scholarly journals Wave Propagation in Thin-Walled Aortic Analogues

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
C. G. Giannopapa ◽  
J. M. B. Kroot ◽  
A. S. Tijsseling ◽  
M. C. M. Rutten ◽  
F. N. van de Vosse
Keyword(s):  
Experimental Data ◽  
Wave Propagation ◽  
Frequency Domain ◽  
Analytical Model ◽  
Viscoelastic Properties ◽  
Numerical Models ◽  
Computational Cost ◽  
One Dimensional ◽  
Arterial Blood

Research on wave propagation in liquid filled vessels is often motivated by the need to understand arterial blood flows. Theoretical and experimental investigation of the propagation of waves in flexible tubes has been studied by many researchers. The analytical one-dimensional frequency domain wave theory has a great advantage of providing accurate results without the additional computational cost related to the modern time domain simulation models. For assessing the validity of analytical and numerical models, well defined in vitro experiments are of great importance. The objective of this paper is to present a frequency domain analytical model based on the one-dimensional wave propagation theory and validate it against experimental data obtained for aortic analogs. The elastic and viscoelastic properties of the wall are included in the analytical model. The pressure, volumetric flow rate, and wall distention obtained from the analytical model are compared with experimental data in two straight tubes with aortic relevance. The analytical results and the experimental measurements were found to be in good agreement when the viscoelastic properties of the wall are taken into account.

scholarly journals Wave Propagation in Thin-Walled Aortic Analogues

2008 ◽  
Author(s):  
C. G. Giannopapa ◽  
J. M. B. Kroot
Keyword(s):  
Experimental Data ◽  
Wave Propagation ◽  
Frequency Domain ◽  
Analytical Model ◽  
Viscoelastic Properties ◽  
Numerical Models ◽  
Computational Cost ◽  
Arterial Blood Flow ◽  
One Dimensional ◽  
Arterial Blood

Research wave propagation in liquid filled vessels is often motivated by the need to understand arterial blood flow. Theoretical and experimental investigation of the propagation of waves in flexible tubes has been studied by many researchers. The analytical one dimensional frequency domain wave theory has a great advantage of providing accurate results without the additional computational cost related to the modern time domain simulation models. For assessing the validity of analytical and numerical models well defined in-vitro experiments are of great importance. The objective of this paper is to present a frequency domain transmission line analytical model based on one-dimensional wave propagation theory and validate it against experimental data obtained for aortic analogues. The elastic and viscoelastic properties of the wall are included in the analytical model. The pressure, flow and wall distention results obtained from the analytical model are compared with experimental data in two straight tubes with aortic relevance. The analytical models and the experimental measurements were found to be in good agreement when the viscoelastic properties of the wall are taken into account.

Multiple Reflection and Transmission Theory for Wave Propagation in the Aorta

2009 ◽  
Author(s):  
C. G. Giannopapa ◽  
J. M. B. Kroot
Keyword(s):  
Experimental Data ◽  
Wave Propagation ◽  
Frequency Domain ◽  
Analytical Model ◽  
Numerical Models ◽  
Computational Cost ◽  
Arterial Blood Flow ◽  
Transition Line ◽  
One Dimensional ◽  
Arterial Blood

Wave propagation in liquid filled vessels is often motivated by the need to understand arterial blood flow. Theoretical and experimental investigations of traveling waves in flexible tubes have been performed by many researchers. The analytical one dimensional frequency domain wave theory has a great advantage of providing accurate results without the additional computational cost involved in the modern time domain simulation models. Transition line theory allows including non uniformities of vessels by capturing them as several uniform segments. For assessing the validity of analytical and numerical models well defined in-vitro experiments are of great importance. The objective of this paper is to present a frequency domain transmission line analytical model based on one-dimensional wave propagation theory and validate it against experimental data obtained for aortic analogues. The analytical model is set up by multiple sections and a formulation is derived that incorporates the multiple reflections and transmissions of propagating waves through the interfaces of these sections. The aortic analogues include straight and tapered tubes. The pressure, flow and wall distention results obtained from the analytical model are compared with experimental data in two straight tubes and one tapered one with aortic relevance. The analytical models and the experimental measurements were found to be in good agreement for both the uniform and tapered tubes.

scholarly journals The Role of Dimensionality in Understanding Granuloma Formation

Computation ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 58 ◽  
Author(s):  
Simeone Marino ◽  
Caitlin Hult ◽  
Paul Wolberg ◽  
Jennifer Linderman ◽  
Denise Kirschner
Keyword(s):  
Experimental Data ◽  
Large Scale ◽  
Bacterial Load ◽  
Computational Cost ◽  
Granuloma Formation ◽  
In Silico Studies ◽  
Cellular Recruitment ◽  
2D And 3D

