Application of the sweep method in solving one-dimensional equations of blood flow and pulse wave propagation in the arterial vascular system

2011 ◽  
Vol 84 (6) ◽  
pp. 1322-1333 ◽  
Author(s):  
V. M. Popov ◽  
V. A. Babenko
Keyword(s):  
Blood Flow ◽  
Wave Propagation ◽  
Pulse Wave ◽  
Vascular System ◽  
Sweep Method ◽  
Pulse Wave Propagation ◽  
One Dimensional

Nonlinear Response of Shells Conveying Pulsatile Flow With Pulse-Wave Propagation

2016 ◽  
Author(s):  
Eleonora Tubaldi ◽  
Marco Amabili ◽  
Michael P. Paidoussis
Keyword(s):  
Blood Flow ◽  
Wave Propagation ◽  
Pulsatile Flow ◽  
Pulse Wave ◽  
Pulse Wave Propagation ◽  
Vascular Prostheses ◽  
Axial Coordinate ◽  
Pulsatile Pressure ◽  
Velocity Changes ◽  
Oscillatory Pressure

In deformable shells conveying pulsatile flow, oscillatory pressure changes cause local movements of the fluid and shell wall, which propagate downstream in the form of a wave. In biomechanics, it is the propagation of the pulse that determines the pressure gradient during the flow at every location of the arterial tree. In this study, a woven Dacron vascular prosthesis is modelled as a transversely isotropic circular cylindrical shell described by means of nonlinear Novozhilov shell theory. Flexible boundary conditions are considered to simulate connection with the remaining tissue. Nonlinear vibrations of the shell conveying pulsatile flow and subjected to pulsatile pressure are investigated taking into account the effects of the pulse-wave propagation. An input oscillatory pressure at the shell entrance is considered and it propagates down the shell causing a wave motion within the shell where, as a consequence, the pressure gradient and the flow velocity are functions of both the axial coordinate and time. For the first time in literature, coupled fluid-structure Lagrange equations for a non-material volume with wave propagation in case of pulsatile flow are developed. The fluid is modeled as a Newtonian inviscid pulsatile flow and it is formulated using a hybrid model based on the linear potential flow theory and considering the unsteady viscous effects obtained from the unsteady time-averaged Navier-Stokes equations. Contributions of pressure and velocity changes’ propagation are also considered in the pressure drop along the shell and in the pulsatile frictional traction on the internal wall in the axial direction. A numerical bifurcation analysis employs a refined reduced order model to investigate the dynamic behavior of a pressurized Dacron vascular graft conveying blood flow. A pulsatile time-dependent blood flow model is considered in order to study the effect of pressurization by applying the first and second harmonic of the physiological waveforms of velocity and pressure during the heart beating period. Geometrically nonlinear vibration response to pulsatile flow and transmural pulsatile pressure considering the propagation of pressure and velocity changes inside the shell are here presented via frequency-response curves and time histories. It is shown how traveling waves of pressure and velocity cause a delay in the radial displacement of the shell at different values of the axial coordinate. This study provides a deep insight into the currently unknown nonlinear behavior of vascular prostheses whose dynamic response can cause unwanted hemodynamic effects leading to failure. Indeed, it is well known that vascular prostheses mechanical properties are very different from those of natural arteries. In particular, the compliance mismatch between the host artery and the prosthesis causes a different wave speed resulting in a change in the performance of the cardiovascular system. In the near future, a more refined model to the one here presented will be applied to reproduce and compare the dynamic behavior of vascular prostheses and the human aorta, helping in vascular prostheses design and implementation.

scholarly journals Simulation of pulse wave propagation using one-dimensional models of hemodynamics

2021 ◽  
Vol 2103 (1) ◽  
pp. 012081
Author(s):  
G V Krivovichev ◽  
N V Egorov
Keyword(s):  
Wave Propagation ◽  
Analytical Solution ◽  
Cross Section ◽  
Pulse Propagation ◽  
Pulse Wave ◽  
Pulse Wave Propagation ◽  
One Dimensional ◽  
Hydrodynamic System ◽  
Dimensional Models ◽  
Inviscid Case

Abstract The models of hemodynamics, corresponding to the inviscid, Newtonian, and non-Newtonian models, are compared. The models are constructed by the averaging of the hydrodynamic system on the vessel cross-section. For the inviscid case, the analytical solution of the problem for pulse propagation is obtained. As the result of the comparison, the deviations of the solutions for non-Newtonian models from the Newtonian and inviscid cases are demonstrated.

scholarly journals Mathematical modeling of pulse wave propagation along human aorta

2018 ◽  
Keyword(s):  
Blood Flow ◽  
Wave Propagation ◽  
Pulse Wave ◽  
Medical Diagnostics ◽  
Human Aorta ◽  
Circulation System ◽  
Pulse Wave Propagation ◽  
Blood Circulation System ◽  
Pulse Waves ◽  
The Individual

