Physical determining factors of the arterial pulse waveform: theoretical analysis and calculation using the 1-D formulation

Alastruey, Jordi; Passerini, Tiziano; Formaggia, Luca; Peiró, Joaquim

doi:10.1007/s10665-012-9555-z

Cited by 67 publications

(98 citation statements)

References 44 publications

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“…This is a short wavelength compared with the 10‐m‐long vessel, which enables showing the full shape of the pulse wave as it propagates along the vessel. For the inviscid problem, theoretical pressure and flow waveforms are in phase, have a constant amplitude and propagate to the right with a wave speed given by Equation . These theoretical results are well predicted by all six numerical schemes.…”

Section: Resultssupporting

confidence: 53%

A benchmark study of numerical schemes for one‐dimensional arterial blood flow modelling

Boileau

Nithiarasu

Blanco

et al. 2015

Numer Methods Biomed Eng

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SUMMARYHaemodynamical simulations using one-dimensional (1D) computational models exhibit many of the features of the systemic circulation under normal and diseased conditions. Recent interest in verifying 1D numerical schemes has led to the development of alternative experimental setups and the use of threedimensional numerical models to acquire data not easily measured in vivo. In most studies to date, only one particular 1D scheme is tested. In this paper, we present a systematic comparison of six commonly used numerical schemes for 1D blood flow modelling: discontinuous Galerkin, locally conservative Galerkin, Galerkin least-squares finite element method, finite volume method, finite difference MacCormack method and a simplified trapezium rule method. Comparisons are made in a series of six benchmark test cases with an increasing degree of complexity. The accuracy of the numerical schemes is assessed by comparison with theoretical results, three-dimensional numerical data in compatible domains with distensible walls or experimental data in a network of silicone tubes. Results show a good agreement among all numerical schemes and their ability to capture the main features of pressure, flow and area waveforms in large arteries. All the information used in this study, including the input data for all benchmark cases, experimental data where available and numerical solutions for each scheme, is made publicly available online, providing a comprehensive reference data set to support the development of 1D models and numerical schemes.

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Section: Resultssupporting

confidence: 53%

A benchmark study of numerical schemes for one‐dimensional arterial blood flow modelling

Boileau

Nithiarasu

Blanco

et al. 2015

Numer Methods Biomed Eng

Self Cite

176

285

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“…The viscoelasticity constant ⌫ is difficult to estimate and is assumed to be zero for the main results; however, we investigated the effect of viscoelasticity in the sensitivity analysis, where we assumed ⌫ ϭ 1,792 r 0 ϩ 1,522 g/s, as approximated from Eq. 32 in Alastruey et al (1), wall viscosity data (7), and wall thickness-diameter ratios (42). Note that although we have chosen a simple Voigt model, more sophisticated viscoelasticity models are available (see for example, Refs.…”

Section: D Model Of Conduit Coronary Arteries Most Sheepmentioning

confidence: 99%

Scalability and in vivo validation of a multiscale numerical model of the left coronary circulation

