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Numerical model of the peripheral circulation and dynamical model of the large vessels and the heart are discussed in this paper. They combined together into the global model of blood circulation. Some results of numerical simulations concerning matter transport through the human organism and heart diseases are represented in the end.
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Context 1
... k , j = 1,..., K — indices of the vessel groups (arteries and veins, if K = 2 ); p — blood k pressure; x, y — spatial coordinates; q ( x , y , p ) — density of the source or the sink of blood (from k j and into appropriate large vessels); r ( x , y , p ) — vascular resistance coefficient (responsible for the k k blood flow in the x − y plane); R ( x , y , p ) — interlayer resistance. The heart functioning under the normal conditions is considered in fig. 2 where results of calculations depicted by the marked curves and all other curves correspond to the experimental data [5]. Slight divergence and in the pressure (fig. 2-a) and volume (fig. 2-b) of the left heart is not significant. The aortic valve stenosis and inter-ventricular partition defect are considered in the further. The stenosis of any valve could be simulated in the same manner as for aortic but this case is considered just as one of the most important. In terms of our model this phenomenon is described simply by increasing the resistance of the appropriate inter-chamber channel. The results of such simulations are shown in fig. 3 where triangles and circles depict the pressure difference before and after the aortic valve. The leftmost circle and triangle corresponds to the normal heart operation. Simulations of the inter-ventricular and inter-atrial partition defects are described by the additional inter-chamber channels (dashed lines in fig. 1). The resistances of these channels are varied in some physiologically tolerant range. The oxygen concentration change in the venous and arterial blood is of particular interest in this case. These changes are shown in fig. 4 for the different values of the inter-ventricular partition resistance. The results concerning matter transport are depicted in fig. 5 and 6. The first simulation (fig. 5) reveals initial stages of the substance propagation through the organism after its inspiration in lungs. Basing on the similar idea it is possible to simulate medicine injection to the arteries or veins (fig. 6). It is supposed constant inflow of substance in the center of the artery supplying right thigh. As one may observe there is limited region that affected by this matter. In general, global model of the blood flow in human organism was presented in this paper. Computational results show great capabilities of using such models for the tasks of global substance transfer and heart diseases. In the future the model may be improved by considering more external effects, pharmacological processes and more detailed cardiovascular graph coupled with all the most important organs that will require parallel ...
Context 2
... k , j = 1,..., K — indices of the vessel groups (arteries and veins, if K = 2 ); p — blood k pressure; x, y — spatial coordinates; q ( x , y , p ) — density of the source or the sink of blood (from k j and into appropriate large vessels); r ( x , y , p ) — vascular resistance coefficient (responsible for the k k blood flow in the x − y plane); R ( x , y , p ) — interlayer resistance. The heart functioning under the normal conditions is considered in fig. 2 where results of calculations depicted by the marked curves and all other curves correspond to the experimental data [5]. Slight divergence and in the pressure (fig. 2-a) and volume (fig. 2-b) of the left heart is not significant. The aortic valve stenosis and inter-ventricular partition defect are considered in the further. The stenosis of any valve could be simulated in the same manner as for aortic but this case is considered just as one of the most important. In terms of our model this phenomenon is described simply by increasing the resistance of the appropriate inter-chamber channel. The results of such simulations are shown in fig. 3 where triangles and circles depict the pressure difference before and after the aortic valve. The leftmost circle and triangle corresponds to the normal heart operation. Simulations of the inter-ventricular and inter-atrial partition defects are described by the additional inter-chamber channels (dashed lines in fig. 1). The resistances of these channels are varied in some physiologically tolerant range. The oxygen concentration change in the venous and arterial blood is of particular interest in this case. These changes are shown in fig. 4 for the different values of the inter-ventricular partition resistance. The results concerning matter transport are depicted in fig. 5 and 6. The first simulation (fig. 5) reveals initial stages of the substance propagation through the organism after its inspiration in lungs. Basing on the similar idea it is possible to simulate medicine injection to the arteries or veins (fig. 6). It is supposed constant inflow of substance in the center of the artery supplying right thigh. As one may observe there is limited region that affected by this matter. In general, global model of the blood flow in human organism was presented in this paper. Computational results show great capabilities of using such models for the tasks of global substance transfer and heart diseases. In the future the model may be improved by considering more external effects, pharmacological processes and more detailed cardiovascular graph coupled with all the most important organs that will require parallel ...
