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.

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.

A convenient formulation of Sadowsky's model for elastic ribbons

2021 ◽  
Vol 477 (2255) ◽  
Author(s):  
Sébastien Neukirch ◽  
Basile Audoly
Keyword(s):  
Differential Equations ◽  
Constitutive Relation ◽  
Classical Problem ◽  
Constitutive Law ◽  
System Of Differential Equations ◽  
Dimensional Model ◽  
Simple Method ◽  
One Dimensional ◽  
Aspect Ratios ◽  
Nonlinear Constitutive Relation

Elastic ribbons are elastic structures whose length-to-width and width-to-thickness aspect ratios are both large. Sadowsky proposed a one-dimensional model for ribbons featuring a nonlinear constitutive relation for bending and twisting: it brings in both rich behaviours and numerical difficulties. By discarding non-physical solutions to this constitutive relation, we show that it can be inverted; this simplifies the system of differential equations governing the equilibrium of ribbons. Based on the inverted form, we propose a natural regularization of the constitutive law that eases the treatment of singularities often encountered in ribbons. We illustrate the approach with the classical problem of the equilibrium of a Möbius ribbon, and compare our findings with the predictions of the Wunderlich model. Overall, our approach provides a simple method for simulating the statics and the dynamics of elastic ribbons.

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 A NUMERICAL MODEL OF THE ST. LAWRENCE RIVER

1972 ◽  
Vol 1 (13) ◽  
pp. 127
Author(s):  
David Prandle
Keyword(s):  
Numerical Model ◽  
Flow Distribution ◽  
Flow Visualisation ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Simple Method ◽  
One Dimensional ◽  
Two Dimensional Model ◽  
The One ◽  
St Lawrence River

A one-dimensional numerical model of a 340 mile section of the St. Lawrence River has been formulated to study tidal propagation. For a more detailed study of the flow distribution in a localised section of the river a two-dimensional model was used. A half mile square grid was used to schematise an area of approximately 20 miles long by 15 miles wide. This two-dimensional model was embodied within the one-dimensional model to permit a free interaction of flow across the boundaries. For the one-dimensional case, a comparison of model and prototype results is included for both elevation and velocity. For the two-dimensional model a comparison of flow distribution was made by using field results obtained from photographing ice movement and from drogue movement. To interpret the results of the two-dimensional model into a simple method of flow visualisation, use was made of animation techniques. A movie film was made that demonstrates both tidal rise and fall and the associated horizontal velocities. Elevation was reproduced by use of varying shades of coloured paper to simulate contours, velocities were represented by simulating drogue movement to produce smoke streaks.

A New Pulse Contour Analysis for Cardiac Output Estimation: The Systolic Volume Balance Method

2012 ◽  
Author(s):  
Orestis Vardoulis ◽  
Theodore G. Papaioannou ◽  
Nikos Stergiopulos
Keyword(s):  
Cardiac Output ◽  
Arterial Compliance ◽  
Intraclass Correlation ◽  
Pulse Contour ◽  
Waveform Analysis ◽  
Dimensional Model ◽  
Arterial Tree ◽  
One Dimensional ◽  
Systolic Volume ◽  
Volume Balance

Cardiac output (CO) monitoring is essential for the optimal management of critically ill patients. Several methods have been proposed for CO estimation based on arterial pressure waveform analysis, known as “pulse contour cardiac output” (PCCO) monitoring. Most of them are based on invasive recording of blood pressure and require repeated calibrations, while they are still subject to inaccuracy under specific conditions. The Systolic Volume Balance (SVB) method was developed as a new non-invasive method based on physical principles and was further validated by a one-dimensional model of the systemic arterial tree. CO estimates were compared against the “real” CO values of the one dimensional model. 507 different hemodynamic cases were simulated by altering heart rate (HR), total arterial compliance (C) and total arterial resistance (R). It was found that CO can be accurately estimated by the new SVB formula. The bias between the brachial PCCO and the model’s CO was 0.042 L/min with 0.341 L/min SD of difference. The limits of agreement were −0.7–0.6 L/min indicating high precision. The intraclass correlation coefficient and the root mean square error between estimated and “real” CO values were 0.861 and 0.041 L/min respectively, indicating good accuracy and agreement.

Modelling Techniques in Applied Glaciology: Numerical Modelling of Avalanches

1983 ◽  
Vol 4 ◽  
pp. 297-297
Author(s):  
G. Brugnot
Keyword(s):  
Finite Difference Method ◽  
Transverse Velocity ◽  
Longitudinal Velocity ◽  
Momentum Conservation ◽  
Dimensional Model ◽  
One Dimensional ◽  
Modelling Techniques ◽  
Reference Grid ◽  
The One ◽  
Near Future

We consider the paper by Brugnot and Pochat (1981), which describes a one-dimensional model applied to a snow avalanche. The main advance made here is the introduction of the second dimension in the runout zone. Indeed, in the channelled course, we still use the one-dimensional model, but, when the avalanche spreads before stopping, we apply a (x, y) grid on the ground and six equations have to be solved: (1) for the avalanche body, one equation for continuity and two equations for momentum conservation, and (2) at the front, one equation for continuity and two equations for momentum conservation. We suppose the front to be a mobile jump, with longitudinal velocity varying more rapidly than transverse velocity.We solve these equations by a finite difference method. This involves many topological problems, due to the actual position of the front, which is defined by its intersection with the reference grid (SI, YJ). In the near future our two directions of research will be testing the code on actual avalanches and improving it by trying to make it cheaper without impairing its accuracy.

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.

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