Blood Flow In Large Arteries Research Articles

Validity of the local nonlinear arterial flow theory: Influence of the upstream and downstream conditions

The “local flow” theory provides a simple way to take into account the nonlinear convective terms associated with blood flow in large arteries. The assumption that blood velocity profiles vary slowly with the longitudinal coordinate allows a simple nonlinear resolution via a mathematical approximation. Although validated in vitro by its authors, this theory still needs to be verified in accordance with the range of variation of the hemodynamical parameters. This constitutes the aim of this work where we assess the validity of two models issued from this theory: the “direct model” using the pressure-gradient as an input for the calculations and the “indirect model” using the centre-line velocity. The assessment of these models is made by comparing their solutions to those of the linear theory using numerical simulations. Our main conclusion is that the indirect model has a wide range of validity while the direct one fails in the presence of a strong reflected wave.

Commentary on Viewpoint “Human experimentation: No accurate, quantitative data?”

LETTERS TO THE EDITORCommentary on Viewpoint “Human experimentation: No accurate, quantitative data?”Douglas R. Seals, Anthony J. Donato, Gary L. Pierce, and Ashley E. WalkerDouglas R. Seals, Anthony J. Donato, Gary L. Pierce, and Ashley E. WalkerPublished Online:01 Mar 2007https://doi.org/10.1152/japplphysiol.01301.2006MoreSectionsPDF (28 KB)Download PDF ToolsExport citationAdd to favoritesGet permissionsTrack citations ShareShare onFacebookTwitterLinkedInEmailWeChat To the Editor: Professor Rowell (4) effectively establishes the position that quantitative and precise methods are (and have been) available to assess regional and systemic cardiovascular function in humans. One of many thoughts stimulated by his comments is the remarkable tools we currently possess for studying vascular function in human subjects. A good example is the continuing evolution of the “closed forearm” technique to study function of peripheral arteries. Combining venous occlusion plethysmography measurements of forearm blood flow and brachial artery catheter delivery of compounds that can stimulate or inhibit specific signaling pathways, this technique allows investigators to “pharmaco-dissect” the neural, humoral, and local (endothelial) mechanisms controlling peripheral blood flow under various conditions (2). Recent advances with this model allow the assessment of other peripheral vascular functions such as arterial fibrinolytic capacity via endothelial release of tissue plasminogen activator (6). Another increasingly valuable tool is vascular ultrasonography. Duplex ultrasonography provides continuous measurements of large artery blood flow and, along with arterial pressure, vascular conductance at rest and during acute stress (3). Duplex ultrasonography also provides a means to noninvasively assess endothelium-dependent dilation (EDD) of peripheral conduit arteries using blood flow-stimulated dilation (flow-mediated dilation; Ref. 1). Administration of substances (e.g., vitamin C) provides an opportunity to study mechanisms influencing conduit artery EDD, albeit limited to nonvasoactive compounds that do not affect systemic arterial pressure and baroreflexes. Finally, B-mode ultrasound combined with applanation tonometry-acquired carotid pressure waveforms can be used to measure directly arterial compliance, particularly in the large elastic arteries that exert an important influence on left ventricular function/structure and systolic blood pressure (5). These techniques represent only part of the impressive contemporary armamentarium available to study circulatory physiology in humans.REFERENCES1 Celermajer DS, Sorensen KE, Gooch VM, Spiegelhalter DJ, Miller OI, Sullivan ID, Lloyd JK, Deanfield JE. Non-invasive detection of endothelial dysfunction in children and adults at risk of atherosclerosis. Lancet 340: 1111–1115, 1992.Crossref | PubMed | ISI | Google Scholar2 Dietz NM, Rivera JM, Eggener SE, Fix RT, Warner DO, Joyner MJ. Nitric oxide contributes to the rise in forearm blood flow during mental stress in humans. J Physiol 480: 361–368, 1994.Crossref | PubMed | ISI | Google Scholar3 Gill RW. Measurement of blood flow by ultrasound: accuracy and sources of error. Ultrasound Med Biol 11: 625–641, 1985.Crossref | PubMed | ISI | Google Scholar4 Rowell LB. Human experimentation: No accurate, quantitative data? J Appl Physiol. In press.Google Scholar5 Tanaka H, Dinenno FA, Monahan KD, Clevenger CM, DeSouza CA, Seals DR. Aging, habitual exercise, and dynamic arterial compliance. Circulation 102: 1270–1275, 2000.Crossref | PubMed | ISI | Google Scholar6 Van Guilder Hoetzer GL, Smith DT, Irmiger HM, Greiner JJ, Stauffer BL, DeSouza CA. Endothelial t-PA release is impaired in overweight and obese adults but can be improved with regular aerobic exercise. Am J Physiol Endocrinol Metab 289: E807–E813, 2005.Link | ISI | Google ScholarAUTHOR NOTESAddress for reprint requests and other correspondence: D. R. Seals, Dept. of Integrative Physiology, Univ. of CO at Boulder, UCB354, Boulder, CO 80309 (e-mail: [email protected]) Download PDF Previous Back to Top Next FiguresReferencesRelatedInformation More from this issue > Volume 102Issue 3March 2007Pages 1294-1294 Copyright & PermissionsCopyright © 2007 the American Physiological Societyhttps://doi.org/10.1152/japplphysiol.01301.2006PubMed17341743History Published online 1 March 2007 Published in print 1 March 2007 Metrics

