scholarly journals On the evolution of shock-waves in mathematical models of the aorta

1981 ◽  
Vol 22 (3) ◽  
pp. 257-269 ◽  
Author(s):  
L. K. Forbes
Keyword(s):  
Shock Wave ◽  
Blood Flow ◽  
Shock Waves ◽  
Gas Dynamics ◽  
Pulse Propagation ◽  
One Dimensional ◽  
Flow Models ◽  
Wave Development ◽  
Blood Flow Models ◽  
The One

AbstractThe one-dimensional, non-linear theory of pulse propagation in large arteries is examined in the light of the analogy which exists with gas dynamics. Numerical evidence for the existence of shock-waves in current one-dimensional blood-flow models is presented. Some methods of suppressing shock-wave development in these models are indicated.

A note on the solution of the one-dimensional unsteady equations of arterial blood flow by the method of characteristics

1979 ◽  
Vol 21 (1) ◽  
pp. 45-52 ◽  
Author(s):  
L. K. Forbes
Keyword(s):  
Blood Flow ◽  
Method Of Characteristics ◽  
Arterial Blood Flow ◽  
Aortic Blood Flow ◽  
Numerical Accuracy ◽  
One Dimensional ◽  
Flow Models ◽  
Arterial Blood ◽  
Blood Flow Models ◽  
The One

AbstractThe “Hartree hybrid method” has recently been employed in one-dimensional non-linear aortic blood-flow models, and the results obtained appear to indicate that shock-waves could only form in distances which exceed physiologically meaningful values. However, when the same method is applied with greater numerical accuracy to these models, the existence of a shock-wave in the vicinity of the heart is predicted. This appears to be contrary to present belief.

Fractional-Order Viscoelasticity in One-Dimensional Blood Flow Models

2014 ◽  
Vol 42 (5) ◽  
pp. 1012-1023 ◽  
Author(s):  
Paris Perdikaris ◽  
George Em. Karniadakis
Keyword(s):  
Blood Flow ◽  
Fractional Order ◽  
One Dimensional ◽  
Flow Models ◽  
Blood Flow Models

scholarly journals Optimization of topological complexity for one-dimensional arterial blood flow models

2018 ◽  
Vol 15 (149) ◽  
pp. 20180546 ◽  
Author(s):  
Fredrik E. Fossan ◽  
Jorge Mariscal-Harana ◽  
Jordi Alastruey ◽  
Leif R. Hellevik
Keyword(s):  
Blood Flow ◽  
Pulse Pressure ◽  
Arterial System ◽  
Arterial Blood Flow ◽  
Patient Specific ◽  
Flow Measurements ◽  
One Dimensional ◽  
Flow Models ◽  
Arterial Blood ◽  
Blood Flow Models

As computational models of the cardiovascular system are applied in modern personalized medicine, maximizing certainty of model input becomes crucial. A model with a high number of arterial segments results in a more realistic description of the system, but also requires a high number of parameters with associated uncertainties. In this paper, we present a method to optimize/reduce the number of arterial segments included in one-dimensional blood flow models, while preserving key features of flow and pressure waveforms. We quantify the preservation of key flow features for the optimal network with respect to the baseline networks (a 96-artery and a patient-specific coronary network) by various metrics and quantities like average relative error, pulse pressure and augmentation pressure. Furthermore, various physiological and pathological states are considered. For the aortic root and larger systemic artery pressure waveforms a network with minimal description of lower and upper limb arteries and no cerebral arteries, sufficiently captures important features such as pressure augmentation and pulse pressure. Discrepancies in carotid and middle cerebral artery flow waveforms that are introduced by describing the arterial system in a minimalistic manner are small compared with errors related to uncertainties in blood flow measurements obtained by ultrasound.

scholarly journals Triangular Gross-Pitaevskii breathers and Damski-Chandrasekhar shock waves

2021 ◽  
Vol 10 (5) ◽  
Author(s):  
Maxim Olshanii ◽  
Dumesle Deshommes ◽  
Jordi Torrents ◽  
Marina Gonchenko ◽  
Vanja Dunjko ◽  
...  
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Initial Conditions ◽  
Broad Class ◽  
Hydrodynamic Equations ◽  
Nonlinear Transport ◽  
One Dimensional ◽  
Nonlinear Transport Equation ◽  
Bosonic Case ◽  
The One

The recently proposed map [5] between the hydrodynamic equations governing the two-dimensional triangular cold-bosonic breathers [1] and the high-density zero-temperature triangular free-fermionic clouds, both trapped harmonically, perfectly explains the former phenomenon but leaves uninterpreted the nature of the initial (t=0) singularity. This singularity is a density discontinuity that leads, in the bosonic case, to an infinite force at the cloud edge. The map itself becomes invalid at times t<0t<0. A similar singularity appears at t = T/4t=T/4, where T is the period of the harmonic trap, with the Fermi-Bose map becoming invalid at t > T/4t>T/4. Here, we first map—using the scale invariance of the problem—the trapped motion to an untrapped one. Then we show that in the new representation, the solution [5] becomes, along a ray in the direction normal to one of the three edges of the initial cloud, a freely propagating one-dimensional shock wave of a class proposed by Damski in [7]. There, for a broad class of initial conditions, the one-dimensional hydrodynamic equations can be mapped to the inviscid Burgers’ equation, which is equivalent to a nonlinear transport equation. More specifically, under the Damski map, the t=0 singularity of the original problem becomes, verbatim, the initial condition for the wave catastrophe solution found by Chandrasekhar in 1943 [9]. At t=T/8t=T/8, our interpretation ceases to exist: at this instance, all three effectively one-dimensional shock waves emanating from each of the three sides of the initial triangle collide at the origin, and the 2D-1D correspondence between the solution of [5] and the Damski-Chandrasekhar shock wave becomes invalid.

scholarly journals Implicit Coupling of One-Dimensional and Three-Dimensional Blood Flow Models with Compliant Vessels

2013 ◽  
Vol 11 (2) ◽  
pp. 474-506 ◽  
Author(s):  
A. Cristiano I. Malossi ◽  
Pablo J. Blanco ◽  
Paolo Crosetto ◽  
Simone Deparis ◽  
Alfio Quarteroni
Keyword(s):  
Blood Flow ◽  
Three Dimensional ◽  
One Dimensional ◽  
Flow Models ◽  
Blood Flow Models
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