parachute shape) in small blood vessels, and the buckling instability is observed when the RBC flow slowly through a micro‐vessel or a converging–diverging capillary. When the vessel diameter is around 10 μm, the reverse Fahraeus‐Lindqvist effect is presented. The blood apparent viscosity shows linear increase with the blood hematocrit. In addition, Malaria infection can make the RBC deformability decreased and the blood apparent viscosity increased. [ABSTRACT FROM AUTHOR]

Summary: The mechanism of many cardiovascular diseases can be understood by studying the pressure distribution in blood vessels. Direct pressure measurements, however, require invasive probing and provide only single‐point data. Alternatively, relative pressure fields can be reconstructed from imaging‐based velocity measurements by considering viscous and inertial forces. Both contributions can be potential troublemakers in pressure reconstruction: the former due to its higher‐order derivatives, and the latter because of the quadratic nonlinearity in the convective acceleration. Viscous and convective terms can be treated in various forms, which, although equivalent for ideal measurements, can perform differently in practice. In fact, multiple versions are often used in literature, with no apparent consensus on the more suitable variants. In this context, the present work investigates the performance of different versions of relative pressure estimators. For viscous effects, in particular, two new modified estimators are presented to circumvent second‐order differentiation without requiring surface integrals. In‐silico and in‐vitro data in the typical regime of cerebrovascular flows are considered, allowing a systematic noise sensitivity study. Convective terms are shown to be the main source of error, even for flows with pronounced viscous component. Moreover, the conservation (often integrated) form of convection exhibits higher noise sensitivity than the standard convective description, in all three families of estimators considered here. For the classical pressure Poisson estimator, the present modified version of the viscous term tends to yield better accuracy than the (recently introduced) integrated form, although this effect is in most cases negligible when compared to convection‐related errors. [ABSTRACT FROM AUTHOR]

Computational hemodynamics is being developed as an alternative approach for assisting clinical diagnosis and treatment planning for liver diseases. The technology is non‐invasive, but the computational time could be high when the full geometry of the blood vessels is taken into account. Existing approaches use either one‐dimensional model of the artery or simplified three‐dimensional tubular geometry in order to reduce the computational time, but the accuracy is sometime compromised, for example, when simulating blood flows in arteries with plaque. In this work, we study a highly parallel method for the transient incompressible Navier–Stokes equations for the simulation of the blood flows in the full three‐dimensional patient‐specific hepatic artery, portal vein and hepatic vein. As applications, we also simulate the flow in a patient with hepatectomy and calculate the S (PPG). One of the advantages of simulating blood flows in all hepatic vessels is that it provides a direct estimate of the PPG, which is a gold standard value to assess the portal hypertension. Moreover, the robustness and scalability of the algorithm are also investigated. A 83% parallel efficiency is achieved for solving a problem with 7 million elements on a supercomputer with more than 1000 processor cores. [ABSTRACT FROM AUTHOR]

In this work, we introduce an algorithmic approach to generate microvascular networks starting from larger vessels that can be reconstructed without noticeable segmentation errors. Contrary to larger vessels, the reconstruction of fine‐scale components of microvascular networks shows significant segmentation errors, and an accurate mapping is time and cost intense. Thus there is a need for fast and reliable reconstruction algorithms yielding surrogate networks having similar stochastic properties as the original ones. The microvascular networks are constructed in a marching way by adding vessels to the outlets of the vascular tree from the previous step. To optimise the structure of the vascular trees, we use Murray's law to determine the radii of the vessels and bifurcation angles. In each step, we compute the local gradient of the partial pressure of oxygen and adapt the orientation of the new vessels to this gradient. At the same time, we use the partial pressure of oxygen to check whether the considered tissue block is supplied sufficiently with oxygen. Computing the partial pressure of oxygen, we use a 3D‐1D coupled model for blood flow and oxygen transport. To decrease the complexity of a fully coupled 3D model, we reduce the blood vessel network to a 1D graph structure and use a bi‐directional coupling with the tissue which is described by a 3D homogeneous porous medium. The resulting surrogate networks are analysed with respect to morphological and physiological aspects. [ABSTRACT FROM AUTHOR]