Mynard

Penny

Smolich

2014

American Journal of Physiology-Heart and Circulatory Physiology

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Mynard JP, Penny DJ, Smolich JJ. Scalability and in vivo validation of a multiscale numerical model of the left coronary circulation. Am J Physiol Heart Circ Physiol 306: H517-H528, 2014. First published December 20, 2013 doi:10.1152/ajpheart.00603.2013.-Multiscale modeling is a promising tool for the study of coronary hemodynamics. A key strength of this approach is that it accounts for microvascular properties and extravascular forces that differ regionally and transmurally, as well as wave propagation effects in the conduit arteries. However, little validation of such models has been reported and no models of the newborn coronary circulation have been described. We therefore validated a multiscale model of the left coronary circulation using high-fidelity data from nine adult sheep and nine newborn lambs and investigated whether wave propagation effects are more prominent in adults, whose body size (and hence wave transit distance) is greater. The model consisted of a one-dimensional (1D) network of the major conduit arteries and a lumped parameter model of microvascular beds. Intramyocardial pressure was considered to arise via contraction-related myocyte thickening and transmission of ventricular cavity pressure into the heart wall. 1D network geometry from published human anatomical data was scaled using myocardial weights, while subject-specific aortic pressure/flow and ventricular pressure formed model inputs. Total vascular resistance was determined iteratively from measured mean circumflex coronary flow (CxQ), but no fitting of phasic aspects of the waveform was performed. Excellent agreement was obtained between simulated and measured CxQ waveforms in most cases. Detailed flow waveform analysis did not clearly reveal a greater prominence of wave propagation effects in adults compared with newborns. This multiscale model is likely to be useful for investigating wave phenomena and phasic aspects of coronary flow in adults and during development. coronary arteries; wave propagation; allometric scaling; computer model; hemodynamics; newborn MATHEMATICAL MODELING, in concert with experimental studies, has played an important role in building our current understanding of coronary hemodynamics, providing insights into the role of intramyocardial pressure, large microvascular compliance, and transmural differences of vascular impedance and flow patterns (4, 9 -12, 18, 64, 67, 70). Many models of the coronary circulation have been of the lumped parameter [or zero-dimensional (0D)] type, where the resistive and capacitive properties of all coronary vessels are combined into a small number of elements. For example, the main conduit coronary arteries lying on the epicardium (or traversing the ventricular septum) have generally been represented by a single compliance (10, 12, 64) or windkessel compartment (4, 9, 18).One limitation of an exclusively 0D modeling approach is that wave propagation effects are neglected. That these effects play a role in shaping the coronary arterial flow waveform was first suggested ...

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“…To reduce the complexity of the numerical model, mixed‐dimension models have been introduced. () Thereby, subnetworks of larger vessels are modelled by three‐dimensional or one‐dimensional (1‐D) PDEs in space. At the inlets and outlets of these networks, the corresponding models are coupled with 1‐D PDEs or zero‐dimensional (0‐D) models (systems of ODEs) incorporating, e.g., the Windkessel effect of the omitted vessels and the pumping of the heart.…”

Section: Introductionmentioning

confidence: 99%

Numerical modelling of a peripheral arterial stenosis using dimensionally reduced models and kernel methods

Köppl

Santin

Haasdonk

et al. 2018

Numer Methods Biomed Eng

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In this work, we consider 2 kinds of model reduction techniques to simulate blood flow through the largest systemic arteries, where a stenosis is located in a peripheral artery, i.e., in an artery that is located far away from the heart. For our simulations, we place the stenosis in one of the tibial arteries belonging to the right lower leg (right posterior tibial artery). The model reduction techniques that are used are on the one hand dimensionally reduced models (1-D and 0-D models, the so-called mixed-dimension model) and on the other hand surrogate models produced by kernel methods. Both methods are combined in such a way that the mixed-dimension models yield training data for the surrogate model, where the surrogate model is parametrised by the degree of narrowing of the peripheral stenosis. By means of a well-trained surrogate model, we show that simulation data can be reproduced with a satisfactory accuracy and that parameter optimisation or state estimation problems can be solved in a very efficient way. Furthermore, it is demonstrated that a surrogate model enables us to present after a very short simulation time the impact of a varying degree of stenosis on blood flow, obtaining a speedup of several orders over the full model.

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Physical determining factors of the arterial pulse waveform: theoretical analysis and calculation using the 1-D formulation

Cited by 67 publications

References 44 publications

A benchmark study of numerical schemes for one‐dimensional arterial blood flow modelling

A benchmark study of numerical schemes for one‐dimensional arterial blood flow modelling

Scalability and in vivo validation of a multiscale numerical model of the left coronary circulation

Numerical modelling of a peripheral arterial stenosis using dimensionally reduced models and kernel methods

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