On the Mechanics Underlying the Reservoir-Excess Separation in Systemic Arteries and their Implications for Pulse Wave Analysis

Several works have separated the pressure waveform p in systemic arteries into reservoir pr and excess pexc components, p = pr + pexc, to improve pulse wave analysis, using windkessel models to calculate the reservoir pressure. However, the mechanics underlying this separation and the physical meaning of pr and pexc have not yet been established. They are studied here using the time-domain, inviscid and linear one-dimensional (1-D) equations of blood flow in elastic vessels. Solution of these equations in a distributed model of the 55 larger human arteries shows that pr calculated using a two-element windkessel model is space-independent and well approximated by the compliance-weighted space-average pressure of the arterial network. When arterial junctions are well-matched for the propagation of forward-travelling waves, pr calculated using a three-element windkessel model is space-dependent in systole and early diastole and is made of all the reflected waves originated at the terminal (peripheral) reflection sites, whereas pexc is the sum of the rest of the waves, which are obtained by propagating the left ventricular flow ejection without any peripheral reflection. In addition, new definitions of the reservoir and excess pressures from simultaneous pressure and flow measurements at an arbitrary location are proposed here. They provide valuable information for pulse wave analysis and overcome the limitations of the current two- and three-element windkessel models to calculate pr

Uncertainty quantification of inflow boundary condition and proximal arterial stiffness coupled effect on pulse wave propagation in a vascular network

International audienceSUMMARY This work aims at quantifying the effect of inherent uncertainties from cardiac output on the sensitivity of a human compliant arterial network response based on stochastic simulations of a reduced-order pulse wave propagation model. A simple pulsatile output form is utilized to reproduce the most relevant cardiac features with a minimum number of parameters associated with left ventricle dynamics. Another source of critical uncertainty is the spatial heterogeneity of the aortic compliance which plays a key role in the propagation and damping of pulse waves generated at each cardiac cycle. A continuous representation of the aortic stiffness in the form of a generic random field of prescribed spatial correlation is then considered. Resorting to a stochastic sparse pseudospectral method, we investigate the spatial sensitivity of the pulse pressure and waves reflection magnitude with respect to the different model uncertainties. Results indicate that uncertainties related to the shape and magnitude of the prescribed inlet flow in the proximal aorta can lead to potent variation of both the mean value and standard deviation of blood flow velocity and pressure dynamics due to the interaction of different wave propagation and reflection features. These results have potential physiological and pathological implications. They will provide some guidance in clinical data acquisition and future coupling of arterial pulse wave propagation reduced-order model with more complex beating heart models

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

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

Methods and Algorithms for Cardiovascular Hemodynamics with Applications to Noninvasive Monitoring of Proximal Blood Pressure and Cardiac Output Using Pulse Transit Time

