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The current management of acute coronary syndromes (ACS) is with an invasive strategy to guide treatment. However, identifying the lesions which are physiologically significant can be challenging. Non-invasive imaging is generally not appropriate or timely in the acute setting, so the decision is generally based upon visual assessment of the angiogram, supplemented in a small minority by invasive pressure wire studies using fractional flow reserve (FFR) or related indices. Whilst pressure wire usage is slowly increasing, it is not feasible in many vessels, patients and situations. Limited evidence for the use of FFR in non-ST elevation (NSTE) ACS suggests a 25% change in management, compared with traditional assessment, with a shift from more to less extensive revascularisation. Virtual (computed) FFR (vFFR), which uses a 3D model of the coronary arteries constructed from the invasive angiogram, and application of the physical laws of fluid flow, has the potential to be used more widely in this situation. It is less invasive, fast and can be integrated into catheter laboratory software. For severe lesions, or mild disease, it is probably not required, but it could improve the management of moderate disease in 'real time' for patients with non-ST elevation acute coronary syndromes (NSTE-ACS), and in bystander disease in ST elevation myocardial infarction. Its practicability and impact in the acute setting need to be tested, but the underpinning science and potential benefits for rapid and streamlined decision-making are enticing.

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Blood flow generates wall shear stress (WSS) which alters endothelial cell (EC) function. Low WSS promotes vascular inflammation and atherosclerosis whereas high uniform WSS is protective. Ivabradine decreases heart rate leading to altered haemodynamics. Besides its cardio-protective effects, ivabradine protects arteries from inflammation and atherosclerosis via unknown mechanisms. We hypothesised that ivabradine protects arteries by increasing WSS to reduce vascular inflammation. Hypercholesterolaemic mice were treated with ivabradine for seven weeks in drinking water or remained untreated as a control. En face immunostaining demonstrated that treatment with ivabradine reduced the expression of pro-inflammatory VCAM-1 (p<0.01) and enhanced the expression of anti-inflammatory eNOS (p<0.01) at the inner curvature of the aorta. We concluded that ivabradine alters EC physiology indirectly via modulation of flow because treatment with ivabradine had no effect in ligated carotid arteries in vivo, and did not influence the basal or TNFα-induced expression of inflammatory (VCAM-1, MCP-1) or protective (eNOS, HMOX1, KLF2, KLF4) genes in cultured EC. We therefore considered whether ivabradine can alter WSS which is a regulator of EC inflammatory activation. Computational fluid dynamics demonstrated that ivabradine treatment reduced heart rate by 20 % and enhanced WSS in the aorta. In conclusion, ivabradine treatment altered haemodynamics in the murine aorta by increasing the magnitude of shear stress. This was accompanied by induction of eNOS and suppression of VCAM-1, whereas ivabradine did not alter EC that could not respond to flow. Thus ivabradine protects arteries by altering local mechanical conditions to trigger an anti-inflammatory response.

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We consider the problem of estimating the stiffness of an artery wall using a data assimilation method applied to a 3D fluid-structure interaction (FSI) model. Recalling previous works, we briefly present the FSI model, the data assimilation procedure and the segmentation algorithm. We present then two examples of the procedure using real data. First, we estimate the stiffness distribution of a silicon rubber tube from image data. Second, we present the estimation of aortic wall stiffness from real clinical data.

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BACKGROUND: Zero-dimensional (lumped parameter) and one dimensional models, based on simplified representations of the components of the cardiovascular system, can contribute strongly to our understanding of circulatory physiology. Zero-D models provide a concise way to evaluate the haemodynamic interactions among the cardiovascular organs, whilst one-D (distributed parameter) models add the facility to represent efficiently the effects of pulse wave transmission in the arterial network at greatly reduced computational expense compared to higher dimensional computational fluid dynamics studies. There is extensive literature on both types of models. METHOD AND RESULTS: The purpose of this review article is to summarise published 0D and 1D models of the cardiovascular system, to explore their limitations and range of application, and to provide an indication of the physiological phenomena that can be included in these representations. The review on 0D models collects together in one place a description of the range of models that have been used to describe the various characteristics of cardiovascular response, together with the factors that influence it. Such models generally feature the major components of the system, such as the heart, the heart valves and the vasculature. The models are categorised in terms of the features of the system that they are able to represent, their complexity and range of application: representations of effects including pressure-dependent vessel properties, interaction between the heart chambers, neuro-regulation and auto-regulation are explored. The examination on 1D models covers various methods for the assembly, discretisation and solution of the governing equations, in conjunction with a report of the definition and treatment of boundary conditions. Increasingly, 0D and 1D models are used in multi-scale models, in which their primary role is to provide boundary conditions for sophisticate, and often patient-specific, 2D and 3D models, and this application is also addressed. As an example of 0D cardiovascular modelling, a small selection of simple models have been represented in the CellML mark-up language and uploaded to the CellML model repository http://models.cellml.org/. They are freely available to the research and education communities. CONCLUSION: Each published cardiovascular model has merit for particular applications. This review categorises 0D and 1D models, highlights their advantages and disadvantages, and thus provides guidance on the selection of models to assist various cardiovascular modelling studies. It also identifies directions for further development, as well as current challenges in the wider use of these models including service to represent boundary conditions for local 3D models and translation to clinical application.

