ASME Centennial Historical Perspective Paper: Mechanics of Blood Flow

1981 ◽  
Vol 103 (2) ◽  
pp. 102-115 ◽  
Author(s):  
R. Skalak ◽  
S. R. Keller ◽  
T. W. Secomb
Keyword(s):  
Blood Flow ◽  
Wave Propagation ◽  
Viscoelastic Behavior ◽  
Leonardo Da Vinci ◽  
Arterial System ◽  
Elastic Membrane ◽  
Biological Knowledge ◽  
Collapsible Tubes ◽  
Precise Understanding ◽  
Leonhard Euler

The historical development of the mechanics of blood flow can be traced from ancient times, to Leonardo da Vinci and Leonhard Euler and up to the present times with increasing biological knowledge and mathematical analysis. In the last two decades, quantitative and numerical methods have steadily given more complete and precise understanding. In the arterial system wave propagation computations based on nonlinear one-dimensional modeling have given the best representation of pulse wave propagation. In the veins, the theory of unsteady flow in collapsible tubes has recently been extensively developed. In the last decade, progress has been made in describing the blood flow at junctions, through stenoses, in bends and in capillary blood vessels. The rheological behavior of individual red blood cells has been explored. A working model consists of an elastic membrane filled with viscous fluid. This model forms a basis for understanding the viscous and viscoelastic behavior of blood.

Control of bat wing capillary pressure and blood flow during reduced perfusion pressure

1988 ◽  
Vol 255 (5) ◽  
pp. H1114-H1129 ◽  
Author(s):  
M. J. Davis
Keyword(s):  
Blood Flow ◽  
Capillary Pressure ◽  
Perfusion Pressure ◽  
Arterial System ◽  
Total Flow ◽  
Capillary Recruitment ◽  
Null System ◽  
Arteriolar Resistance ◽  
Sampling Procedures ◽  
Bat Wing

Regulation of blood flow depends on changes in the sum of arterial (Ra) and venous (Rv) resistances, whereas regulation of capillary pressure (Pc) depends on the ratio of Rv to Ra. If the myogenic response of the arterial system (i.e., delta Ra) is the primary mechanism for controlling pressure and flow when perfusion pressure is lowered, then Pc and total flow should be regulated to the same degree under these conditions. This hypothesis was tested by making direct measurements of Pc and flow in skin and skeletal muscle in the wings of unanesthetized bats. The box method was used to reduce perfusion pressure to the wing. Pressures were measured with a servo-null system; flows were computed from measurements of vascular diameters and red cell velocities using intravital microscopy. All branching orders of arterioles dilated significantly during decreases in box pressure (Pb). For 0 less than Pb less than or equal to -30 mmHg, total flow (1st-order arteriolar flow) remained nearly constant, whereas Pc was "regulated" only approximately 60%. These results cannot be explained by changes in arteriolar resistance alone and suggest that changes in Rv may be important. The possible consequences of flow redistribution, capillary recruitment, and micropressure sampling procedures are discussed in relationship to local regulation of capillary pressure and flow.

scholarly journals The approximation of the solution of wave problems by spectral expansions connected with elliptic differential operators

2021 ◽  
Vol 86 (2) ◽  
pp. 101-106
Author(s):  
Abdulkasim Akhmedov ◽  
Mohd Zuki Salleh ◽  
Abdumalik Rakhimov
Keyword(s):  
Wave Propagation ◽  
Differential Operators ◽  
Sufficient Conditions ◽  
Elastic Membrane ◽  
Conductive Material ◽  
Spectral Expansions ◽  
Vibration Process ◽  
Thermally Conductive ◽  
Elliptic Differential Operators ◽  
Wave Problems

In this research, we investigate the spectral expansions connected with elliptic differential operators in the space of singular distributions, which describes the vibration process made of thin elastic membrane stretched tightly over a circular frame. The sufficient conditions for summability of the spectral expansions connected with wave problems on the disk are obtained by taking into account that the deflection of the membrane during the motion remains small compared to the size of the membrane and for wave propagation problems, the disk is made of some thermally conductive material.

scholarly journals Blood Flow in Human Arterial System-A Review

2016 ◽  
Vol 24 ◽  
pp. 339-346 ◽  
Author(s):  
Blessy Thomas ◽  
K.S. Sumam
Keyword(s):  
Blood Flow ◽  
Arterial System ◽  
System A

