A well‐balanced positivity‐preserving central‐upwind scheme for one‐dimensional blood flow models

2020 ◽  
Author(s):  
Gerardo Hernandez‐Duenas ◽  
Guillermo Ramirez‐Santiago
Keyword(s):  
Blood Flow ◽  
Upwind Scheme ◽  
Positivity Preserving ◽  
One Dimensional ◽  
Flow Models ◽  
Blood Flow Models

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 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

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.

scholarly journals Comparison of blood flow models and acquisitions for quantitative myocardial perfusion estimation from dynamic CT

2014 ◽  
Vol 59 (7) ◽  
pp. 1533-1556 ◽  
Author(s):  
Michael Bindschadler ◽  
Dimple Modgil ◽  
Kelley R Branch ◽  
Patrick J La Riviere ◽  
Adam M Alessio
Keyword(s):  
Blood Flow ◽  
Myocardial Perfusion ◽  
Dynamic Ct ◽  
Flow Models ◽  
Quantitative Myocardial Perfusion ◽  
Blood Flow Models
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