Simulation numérique du système cardiovasculaire

In this article, we aim at giving a non-technical overview of some mathematical models currently used in the numerical simulation of the cardiovascular system. A hierarchy of models for blood flows in large arteries is briefly described as well as an electromechanical model for the heart. We discuss some possible applications of the numerical simulations of such models, for example the optimization of prostheses. We also address the issue of the data assimilation for the calibration of the models.

Freezing by a Flat, Circular Surface Cryoprobe of a Tissue Phantom With an Embedded Cylindrical Heat Source Simulating a Blood Vessel

The effects of a thermally-significant blood vessel, simulated by an embedded acrylic tube, 4.8 mm outer diameter on the freezing field caused by a surface cryoprobe were studied experimentally in a tissue phantom. The flat, 15 mm diameter, circular cryoprobe was operated at a constant cooling rate of -8 degrees C/min by liquid nitrogen down to -60 degrees C. Water flow rates of 30 and 100 ml/min, at a constant temperature of 32.5 degrees C, were maintained in the embedded tube. The latter flow rate is typical to the lower range of blood flows in large arteries in the human body. The phase changing medium (PCM) used was a 30/70% by volume mashed potatoes flakes-water solution. Temperature measurements inside the PCM were performed in one plane perpendicular to the embedded tube, relative to which the cryoprobe was placed at 5 locations in separate experiments. This novel experimental method reduced the perturbation caused by the thermocouple junctions while facilitating rather detailed measurements of the temperature fields developing in the PCM. Results show the development of two hump-like formations on either side of the embedded tube. Freezing was retarded in the region away from the surface cryoprobe and under the tube. This accentuated the dominance of the axial effects, due to the embedded tube, over the radial ones due to the cryoprobe. Results of this study should be considered in designing protocols of cryosurgical procedures performed in the vicinity of thermally-significant blood vessels.

Persistent Autoregulatory Disturbance after Angioplasty for Cerebral Vasospasm

Hyperdynamic therapy, consisting of hypervolemia, haemodilution, and hypertension, is an established treatment for cerebral vasospasm following subarachnoid haemorrhage. Angioplasty has emerged as an additional, effective treatment for symptomatic vasospasm. Loss of autoregulation, however, can occur despite effective angioplasty, underscoring the need for treatment with hyperdynamic therapy in combination with angioplasty. A 43-year-old woman underwent endovascular coiling of a ruptured left posterior communicating artery aneurysm. The patient went on to develop symptomatic vasospasm and was treated with hyperdynamic therapy and angioplasty. Autoregulation was assessed with xenon CT cerebral blood flow (CBF) measurement. An initial CBF study was obtained when the patient received dopamine and dobutamine infusions to maintain systolic blood pressure at 160 mmHg. The vasopressor drips were then temporarily held for twenty minutes, allowing the patient's systolic blood pressure to drop to 140 mmHg, and a repeat CBF study was obtained. Several days after angioplasty, CBF decreased significantly when the patient was taken off vasopressors, indicating impaired autoregulation. Hyperdynamic therapy was continued, and another CBF study one week later showed a return of autoregulation and normalization of CBF without induced hypertension. Autoregulation is disturbed during vasospasm. Although angioplasty can improve large artery blood flow during vasospasm, hyperdynamic therapy is also needed to maintain cerebral perfusion, particularly in the face of impaired autoregulation. Quantitative CBF measurement permits the maintenance of optimal CBF and monitoring of response to therapy.

