Yubing Shi

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

BackgroundZero-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 ResultsThe 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.ConclusionEach 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.

Accuracy vs. computational time: Translating aortic simulations to the clinic

State of the art simulations of aortic haemodynamics feature full fluid-structure interaction (FSI) and coupled 0D boundary conditions. Such analyses require not only significant computational resource but also weeks to months of run time, which compromises the effectiveness of their translation to a clinical workflow. This article employs three computational fluid methodologies, of varying levels of complexity with coupled 0D boundary conditions, to simulate the haemodynamics within a patient-specific aorta. The most comprehensive model is a full FSI simulation. The simplest is a rigid walled incompressible fluid simulation while an alternative middle-ground approach employs a compressible fluid, tuned to elicit a response analogous to the compliance of the aortic wall. The results demonstrate that, in the context of certain clinical questions, the simpler analysis methods may capture the important characteristics of the flow field.

Computational modelling and evaluation of cardiovascular response under pulsatile impeller pump support

This study presents a numerical simulation of cardiovascular response in the heart failure condition under the support of a Berlin Heart INCOR impeller pump-type ventricular assist device (VAD). The model is implemented using the CellML modelling language. To investigate the potential of using the Berlin Heart INCOR impeller pump to produce physiologically meaningful arterial pulse pressure within the various physiological constraints, a series of VAD-assisted cardiovascular cases are studied, in which the pulsation ratio and the phase shift of the VAD motion profile are systematically changed to observe the cardiovascular responses in each of the studied cases. An optimization process is proposed, including the introduction of a cost function to balance the importance of the characteristic cardiovascular variables. Based on this cost function it is found that a pulsation ratio of 0.35 combined with a phase shift of 200° produces the optimal cardiovascular response, giving rise to a maximal arterial pulse pressure of 12.6 mm Hg without inducing regurgitant pump flow while keeping other characteristic cardiovascular variables within appropriate physiological ranges.

Importance of realistic LVAD profiles for assisted aortic simulations: evaluation of optimal outflow anastomosis locations.

Left ventricular assist devices (LVADs) are carefully designed, but the significance of the implantation configuration and interaction with the vasculature is complex and not fully determined. The present study employs computational fluid dynamics to investigate the importance of applying a realistic LVAD profile when evaluating assisted aortic flow fields and subsequently compares a number of potential anastomosis locations in a patient-specific aortic geometry. The outflow profile of the Berlin Heart INCOR® device was provided by Berlin Heart GmbH (Berlin, Germany) and the cannula was attached at a number of locations on the aorta. Simulations were conducted to compare a flat profile against the real LVAD profile. The results illustrate the importance of applying an LVAD profile. It not only affects the magnitude and distribution of oscillatory shear index, but also the distribution of flow to the great arteries. The ascending aorta was identified as the optimal location for the anastomosis.

Generating anatomical models of the heart and the aorta from medical images for personalized physiological simulations

The anatomy and motion of the heart and the aorta are essential for patient-specific simulations of cardiac electrophysiology, wall mechanics and hemodynamics. Within the European integrated project euHeart, algorithms have been developed that allow to efficiently generate patient-specific anatomical models from medical images from multiple imaging modalities. These models, for instance, account for myocardial deformation, cardiac wall motion, and patient-specific tissue information like myocardial scar location. Furthermore, integration of algorithms for anatomy extraction and physiological simulations has been brought forward. Physiological simulations are linked closer to anatomical models by encoding tissue properties, like the muscle fibers, into segmentation meshes. Biophysical constraints are also utilized in combination with image analysis to assess tissue properties. Both examples show directions of how physiological simulations could provide new challenges and stimuli for image analysis research in the future.

Predicting hemodynamics in native and residual coarctation: preliminary results of a Rigid-Wall Computational-Fluid-Dynamics model (RW-CFD) validated against clinically invasive pressure measures at rest and during pharmacological stress

Current clinical assessment of borderline aortic coarctation may involve cardiovascular magnetic resonance(CMR) but if inconclusive, invasive catheterization pressure measurements are required to evaluate the pressure gradient at rest and during pharmacological stress(isoprenaline).

Closing the loop: modelling of heart failure progression from health to end-stage using a meta-analysis of left ventricular pressure-volume loops.