In recent years, the complexity of vessel networks for one-dimensional blood flow models has significantly increased, because of enhanced anatomical detail or automatic peripheral vasculature generation, for example. This fact, along with the application of these models in uncertainty quantification and parameter estimation poses the need for extremely efficient numerical solvers. The aim of this work is to present a finite volume solver for one-dimensional blood flow simulations in networks of elastic and viscoelastic vessels, featuring high-order space-time accuracy and local time stepping (LTS). The solver is built on (i) a high-order finite volume type numerical scheme, (ii) a high-order treatment of the numerical solution at internal vertexes of the network, often called junctions, and (iii) an accurate LTS strategy. The accuracy of the proposed methodology is verified by empirical convergence tests. Then, the resulting LTS scheme is applied to arterial networks of increasing complexity and spatial scale heterogeneity, with a number of one-dimensional segments ranging from a few tens up to several thousands and vessel lengths ranging from less than a millimeter up to tens of centimeters, in order to evaluate its computational cost efficiency. The proposed methodology can be extended to any other hyperbolic system for which network applications are relevant. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY An extension of a total variation diminishing (TVD) scheme to solve one-dimensional (1D) blood flow for human circulation is proposed. This method is simple as it involves only a few modifications to existing shock-capturing TVD schemes. We have applied the method to a wide range of test cases including a complete simulation of the human vascular network. Excellent solutions have been demonstrated for problems involving varying and discontinuous mechanical properties of blood vessels. For 1D network simulations, the method has been shown to agree well with the reported computational results. Finally, the method has been demonstrated to compare favorably with in vivo experiments set up to study the impact of circle of Willis anomalies on flow patterns in the cerebral arterial system. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY A coupled computational model of the foot consisting of a three-dimensional soft tissue continuum and a one-dimensional (1D) transient blood flow network is presented in this article. The primary aim of the model is to investigate the blood flow in major arteries of the pathologic foot where the soft tissue stiffening occurs. It has been reported in the literature that there could be up to about five-fold increase in the mechanical stiffness of the plantar soft tissues in pathologic (e.g. diabetic) feet compared with healthy ones. The increased stiffness results in higher tissue hydrostatic pressure within the plantar area of the foot when loaded. The hydrostatic pressure acts on the external surface of blood vessels and tend to reduce the flow cross-section area and hence the blood supply. The soft tissue continuum model of the foot was modelled as a tricubic Hermite finite element mesh representing all the muscles, skin and fat of the foot and treated as incompressible with transversely isotropic properties. The details of the mechanical model of soft tissue are presented in the companion paper, Part 1. The deformed state of the soft tissue continuum because of the applied ground reaction force at three foot positions (heel-strike, midstance and toe-off) was obtained by solving the Cauchy equations based on the theory of finite elasticity using the Galerkin finite element method. The geometry of the main arterial network in the foot was represented using a 1D Hermite cubic finite element mesh. The flow model consists of 1D Navier-Stokes equations and a nonlinear constitutive equation to describe vessel radius-transmural pressure relation. The latter was defined as the difference between the fluid and soft tissue hydrostatic pressure. Transient flow governing equations were numerically solved using the two-step Lax-Wendroff finite difference method. The geometry of both the soft tissue continuum and arterial network is anatomically-based and was developed using the data derived from visible human images and magnetic resonance images of a healthy male volunteer. Simulation results reveal that a two-fold increase in tissue stiffness leads to about 28% reduction in blood flow to the affected region.Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this study, a coupled dimensionally-heterogeneous model of the systemic circulation is applied in order to study computationally the influence of the heart rate in the local hemodynamics. This is achieved by using a 3D-1D-0D model of the whole arterial tree accounting for: details of the local blood flow in the vessel of interest through 3D models, the wave propagation phenomena in the larger arteries by means of 1D models and, the peripheral microvascular beds via 0D models. Two applications are presented which aim at assessing the influence of the global setting of the vascular network on the local hemodynamics. In the first example, the hemodynamics in a patient-specific model of the abdominal aorta is studied for two different systemic scenarios corresponding to different resting heart rates. In the second example, the blood flow in a standardized model of the carotid artery is analyzed for different heart rates including the resting state and several other exercise regimes. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We present a multi-model approach to the study of side-effects of endovascular implants. A 2D model of elastic walls and a local 3D model of blood flow are combined with a 1D network blood circulation model. The three numerical models form an endovascular computational stand. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Tortuous vessels are often observed in vivo and could hinder or even disrupt blood flow to distal organs. Besides genetic and biological factors, the in vivo mechanical loading seems to play a role in the formation of tortuous vessels, but the mechanism for formation of helical vessel shape remains unclear. Accordingly, the aim of this study was to investigate the biomechanical loads that trigger the occurrence of helical buckling in blood vessels using finite element analysis. Porcine carotid arteries were modeled as thick‐walled cylindrical tubes using generalized Fung and Holzapfel‐Gasser‐Ogden constitutive models. Physiological loadings, including axial tension, lumen pressure, and axial torque, were applied. Simulations of various geometric dimensions, different constitutive models and at various levels of axial stretch ratios, lumen pressures, and twist angles were performed to identify the mechanical factors that determine the helical stability. Our results demonstrated that axial torsion can cause wringing (twist buckling) that leads to kinking or helical coiling and even looping and winding. The specific buckling patterns depend on the combination of lumen pressure, axial torque, axial tension, and the dimensions of the vessels. This study elucidates the mechanism of how blood vessels buckle under various mechanical loads and how complex mechanical loads yield helical buckling. The novelties of this research article include the following: Illustrated that mechanical loadings such as lumen pressure, axial tension, and axial torque could lead to the formation of tortuous vessels (curving, wringing, kinking, helical coiling, looping, and winding).Determined the biomechanical loads that trigger helical buckling in blood vessels.Compared the effect of different constitutive models. [ABSTRACT FROM AUTHOR]

