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

ANALYSE NUMÉRIQUE ET SIMULATIONS DE PROBLÈMES COUPLÉS POUR LE SYSTÈME CARDIOVASCULAIRE

In this thesis we present the numerical analysis and the development of partitioned algorithms in order to couple the blood dynamics in different cardiovascular compartments (3D-3D, 3D-0D). In the first par t a fluid-fluid coupled problem is introduced. On the interface between the domains Robin-Robin boundary conditions, derived from the Nitsche’s interface formulation, are considered. We suggest different staggered explicit schemes whose stability is analyzed in the energy norm. Extensive numerical experiments illustrate the accuracy of the methods presented. The second par t deals with more realistic cardiovascular applications. First a reduced order model for the hear t valves is described. Without dealing with fluid-structure interaction with the blood flow, the valves are replaced by immersed surfaces acting as resistances on the fluid. Numerical simulations show the efficiency and the robustness of this model in the framework of a fluid-fluid interaction scheme. In the end, an ALE formulation is used to solve a fluid model in a moving domain. We show that adding a suitable consistent term, a stable energy inequality can be obtained without considering any Geometric Conservation Laws. The work ends with numerical simulations on blood dynamics in the left ventricle coupled with the blood flowing in the aortaDans cette thèse, nous proposons l’analyse numérique et le développement d’algorithmes par titionnés pour coupler l’écoulement du sang dans différents compar ti- ments cardiovasculaires (3D-3D, 3D-0D). Dans une première par tie, un problème couplé fluide-fluide est introduit. Sur l’interface qui sépare les domaines, des conditions aux limites de type Robin-Robin dérivées de la formulation d’interface de Nitsche sont considérées. Nous proposons différents schémas explicites dont la stabilité est analysée dans la norme de l’énergie. Des simulations numé- riques illustrent le potentiel des méthodes présentées. La deuxième par tie propose des applications cardiovasculaires plus réalistes. Tout d’abord, un modèle d’ordre réduit pour les valves cardiaques est décrit. Sans traiter l’interaction fluide-structure avec le sang, les valves sont remplacées par des surfaces agissant comme des résistances immergées dans le fluide. Des simulations numériques montrent l’efficacité et la robustesse de ce modèle. Pour finir, une formulation ALE est utilisée pour la résolution d’un modèle fluide sur un domaine mobile. Nous montrons qu’en ajoutant un terme consistent, une inégalité d’énergie stable peut être obtenue sans considérer aucune hypothèse de Loi de Conser vation Géométrique. Le travail se termine avec des simulations numériques sur la dynamique du sang dans le ventricule gauche, couplé avec l’écoulement du sang dans l’aorte

A Computational Approach To The Study Of Trauma

Trauma with hypovolemic shock is an extreme pathological state that challenges the body to maintain blood pressure and oxygenation in the face of hemorrhagic blood loss. In conjunction with surgical actions and transfusion therapy, survival requires the patient’s blood to maintain hemostasis to stop bleeding. The physics of the problem are multiscale: (1) the systemic circulation sets the global blood pressure in response to blood loss and resuscitation therapy, (2) local tissue perfusion is altered by localized vasoregulatory mechanisms and bleeding, and (3) altered blood and vessel biology resulting from the trauma as well as local hemodynamics control the assembly of clotting components at the site of injury. Building upon ongoing modeling efforts to simulate arterial or venous thrombosis in a diseased vasculature, we have developed models of trauma (both multiscale and machine-learning based) to understand patient risk and predict response. Key results were: (1) the upstream vascular network rapidly depressurizes to reduce blood loss, (2) wall shear rates at the hemorrhaging wound exit are sufficiently high (~10,000 s-1) to drive von Willebrand Factor unfolding, (3) full coagulopathy results in \u3e2L blood loss in 2 hours for severing all vessels of 0.13 to 0.005 mm diameter within the bifurcating network, whereas full hemostasis limits blood loss to \u3c100 mL within 2 min, and (4) hemodilution from transcapillary refill increases blood loss and could be implicated in trauma induced coagulopathy. Machine learning based methods were also implemented to understand trauma patient outcomes. A 400-estimator gradient boosting classifier was trained to predict survival probability and the model is able to predict a survival probability for any trauma patient and accurately distinguish between a deceased and survived patient in 92.4% of all cases. Partial dependence curves (Psurvival vs. feature value) obtained from the trained model revealed the global importance of Glasgow coma score, age, and systolic blood pressure while pulse rate, respiratory rate, temperature, oxygen saturation, and gender had more subtle single variable influences. Shapley values, which measure the relative contribution of each of the 8 features to individual patient risk, were computed for several patients and quantified patient-specific warning signs

Transient Cardiovascular Hemodynamics In A Patient-Specific Arterial System

The ultimate goal of the present study is to aid in the development of tools to assist in the treatment of cardiovascular disease. Gaining an understanding of hemodynamic parameters for medical implants allow clinicians to have some patient-specific proposals for intervention planning. In the present study a full cardiovascular experimental phantom and digital phantom (CFD model) was fabricated to study: (1) the effects of local hemodynamics on global hemodynamics, (2) the effects of transition from bed-rest to upright position, and (3) transport of dye (drug delivery) in the arterial system. Computational three dimensional (3-D) models (designs A, B, and C) stents were also developed to study the effects of stent design on hemodynamic flow and the effects of drug deposition into the arterial wall. The experimental phantom used in the present study is the first system reported in literature to be used for hemodynamic assessment in static and orthostatic posture changes. Both the digital and experimental phantom proved to provide different magnitudes of wall shear and normal stresses in sections where previous studies have only analyzed single arteries. The dye mass concentration study for the digital and experimental cardiovascular phantom proved to be useful as a surrogate for medical drug dispersion. The dye mass concentration provided information such as transition time and drug trajectory paths. For the stent design CFD studies, hemodynamic results (wall shear stress (WSS), normal stress, and vorticity) were assessed to determine if simplified stented geometries can be used as a surrogate for patient-specific geometries and the role of stent design on flow. Substantial differences in hemodynamic parameters were found to exist which confirms the need for patient-specific modeling. For drug eluting stent studies, the total deposition time for the drug into the arterial wall was approximately 3.5 months