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

Hemodynamics of aortic valve stenoses

The aortic valve of a human heart is located between the left ventricle and the aorta. Its function is to open during the systole, allowing the blood to flow to the aorta in order to feed the organs and close during the diastole, preventing blood flow back into the left ventricle. Disease can lead to dysfunctionalities of the aortic valve and affect its performance. Calcific aortic valve disease (CAVD) is one of the most common valvular heart diseases which causes malfunctioning of the aortic valve leading to stroke, aortic aneurysm, heart attack and failure over time. Over the past few decades, researchers have investigated the effects of stenosis of the aortic valve on its hemodynamics and performance using in-vitro and in-vivo experiments, as well as numerical models. In-vitro experimentation and in-vivo measurements are broadly used for the investigation of the effect of aortic valve stenosis on the hemodynamics in the aortic root and the performance of the aortic valve. Numerical methods also play an important role in the modelling of the stenosis of the aortic valve and have obtained considerable attention in biomechanics application due to their very cost effective nature. Significant developments have been made in modelling the stenosis of the aortic valve and the effects on its hemodynamics and malfunctioning, however, the influence of vortex structures in the sinus on the aortic root and the coronary artery hemodynamics, as well as the performance of the valve and its correlation with the development of CAVD, are still unknown. The aim of this thesis is to develop an understanding of the flow behaviour inside the sinus cavity of the aortic valve in order to predict the shear stress distribution on the aortic valve leaflets and its correlation with CAVD. This aim has been achieved by answering the following research questions: (i) how stenosis of the aortic valve affects the aortic root and coronary artery hemodynamics; (ii) how the geometrical parameters of the aortic valve, such as the locations of the coronary artery ostia and the shape of the sinuses, influences the sinus hemodynamics, especially vortex structures within the sinuses; (iii) what are the effects of coronary artery stenosis on the shear stress distribution on the aortic valve leaflets; (iv) how vortex structures in the sinuses can change the wall shear stress distribution on the leaflets and its correlation with CAVD. In order to answer all of the above-mentioned questions and achieve the main objective of the project, the following tasks have been defined: • A brief overview of cardiovascular heart diseases with a focus on valvular heart diseases, and various techniques frequently used for diagnostics and treatment of stenosis of the aortic valve has been provided. • A comprehensive review of different techniques used for modelling aortic valve stenosis has been provided with a focus on the numerical Fluid-Structure Interaction (FSI) method and its advantages in modelling. • Two dimensional models of a healthy and a stenosed aortic valve have been extracted from the 2D echocardiography images available in the literature and developed in ANSYS- Fluent software. • Dynamic motion simulation of the aortic valve leaflets have been used to investigate the effects of stenosis of the aortic valve on the sinus vortex structures, coronary artery hemodynamics, wall shear stress on the leaflets and its correlation with CAVD. • A unique test rig has been designed, fabricated, and used for validation of the transvalvular pressure gradient and flow rate profile of the aortic valve. The test rig experimentally replicates the left ventricle of the heart and is capable of producing the heart beat flow conditions of different patients. The flow rate profile of the aortic valve and the pressure difference through the aortic valve are measured and compared with the simulated results. The developed model is capable of mimicking the dynamic motion of the aortic valve leaflets and predicting the wall shear stress distribution on the leaflets, which is associated with CAVD. The most important findings of the project showed that the wall shear stress distribution on the leaflets is highly dependent on the geometrical parameters of the aortic valve, such as the locations of the coronary artery ostia, as well as the shape of the sinuses. For example, an aortic valve with proximal coronary artery ostia experiences lower ranges of wall shear stress distribution on the leaflets. This means that a healthy valve with proximal coronary artery ostia are more prone to calcification over time in comparison with a healthy valve with distal and middle coronary artery ostia. Furthermore, the results demonstrated that a severely calcified aortic valve exhibits a lower range of wall shear stress distribution on the leaflets with higher probability of having smaller wall shear stress on the leaflets compared to a healthy valveThesis (Ph.D.) -- University of Adelaide, School of Mechanical Engineering, 202