Introduction The American Heart Association (AHA)/American College of Cardiology (ACC) guidelines for the classification of heart failure (HF) are descriptive but lack precise and objective measures which would assist in categorising such patients. Our aim was two fold, firstly to demonstrate quantitatively the progression of HF through each stage using a meta-analysis of existing left ventricular (LV) pressure-volume (PV) loop data and secondly use the LV PV loop data to create stage specific HF models. Methods and Results A literature search yielded 31 papers with PV data, representing over 200 patients in different stages of HF. The raw pressure and volume data were extracted from the papers using a digitising software package and the means were calculated. The data demonstrated that, as HF progressed, stroke volume (SV), ejection fraction (EF%) decreased while LV volumes increased. A 2-element lumped parameter model was employed to model the mean loops and the error was calculated between the loops, demonstrating close fit between the loops. The only parameter that was consistently and statistically different across all the stages was the elastance (Emax). Conclusions For the first time, the authors have created a visual and quantitative representation of the AHA/ACC stages of LVSD-HF, from normal to end-stage. The study demonstrates that robust, load-independent and reproducible parameters, such as elastance, can be used to categorise and model HF, complementing the existing classification. The modelled PV loops establish previously unknown physiological parameters for each AHA/ACC stage of LVSD-HF, such as LV elastance and highlight that it this parameter alone, in lumped parameter models, that determines the severity of HF. Such information will enable cardiovascular modellers with an interest in HF, to create more accurate models of the heart as it fails.

Derivation of aortic distensibility and pulse wave velocity by image registration with a physics-based regularisation term

Analysis of the cardiovascular system represents a classical problem in which the solid and fluid phases interact intimately, and so is a rich field of application for state-of-the-art fluid-solid interaction (FSI) analyses. In this paper, we focus on the human aorta. Solution of the full FSI problem requires knowledge of the material properties of the wall and information on vessel support. We show that variation of distensibility along the aorta can be obtained from four-dimensional image data using image registration. If pressure data at one point in the vessel are available, these can be converted to absolute values. Alternatively, values of pulse wave velocity along the vessel can be obtained. The quality of the extracted data is improved by the incorporation into the registration of a regularisation term based on the one-dimensional wave equation. The method has been validated using simulated data. For idealised vessels, the accuracy with which the distensibility and wave velocity can be extracted is high (1%-2%). The method is applied to six clinical datasets from patients with mild coarctation, for which it is shown that wave velocity along the aorta is relatively constant.

ONE-DIMENSIONAL SIMULATION OF HAEMODYNAMICS IN AORTIC COARCTATION

Aortic coarctation is a narrowing of part of the aorta due to the congenital defect. It causes abnormally elevated after-load to the left heart and thus impaired blood supply to the peripheral organs. Currently diagnosis and treatment of aortic coarctation are still difficult issues due to the complex haemodynamic changes involved [Keshavarz-Motamed, 2011]. The EU FP7 euHeart project is developing numerical tools to assist clinicians in the diagnostic evaluation of aortic coarctation based on MRI images of patients. The pressure gradient across the aorta in a patient-specific anatomy is computed by 3D computational fluid dynamics, but the result is critically dependent on the balance of the measured ascending aortic flow that is distributed to the supra-aortic vessels and the descending aorta. The balance is achieved using Windkessel models at the four outlets. The process of tuning the Windkessels in combination with the 3D model to match the (noisy) clinical flow measurements is computationally expensive and is sensitive to the initialisation. We propose the use of an intermediate 1D/0D model, based on the geometry of the patient aorta, to pre-tune the system.

CellML Implementation of a Numerical Model for the Cardiovascular System under VAD Support

In this study numerical simulation is carried out to investigate cardiovascular response under the support of a displacement pump type ventricular assist device (VAD). The native cardiovascular system model employed in this study is a simplified version of a published system model, and the VAD is characterized by prescribed flow-rate changes in the VAD inlet and outlet. The CellML markup language is used for the description of the numerical model, and the resulting model is executed in the PCEnv simulation environment for the calculation of cardiac responses. Simulation results show that the VAD provides satisfactory support to the diseased heart. CellML, combined with PCEnv, provides a flexible and cohesive environment for the description of models represented by systems of ordinary differential equations, and thus facilitates the study of the dynamics of the circulation.