Within the first 2–3 months of a Mycobacterium tuberculosis (Mtb) infection, 2–4 mm spherical structures called granulomas develop in the lungs of the infected hosts. These are the hallmark of tuberculosis (TB) infection in humans and non-human primates. A cascade of immunological events occurs in the first 3 months of granuloma formation that likely shapes the outcome of the infection. Understanding the main mechanisms driving granuloma development and function is key to generating treatments and vaccines. In vitro, in vivo, and in silico studies have been performed in the past decades to address the complexity of granuloma dynamics. This study builds on our previous 2D spatio-temporal hybrid computational model of granuloma formation in TB (GranSim) and presents for the first time a more realistic 3D implementation. We use uncertainty and sensitivity analysis techniques to calibrate the new 3D resolution to non-human primate (NHP) experimental data on bacterial levels per granuloma during the first 100 days post infection. Due to the large computational cost associated with running a 3D agent-based model, our major goal is to assess to what extent 2D and 3D simulations differ in predictions for TB granulomas and what can be learned in the context of 3D that is missed in 2D. Our findings suggest that in terms of major mechanisms driving bacterial burden, 2D and 3D models return very similar results. For example, Mtb growth rates and molecular regulation mechanisms are very important both in 2D and 3D, as are cellular movement and modulation of cell recruitment. The main difference we found was that the 3D model is less affected by crowding when cellular recruitment and movement of cells are increased. Overall, we conclude that the use of a 2D resolution in GranSim is warranted when large scale pilot runs are to be performed and if the goal is to determine major mechanisms driving infection outcome (e.g., bacterial load). To comprehensively compare the roles of model dimensionality, further tests and experimental data will be needed to expand our conclusions to molecular scale dynamics and multi-scale resolutions.

Wave propagation in heterogeneous porous media formulated in the frequency-space domain using a discontinuous Galerkin method

Geophysics ◽  
2011 ◽  
Vol 76 (4) ◽  
pp. N13-N28 ◽  
Author(s):  
Bastien Dupuy ◽  
Louis De Barros ◽  
Stephane Garambois ◽  
Jean Virieux
Keyword(s):  
Porous Media ◽  
Wave Propagation ◽  
Galerkin Method ◽  
Frequency Domain ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Solid Phase ◽  
Numerical Models ◽  
Fluid Phase ◽  
Heterogeneous Porous Media

Biphasic media with a dynamic interaction between fluid and solid phases must be taken into account to accurately describe seismic wave amplitudes in subsurface and reservoir geophysical applications. Consequently, the modeling of the wave propagation in heteregeneous porous media, which includes the frequency-dependent phenomena of the fluid-solid interaction, is considered for 2D geometries. From the Biot-Gassmann theory, we have deduced the discrete linear system in the frequency domain for a discontinuous finite-element method, known as the nodal discontinuous Galerkin method. Solving this system in the frequency domain allows accurate modeling of the Biot wave in the diffusive/propagative regimes, enhancing the importance of frequency effects. Because we had to consider finite numerical models, we implemented perfectly matched layer techniques. We found that waves are efficiently absorbed at the model boundaries, and that the discretization of the medium should follow the same rules as in the elastodynamic case, that is, 10 grids per minimum wavelength for a P0 interpolation order. The grid spreading of the sources, which could be stresses or forces applied on either the solid phase or the fluid phase, did not show any additional difficulties compared to the elastic problem. For a flat interface separating two media, we compared the numerical solution and a semianalytic solution obtained by a reflectivity method in the three regimes where the Biot wave is propagative, diffusive/propagative, and diffusive. In all cases, fluid-solid interactions were reconstructed accurately, proving that attenuation and dispersion of the waves were correctly accounted for. In addition to this validation in layered media, we have explored the capacities of modeling complex wave propagation in a laterally heterogeneous porous medium related to steam injection in a sand reservoir and the seismic response associated to a fluid substitution.

scholarly journals Arterial pulse wave propagation across stenoses and aneurysms: assessment of one-dimensional simulations against three-dimensional simulations and in vitro measurements

2021 ◽  
Vol 18 (177) ◽  
Author(s):  
Weiwei Jin ◽  
Jordi Alastruey
Keyword(s):  
Abdominal Aorta ◽  
Three Dimensional ◽  
Experimental Models ◽  
Arterial Blood Flow ◽  
Future Research ◽  
One Dimensional ◽  
Arterial Blood ◽  
Mean Square Errors ◽  
Pressure And Flow Waves

One-dimensional (1-D) arterial blood flow modelling was tested in a series of idealized vascular geometries representing the abdominal aorta, common carotid and iliac arteries with different sizes of stenoses and/or aneurysms. Three-dimensional (3-D) modelling and in vitro measurements were used as ground truth to assess the accuracy of 1-D model pressure and flow waves. The 1-D and 3-D formulations shared identical boundary conditions and had equivalent vascular geometries and material properties. The parameters of an experimental set-up of the abdominal aorta for different aneurysm sizes were matched in corresponding 1-D models. Results show the ability of 1-D modelling to capture the main features of pressure and flow waves, pressure drop across the stenoses and energy dissipation across aneurysms observed in the 3-D and experimental models. Under physiological Reynolds numbers ( Re ), root mean square errors were smaller than 5.4% for pressure and 7.3% for the flow, for stenosis and aneurysm sizes of up to 85% and 400%, respectively. Relative errors increased with the increasing stenosis and aneurysm size, aneurysm length and Re , and decreasing stenosis length. All data generated in this study are freely available and provide a valuable resource for future research.

