scholarly journals A One-Dimensional Hemodynamic Model of the Coronary Arterial Tree

2019 ◽  
Vol 10 ◽  
Author(s):  
Zheng Duanmu ◽  
Weiwei Chen ◽  
Hao Gao ◽  
Xilan Yang ◽  
Xiaoyu Luo ◽  
...  
Keyword(s):  
Arterial Tree ◽  
One Dimensional ◽  
Hemodynamic Model

scholarly journals Validation of a one-dimensional model of the systemic arterial tree

2009 ◽  
Vol 297 (1) ◽  
pp. H208-H222 ◽  
Author(s):  
Philippe Reymond ◽  
Fabrice Merenda ◽  
Fabienne Perren ◽  
Daniel Rüfenacht ◽  
Nikos Stergiopulos
Keyword(s):  
Constitutive Law ◽  
Distributed Model ◽  
Arterial Tree ◽  
One Dimensional ◽  
Continuity Equations ◽  
Nonlinear Viscoelastic ◽  
Model Predictions ◽  
The One ◽  
D Model ◽  
Systemic Arterial Tree

A distributed model of the human arterial tree including all main systemic arteries coupled to a heart model is developed. The one-dimensional (1-D) form of the momentum and continuity equations is solved numerically to obtain pressures and flows throughout the systemic arterial tree. Intimal shear is modeled using the Witzig-Womersley theory. A nonlinear viscoelastic constitutive law for the arterial wall is considered. The left ventricle is modeled using the varying elastance model. Distal vessels are terminated with three-element windkessels. Coronaries are modeled assuming a systolic flow impediment proportional to ventricular varying elastance. Arterial dimensions were taken from previous 1-D models and were extended to include a detailed description of cerebral vasculature. Elastic properties were taken from the literature. To validate model predictions, noninvasive measurements of pressure and flow were performed in young volunteers. Flow in large arteries was measured with MRI, cerebral flow with ultrasound Doppler, and pressure with tonometry. The resulting 1-D model is the most complete, because it encompasses all major segments of the arterial tree, accounts for ventricular-vascular interaction, and includes an improved description of shear stress and wall viscoelasticity. Model predictions at different arterial locations compared well with measured flow and pressure waves at the same anatomical points, reflecting the agreement in the general characteristics of the “generic 1-D model” and the “average subject” of our volunteer population. The study constitutes a first validation of the complete 1-D model using human pressure and flow data and supports the applicability of the 1-D model in the human circulation.

Toward a noninvasive subject-specific estimation of abdominal aortic pressure

2008 ◽  
Vol 295 (3) ◽  
pp. H1156-H1164 ◽  
Author(s):  
Carl-Johan Thore ◽  
Jonas Stålhand ◽  
Matts Karlsson
Keyword(s):  
Aortic Pressure ◽  
Processing Technique ◽  
Distributed Model ◽  
Specific Information ◽  
Peripheral Artery ◽  
Tree Model ◽  
Signal Processing Technique ◽  
Arterial Tree ◽  
One Dimensional ◽  
Abdominal Aortic

A method for estimation of central arterial pressure based on linear one-dimensional wave propagation theory is presented in this paper. The equations are applied to a distributed model of the arterial tree, truncated by three-element windkessels. To reflect individual differences in the properties of the arterial trees, we pose a minimization problem from which individual parameters are identified. The idea is to take a measured waveform in a peripheral artery and use it as input to the model. The model subsequently predicts the corresponding waveform in another peripheral artery in which a measurement has also been made, and the arterial tree model is then calibrated in such a way that the computed waveform matches its measured counterpart. For the purpose of validation, invasively recorded abdominal aortic, brachial, and femoral pressures in nine healthy subjects are used. The results show that the proposed method estimates the abdominal aortic pressure wave with good accuracy. The root mean square error (RMSE) of the estimated waveforms was 1.61 ± 0.73 mmHg, whereas the errors in systolic and pulse pressure were 2.32 ± 1.74 and 3.73 ± 2.04 mmHg, respectively. These results are compared with another recently proposed method based on a signal processing technique, and it is shown that our method yields a significantly ( P < 0.01) lower RMSE. With more extensive validation, the method may eventually be used in clinical practice to provide detailed, almost individual, specific information as a valuable basis for decision making.