Contribution of Inertia on Venous Flow in the Lower Limb during Stationary Gait

2004 ◽  
Vol 20 (2) ◽  
pp. 115-128 ◽  
Author(s):  
Jean-Thomas Aubert ◽  
Christian Ribreau
Keyword(s):  
Blood Flow ◽  
Gait Cycle ◽  
Strong Dependence ◽  
Venous Blood ◽  
Kinematic Model ◽  
The Body ◽  
Axial Component ◽  
Venous Blood Flow ◽  
Collapsible Tubes ◽  
Body Forces

Blood flows toward the heart through collapsible vessels, the veins. The equations of flow in collapsible tubes in motion show a strong dependence on body forces resulting from gravity and acceleration. This paper analyzes the contribution of body forces to venous blood flow during walking on level ground. It combines the biomechanics of gait and theory of collapsible tubes to point out that body forces due to gravity and limb acceleration cannot be overlooked when considering the determinants of venous blood flow during locomotion. The study involved the development of a kinematic model of the limb as a multi-pendulum arrangement in which the limb segments undergo angular displacements. Angular velocities and accelerations were determined and the body forces were calculated during various phases of the gait cycle. A vascular model of the leg's major venous system was also constructed, and the accelerations due to body and gravity forces were calculated in specific venous segments, using the data from the kinematic model. The results showed there were large, fast variations in the axial component (Gx–Mx) of the body forces in veins between the hip and the ankle. Acceleration peaks down to –2G were obtained at normal locomotion. At fast locomotion, a distal vein in the shank displayed values of (Gx–Mx)/G equal to –3.2. Given the down-to-up orientation of the x-axis, the axial component Mx was usually positive in the axial veins, and Mx could shift from positive to negative during the gait cycle in the popliteal vein and the dorsal venous arch.

The numerical analysis of fluid-solid interactions for blood flow in arterial structures Part 2: Development of coupled fluid-solid algorithms

1998 ◽  
Vol 212 (4) ◽  
pp. 241-252 ◽  
Author(s):  
S Z Zhao ◽  
X Y Xu ◽  
M W Collins
Keyword(s):  
Blood Flow ◽  
Wave Propagation ◽  
Numerical Analysis ◽  
Blood Vessels ◽  
Applied Mechanics ◽  
Specific Topic ◽  
Numerical Techniques ◽  
Wall Effects ◽  
Clinical Context ◽  
Local Flow

In this paper, the authors extend their study of wall mechanics given in Part 1 to the overall problem of fluid-solid interactions in arterial flows. Fluid-solid coupling has become a specific topic in computational methods and applied mechanics. In this review, firstly, the effects of elasticity of blood vessels on wave propagation and local flow patterns in large arteries are discussed. Then, numerical techniques are reviewed together with the alternative coupled methods available in fluid—wall models. Finally, a novel numerical algorithm combining two commercial codes for coupled solid/fluid problems is presented. As a consequence of the present studies, wall effects are now able to be included in predictions of haemodynamics in a clinical context.

The Rheology of Blood Flow in a Branched Arterial System

2005 ◽  
Vol 15 (6) ◽  
pp. 398-405 ◽  
Author(s):  
Shewaferaw S. Shibeshi ◽  
William E. Collins
Keyword(s):  
Blood Flow ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Power Law ◽  
Numerical Study ◽  
Arterial System ◽  
Magnitude Distribution ◽  
Velocity Magnitude ◽  
Percentage Difference ◽  
Volume Method

AbstractBlood flow rheology is a complex phenomenon. Presently there is no universally agreed upon model to represent the viscous property of blood. However, under the general classification of non-Newtonian models that simulate blood behavior to different degrees of accuracy, there are many variants. The power law, Casson and Carreau models are popular non-Newtonian models and affect hemodynamics quantities under many conditions. In this study, the finite volume method is used to investigate hemodynamics predictions of each of the models. To implement the finite volume method, the computational fluid dynamics software Fluent 6.1 is used. In this numerical study the different hemorheological models are found to predict different results of hemodynamics variables which are known to impact the genesis of atherosclerosis and formation of thrombosis. The axial velocity magnitude percentage difference of up to 2 % and radial velocity difference up to 90 % is found at different sections of the T-junction geometry. The size of flow recirculation zones and their associated separation and reattachment point’s locations differ for each model. The wall shear stress also experiences up to 12 % shift in the main tube. A velocity magnitude distribution of the grid cells shows that the Newtonian model is close dynamically to the Casson model while the power law model resembles the Carreau model.

