A MATHEMATICAL MODEL FOR BLOOD FLOW UNDER PERIODIC ACCELERATION

2010 ◽  
Author(s):  
Abdalla Wassf Isaac ◽  
Mikhial Maher Mathuieu
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Periodic Acceleration

A MATHEMATICAL MODEL OF ANEURYSM OF CIRCLE OF WILLIS

1995 ◽  
Vol 03 (03) ◽  
pp. 653-659 ◽  
Author(s):  
J. J. NIETO ◽  
A. TORRES
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Ordinary Differential Equation ◽  
Blood Flow ◽  
Nonlinear Analysis ◽  
Existence Of Solutions ◽  
Circle Of Willis ◽  
Second Order ◽  
Qualitative Properties

We introduce a new mathematical model of aneurysm of the circle of Willis. It is an ordinary differential equation of second order that regulates the velocity of blood flow inside the aneurysm. By using some recent methods of nonlinear analysis, we prove the existence of solutions with some qualitative properties that give information on the causes of rupture of the aneurysm.

Mathematical model of the capillary blood flow and transcapillary fluid exchange

1976 ◽  
Vol 11 (5) ◽  
pp. 748-752
Author(s):  
V. M. Zaiko ◽  
V. G. Aleksandrov
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Capillary Blood ◽  
Capillary Blood Flow ◽  
Fluid Exchange

Interaction among autoregulation, CO2 reactivity, and intracranial pressure: a mathematical model

1998 ◽  
Vol 274 (5) ◽  
pp. H1715-H1728 ◽  
Author(s):  
Mauro Ursino ◽  
Carlo Alberto Lodi
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Cerebral Blood Flow ◽  
Intracranial Pressure ◽  
Nonlinear Interaction ◽  
Cerebral Blood Volume ◽  
Cerebral Hemodynamics ◽  
Pial Arteries ◽  
Arterial Circulation ◽  
Neurosurgical Patients

The relationships among cerebral blood flow, cerebral blood volume, intracranial pressure (ICP), and the action of cerebrovascular regulatory mechanisms (autoregulation and CO2 reactivity) were investigated by means of a mathematical model. The model incorporates the cerebrospinal fluid (CSF) circulation, the intracranial pressure-volume relationship, and cerebral hemodynamics. The latter is based on the following main assumptions: the middle cerebral arteries behave passively following transmural pressure changes; the pial arterial circulation includes two segments (large and small pial arteries) subject to different autoregulation mechanisms; and the venous cerebrovascular bed behaves as a Starling resistor. A new aspect of the model exists in the description of CO2 reactivity in the pial arterial circulation and in the analysis of its nonlinear interaction with autoregulation. Simulation results, obtained at constant ICP using various combinations of mean arterial pressure and CO2 pressure, substantially support data on cerebral blood flow and velocity reported in the physiological literature concerning both the separate effects of CO2 and autoregulation and their nonlinear interaction. Simulations performed in dynamic conditions with varying ICP underline the existence of a significant correlation between ICP dynamics and cerebral hemodynamics in response to CO2 changes. This correlation may significantly increase in pathological subjects with poor intracranial compliance and reduced CSF outflow. In perspective, the model can be used to study ICP and blood velocity time patterns in neurosurgical patients in order to gain a deeper insight into the pathophysiological mechanisms leading to intracranial hypertension and secondary brain damage.

Shock Waves in Mathematical Models of the Aorta

1970 ◽  
Vol 37 (1) ◽  
pp. 34-37 ◽  
Author(s):  
George Rudinger
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Shock Waves ◽  
Method Of Characteristics ◽  
Wave Form ◽  
Shock Formation ◽  
Rapid Flow ◽  
Latex Tube ◽  
Flow Changes ◽  
The Mathematical Model

If the nonlinear equations for nonsteady blood flow are solved by the method of characteristics, shock discontinuities may develop as a result of omitting from the mathematical model some aspect of the system that becomes significant at rapid flow changes. As an illustration, the flow from the heart into the aorta at the beginning of systole is analyzed. An equation is derived which yields shock formation distances between a few centimeters and several meters depending on the elastic properties of the aorta. Since knowledge of the actual wave form would be useful for computer programming, a few exploratory experiments were performed with an unrestrained latex tube. They indicated wave transitions extending over several tube diameters, but maximum steepening of the wave has not yet been achieved.

Continuous mathematical model of platelet thrombus formation in blood flow

2012 ◽  
Vol 27 (2) ◽  
Author(s):  
A. Tokarev ◽  
I. Sirakov ◽  
G. Panasenko ◽  
V. Volpert ◽  
E. Shnol ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Thrombus Formation ◽  
Platelet Thrombus

scholarly journals A Model of Brain Arteriolar Oxygen and Carbon Dioxide Transport during Anemia

1993 ◽  
Vol 13 (5) ◽  
pp. 872-880 ◽  
Author(s):  
Richard S. Schacterle ◽  
Robert J. Ribando ◽  
J. Milton Adams
Keyword(s):  
Carbon Dioxide ◽  
Mathematical Model ◽  
Blood Flow ◽  
Tissue Oxygenation ◽  
Normal Values ◽  
Experimental Studies ◽  
Limited Information ◽  
Carbon Dioxide Transport ◽  
Theoretical Evidence ◽  
Predicted Values

Existing experimental and theoretical evidence suggests that precapillary diffusion of O2 and CO2 occurs between arterioles and tissue under normal physiologic conditions. However, limited information is available on arteriolar gas transport during anemia. With use of a mathematical model of an arteriolar network in brain tissue, anemic hematocrits of 35, 25, and 15% were modeled to determine the effect of anemia on the exchange, the change in the equilibrium tissue O2 and CO2 tensions, and the increase in blood flow needed to restore tissue oxygenation. We found that the blood Po2 exiting the network fell from 66 mm Hg normally to 48 mm Hg during the severest anemia. Concurrently, the equilibrium tissue O2 tensions dropped from 44 to 23 mm Hg. For CO2 the exit blood Pco2 was 58 mm Hg for a 15% hematocrit, an increase of 4 mm Hg from the normal value, and equilibrium tissue Pco2 increased from 56 to 61 mm Hg. Blood flow increases from normal values necessary to offset the effects of the decreased O2 delivery to the tissue were 26, 86, and 222%, respectively, for hematocrits of 35, 25, and 15%. We compared our model results with recent experimental studies that have suggested that the amount of O2 diffusion is much higher than predicted values. We found that these experimental O2 gradients are three to four times larger than theoretical.

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