One Dimensional Model of the Systemic Arterial Tree Including Cerebral Circulation

2007 ◽  
Author(s):  
Philippe Reymond ◽  
Fabrice Merenda ◽  
Fabienne Perren ◽  
Daniel Rüfenacht ◽  
Nikos Stergiopulos
Keyword(s):  
Cerebral Circulation ◽  
Cerebral Arteries ◽  
Distributed Model ◽  
Dimensional Model ◽  
Heart Model ◽  
Arterial Tree ◽  
One Dimensional ◽  
Distributed Models ◽  
The Past ◽  
Systemic Arterial Tree

The aim of this study is to develop a distributed model of the entire systemic arterial tree, coupled to a heart model and including a detailed description of the cerebral arteries. Distributed models of the arterial tree have been studied extensively in the past (Avolio [1]; Cassot et al [2]; Meister [3]; Schaaf and Abbrecht [4]; Stergiopulos et al [5]; Westerhof et al [6]; Zagzoule and Marc-Vergnes [7]), however, no model has been developed so far that offers a physiologically relevant coupling to the heart and includes the entire cerebral artery network.

scholarly journals AN IMPROVED MODEL FOR REDUCED-ORDER PHYSIOLOGICAL FLUID FLOWS

2012 ◽  
Vol 12 (03) ◽  
pp. 1250052 ◽  
Author(s):  
OMER SAN ◽  
ANNE E. STAPLES
Keyword(s):  
Fluid Flows ◽  
Momentum Equation ◽  
System Level ◽  
Arterial Tree ◽  
Reduced Order ◽  
One Dimensional ◽  
Proposed Model ◽  
Nonlinear Coupled System ◽  
Physiological Fluid ◽  
Physiological Systems

An improved one-dimensional mathematical model based on the Pulsed Flow Equations (PFE) is derived by integrating the axial component of the momentum equation over the transient Womersley velocity profile, providing a dynamic momentum equation whose coefficients are smoothly varying functions of the spatial variable. The resulting momentum equation along with the continuity equation and pressure-area relation form our reduced-order model for physiological fluid flows in one dimension and are aimed at providing accurate and fast-to-compute global models for physiological systems represented as networks of quasi one-dimensional fluid flows. The consequent nonlinear coupled system of equations is solved by the Lax-Wendroff scheme and is then applied to an open model arterial network of the human vascular system containing the largest 55 arteries. The proposed model with functional coefficients is compared with current classical one-dimensional theories which assume steady state Hagen-Poiseuille velocity profiles, either parabolic or plug-like, throughout the whole arterial tree. The effects of the nonlinear term in the momentum equation and different strategies for bifurcation points in the network, as well as the various lumped parameter outflow boundary conditions for distal terminal points are also analyzed. The results show that the proposed model can be used as an efficient tool for investigating the dynamics of reduced-order models of flows in physiological systems and would, in particular, be a good candidate for the one-dimensional, system-level component of geometric multiscale models of physiological systems.

Validation of a patient-specific one-dimensional model of the systemic arterial tree

2011 ◽  
Vol 301 (3) ◽  
pp. H1173-H1182 ◽  
Author(s):  
Philippe Reymond ◽  
Yvette Bohraus ◽  
Fabienne Perren ◽  
Francois Lazeyras ◽  
Nikos Stergiopulos
Keyword(s):  
Arterial Wall ◽  
Specific Model ◽  
Constitutive Law ◽  
Distributed Model ◽  
Patient Specific ◽  
Dimensional Model ◽  
Arterial Tree ◽  
One Dimensional ◽  
Flow Waveforms ◽  
Systemic Arterial Tree

The aim of this study is to develop and validate a patient-specific distributed model of the systemic arterial tree. This model is built using geometric and hemodynamic data measured on a specific person and validated with noninvasive measurements of flow and pressure on the same person, providing thus a patient-specific model and validation. The systemic arterial tree geometry was obtained from MR angiographic measurements. A nonlinear viscoelastic constitutive law for the arterial wall is considered. Arterial wall distensibility is based on literature data and adapted to match the wave propagation velocity of the main arteries of the specific subject, which were estimated by pressure waves traveling time. The intimal shear stress is modeled using the Witzig-Womersley theory. Blood pressure is measured using applanation tonometry and flow rate using transcranial ultrasound and phase-contrast-MRI. The model predicts pressure and flow waveforms in good qualitative and quantitative agreement with the in vivo measurements, in terms of wave shape and specific wave features. Comparison with a generic one-dimensional model shows that the patient-specific model better predicts pressure and flow at specific arterial sites. These results obtained let us conclude that a patient-specific one-dimensional model of the arterial tree is able to predict well pressure and flow waveforms in the main systemic circulation, whereas this is not always the case for a generic one-dimensional model.

scholarly journals On the importance of the nonuniform aortic stiffening in the hemodynamics of physiological aging

2019 ◽  
Vol 317 (5) ◽  
pp. H1125-H1133
Author(s):  
Stamatia Z. Pagoulatou ◽  
Vasiliki Bikia ◽  
Bram Trachet ◽  
Theodore G. Papaioannou ◽  
Athanase D. Protogerou ◽  
...  
Keyword(s):  
Aortic Flow ◽  
Patient Specific ◽  
Diagnostic Tools ◽  
Dimensional Model ◽  
Arterial Tree ◽  
Simple Method ◽  
Peripheral Vessel ◽  
One Dimensional ◽  
Noninvasive Measurements ◽  
Effects Of Aging