Multi- Modal Characterization Of Left Ventricular Diastolic Filling Physiology

Multiple modalities are clinically used to quantify cardiovascular function. Most clinical indexes derived from these modalities are empirically derived or correlation- based rather than causality based. Hence these indexes don\u27t provide insight into cardiac physiology and the mechanism of dysfunction. Our group has previously developed and validated a mathematical model using a kinematic paradigm of suction- initiated ventricular filling to understand the mechanics of early transmitral flow and the associated physiology/ pathophysiology. The model characterizes the kinematics of early transmitral flow analogous to a damped simple harmonic oscillator with lumped parameters- ventricular stiffness, ventricular viscoelasticity/ relaxation and ventricular load. The current research develops the theme of causal mechanism based quantification of physiology and uses the kinematic model to study intraventricular fluid mechanics in diastole. In the first project, the role of vortex rings in efficient diastolic filling was investigated. Vortex rings had been previously characterized by a dimensionless index called vortex formation time (VFT). We re- expressed VFT in terms of ventricular kinematic properties- stiffness, viscoelasticity and volumetric preload, using the kinematic model. This VFTkinematic could be calculated using data from a clinical echocardiographic study. The VFTkinematic was a sensitive to physiologic changes as verified by its correlation with a clinically used echo- based index of filling pressure. Additionally, we demonstrated that VFTkinematic, by factoring the ventricular expansion rate, could differentiate between normal filling pattern and pseudonormal filling pattern which is characteristic of moderate DD. Continuing on our study of intraventricular fluid mechanics, we next studied the development of vortex ring in the ventricle. We discovered that as the vortex ring develops, the leading edge of the circulating flow passes through the main inflow tract. This causes an extra flow wave recorded in transmitral Doppler echocardiography (in addition to early and late filling waves) that had been observed previously. By using cardiac magnetic resonance (CMR) and echocardiography to independently measure intraventricular vortexes we were able to provide a causal explanation for the extra flow wave and its clinical consequences. We developed another approach to quantify the effect of chamber kinematics on filling via directional flow impedances. In the ventricle, both pressure and flow rate are oscillatory and pressure oscillations cause flow rate changes. Hence a frequency based approach via impedance, to quantify the relationship between pressure and flow rate is intuitive. We developed expressions for longitudinal and transverse flow impedances which could be computed from cardiac catheterization and echocardiographic data. Longitudinal and transverse flow impedances allowed us to quantify the previously observed directionality of filling as a function of harmonics and use it as an index to measure pathophysiologic changes. While fluid mechanics based indexes provide a method to evaluate LV chamber kinematics in diastole, an alternate approach for DF quantification is LV hemodynamic assessment. Since, LV filling is influenced by pressure changes before and during filling, we investigated the spatial pressure gradient in the LV. We measured the pressure difference between the LV apex and mid-LV using catheterization and we found a larger gradient exists during isovolumic relaxation (2- 3 times) as compared to filling. Additionally, the rate of pressure decay as quantified by different models of relaxation was also significantly different at the two locations. Additionally, we developed a new method for load independent hemodynamic analysis of the cardiac cycle. Load represents the pressure against which the ventricle has to fill and eject and most LV function indexes are load dependent, which can confound the diagnosis of dysfunction. We computed load independent cardiac cycle hemodynamics by normalizing LV pressure and the rate of change of pressure (dP/dt). Normalization revealed the presence of conserved kinematics during isovolumic relaxation particularly the normalized pressure at peak negative dP/dt while a similar feature was not observed during the contraction. These studies demonstrate the advantage of mechanism based approaches to quantify diastolic physiology

Boundary condition assessment and geometrical accuracy enhancement for computational haemodynamics

Cardiovascular diseases cause over 47 % of all deaths in Europe each year. Computational fluid dynamics provides the research community with a unique opportunity to investigate cardiovascular diseases with the intent of enabling optimised, patient-specific medical therapies. Incorporating physiologically accurate geometries and boundary conditions into computational fluid dynamics simulations can be difficult tasks and are a concern for researchers. This thesis analyses the impact various inlet and outlet boundary conditions can have on the outcome of a simulation. It also presents a novel, semi-automated process that prepares accurate geometrical models for haemodynamic simulations. Firstly, rabbit and human aorta models were used to analyse the impacts of boundary conditions on haemodynamic metrics used for understanding cardiovascular disease pathology. Comparisons were made between traction free, Murray’s Law, three-element Windkessel, and Murray’s Law/in vivo data hybrid outlet boundary conditions. Steady-state, transient, fully-developed and plug-type inlet boundary conditions were also investigated. Results showed that when advanced models such as the three-element Windkessel are unavailable, the Murray’s Law based outlet returns the most physiologically accurate haemodynamics. Results also showed that prescribing a transient simulation and a fully-developed flow at the inlet are not required when the focus is only on the flow within the aorta and around the intercostal branches. Secondly, a sensitivity test was conducted on the simulation of Left Ventricular Assistive Device (LVAD) configurations. The effects of flow ratios between the LVAD and aortic root on haemodynamic metrics were quantified. The general irregular sensitivity of the subclavian and carotid arteries to flow ratios indicates that the perfusion and wall shear stress-based haemodynamic metrics within these arteries cannot be accurately predicted unless the flow ratios are incorporated into the preoperative planning of the optimal LVAD configuration. Finally, a semi-automated reconstruction process combining magnetic resonance angiography and optical coherence tomography data was developed. The process was successful in its ability to create an accurate geometry in a relatively short time. This forms the foundation on which more sophisticated methods can be developed