Context 3
... k , j = 1,..., K — indices of the vessel groups (arteries and veins, if K = 2 ); p — blood k pressure; x, y — spatial coordinates; q ( x , y , p ) — density of the source or the sink of blood (from k j and into appropriate large vessels); r ( x , y , p ) — vascular resistance coefficient (responsible for the k k blood flow in the x − y plane); R ( x , y , p ) — interlayer resistance. The heart functioning under the normal conditions is considered in fig. 2 where results of calculations depicted by the marked curves and all other curves correspond to the experimental data [5]. Slight divergence and in the pressure (fig. 2-a) and volume (fig. 2-b) of the left heart is not significant. The aortic valve stenosis and inter-ventricular partition defect are considered in the further. The stenosis of any valve could be simulated in the same manner as for aortic but this case is considered just as one of the most important. In terms of our model this phenomenon is described simply by increasing the resistance of the appropriate inter-chamber channel. The results of such simulations are shown in fig. 3 where triangles and circles depict the pressure difference before and after the aortic valve. The leftmost circle and triangle corresponds to the normal heart operation. Simulations of the inter-ventricular and inter-atrial partition defects are described by the additional inter-chamber channels (dashed lines in fig. 1). The resistances of these channels are varied in some physiologically tolerant range. The oxygen concentration change in the venous and arterial blood is of particular interest in this case. These changes are shown in fig. 4 for the different values of the inter-ventricular partition resistance. The results concerning matter transport are depicted in fig. 5 and 6. The first simulation (fig. 5) reveals initial stages of the substance propagation through the organism after its inspiration in lungs. Basing on the similar idea it is possible to simulate medicine injection to the arteries or veins (fig. 6). It is supposed constant inflow of substance in the center of the artery supplying right thigh. As one may observe there is limited region that affected by this matter. In general, global model of the blood flow in human organism was presented in this paper. Computational results show great capabilities of using such models for the tasks of global substance transfer and heart diseases. In the future the model may be improved by considering more external effects, pharmacological processes and more detailed cardiovascular graph coupled with all the most important organs that will require parallel ...
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Using simple physical and mathematical models we studied the possible role of asymmetry of the cardiovascular system which evolves in early embryonic life. During this phase of life blood circulates in one direction through the system in spite of the complete lack of valves. In our model we were able to show that asymmetry is a precaution for a val...
Citations
... If applied to the tasks of global circulation such approaches require huge computational resources. One-dimensional models [4,[9][10][11][12][13][14][15][16] are often exploited for investigations of the pulse wave propagation and reflection from the vessel bifurcation. Such approach is more effective for the tasks of global circulation but it requires identification of the great number of ill-conditioned and strongly variable parameters describing the model. ...
... As a basis for such model, we propose to use the model of non-linear pulsative flow of viscous incompressible fluid streaming through the collapsible tube [14][15][16]. The flow is supposed to be pseudo one-dimensional as all values are supposed to be averaged over crosssectional area of the vessel. ...
... For every vessel of k th generation the mass and momentum conservation are [4,[9][10][11][12][13][14][15][16]: ( ) , k p t x -pressure in the vessel counted off from atmospheric; k ψ -the impact from the external forces (gravitation, friction and others); ki χ -parameters describing the impact i on the vessel k. ...
