Review of Zero-D and 1-D Models of Blood Flow in the Cardiovascular System

<p>Abstract</p> <p>Background</p> <p>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.</p> <p>Method and Results</p> <p>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 <url>http://models.cellml.org/</url>. They are freely available to the research and education communities.</p> <p>Conclusion</p> <p>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.</p

Refining Our Understanding of the Flow Through Coronary Artery Branches; Revisiting Murray's Law in Human Epicardial Coronary Arteries

Background: Quantification of coronary blood flow is used to evaluate coronary artery disease, but our understanding of flow through branched systems is poor. Murray’s law defines coronary morphometric scaling, the relationship between flow (Q) and vessel diameter (D) and is the basis for minimum lumen area targets when intervening on bifurcation lesions. Murray’s original law (Q α D(P)) dictates that the exponent (P) is 3.0, whilst constant blood velocity throughout the system would suggest an exponent of 2.0. In human coronary arteries, the value of Murray’s exponent remains unknown. Aim: To establish the exponent in Murray’s power law relationship that best reproduces coronary blood flows (Q) and microvascular resistances (Rmicro) in a bifurcating coronary tree. Methods and Results: We screened 48 cases, and were able to evaluate inlet Q and Rmicro in 27 branched coronary arteries, taken from 20 patients, using a novel computational fluid dynamics (CFD) model which reconstructs 3D coronary anatomy from angiography and uses pressure-wire measurements to compute Q and Rmicro distribution in the main- and side-branches. Outputs were validated against invasive measurements using a Rayflow™ catheter. A Murray’s power law exponent of 2.15 produced the strongest correlation and closest agreement with inlet Q (zero bias, r = 0.47, p = 0.006) and an exponent of 2.38 produced the strongest correlation and closest agreement with Rmicro (zero bias, r = 0.66, p = 0.0001). Conclusions: The optimal power law exponents for Q and Rmicro were not 3.0, as dictated by Murray’s Law, but 2.15 and 2.38 respectively. These data will be useful in assessing patient-specific coronary physiology and tailoring revascularisation decisions

The Role of Computational Fluid Dynamics in the Management of Unruptured Intracranial Aneurysms: A Clinicians' View

Objective. The importance of hemodynamics in the etiopathogenesis of intracranial aneurysms (IAs) is widely accepted. Computational fluid dynamics (CFD) is being used increasingly for hemodynamic predictions. However, alogn with the continuing development and validation of these tools, it is imperative to collect the opinion of the clinicians. Methods. A workshop on CFD was conducted during the European Society of Minimally Invasive Neurological Therapy (ESMINT) Teaching Course, Lisbon, Portugal. 36 delegates, mostly clinicians, performed supervised CFD analysis for an IA, using the @neuFuse software developed within the European project @neurIST. Feedback on the workshop was collected and analyzed. The performance was assessed on a scale of 1 to 4 and, compared with experts' performance. Results. Current dilemmas in the management of unruptured IAs remained the most important motivating factor to attend the workshop and majority of participants showed interest in participating in a multicentric trial. The participants achieved an average score of 2.52 (range 0–4) which was 63% (range 0–100%) of an expert user. Conclusions. Although participants showed a manifest interest in CFD, there was a clear lack of awareness concerning the role of hemodynamics in the etiopathogenesis of IAs and the use of CFD in this context. More efforts therefore are required to enhance understanding of the clinicians in the subject

Sex differences in coronary microvascular resistance measured by a computational fluid dynamics model

BackgroundIncreased coronary microvascular resistance (CMVR) is associated with coronary microvascular dysfunction (CMD). Although CMD is more common in women, sex-specific differences in CMVR have not been demonstrated previously.AimTo compare CMVR between men and women being investigated for chest pain.Methods and resultsWe used a computational fluid dynamics (CFD) model of human coronary physiology to calculate absolute CMVR based on invasive coronary angiographic images and pressures in 203 coronary arteries from 144 individual patients. CMVR was significantly higher in women than men (860 [650–1,205] vs. 680 [520–865] WU, Z = −2.24, p = 0.025). None of the other major subgroup comparisons yielded any differences in CMVR.ConclusionCMVR was significantly higher in women compared with men. These sex-specific differences may help to explain the increased prevalence of CMD in women

Patient-specific non-invasive estimation of pressure gradient across aortic coarctation using magnetic resonance imaging