Computer Simulation of Non-Newtonian Effects on Blood Flow in Large Arteries

The influence of viscoelastic effects on blood flow in large arteries is studied numerically. The description of the blood flow uses the conservation of mass and momentum and a constitutive relation of Jeffreys type (Oldroyd-B) and appropriate relations to describe the shear thinning behaviour. The steady flow studies are carried out in an axisymmetric tube with a local constriction modelling a stenosed blood vessel and in a three-dimensional 90° curved tube. The numerical approach applies a decoupled technique where the computation of kinematics and stresses is separated. The governing equations are solved by means of an upwind stabilised Galerkin finite element method. The numerical results indicate significant influence of viscoelastic effects in the stenosed model. The flow through the curved tube shows minor quantitative viscoelastic influence. The influence of the shear thinning effect can be observed in both geometries. The results demonstrate that the viscoelastic behaviour of the local flow patterns in large arteries is dependent on the shape of the flow domain.

1228 球とばねによる赤血球のモデル化と血液の定ずり流動解析

The blood flow in large arteries is commonly analyzed by means of the constitutive equations. However, it is not appropriate to use constitutive equations for small arteries because of the heterogeneity of the blood. In this paper, a new method to model an erythrocyte by using beads and springs is proposed as an alternative to analyze the blood flow. The behavior of a single erythrocyte is computed under a constant shear field. The rotating attitude of an erythrocyte, shear viscosity, normal stress difference coefficient and stress thinning are discussed. The results show that the bead-spring model appropriately can simulate the tank tread motion of an erythrocyte under a high shear field and stress thinning. It is therefore considered that the bead-spring erythrocyte model is able to consistently express blood characteristics.

Modeling of an Erythrocyte by Beads and Springs and the Numerical Analysis of Blood Flow under the Constant Shear Field.

The blood flow in large arteries is commonly analyzed by means of the constitutive equations. However, it is not appropriate to use constitutive equations for small arteries because of the heterogeneity of the blood. In this paper, a new method to model an erythrocyte by using beads and springs is proposed as an alternative to analyze the blood flow. The behavior of a single erythrocyte is computed under a constant shear field. The rotating attitude of an erythrocyte, shear viscosity, normal stress difference coefficient and stress thinning are discussed. The results show that the bead-spring model appropriately can simulate the tank tread motion of an erythrocyte under a high shear field and stress thinning. It is therefore considered that the bead-spring erythrocyte model is able to consistently express blood characteristics.

A numerical study of blood flow patterns in anatomically realistic and simplified end-to-side anastomoses.

Recently, some numerical and experimental studies of blood flow in large arteries have attempted to accurately replicate in vivo arterial geometries, while others have utilized simplified models. The objective of this study was to determine how much an anatomically realistic geometry can be simplified without the loss of significant hemodynamic information. A human femoral-popliteal bypass graft was used to reconstruct an anatomically faithful finite element model of an end-to-side anastomosis. Nonideal geometric features of the model were removed in sequential steps to produce a series of successively simplified models. Blood flow patterns were numerically computed for each geometry, and the flow and wall shear stress fields were analyzed to determine the significance of each level of geometric simplification. The removal of small local surface features and out-of-plane curvature did not significantly change the flow and wall shear stress distributions in the end-to-side anastomosis. Local changes in arterial caliber played a more significant role, depending upon the location and extent of the change. The graft-to-host artery diameter ratio was found to be a strong determinant of wall shear stress patterns in regions that are typically associated with disease processes. For the specific case of an end-to-side anastomosis, simplified models provide sufficient information for comparing hemodynamics with qualitative or averaged disease locations, provided the "primary" geometric features are well replicated. The ratio of the graft-to-host artery diameter was shown to be the most important geometric feature. "Secondary" geometric features such as local arterial caliber changes, out-of-plane curvature, and small-scale surface topology are less important determinants of the wall shear stress patterns. However, if patient-specific disease information is available for the same arterial geometry, accurate replication of both primary and secondary geometric features is likely required.