Background: Physical characteristics of pulse waves, which are generated by the heart contractions and propagated along the arteries, are used in medicine for diagnostics of the blood circulation system and blood supply to the organs and tissues. At the sites with significant wave reflections the high local pressure oscillations appear that may lead to damage of the endothelium, development of atherosclerotic plaques and aortic aneurysm. Therefore, elaboration of a detailed biophysical model of the individual aorta based on tomography and determination of the dangerous sites with high wave reflections are important for medical diagnostics. Objectives: The aim of the work is to study the regularities of the pulse wave propagation and reflection along the aorta and to propose new methods for early diagnosis of disorders in the blood circulation system. Materials and methods: The measurement data on diameters and lengths of segments of aorta and its branches conducted on 5 corpses have been used. Calculations of the wave conduction and reflection coefficients are based on the linear theory of pulse waves developed by J. Lighthill. Results: It is shown that from the biophysical point of view, the aorta is an optimal waveguide, which provides almost zero local reflections of the pulse waves. Most of the branches possess negative reflection, which accelerates the blood flow and decreases the load on the heart due to the suction effect. The calculated values of the branching coefficients and pulse waves speeds correspond to the data of the previous experimental measurements. It is shown that most of the branches have an optimal Murray coefficient close to one. It implies, aorta also provides the optimal volumetric blood flow over the period of cardiac contraction with minimal energy expenses. Conclusions: Human aorta and its branches possess optimal biophysical properties, which ensure the blood flow with minimal energy consumption. Aorta as an optimal waveguide provides pulse wave propagation with almost without reflection. The proposed method of estimation of the biophysical properties of aorta as a waveguide can be useful for medical diagnostics, allowing early identification of the regions which are dangerous in terms of the progressive development of vascular pathologies in the individual geometry of the patient's vasculature.

Effect of Bifurcation on Pulse Wave Propagation in Human Arteries

2010 ◽  
Author(s):  
Yusuke Kawai ◽  
Shigehiko Kaneko
Keyword(s):  
Wave Propagation ◽  
Pulse Wave ◽  
Estimation Method ◽  
Momentum Conservation ◽  
Reactive Force ◽  
Dimensional Model ◽  
Pulse Wave Propagation ◽  
One Dimensional ◽  
Elastic Tubes ◽  
Human Arteries

In recent years, arteriosclerotic cardiovascular disease becomes a serious problem in the developed countries. The degree of the arteriosclerosis should be examined routinely and invasively, and the measurement of pulse wave is considered as an effective estimation method. Nowadays, pulse wave is widely used in clinical practice as a noninvasive method of examining circulatory kinetics, but the mechanism in the process of the systolic wave generated at heart and propagating to the peripheral artery remains to be elucidated. In this research, to investigate the effect of bifurcation on pulse wave propagation, numerical simulations by a dynamic model of arteries and in vitro experiments were conducted. A one-dimensional model of arteries is coupled by partial differential equations describing mass and momentum conservation with the tube law that relates the local cross-sectional area to the local radial pressure difference. In the case of a bifurcated artery model, the governing equations were solved by introducing the momentum caused by the reactive force at bifurcation into the equation of momentum conservation. The momentum by the reactive force at bifurcation was supposed to be proportional to the momentum flowing into the bifurcation, and the proportionality coefficient was derived from experiments. Then, the proposed one-dimensional model was validated by a comparison to experimental data. In the experimental setup, elastic tubes with different values of Young’s modulus were tested to simulate human arteries. From the numerical and experimental results, it turns out that the characteristic waveforms of the pressure and velocity obtained from experiments are also captured by the numerical calculations.

scholarly journals Alterations in pulse wave propagation reflect the degree of outflow tract banding in HH18 chicken embryos

2013 ◽  
Vol 305 (3) ◽  
pp. H386-H396 ◽  
Author(s):  
Liang Shi ◽  
Sevan Goenezen ◽  
Stephen Haller ◽  
Monica T. Hinds ◽  
Kent L. Thornburg ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Blood Flow ◽  
Wave Propagation ◽  
Transit Time ◽  
Congenital Heart ◽  
Cardiac Cycle ◽  
Pulse Wave ◽  
Pulse Transit Time ◽  
Pulse Wave Propagation ◽  
Chicken Embryos

Hemodynamic conditions play a critical role in embryonic cardiovascular development, and altered blood flow leads to congenital heart defects. Chicken embryos are frequently used as models of cardiac development, with abnormal blood flow achieved through surgical interventions such as outflow tract (OFT) banding, in which a suture is tightened around the heart OFT to restrict blood flow. Banding in embryos increases blood pressure and alters blood flow dynamics, leading to cardiac malformations similar to those seen in human congenital heart disease. In studying these hemodynamic changes, synchronization of data to the cardiac cycle is challenging, and alterations in the timing of cardiovascular events after interventions are frequently lost. To overcome this difficulty, we used ECG signals from chicken embryos (Hamburger-Hamilton stage 18, ∼3 days of incubation) to synchronize blood pressure measurements and optical coherence tomography images. Our results revealed that, after 2 h of banding, blood pressure and pulse wave propagation strongly depend on band tightness. In particular, while pulse transit time in the heart OFT of control embryos is ∼10% of the cardiac cycle, after banding (35% to 50% band tightness) it becomes negligible, indicating a faster OFT pulse wave velocity. Pulse wave propagation in the circulation is likewise affected; however, pulse transit time between the ventricle and dorsal aorta (at the level of the heart) is unchanged, suggesting an overall preservation of cardiovascular function. Changes in cardiac pressure wave propagation are likely contributing to the extent of cardiac malformations observed in banded hearts.

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