Mathematical models of the arterial tree constitute a valuable tool to investigate the hemodynamics of aging and pathology. Rendering such models as patient specific could allow for the assessment of central hemodynamic variables of clinical interest. However, this task is challenging, particularly with respect to the tuning of the local area compliance that varies significantly along the arterial tree. Accordingly, in this study, we demonstrate the importance of taking into account the differential effects of aging on the stiffness of central and peripheral arteries when simulating a person’s hemodynamic profile. More specifically, we propose a simple method for effectively adapting the properties of a generic one-dimensional model of the arterial tree based on the subject’s age and noninvasive measurements of aortic flow and brachial pressure. A key element for the success of the method is the implementation of different mechanisms of arterial stiffening for young and old individuals. The designed methodology was tested and validated against in vivo data from a population of n = 20 adults. Carotid-to-femoral pulse wave velocity was accurately predicted by the model (mean error = 0.14 m/s, SD = 0.77 m/s), with the greatest deviations being observed for older subjects. In regard to aortic pressure, model-derived systolic blood pressure and augmentation index were both in good agreement (mean difference of 2.3 mmHg and 4.25%, respectively) with the predictions of a widely used commercial device (Mobil-O-Graph). These preliminary results encourage us to further validate the method in larger samples and consider its potential as a noninvasive tool for hemodynamic monitoring. NEW & NOTEWORTHY We propose a technique for adapting the parameters of a validated one-dimensional model of the arterial tree using noninvasive measurements of aortic flow and brachial pressure. Emphasis is given on the adjustment of the arterial tree distensibility, which incorporates the nonuniform effects of aging on central and peripheral vessel elasticity. Our method could find application in the derivation of important hemodynamic indices, paving the way for novel diagnostic tools.

A hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree

2007 ◽  
Vol 292 (6) ◽  
pp. H2623-H2633 ◽  
Author(s):  
Yunlong Huo ◽  
Ghassan S. Kassab
Keyword(s):  
Blood Flow ◽  
Large Scale ◽  
Stokes Equations ◽  
Energy Losses ◽  
Type Model ◽  
Pulsatile Blood Flow ◽  
Arterial Tree ◽  
Main Trunk ◽  
Mean Values ◽  
One Dimensional

Using a frequency-domain Womersley-type model, we previously simulated pulsatile blood flow throughout the coronary arterial tree. Although this model represents a good approximation for the smaller vessels, it does not take into account the nonlinear convective energy losses in larger vessels. Here, using Womersley's theory, we present a hybrid model that considers the nonlinear effects for the larger epicardial arteries while simulating the distal vessels (down to the 1st capillary segments) with the use of Womersley's Theory. The main trunk and primary branches were discretized and modeled with one-dimensional Navier-Stokes equations, while the smaller-diameter vessels were treated as Womersley-type vessels. Energy losses associated with vessel bifurcations were incorporated in the present analysis. The formulation enables prediction of impedance and pressure and pulsatile flow distribution throughout the entire coronary arterial tree down to the first capillary segments in the arrested, vasodilated state. We found that the nonlinear convective term is negligible and the loss of energy at a bifurcation is small in the larger epicardial vessels of an arrested heart. Furthermore, we found that the flow waves along the trunk or at the primary branches tend to scale (normalized with respect to their mean values) to a single curve, except for a small phase angle difference. Finally, the model predictions for the inlet pressure and flow waves are in excellent agreement with previously published experimental results. This hybrid one-dimensional/Womersley model is an efficient approach that captures the essence of the hemodynamics of a complex large-scale vascular network. The present model has numerous applications to understanding the dynamics of coronary circulation.

scholarly journals A fast method for solving a linear model of one-dimensional blood flow in a viscoelastic arterial tree

2017 ◽  
Vol 231 (3) ◽  
pp. 203-212 ◽  
Author(s):  
Ivan Korade ◽  
Zdravko Virag ◽  
Severino Krizmanić
Keyword(s):  
Blood Flow ◽  
Transmission Line ◽  
Method Of Characteristics ◽  
Fast Method ◽  
Arterial Tree ◽  
One Dimensional ◽  
The Method Of Characteristics ◽  
Line Method ◽  
Transmission Line Method ◽  
Linearized Model

For the purpose of optimization of the whole arterial tree, a fast method for solving of one-dimensional model of blood flow is required. A semi-analytic transmission line method for solving a linearized one-dimensional model of blood flow in an arterial tree with viscoelastic walls is proposed. The transmission line method that solves the linearized model in the frequency domain and the method of characteristics that solves either linearized or non-linear one-dimensional models in the time domain are compared regarding accuracy and computational time. For this purpose, the benchmark problem of a 37-artery network with available experimental data is used. In the case of the linearized model, the results from the transmission line method and the method of characteristics are practically the same. The difference between the transmission line method solution of the linearized model and the method of characteristics solution of the non-linear model is much smaller than the error of either method of characteristics or transmission line method numerical solutions with respect to the experimental data. For typical applications, the transmission line method is at least two orders of magnitude faster than the method of characteristics.

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