Hypergravity and Multiple Reflections in Wave Propagation in the Aorta

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
J. M. B. Kroot ◽  
C. G. Giannopapa
Keyword(s):  
Blood Flow ◽  
Wave Propagation ◽  
Cerebral Blood Flow ◽  
Total Pressure ◽  
Loss Of Consciousness ◽  
Pressure Waves ◽  
Multiple Reflections ◽  
One Dimensional ◽  
Gravity Changes ◽  
Pressure Part

Hypergravity and gravity changes encountered in, e.g., airplanes, rollercoasters, and spaceflight can result in headaches or loss of consciousness due to decreased cerebral blood flow. This paper describes the effect of hypergravity and gravity changes on the pressure in the aorta and the distension of its wall. The model presented consists of a pressure part caused by gravity and a part representing pressure waves propagating through the vessel. The total pressure is described by a one-dimensional formulation in the frequency domain. To accommodate for geometrical and material variations, the vessel is modeled as a series of sections in which multiple reflections can occur. Results are presented for constant and varying gravity in straight and tapered flexible vessels.

Differential Effects of Isoflurane and Halothane on Aortic Input Impedance Quantified Using a Three-element Windkessel Model

1995 ◽  
Vol 83 (2) ◽  
pp. 361-373. ◽  
Author(s):  
Douglas A. Hettrick ◽  
Paul S. Pagel ◽  
David C. Warltier
Keyword(s):  
Blood Flow ◽  
Input Impedance ◽  
Wave Reflection ◽  
Conscious State ◽  
Left Ventricular ◽  
Arterial System ◽  
Windkessel Model ◽  
Frequency Dependent ◽  
Aortic Input Impedance ◽  
Arterial Wave Reflection

Background Systemic vascular resistance (the ratio of mean aortic pressure [AP] and mean aortic blood flow [AQ]) does not completely describe left ventricular (LV) afterload because of the phasic nature of pressure and blood flow. Aortic input impedance (Zin) is an established experimental description of LV afterload that incorporates the frequency-dependent characteristics and viscoelastic properties of the arterial system. Zin is most often interpreted through an analytical model known as the three-element Windkessel. This investigation examined the effects of isoflurane, halothane, and sodium nitroprusside (SNP) on Zin. Changes in Zin were quantified using three variables derived from the Windkessel: characteristic aortic impedance (Zc), total arterial compliance (C), and total arterial resistance (R). Methods Sixteen experiments were conducted in eight dogs chronically instrumented for measurement of AP, LV pressure, maximum rate of change in left ventricular pressure, subendocardial segment length, and AQ. AP and AQ waveforms were recorded in the conscious state and after 30 min equilibration at 1.25, 1.5, and 1.75 minimum alveolar concentration (MAC) isoflurane and halothane. Zin spectra were obtained by power spectral analysis of AP and AQ waveforms and corrected for the phase responses of the transducers. Zc and R were calculated as the mean of Zin between 2 and 15 Hz and the difference between Zin at zero frequency and Zc, respectively. C was determined using the formula C = (Ad.MAP).[MAQ.(Pes-Ped)]-1, where Ad = diastolic AP area; MAP and MAQ = mean AP and mean AQ, respectively; and Pes and Ped = end-systolic and end-diastolic AP, respectively. Parameters describing the net site and magnitude of arterial wave reflection were also calculated from Zin. Eight additional dogs were studied in the conscious state before and after 15 min equilibration at three equihypotensive infusions of SNP. Results Isoflurane decreased R (3,205 +/- 315 during control to 2,340 +/- 2.19 dyn.s.cm-5 during 1.75 MAC) and increased C(0.55 +/- 0.02 during control to 0.73 +/- 0.06 ml.mmHg-1 during 1.75 MAC) in a dose-related manner. Isoflurane also increased Zc at the highest dose. Halothane increased C and Zc but did not change R. Equihypotensive doses of SNP decreased R and produced marked increases in C without changing Zc. No changes in the net site or the magnitude of arterial wave reflection were observed with isoflurane and halothane, in contrast to the findings with SNP. Conclusions The major difference between the effects of isoflurane and halothane on LV afterload derived from the Windkessel model of Zin was related to R, a property of arteriolar resistance vessels, and not to Zc or C, the mechanical characteristics of the aorta. No changes in arterial wave reflection patterns determined from Zin spectra occurred with isoflurane and halothane. These results indicate that isoflurane and halothane have no effect on frequency-dependent arterial properties.

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