The aim of this work is to develop a novel computational approach to facilitate the modeling of angiogenesis during tumor growth. The preexisting vasculature is modeled as a 1D inclusion and embedded into the 3D tissue through a suitable coupling method, which allows for nonmatching meshes in 1D and 3D domain. The neovasculature, which is formed during angiogenesis, is represented in a homogenized way as a phase in our multiphase porous medium system. This splitting of models is motivated by the highly complex morphology, physiology, and flow patterns in the neovasculature, which are challenging and computationally expensive to resolve with a discrete, 1D angiogenesis and blood flow model. Moreover, it is questionable if a discrete representation generates any useful additional insight. By contrast, our model may be classified as a hybrid vascular multiphase tumor growth model in the sense that a discrete, 1D representation of the preexisting vasculature is coupled with a continuum model describing angiogenesis. It is based on an originally avascular model which has been derived via the thermodynamically constrained averaging theory. The new model enables us to study mass transport from the preexisting vasculature into the neovasculature and tumor tissue. We show by means of several illustrative examples that it is indeed capable of reproducing important aspects of vascular tumor growth phenomenologically. [ABSTRACT FROM AUTHOR]

Upon injury to a blood vessel, flowing platelets will aggregate at the injury site, forming a plug to prevent blood loss. Through a complex system of biochemical reactions, a stabilizing mesh forms around the platelet aggregate forming a blood clot that further seals the injury. Computational models of clot formation have been developed to a study intravascular thrombosis, where a vessel injury does not cause blood leakage outside the blood vessel but blocks blood flow. To model scenarios in which blood leaks from a main vessel out into the extravascular space, new computational tools need to be developed to handle the complex geometries that represent the injury. We have previously modeled intravascular clot formation under flow using a continuum approach wherein the transport of platelet densities into some spatial location is limited by the platelet fraction that already reside in that location, i.e., the densities satisfy a maximum packing constraint through the use of a hindered transport coefficient. To extend this notion to extravascular injury geometries, we have modified a finite element method flux‐corrected transport (FEM‐FCT) scheme by prelimiting antidiffusive nodal fluxes. We show that our modified scheme, under a variety of test problems, including mesh refinement, structured vs unstructured meshes, and for a range of reaction rates, produces numerical results that satisfy a maximum platelet‐density packing constraint. [ABSTRACT FROM AUTHOR]