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 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.

The importance of viscoelasticity in arterial blood flow models

1975 ◽  
Vol 8 (3-4) ◽  
pp. 237-245 ◽  
Author(s):  
Gary E. Saito ◽  
Terry J. Vander Werff
Keyword(s):  
Blood Flow ◽  
Arterial Blood Flow ◽  
Flow Models ◽  
Arterial Blood ◽  
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.

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 A benchmark study of numerical schemes for one-dimensional arterial blood flow modelling

2015 ◽  
Vol 31 (10) ◽  
pp. e02732 ◽  
Author(s):  
Etienne Boileau ◽  
Perumal Nithiarasu ◽  
Pablo J. Blanco ◽  
Lucas O. Müller ◽  
Fredrik Eikeland Fossan ◽  
...  
Keyword(s):  
Blood Flow ◽  
Arterial Blood Flow ◽  
Numerical Schemes ◽  
One Dimensional ◽  
Flow Modelling ◽  
Benchmark Study ◽  
Arterial Blood

Effects of systemic arterial hypoperfusion on splanchnic hemodynamics and hepatic arterial buffer response in pigs

2001 ◽  
Vol 280 (5) ◽  
pp. G819-G827 ◽  
Author(s):  
S. M. Jakob ◽  
J. J. Tenhunen ◽  
S. Laitinen ◽  
A. Heino ◽  
E. Alhava ◽  
...  
Keyword(s):  
Blood Flow ◽  
Cardiac Tamponade ◽  
Venous Blood ◽  
Liver Blood Flow ◽  
Hepatic Function ◽  
Arterial Blood Flow ◽  
Cellular Damage ◽  
Aortic Blood Flow ◽  
Venous Blood Flow ◽  
Arterial Blood

The hepatic arterial buffer response (HABR) tends to maintain liver blood flow under conditions of low mesenteric perfusion. We hypothesized that systemic hypoperfusion impairs the HABR. In 12 pigs, aortic blood flow was reduced by cardiac tamponade to 50 ml · kg−1 · min−1 for 1 h (short-term tamponade) and further to 30 ml · kg−1 · min−1 for another hour (prolonged tamponade). Twelve pigs without tamponade served as controls. Portal venous blood flow decreased from 17 ± 3 (baseline) to 6 ± 4 ml · kg−1 · min−1 (prolonged tamponade; P = 0.012) and did not change in controls, whereas hepatic arterial blood flow decreased from 2 ± 1 (baseline) to 1 ± 1 ml · kg−1 · min−1 (prolonged tamponade; P = 0.050) and increased from 2 ± 1 to 4 ± 2 ml · kg−1 · min−1in controls ( P = 0.002). The change in hepatic arterial conductance (Δ C ha) during acute portal vein occlusion decreased from 0.1 ± 0.05 (baseline) to 0 ± 0.01 ml · kg−1 · min−1 · mmHg−1(prolonged tamponade; P = 0.043). In controls, Δ C ha did not change. Hepatic lactate extraction decreased, but hepatic release of glutathione S-transferase A did not change during cardiac tamponade. In conclusion, during low systemic perfusion, the HABR is exhausted and hepatic function is impaired without signs of cellular damage.

Transient analysis of cardiopulmonary interactions. I. Diastolic events

1988 ◽  
Vol 64 (4) ◽  
pp. 1506-1517 ◽  
Author(s):  
J. Peters ◽  
M. K. Kindred ◽  
J. L. Robotham
Keyword(s):  
Blood Flow ◽  
Intrathoracic Pressure ◽  
Left Ventricular ◽  
Arterial Blood Flow ◽  
Aortic Blood Flow ◽  
Cross Sectional ◽  
Arterial Blood ◽  
Run Off ◽  
In Series ◽  
Antegrade Flow

The etiology of the fall in left ventricular stroke volume (LVSV) with negative intrathoracic pressure (NITP) during inspiration has been ascribed to a reduction in LV preload. This study evaluated the effects of NITP with and without airway obstruction confined to early (ED), mid- (MD), or late diastole (LD) on the subsequent LVSV, anteroposterior (AP), and right-to-left (RL) aortic diameters (DAO) (series I, n = 6) as well as on phasic arterial blood flow out of the thorax (series II, n = 6) in anesthetized dogs. Transient NITP was obtained by electrocardiogram-triggered phrenic nerve stimulation. In series I, NITP applied for 60% of diastole with the airway obstructed caused decreases of LVSV during ED [-7.7 +/- 3.2% (SE) NS], MD (-11.7 +/- 3.9%, P less than 0.05), and LD (-14.6 +/- 1.5%, P less than 0.01) associated with significant increases of left ventricular end-diastolic pressures relative to both atmospheric and esophageal pressures during MD and LD. NITP increased DAO(AP) and DAO(RL), resulting in increases in diastolic aortic cross-sectional area by an average of 6.1-8.3% (P less than 0.01). Similar changes were seen with the airway unobstructed during NITP. In series II, NITP caused diminished diastolic antegrade carotid artery and/or descending aortic flow run off in all dogs. Transient retrograde arterial flows with NITP were observed in more than half of the animals consistent with increases in aortic diameters. We conclude that a decrease of intrathoracic pressure confined to diastole can 1) diminish the ensuing LVSV, presumptively reducing preload by ventricular interdependence; 2) distend the intrathoracic aorta; 3) diminish antegrade flow out of the thorax independent of effects on cardiac performance; and 4) cause transient retrograde carotid and aortic blood flow. The intrathoracic aorta and, presumably, the arterial intrathoracic vascular compartment can be viewed as an elastic container driven by changes in intrathoracic pressure.

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