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.

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 Pulse wave propagation along human aorta: a model study

2020 ◽  
Vol 58 (1) ◽  
pp. 17-34
Author(s):  
Natalya Kizilova ◽  
Jeremi Mizerski ◽  
Helen Solovyova
Keyword(s):  
Wave Propagation ◽  
Pulse Wave ◽  
Human Aorta ◽  
Pulse Wave Propagation ◽  
Model Study

scholarly journals FSI Simulations of Pulse Wave Propagation in Human Abdominal Aortic Aneurysm: The Effects of Sac Geometry and Stiffness

2016 ◽  
Vol 7 ◽  
pp. BECB.S40094 ◽  
Author(s):  
Han Li ◽  
Kexin Lin ◽  
Danial Shahmirzadi
Keyword(s):  
Wave Propagation ◽  
Abdominal Aortic Aneurysm ◽  
Aortic Aneurysm ◽  
Pulse Wave ◽  
Fluid Velocity ◽  
In Vivo Studies ◽  
Pulse Wave Propagation ◽  
Wall Displacement ◽  
Abdominal Aortic ◽  
Pulse Waves

This study aims to quantify the effects of geometry and stiffness of aneurysms on the pulse wave velocity (PWV) and propagation in fluid-solid interaction (FSI) simulations of arterial pulsatile flow. Spatiotemporal maps of both the wall displacement and fluid velocity were generated in order to obtain the pulse wave propagation through fluid and solid media, and to examine the interactions between the two waves. The results indicate that the presence of abdominal aortic aneurysm (AAA) sac and variations in the sac modulus affect the propagation of the pulse waves both qualitatively (eg, patterns of change of forward and reflective waves) and quantitatively (eg, decreasing of PWV within the sac and its increase beyond the sac as the sac stiffness increases). The sac region is particularly identified on the spatiotemporal maps with a region of disruption in the wave propagation with multiple short-traveling forward/reflected waves, which is caused by the change in boundary conditions within the saccular region. The change in sac stiffness, however, is more pronounced on the wall displacement spatiotemporal maps compared to those of fluid velocity. We conclude that the existence of the sac can be identified based on the solid and fluid pulse waves, while the sac properties can also be estimated. This study demonstrates the initial findings in numerical simulations of FSI dynamics during arterial pulsations that can be used as reference for experimental and in vivo studies. Future studies are needed to demonstrate the feasibility of the method in identifying very mild sacs, which cannot be detected from medical imaging, where the material property degradation exists under early disease initiation.

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.

РULSE WAVES РROPAGATION IN SMALL VESSELS: MEASUREMENT RESULTS AND MODELLING APPROACHES

2020 ◽  
Vol 4 (2) ◽  
pp. 1037-1044
Author(s):  
A.I. Kubarko ◽  
◽  
V.A. Mansurov ◽  
A.D. Svetlichny ◽  
L.D. Ragunovich ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Computer Simulation ◽  
Wave Propagation ◽  
Propagation Velocity ◽  
Pulse Wave ◽  
Wave Propagation Velocity ◽  
Pulse Wave Propagation ◽  
Small Vessels ◽  
Pulse Waves ◽  
Simulation Results

The objective of the research work was to develop devices and algorithm for synchronous recording of pulse waves and ECG for measuring the delay time of pulse waves in the branches of various arteries relative to the R wave on an ECG, and to carry out computer simulation of the pulse wave propagation process to determine the dependence of the pulse wave propagation velocity on branching and other hemodynamic and morphological parameters of blood vessels. Material and methods. The study was conducted in 74 healthy subjects aged 18-23 years. The propagation time of the pulse wave by the arterial branches of the vessels of the common carotid, internal, external carotid and radial arteries was measured. The time was calculated by the delay of the beginning of the pulse wave relative to the tip of the R wave on the ECG. Vascular pulsations were recorded using mechanical sensitive and photosensitive sensors, which signals were amplified, digitized, recorded and analyzed using original computer soft wares. Computer simulation of the propagation of pulse waves along the wall of an “equivalent” vessel corresponding to the branching of several arterial vessels was carried out. Results. The velocity of propagation of a pulse wave along the branches of small arterial vessels was lower than its value for larger main arteries. The simulation results confirmed that the propagation velocity of a pulse wave can significantly slow down its movement along branched arterial vessels, which differ in the mechanical properties of the main arteries. Conclusion. The data obtained indicate that the developed devices and measurement algorithms make it possible to register pulse waves of various small arteries and obtain reproducible indices of the delay time of the pulse wave relative to the R wave on the ECG. The time and velocity of the pulse wave propagation depends on the length of the studied vessels, the mechanical properties of the walls of the vessels, which follows from the comparison of the obtained data with the morphological features of the structure of vascular networks. Simulation results for an “equivalent” vessel show that one of the possible causes of a lower pulse wave propagation velocity in small vessels is lower mechanical properties of the branches of small vessels compared with those of larger arteries. However, the identification of the nature of these dependencies and their connection with stiffness of the walls of small vessels requires further study.

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