Model-based quantification of systolic and diastolic left ventricular mechanics

Het linker ventrikel (LV) is de meest gespierde kamer van het hart. Door het gecoördineerd samentrekken van de spiercellen in de LV-wand wordt zuurstofrijk bloed in de aorta gepompt (systolische fase). Daarna ontspannen de spiercellen zich snel waardoor het LV opnieuw met bloed wordt gevuld (diastolische fase). In de kliniek en de onderzoekswereld bestaat er een waaier van modelgebaseerde methoden en concepten om de performantie en de mechanische eigenschappen van het LV te kwantificeren. Invasief bekomen druk- en volumedata laten toe om de systolische en diastolische mechanica van het LV met grote nauwkeurigheid te kennen. In de klinische praktijk wordt echter vaker gebruik gemaakt van (Doppler-) echocardiografie, een snelle en veilige niet-invasieve beeldtechniek. In een eerste deel van dit doctoraatsonderzoek werd een originele methode voorgesteld om, op basis van echocardiografie en klassieke bloeddrukmetingen, de intrinsieke krachtontwikkeling (contractiliteit) van het LV te schatten. De methode werd toegepast bij 2524 mensen die deelnemen aan de Asklepios-studie. De onderzoeksresultaten verschaften ons nieuwe informatie over hoe de evolutie van de krachtontwikkeling verschilt tussen gezonde mannen en vrouwen. De mechanische en vloeistofdynamische fenomenen tijdens de diastole vormden het onderwerp van het tweede deel van het onderzoek. Met behulp van een hydraulisch model van het LV werd nagegaan welke factoren een belangrijke invloed uitoefenen op het gedrag van het LV tijdens de isovolumetrische ontspanningsfase. In dit deel werd eveneens een uitgebreid overzicht gegeven van de meest recente echocardiografische methoden om de diastolische LV-mechanica te begroten. Daarbij werden de bloedstroming, de wandbeweging en de interactie tussen beiden gedetailleerd behandeld

Pressure drop and recovery in cases of cardiovascular disease: a computational study

The presence of disease in the cardiovascular system results in changes in flow and pressure patterns. Increased resistance to the flow observed in cases of aortic valve and coronary artery disease can have as a consequence abnormally high pressure gradients, which may lead to overexertion of the heart muscle, limited tissue perfusion and tissue damage. In the past, computational fluid dynamics (CFD) methods have been used coupled with medical imaging data to study haemodynamics, and it has been shown that CFD has great potential as a way to study patient-specific cases of cardiovascular disease in vivo, non-invasively, in great detail and at low cost. CFD can be particularly useful in evaluating the effectiveness of new diagnostic and treatment techniques, especially at early ‘concept’ stages. The main aim of this thesis is to use CFD to investigate the relationship between pressure and flow in cases of disease in the coronary arteries and the aortic valve, with the purpose of helping improve diagnosis and treatment, respectively. A transitional flow CFD model is used to investigate the phenomenon of pressure recovery in idealised models of aortic valve stenosis. Energy lost as turbulence in the wake of a diseased valve hinders pressure recovery, which occurs naturally when no energy losses are observed. A “concept” study testing the potential of a device that could maximise pressure recovery to reduce the pressure load on the heart muscle was conducted. The results indicate that, under certain conditions, such a device could prove useful. Fully patient-specific CFD studies of the coronary arteries are fewer than studies in larger vessels, mostly due to past limitations in the imaging and velocity data quality. A new method to reconstruct coronary anatomy from optical coherence tomography (OCT) data is presented in the thesis. The resulting models were combined with invasively acquired pressure and flow velocity data in transient CFD simulations, in order to test the ability of CFD to match the invasively measured pressure drop. A positive correlation and no bias were found between the calculated and measured results. The use of lower resolution reconstruction methods resulted in no correlation between the calculated and measured results, highlighting the importance of anatomical accuracy in the effectiveness of the CFD model. However, it was considered imperative that the limitations of CFD in predicting pressure gradients be further explored. It was found that the CFD-derived pressure drop is sensitive to changes in the volumetric flow rate, while bench-top experiments showed that the estimation of volumetric flow rate from invasively measured velocity data is subject to errors and uncertainties that may have a random effect on the CFD pressure result. This study demonstrated that the relationship between geometry, pressure and flow can be used to evaluate new diagnostic and treatment methods. In the case of aortic stenosis, further experimental work is required to turn the concept of a pressure recovery device into a potential clinical tool. In the coronary study it was shown that, though CFD has great power as a study tool, its limitations, especially those pertaining to the volumetric flow rate boundary condition, must be further studied and become fully understood before CFD can be reliably used to aid diagnosis in clinical practice.Open Acces