Blood system functions are very diverse and important for most processes in human organism. One of its primary functions is matter transport among different parts of the organism including tissue supplying with oxygen, carbon dioxide excretion, drug propagation etc. Forecasting of these processes under normal conditions and in the presence of different pathologies like atherosclerosis, loss of blood, anatomical abnormalities, pathological changing in chemical transformations and others is significant issue for many physiologists. In this connection should be pointed out that global processes are of special interest as they include feedbacks and interdependences among different regions of the organism. At the modern level of computer engineering the most adequate physical model for the dynamical description of cardiovascular system is the model of non-stationary flow of incompressible fluid through the system of elastic tubes. Mechanics of such flow is described by nonlinear set of hyperbolic equations including mass and momentum conservation joined with equation of state that determines elastic properties of the tube [1]. As we interested in global processes the models of the four vascular trees (arterial and venous parts of systemic and pulmonary circulation) must be closed with heart and peripheral circulation models. Heart operation is described by the model of fluid flow averaged by volume through the system of extensible chambers that results in the set of stiff ordinary differential equations [1]. When combined these models allow us to consider functional changes and responses as during one cardiac cycle and at a longer periods upon 10 minutes that
Fig. 1.
Pressure wave propagation through the large pulmonary arteries during one cardiac cycle. Grayscale designates divergence from the minimum pressure in each vessel.
... If applied to the tasks of global circulation such approaches require huge computational resources. One-dimensional models [4,[9][10][11][12][13][14][15][16] are often exploited for investigations of the pulse wave propagation and reflection from the vessel bifurcation. Such approach is more effective for the tasks of global circulation but it requires identification of the great number of ill-conditioned and strongly variable parameters describing the model. ...
... As a basis for such model, we propose to use the model of non-linear pulsative flow of viscous incompressible fluid streaming through the collapsible tube [14][15][16]. The flow is supposed to be pseudo one-dimensional as all values are supposed to be averaged over crosssectional area of the vessel. ...
... For every vessel of k th generation the mass and momentum conservation are [4,[9][10][11][12][13][14][15][16]: ( ) , k p t x -pressure in the vessel counted off from atmospheric; k ψ -the impact from the external forces (gravitation, friction and others); ki χ -parameters describing the impact i on the vessel k. ...
Blood system functions are very diverse and important for most processes in human organism. One of its primary functions is matter transport among different parts of the organism including tissue supplying with oxygen, carbon dioxide excretion, drug propagation etc. Forecasting of these processes under normal conditions and in the presence of different pathologies like atherosclerosis, loss of blood, anatomical abnormalities, pathological changing in chemical transformations and others is significant issue for many physiologists. In this connection should be pointed out that global processes are of special interest as they include feedbacks and interdependences among different regions of the organism. Thus the main goal of this work is to develop the model allowing to describe effectively blood flow in the whole organism. As we interested in global processes the models of the four vascular trees (arterial and venous parts of systemic and pulmonary circulation) must be closed with heart and peripheral circulation models. As one of the model applications the processes of the blood loss is considered in the end of the paper.
... Characteristic form of equations (1)- (2) has been used to calculate values at the junction points of respiratory tubes [18][19][20]. ...
... It turns out that acoustical disturbances of the lungs discussed above significantly affect hemodynamics of the pulmonary circulation. The earlier developed dynamical model of the flow of viscous incompressible fluid [18][19][20] allowed us to simulate this effect. To do this the models of the air and blood flows were joined together by means of common boundary conditions. ...
Frequently during its lifetime a human organism is subjected to the acoustical and similar to them vibrating impacts. Under the certain conditions such influence may cause physiological changes in the organs functioning. Thus the study of the oscillatory mechanical impacts to the organism is very important task of the numerical physiology. It allows to investigate the endurance limits of the organism and to develop protective measures in order to extend them. The noise nuisances affects to the most parts of the organism disrupting their functions. The vibrating disturbances caused to the lung function as one of the most sensitive to the acoustical impacts is considered in this work. The model proposed to describe the air motion in trachea-bronchial tree is based on the one dimensional no-linear theory including mass and momentum conservation for the air flow in flexible tubes.
Using the Duhamel–Neumann equations, we consider the stationary heat-loading problem of a bulk specimen of a two-dimensional material (like grapheme) as an approximation of small elastic deformations. We present a numerical method for solving the heat-loading problem of a specimen of a complex shape with the use of a Friedrichs-monotonic finite-difference scheme on chaotic grids in a multiply connected integration domain. Then we demonstrate the results of the computational experiments.
