I strongly recommend this book as a fairly complete trea- tise on an ever- enlarging subject. The frequent correlations with pathological specimens improve clarity. William R. Milnor. mind, and it is desirable to adopt a terminology that 8. Milnor, W.R. (). Hemodynamics, 2nd ed. Baltimore, Williams & Wilkins. 9. Hemodynamics by Milnor, William R. and a great selection of related books, art and collectibles available now at

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A key phenomenon underlying these non-continuum effects is the tendency for red blood cells milnoor near vessel walls to migrate away from the walls, forming a cell-free or cell-depleted layer. As already mentioned, the variation of volume contained in a compliant vessel is represented by including a capacitance.

The alternative approach adopted here is based on a force-balance argument analogous to that used above for the thin-walled case, which provides some physical insight into the mechanics of the system. The flow rates and lengths of corresponding arterial and venous vessels are necessarily virtually equivalent, because they must carry the same flows over the same distances.

The decrease in pulse pressure amplification with age can be explained in terms of the increasing stiffness of the aorta, which as mentioned earlier, milnro to an approximate doubling of wave speed. With this approach, Eqs.

Despite its simplicity, this model is quite successful in representing the exponential decay of hekodynamics pressure during diastole 64 Velocity fields are conventionally represented graphically by plotting velocity as a mjlnor of position, giving a velocity profile, which in this case is a parabola with its vertex on the center-line Figure 5B.

Observed wave speeds in arteries have been tabulated for various species and anatomical locations The cellular components include red blood cells erythrocytesseveral types of white blood cells leukocytesand platelets. Next, we consider the mechanical equilibrium of a thin shell within the wall, of radius r and thickness dragain considering only the upper half of the vessel Figure 10B.


While the direction of the stress may also change by the reverse flow, depending on the hemodynamic conditions.

Blood being pumped out of the heart first enters the aortathe largest artery of the body. In a first approach based on fluids, as indicated by the Hagen—Poiseuille equation.

The parameters AB and X 0 mlinor given by:. First published in print The variation is over about six orders of magnitude. The Mechanics of The Circulation. Apund Eggers et Socios; Other factors affecting arterial compliance It should be emphasized that the actual behavior of arteries deviates in important respects from the assumptions made in the above analyses, including the assumptions of linear elastic material properties, small strain, isotropy, and the existence of a stress-free reference state.

This implies that the ratio of velocity to diameter remains approximately constant. Hemodtnamics example, this approach can be used predict the deformation of a blood vessel subjected to a time-varying transmural pressure, as it experiences during each cardiac cycle, and the dependence of the deformation on the material properties of the artery wall, as discussed in more detail below. The larger the total cross-sectional area, the lower the mean velocity as well as the pressure.

The solution to the wave equation given in Eq. This result shows that the deformability of red blood cells is mainly responsible for the reduction in blood viscosity at higher shear rates. Dependence of the bulk viscosity of human blood on hematocrit, for indicated shear rates. The data presented in Figure 8 imply an enormous range of Reynolds numbers in the circulatory system.

Hemodynamics – Wikipedia

Curves are derived from polynomial expressions given by Chien et al. Other major arteries have similar levels of blood pressure recordings indicating very low disparities among major arteries. Lakatta EG, Minlor D.

Because of this arrangement, the consequences of venous valve failure depend on the location of valves that are not competent 88 With increasing shear rates, individual cells are more readily deformed by flow forces. These results also show a large increase in the viscosity of blood at very low shear rates 0. As early asthe great Swiss mathematician Leonhard Euler formulated the key equations needed for an analysis of this problem 19although he was apparently frustrated by the difficulty of solving these equations Clearly, the greater the H i and the greater the number of units removed during hemodilution, the more effective ANH is for preventing homologous blood transfusion.

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One of the several contributions of Otto Frank — to physiology was his development of the Windkessel model to describe the mechanical interaction between the ejection of blood from the left ventricle during systole and the elasticity of the aorta and the major arteries In order to represent pulse wave propagation in arteries, analyses with one spatial dimension are generally milnod 1. The main cause of this reduction in apparent viscosity of blood in narrow tubes is the formation of a layer of cell-free or cell-depleted plasma near the tube wall, as already discussed.


Under a broad range of conditions, the flow resistance of a blood vessel is approximately independent of the flow rate, and depends only on the geometrical properties of the vessel mjlnor on the viscosity of blood, as discussed below. One-dimensional theory of pulse wave propagation In order to represent pulse wave propagation in arteries, analyses with one spatial dimension are generally used 1. Retrieved 16 September Williams and Wilkins; English translation with annotations, C.

Mechanism bemodynamics as in A, but with reversed velocities. Shaded area indicates region of flow separation, with separation point at the upstream end and reattachment point at the downstream end.