The Development of a Patient-Specific, Open Source Computational Fluid Dynamics Tool to Comprehensively and Innovatively Study Coarctation of the Aorta in a Limited Resource Clinical Context

Congenital heart disease (CHD) has a global prevalence of 8 per 1000 births [1] and coarctation of the aorta (CoA) is one of the most common defects with a prevalence of 7% of all cases. The occurrence of CHD in Africa is estimated to be significantly lower, which is attributed to a lack of data [2]. This emphasises the restricted human resources, as well as diagnostic and intervention capacity of specialists in Africa which leads to delayed treatment, presentation with established severity and, consequently, a worse prognosis. Computational Fluid Dynamics (CFD) is seen as the tool that will lead to a better understanding of the haemodynamic effects caused by the malformations related to CoA and provide insights into post-repair morbidity. In addition, the development of a computational tool is envisaged to improve the clinical capacity for diagnosis as well as provide a tool to conduct in silico repair planning. In a low and lower-middle income country healthcare facility, the supplementary data that CFD can provide can add diagnostic value, plan interventions to be more effective and efficient, as well as provide data that may improve postrepair patient management. The aim of this project is to develop a patient-specific, open source, computational fluid dynamics toolchain that is able to study the haemodynamics relating to CoA. In order to do so, a protocol for the collection of doppler echocardiography (echo) and CTA data is proposed. The method for processing the echo data and manually segmenting the CTA data is presented and evaluated. The open source, OpenFOAM code is used to simulate a patient-specific CoA case as well as two in silico designs of coarctation repairs based on expanding the coarctation from the original dataset. The CFD toolchain was developed such that patient data collected from the hospital could be processed to present key haemodynamic metrics such as velocities in the field at the coarctation zone, the pressure gradient across the coarctation and volumetric flow rates through each supra-aortic branch. These results are obtained for each case's geometry, and the trends and impacts that increasing the coarctation ratio has on each of the haemodynamic metrics is presented. The results show that the coarctation pressure gradient and maximum coarctation velocity decrease while perfusion of the lower limbs recovers with expanding coarctation ratio. Following an analysis of the results, it is evident that the pipeline is capable of running patient-specific CFD simulations and can present clinically relevant results. It is noted that this work is a proof of concept and so several steps are discussed that will improve the pipeline

Patient-specific modelling of the cerebral circulation for aneurysm risk assessment

Cerebral aneurysms are localised pathological dilatations of cerebral arteries, most commonly found in the circle of Willis. Although not all aneurysms are unstable, the major clinical concern involved is the risk of rupture. High morbidity and mortality rates are associated with the haemorrhage resulting from rupture. New indicators of aneurysm stability are sought, since current indicators based on morphological factors have been shown to be unreliable. Haemodynamical factors are known to be relevant in vascular wall remodelling, and therefore believed to play an important role in aneurysmdevelopment and stability. Studies suggest that intra-aneurysmal wall shear stress and flow patterns, for example, are candidate parameters in aneurysm stability assessment. These factors can be estimated if the 3D patient-specific intra-aneurysmal velocity is known, which can be obtained via a combination of in vivo measurements and computational fluid dynamics models. The main determinants of the velocity field are the vascular geometry and flow through this geometry. Over the last decade the extraction of the vascular geometry has become well established. More recently, there has been a shift of attention towards extracting boundary conditions for the 3D vascular segment of interest. The aim of this research is to improve the reliability of the model-based representation of the velocity field in the aneurysmal sac. To this end, a protocol is proposed such that patient-specific boundary conditions for the 3D segment of interest can be estimated without the need for added invasive procedures. This is facilitated by a 1D wave propagation model based on patient-specific geometry and boundary conditions measured non-invasively in more accessible regions. Such a protocol offers improved statistical reliability owing to the increased number of patients that can participate in studies aiming to identify parameters of interest in aneurysm stability assessment. In chapter 2 the intra-aneurysmal velocity field in an idealised aneurysm model is validated with particle image velocimetry experiments, after which the flow patterns are evaluated using a vortex identification method. Chapter 3 describes a 1D model wave propagation model of the cerebral circulation with a patient-specific vascular geometry. The resulting flow pulses at the boundaries of the 3D segment of interest are compared to those obtained with a patient-generic geometry. The influence of these different boundary conditions on the 3D intra-aneurysmal velocity field is evaluated in chapter 4 by prescribing the end-diastolic flows extracted from the 1D models. In order to measure blood flow with videodensitometric methods, an injection of contrast agent is required. The effect of this injection on the flow of interest is assessed in chapter 5. In chapter 6, pressure measurements in the internal carotid are used to evaluate the variability of pressure waveform and its effect on the boundary conditions for the 1D model. Finally, a protocol for full patient-specific modelling is discussed in chapter 7