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OBJECTIVES: Hemodynamic changes in the cerebral circulation in presence of coarctation of aorta (CoA) and their significance in the increased intracranial aneurysms (IAs) formation in these patients remain unclear. In the present study, we measured the flow-rate waveforms in the cerebral arteries of a patient with CoA, followed by an analysis of different hemodynamic indices in a coexisting IA. MATERIALS AND METHODS: Phase-contrast Magnetic Resonance (pc-MR) volumetric flow-rate (VFR) measurements were performed in cerebral arteries of a 51 years old woman with coexisting CoA, and five healthy volunteers. Numerical predictions of a number of relevant hemodynamic indices were performed in an IA located in sub-clinoid part of left internal carotid artery (ICA) of the patient. Computations were performed using Ansys(®)-CFX(™) solver using the VFR values measured in the patient as boundary conditions (BCs). A second analysis was performed using the average VFR values measured in healthy volunteers. The VFR waveforms measured in the patient and healthy volunteers were compared followed by a comparison of the hemodynamic indices obtained using both approaches. The results are discussed in the background of relevant literature. RESULTS: Mean flow-rates were increased by 27.1% to 54.9% (2.66-5.44 ml/sec) in the cerebral circulation of patients with CoA as compared to healthy volunteers (1.2-3.95 ml/sec). Velocities were increased inside the IA by 35-45%. An exponential rise of 650% was observed in the area affected by high wall shear stress (WSS>15Pa) when flow-rates specific to CoA were used as compared to population average flow-rates. Absolute values of space and time averaged WSS were increased by 65%. Whereas values of maximum pressure on the IA wall were increased by 15% the area of elevated pressure was actually decreased by 50%, reflecting a more focalized jet impingement within the IA of the CoA patient. CONCLUSIONS: IAs can develop in patients with CoA several years after the surgical repair. Cerebral flow-rates in CoA patients are significantly higher as compared to average flow-rates in healthy population. The increased supra-physiological WSS (>15Pa), OSI (>0.2) and focalized pressure may play an important role in the etiopathogenesis of IAs in patients with CoA.

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Haemodynamics is believed to play an important role in the initiation, growth and rupture of intracranial aneurysms. In this context, computational haemodynamics has been extensively used in an effort to establish correlations between flow variables and clinical outcome. It is common practice in the application of Dirichlet boundary conditions at domain inlets to specify transient velocities as either a flat (plug) profile or a spatially developed profile based on Womersley's analytical solution. This paper provides comparative haemodynamics measures for three typical cerebral aneurysms. Three dimentional rotational angiography images of aneurysms at three common locations, viz. basilar artery tip, internal carotid artery and middle cerebral artery were obtained. The computational tools being developed in the European project @neurIST were used to reconstruct the fluid domains and solve the unsteady Navier-Stokes equations, using in turn Womersley and plug-flow inlet velocity profiles. The effects of these assumptions were analysed and compared in terms of relevant haemodynamic variables within the aneurismal sac. For the aneurysm at the basilar tip geometries with different extensions of the afferent vasculature were considered to study the plausibility of a fully-developed axial flow at the inlet boundaries. The study shows that assumptions made on the velocity profile while specifying inlet boundary conditions have little influence on the local haemodynamics in the aneurysm, provided that a sufficient extension of the afferent vasculature is considered and that geometry is the primary determinant of the flow field within the aneurismal sac. For real geometries the Womersley profile is at best an unnecessary over-complication, and may even be worse than the plug profile in some anatomical locations (e.g. basilar confluence).

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An in vitro model of blood clotting is presented using hypercoaguable milk as an analog for blood. Milk clot formation was studied for periods of 2, 5, 10, 20, and 30 min within an idealized stenosis geometry. Clot formation was recorded using photography, clot casting, and clot mass calculation. The distribution of clot within the fluid was seen to be in good agreement with a previous study that used a residence time model to predict areas of clot formation in thrombin solution. A numerical model was formulated within computational fluid dynamics package CFX that allowed local activation of blood clotting to be simulated. This model was applied to the analysis of an idealized cerebral aneurysm geometry. An idealized coil geometry was included within the aneurysm and clotting fluid concentration and fluid residence time were modeled using transport equations within CFX. The viscosity of the fluid was defined as a function of both residence time and clotting fluid concentration. The model was seen to produce features consistent with observations of thrombosis within cerebral aneurysms, while avoiding the unrealistic build up of clot in near-wall regions that is associated with a pure residence time model.

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