Advanced health monitoring and diagnostics technology are essential to reduce the unrivaled number of human fatalities due to cardiovascular diseases (CVDs). Traditionally, gold standard CVD diagnosis involves direct measurements of the aortic blood pressure (central BP) and flow by cardiac catheterization, which can lead to certain complications. Understanding the inner-workings of the cardiovascular system through patient-specific cardiovascular modeling can provide new means to CVD diagnosis and relating treatment. BP and flow waves propagate back and forth from heart to the peripheral sites, while carrying information about the properties of the arterial network. Their speed of propagation, magnitude and shape are directly related to the properties of blood and arterial vasculature. Obtaining functional and anatomical information about the arteries through clinical measurements and medical imaging, the digital twin of the arterial network of interest can be generated. The latter enables prediction of BP and flow waveforms along this network. Point of care devices (POCDs) can now conduct in-home measurements of cardiovascular signals, such as electrocardiogram (ECG), photoplethysmogram (PPG), ballistocardiogram (BCG) and even direct measurements of the pulse transit time (PTT). This vital information provides new opportunities for designing accurate patient-specific computational models eliminating, in many cases, the need for invasive measurements. One of the main efforts in this area is the development of noninvasive cuffless BP measurement using patient’s PTT. Commonly, BP prediction is carried out with regression models assuming direct or indirect relationships between BP and PTT. However, accounting for the nonlinear FSI mechanics of the arteries and the cardiac output is indispensable. In this work, a monotonicity-preserving quasi-1D FSI modeling platform is developed, capable of capturing the hyper-viscoelastic vessel wall deformation and nonlinear blood flow dynamics in arbitrary arterial networks. Special attention has been dedicated to the correct modeling of discontinuities, such as mechanical properties mismatch associated with the stent insertion, and the intertwining dynamics of multiscale 3D and 1D models when simulating the arterial network with an aneurysm. The developed platform, titled Cardiovascular Flow ANalysis (CardioFAN), is validated against well-known numerical, in vitro and in vivo arterial network measurements showing average prediction errors of 5.2%, 2.8% and 1.6% for blood flow, lumen cross-sectional area, and BP, respectively. CardioFAN evaluates the local PTT, which enables patient-specific calibration and its application to input signal reconstruction. The calibration is performed based on BP, stroke volume and PTT measured by POCDs. The calibrated model is then used in conjunction with noninvasively measured peripheral BP and PTT to inversely restore the cardiac output, proximal BP and aortic deformation in human subjects. The reconstructed results show average RMSEs of 1.4% for systolic and 4.6% for diastolic BPs, as well as 8.4% for cardiac output. This work is the first successful attempt in implementation of deterministic cardiovascular models as add-ons to wearable and smart POCD results, enabling continuous noninvasive monitoring of cardiovascular health to facilitate CVD diagnosis

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

Computational estimation of haemodynamics and tissue stresses in abdominal aortic aneurysms

&apos;o e Abdominal aortic aneurysm is a vascular disease involving a focal dilation of the aorta. The exact cause is unknown but possibilities include infection and weakening of the connective tissue. Risk factors include a history of atherosclerosis, current smoking and a close relative with the disease. Although abdominal aortic aneurysm can affect anyone, it is most often seen in older men, and may be present in up to 5.9 % of the population aged 80 years. Biomechanical factors such as tissue stresses and shear stresses have been shown to play a part in aneurysm progression, although the specific mechanisms are still to be determined. The growth rate of the abdominal aortic aneurysm has been found to correlate with the peak stress in the aneurysm wall and the blood flow is thought to influence disease development. In order to resolve the connections between biology and biomechanics, accurate estimations of the forces involved are required. The first part of this thesis assesses the use of computational fluid dynamics for modelling haemodynamics in abdominal aortic aneurysms. Boundary conditions from the literature o

Measurement of Wall Shear Stress Exerted by Flowing Blood in the Human Carotid Artery: Ultrasound Doppler Velocimetry and Echo Particle Image Velocimetry

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordVascular endothelial cells lining the arteries are sensitive to wall shear stress (WSS) exerted by flowing blood. An important component of the pathophysiology of vascular diseases, WSS is commonly estimated by centerline ultrasound Doppler velocimetry (UDV). However, the accuracy of this method is uncertain. We have previously validated the use of a novel, ultrasound-based, particle image velocimetry technique (echo PIV) to compute 2-D velocity vector fields, which can easily be converted into WSS data. We compared WSS data derived from UDV and echo PIV in the common carotid artery of 27 healthy participants. Compared with echo PIV, time-averaged WSS was lower using UDV (28 ± 35%). Echo PIV revealed that this was due to considerable spatiotemporal variation in the flow velocity profile, contrary to the assumption that flow is steady and the velocity profile is parabolic throughout the cardiac cycle. The largest WSS underestimation by UDV was found during peak systole (118 ± 16%) and the smallest during mid-diastole (4.3± 46%). The UDV method underestimated WSS for the accelerating and decelerating systolic measurements (68 ± 30% and 24 ± 51%), whereas WSS was overestimated for end-diastolic measurements (−44 ± 55%). Our data indicate that UDV estimates of WSS provided limited and largely inaccurate information about WSS and that the complex spatiotemporal flow patterns do not fit well with traditional assumptions about blood flow in arteries. Echo PIV-derived WSS provides detailed information about this important but poorly understood stimulus that influences vascular endothelial pathophysiology.National Institute of HealthNational Institute for Health Research (NIHR