Development of a prosthetic heart valve with inbuilt sensing technology, to aid in continuous monitoring of function under various stenotic conditions

In spite of technological advances in the design of prosthetic heart valves, they are still often subject to complications after implantation. One of the common complications is valve stenosis, which involves the obstruction of the valve orifice caused by biological processes. The greatest challenge in diagnosing the development of valve failure and complications is related to the fact that the valve is implanted and isolated. To continuously monitor the state of the valve and its performance would be of great benefit but practically can only be achieved by instrumenting the implanted valve. In this thesis, we explore the development of a prosthetic valve with inbuilt sensing technology to aid in continuous monitoring of valve function under various stenotic conditions. 22mm polyurethane valves were designed via dipcoating. A custom made mock circulatory system was designed and hydrodynamic testing of the polyurethane valves under different flow rates were performed with Effective orifice area (EOA) and Transvalvular Pressure Gradient (TVPG) being the parameters of interest. Valves were subjected to varying levels of obstruction to investigate the effect obstruction has on the pressure gradient across the valves. Similar tests were performed on a Carpentier Edwards SAV 2650 model bioprosthetic valve for comparison. Polyurethane valves were then instrumented with strain gauges to measure peak to peak strain difference, in response to varying levels of obstructions. All the polyurethane valves exhibited good hydrodynamic performance with EOA (>1cm2) under baseline physiological conditions. It was also discovered that pressure difference across the valves was directly proportional to the flow rate. The pressure difference also demonstrated a slow increase during the initial stages of simulated stenosis and a sudden increase as the obstruction became severe. This provides further evidence to support the ideal that stenosis is a slow progressive disease which may not present symptoms until severe. The peak to peak strain differences also tend to decrease as the severity of the obstruction was increased. The peak to peak strain difference is indicative of the pressures within the valve (intravalvular pressure). The results suggest that directly monitoring the pressures within the valve could be a useful diagnostic tool for detecting valve stenosis. Future works involves miniaturisation of the sensors and also the incorporation of telemetry into the sensor design.In spite of technological advances in the design of prosthetic heart valves, they are still often subject to complications after implantation. One of the common complications is valve stenosis, which involves the obstruction of the valve orifice caused by biological processes. The greatest challenge in diagnosing the development of valve failure and complications is related to the fact that the valve is implanted and isolated. To continuously monitor the state of the valve and its performance would be of great benefit but practically can only be achieved by instrumenting the implanted valve. In this thesis, we explore the development of a prosthetic valve with inbuilt sensing technology to aid in continuous monitoring of valve function under various stenotic conditions. 22mm polyurethane valves were designed via dipcoating. A custom made mock circulatory system was designed and hydrodynamic testing of the polyurethane valves under different flow rates were performed with Effective orifice area (EOA) and Transvalvular Pressure Gradient (TVPG) being the parameters of interest. Valves were subjected to varying levels of obstruction to investigate the effect obstruction has on the pressure gradient across the valves. Similar tests were performed on a Carpentier Edwards SAV 2650 model bioprosthetic valve for comparison. Polyurethane valves were then instrumented with strain gauges to measure peak to peak strain difference, in response to varying levels of obstructions. All the polyurethane valves exhibited good hydrodynamic performance with EOA (>1cm2) under baseline physiological conditions. It was also discovered that pressure difference across the valves was directly proportional to the flow rate. The pressure difference also demonstrated a slow increase during the initial stages of simulated stenosis and a sudden increase as the obstruction became severe. This provides further evidence to support the ideal that stenosis is a slow progressive disease which may not present symptoms until severe. The peak to peak strain differences also tend to decrease as the severity of the obstruction was increased. The peak to peak strain difference is indicative of the pressures within the valve (intravalvular pressure). The results suggest that directly monitoring the pressures within the valve could be a useful diagnostic tool for detecting valve stenosis. Future works involves miniaturisation of the sensors and also the incorporation of telemetry into the sensor design