Analytical Model of the Soil Temperature Distribution Based on Weather Data

2020 ◽  
Author(s):  
M. Naser Reda ◽  
Markus Spinnler ◽  
Rajib Mahamud ◽  
Thomas Sattelmayer
Keyword(s):  
Temperature Distribution ◽  
Soil Temperature ◽  
Analytical Model ◽  
Numerical Models ◽  
Computational Cost ◽  
Weather Conditions ◽  
Solar Irradiation ◽  
Weather Data ◽  
Data Sets ◽  
Temperature Profiles

Abstract The measurement of soil temperature profiles for different locations or climates is essential for calculating the thermal performance of applications connected with the soil, e.g., underground heat storage systems. Estimating soil temperature profiles is identified as crucial knowledge for plant and crop growth as well as for germination in all agricultural tasks. The ground temperature depends on weather conditions (ambient temperature, solar irradiation, wind velocity, sky radiation, etc.) that contribute to the resulting temperature distribution within the soil close to the surface. In literature, several approaches have been discussed to predict soil temperature in different climates and locations, such as data-driven models, wavelet transform artificial neural networks, statistical models, etc. However, these models require extensive data sets from literature and high computational efforts. In the present study, a one-dimensional analytical model will be presented, which is based on the Green’s Function (GF) method. The model can estimate the daily and annual variation of the soil temperature distribution at different depths from real-time weather data sets. The model was experimentally validated with an accuracy of more than 96%. The significant advantage of the presented analytical method is the low computational cost, which is lower than that of numerical models by approximately two orders of magnitude.

A wavelet-based model of one-dimensional periodic structure for wave-propagation analysis

2009 ◽  
Vol 466 (2113) ◽  
pp. 263-281 ◽  
Author(s):  
Parikshit Sonekar ◽  
Mira Mitra
Keyword(s):  
Wave Propagation ◽  
Frequency Domain ◽  
Periodic Structure ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Fe Model ◽  
Loading Conditions ◽  
Dynamic Stiffness Matrix ◽  
One Dimensional ◽  
Propagation Analysis

In this paper, a wavelet-based method is developed for wave-propagation analysis of a generic multi-coupled one-dimensional periodic structure (PS). The formulation is based on the periodicity condition and uses the dynamic stiffness matrix of the periodic cell obtained from finite-element (FE) or other numerical methods. Here, unlike its conventional definition, the dynamic stiffness matrix is obtained in the wavelet domain through a Daubechies wavelet transform. The proposed numerical scheme enables both time- and frequency-domain analysis of PSs under arbitrary loading conditions. This is in contrast to the existing Fourier-transform-based analysis that is restricted to frequency-domain study. Here, the dispersion characteristics of PSs, especially the band-gap features, are studied. In addition, the method is implemented to simulate time-domain wave response under impulse loading conditions. The two examples considered are periodically simply supported beam and periodic frame structures. In all cases, the responses obtained using the present periodic formulation are compared with the response simulated using the FE model without the periodicity assumption, and they show an exact match. This validates the accuracy of the periodic assumption to obtain the time- and frequency-domain wave responses up to a high-frequency range. Apart from this, the proposed method drastically reduces the computational cost and can be implemented for homogenization of PSs.

Numerical Solution for Two-Dimensional Elastic Wave Propagation in Finite Bars

1967 ◽  
Vol 34 (3) ◽  
pp. 725-734 ◽  
Author(s):  
L. D. Bertholf
Keyword(s):  
Experimental Data ◽  
Wave Propagation ◽  
Elastic Wave ◽  
Numerical Solutions ◽  
Step Change ◽  
Two Dimensional ◽  
One Dimensional ◽  
Elastic Bar ◽  
The One ◽  
The Impact

Numerical solutions of the exact equations for axisymmetric wave propagation are obtained with continuous and discontinuous loadings at the impact end of an elastic bar. The solution for a step change in stress agrees with experimental data near the end of the bar and exhibits a region that agrees with the one-dimensional strain approximation. The solution for an applied harmonic displacement closely approaches the Pochhammer-Chree solution at distances removed from the point of application. Reflections from free and rigid-lubricated ends are studied. The solutions after reflection are compared with the elementary one-dimensional stress approximation.

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