[Background] Non-invasive estimation of the pressure gradient in aortic coarctation has much clinical importance in assisting the diagnosis and treatment of the disease. Previous researchers applied computational fluid dynamics for the prediction of the pressure gradient in aortic coarctation. The accuracy of the prediction was satisfactory but the procedure was time-consuming and resource-demanding.[Method] In this research a magnetic resonance imaging (MRI)-based non-invasive modeling procedure is implemented to predict the pressure gradient in 14 patient cases of aortic coarctation. Multi-cycle patient flow and pressure data are processed to produce the flow and pressure conditions in the patient cases. Bernoulli equation-based friction loss model combined with the inertial effect of the blood flow in the vessel segments are applied to model the pressure gradient in the aortic coarctation. The model-predicted pressure gradient data are then compared with the catheter in vivo measurement data for validation.[Results] The MRI-based model prediction technique produces results that are consistent with those from the catheter measurement, based on the criteria of both the cycle-averaged instantaneous pressure gradient and the peak-to-peak pressure gradient.[Conclusion] This study suggests that the MRI-based non-invasive modeling procedure has much potential to be applied in clinical practice for the prediction of the pressure gradient in aortic coarctation patients.This research was supported by the European Commission's Seventh Framework Programme (FP7/2007-2013) under the grant agreement number 224495 (euHeart project).Peer reviewe

Influence of inlet boundary conditions on the local haemodynamics of intracranial aneurysms

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)

Contribution of Mechanical and Fluid Stresses to the Magnitude of In-stent Restenosis at the Level of Individual Stent Struts

Structural and fluid stresses acting on the artery wall are proposed as mechanical mediators of in-stent restenosis (ISR). This study reports an investigation of the correlation between stresses obtained from computational simulations with the magnitude of ISR at the level of individual stent struts observed in an in vivo model of restenosis. Structural and fluid dynamic analyses were undertaken in a model based on volumetric micro-CT data from an in vivo stent deployment in a porcine right coronary artery. Structural and fluid mechanics were compared with histological data from the same stented vessel sample. Interpretation of the combined data at the level of individual stent struts was possible by identifying the location of each 2-D histological section within the 3-D micro-CT volume. Linear correlation between structural and fluid stimuli and neointimal thickness at the level of individual struts is less clear when individual stimuli are considered [compressive force (CF), R 2 = 0.19, wall shear stress (WSS), R 2 = 0.25, oscillatory shear index (OSI), R 2 = 0.28]. Closer correlation is observed if combined structural and fluid stimuli are assumed to stimulate ISR (CF/WSS, R 2 = 0.64). The use of micro-CT to characterise stent geometry after deployment enhances the clinical relevance of computational simulations, allowing direct comparison with histology. The results support the combined role of both structural and fluid mechanics to determine the magnitude of ISR at the level of individual struts. This finding is consistent with other studies which consider these stimuli averaged over a transverse section of the vessel

Rethinking the Neolithic from Iberian Archaeology

European Journal of Archeology, 3 (2):283-284. (año 2000)[ES] Reseña bibliográfica del libro de Almudena Hernado, 'Los primeros agricultores de la Península Ibérica. Una historiografía crítica del Neolítico' (Madrid: Editorial Síntesis, 1999, 315 pp.). [EN]bliographic Almudena Hernando book, 'The first farmers in the Iberian Peninsula. A critical historiography of the Neolithic '(Madrid: Editorial Síntesis, 1999, 315 pp.)Peer reviewe

Comparison of stenosis models for usage in the estimation of pressure gradient across aortic coarctation

Non-invasive estimation of the pressure gradient in cardiovascular stenosis has much clinical importance in assisting the diagnosis and treatment of stenotic diseases. In this research, a systematic comparison is conducted to investigate the accuracy of a group of stenosis models against the MRI- and catheter-measured patient data under the aortic coarctation condition. Eight analytical stenosis models, including six from the literature and two proposed in this study, are investigated to examine their prediction accuracy against the clinical data. The two improved models proposed in this study consider comprehensively the Poiseuille loss, the Bernoulli loss in its exact form, and the entrance effect, of the blood flow. Comparison of the results shows that one of the proposed models demonstrates a cycle-averaged mean prediction error of −0.15 ± 3.03 mmHg, a peak-to-peak prediction error of −1.8 ± 6.89 mmHg, which is the best among the models studied.This research was funded by the European Community’s Seventh Framework Programme (FP7/2007–2013) under the grant agreement number 224495 (euHeart project)