Influence of Non‐newtonian Flow Behavior on Local Hemodynamics

AbstractThe influence of non‐Newtonian blood flow in large arteries is studied numerically. The model studies are carried out to demonstrate the shear thinning effect at increased shear rates resulting from the reversible destruction of red blood cell aggregates and to show basic viscoelastic effects. The mathematical models considered use the conservation of momentum and of mass and constitutive relations describing the shear thinning behavior and relations of Jeffreys type (Oldroyd‐B model). The numerical approach applies the finite element method. The non‐Newtonian inelastic effects are demonstrated in a curved tube model and in an anatomically and physiologically realistic artery bifurcation model. The viscoelastic flow study is carried out using an axisymmetric tube with a local constriction modeling a stenosed blood vessel. The assumption of physiologically realistic shear thinning behavior shows a minor quantitative influence on local flow patterns compared with Newtonian reference flow.

Remodeling of the Radial Artery in Response to a Chronic Increase in Shear Stress

Chronic changes in large artery blood flow rates induce corresponding adjustments in arterial diameter, but little is known about structural adaptations of the vessel wall in humans. We used a high-resolution echo-tracking system to measure radial artery internal diameter, wall thickness, and mean blood flow on both arms of 11 patients with end-stage renal disease. Measurements were performed on the wrist side of the arteriovenous fistula. The contralateral radial artery was investigated as control. Wall cross-sectional area, circumferential wall stress, and mean wall shear stress were calculated. Results indicate a sixfold increase in blood flow on the side of the arteriovenous fistula compared with the control side, with a 1.4-fold increase in internal diameter. The diameter enlargement was sufficient to normalize wall shear stress. Changes in diameter were not associated with arterial wall hypertrophy because wall cross-sectional area was not increased and rather suggest a "remodeling" of the arterial wall. For the same level of blood pressure, circumferential wall stress was increased on the side of the arteriovenous fistula. These results suggest that the structural adaptations of the arterial wall to a chronic increase in blood flow normalize wall shear stress and overcome stretch-induced changes in the particular circumstance of arteriovenous fistula.

Exercise Rehabilitation for Treatment of Claudication

In Reply. —We fully agree with the statement by Dr Hirsch and colleagues that exercise performance is not solely dependent on large artery blood flow and that intermittent claudication can be improved without revascularization. Our meta-analysis, along with the additional articles cited by Hirsch and colleagues, supports the notion that exercise rehabilitation is an effective treatment for patients with peripheral arterial occlusive disease and disabling claudication pain. Hirsch and colleagues raise another key point concerning the availability of vascular rehabilitation programs in health care facilities. Patients with intermittent claudication frequently have concomitant atherosclerosis in the coronary and cerebrovascular arteries, as well as a host of other comorbidities. Consequently, the risks associated with exercise in patients with claudication are similar to those of patients with cardiac disease, emphasizing the need for a closely supervised program that can only be accomplished in a health care facility. An additional benefit of a supervised

Book review : DW Liepsch ed 1990: Blood flow in large arteries: applications to atherogenesis and clinical medicine. Basel, Karger Scientific Publications. 281pp; figs

Book review : DW Liepsch ed 1990: Blood flow in large arteries: applications to atherogenesis and clinical medicine. Basel, Karger Scientific Publications. 281pp; figs

Solitary Waves in Large Blood Vessels

In order to elucidate the dynamical features of the pulsatile blood flow in large arteries, we propose a soliton theory for a simplified and an idealized model-system of the blood motion in large blood vessels. The theory is performed for an infinitely long, straight, circular, homogeneous thin-walled elastic tube filled with an ideal fluid. It is shown the pulse waves of pressure and flow propagating through the arteries can be described as solitary waves excited by cardiac ejections of blood and the features of the pulse wave such as “peaking” and “steepening” are interpreted in the viewpoint of soliton. The clinical importance of the “lowest blood pressure” and the “pulse-pressure”, which corresponds to the amplitude of pressure pule-wave, is physically explained by the formula obtained from our theory.

Blood flow in the heart and large vessels.

The rapid progress in haemodynamics over the last twenty years has depended greatly on the development of instrumentation. The quantities necessary for the description of blood flow are the pressure and velocity (or flow-rate) of the blood. Since the blood flow in large arteries has periodic, transient, and sometimes random characteristics, a system for measuring pressure or velocity must have a sufficiently large frequency response to cover the spectrum associated with the pressure or velocity waveform. The practical application of the catheter-tip transducer led to the improvement of the quality of blood pressure data even in terms of fluid dynamics. Various systems for measuring the blood velocity, each having its merits and faults, have been developed, and a considerable amount of experimental and clinical data are now available. The present stage of research in cardiovascular fluid dynamics is described here in relation to several methods of measurement.

Effects of velocity jumps on blood flow in large arteries

When a human being experiences a sudden velocity change, the blood flow is disturbed. A theoretical analysis to predict the effects of sudden velocity changes on blood flow in large arteries is presented. The situations is modelled as a one-dimensional flow problem in a viscoelastic tube where the fluid viscosity convective term in the equation of motion and nonlinearity in the elastic modulus of the tube wall are neglected. The governing equations of the model are solved by Laplace transformation. The computed results show that relatively high blood pressures, capable of harming circulation, are produced even by relatively moderate velocity jumps.

Finite element methods of studying mechanical factors in blood flow.

This paper reviews some biomechanical analyses of blood flow in large arteries based on a general computer modeling using the finite element method. We study the following question: What is the role played by the interrelated factors of mechanical stress, flow irregularities, and diffusion through the endothelium on the etiology of atherosclerosis or the aggravation of vascular injury. It presents the computational features of the method and stresses the physiological significance of the results, such as the effect of geometric complexities, material nonlinearities, and non-Newtonian rheology of the blood. The specific mechanical and fluid dynamic factors analyzed are wall shear stress, flow profiles, and pressure variations. After simulating tubes of circular cross section, we apply the analysis to a number of physiological situations of significance, including blood flow in the entrance region, at bifurcations, in the annular region between an inserted catheter of varying diameter and the vessel. A model study of pulsatile flow in a 60 degree bifurcated channel of velocity profiles provided corroborative measurements of these processes with special emphasis on reversed or distributed flow conditions. The corresponding analysis was extended to the situation in which flow separates and reverses in the neighborhood of stagnation points. This required developing the nonlinear expression for the convective velocity change in the medium. A computer algorithm was developed to handle simultaneous effects of pressure and viscous forces on velocity change across the element and applied to the canine prebranch arterial segment. For mean physiological flow conditions, low shear stresses (0-10 dynes/cm2) are predicted near the wall in the diverging plane, higher values (50 dynes/cm2) along the converging sides of the wall. Backflow is predicted along the outer wall, pressure recovery prior to and into the branches, and a peak shear at the divider lip.

Analysis of non-linear pulsatile blood flow in arteries

Some aspects of the problem of computation of non-linear pulsatile blood flow in large arteries are investigated, in the context of the computational method developed by Ling and Atabek (1972). As examples, the following aspects are considered: stability of the computations; representation of higher-frequency components of the flow; effects of keeping or omitting non-linear terms in the equations; effects of varying the dimensionless parameters of the problem. The computational method is extended to include effects of viscoelasticity of arterial walls.

Recorder for blood-flow determination.

Summary.An apparatus is described for direct, exact determination of the blood flow in large arteries of anesthetized animals. It permits direct recording on the kymograph curve of the blood flow per time unit (0.5 ‐ 2 sec).