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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This arrival time varies substantially with age, due to changes in arterial size and stiffness as mentioned earlier The velocity profile is almost uniform across hemodyjamics diameter of the tube, with narrow viscous boundary layers at the walls.

Despite its simplicity, this model is quite successful in representing the exponential decay of arterial pressure during diastole 64 Journal milnot Applied Physiology. This migration occurs as a consequence of the deformability of red blood cells. The effect is strongest in young individuals and diminishes with age In arteries, the dominant wave travels away from the heart, but reflected components are generated at branch points and as a result of variations in vessel diameter or stiffness.

This case is known as Stokes flow. However, this does not necessarily weaken the reflections returned to the heart, as hemodynamicz below. Depending on the vessel diameter and other physical parameters, a wide variety of flow phenomena can occur.

Blood flow in veins In the veins, blood pressure and flow velocity are relatively low, with increased possibility of thrombus formation, and valves maintain the flow direction. The development of the parabolic flow profile with distance along a tube is illustrated milnot Figure 14assuming steady flow, for the case when the fluid enters the tube with almost uniform velocity over the cross-section. Network analysis of mjlnor of cat milmor. A second factor contributing to pulse pressure amplification is the nonlinearity of the elastic properties, leading to steepening of the leading edge of the pressure pulse Inertia-dependent phenomena such as flow instability, flow separation, turbulence, and generation of secondary flows in curved tubes do not occur.


For a review of the mechanics of blood flow in smaller tubes, particularly in the diameter range of capillaries, see The mean velocity of flow in the tube is. Analysis of stresses in a pressurized cylindrical tube. Calculations of the circumferential stress in vessel walls according to Eq.

Hemodynamics / William R. Milnor – Details – Trove

The hwmodynamics arises because the latter result assumes that the wall is not tethered in the axial direction, whereas the present analysis assumes that it is tethered. Large arrow shows direction of propagation.

The results were given in terms of relative viscosity, i. Since the same cardiac output that flows through the aorta must also flow through the capillaries, the velocity is about times slower in the capillaries. In a Newtonian fluid, the non-isotropic components of stress are proportional to the local velocity gradients. If the strain was zero in the unloaded state, this would lead to a large radial gradient of strain in the loaded state.

More detailed discussions of many of the topics mentioned here can be found in several books 71228646671 In particular, the venous vessels are larger than corresponding arterial vessels, with typically about twice the diameter see Figure 8. The maximum SBL that is possible when ANH is used without falling below Hm BLH is found by assuming that all the blood removed during ANH is returned to the patient at a rate sufficient to maintain the hematocrit at the minimum safe level.

The same mechanism also permits imlnor propagation of a pulse wave in the opposite direction, which can arise because of reflection of the primary wave generated by left ventricular systole. The peak velocity occurs on the center-line and is given by.


Given a system x 1x 2x 3 of Cartesian coordinates in three dimensions, T can be represented in terms of its components T 1T 2T 3 or briefly as T i where i is understood to take the values 1, 2 or 3.

However, given that the site of the reflections leading to the augmentation of pulse pressure is not well defined, and that left ventricular contractility influences the pressure hemodynamucsthe augmentation index cannot be considered a direct measure of stiffness Vertical arrows indicate effect of aggregation to increase viscosity relative to non-aggregating cells at very low shear rates, and effect of deformation to decrease viscosity relative to rigid mi,nor, an effect that increases with shear rate.

The concepts of hemodynamics, and their basis in the understanding of fluid and solid mechanics, will retain their importance, as they provide the necessary framework for interpreting cellular responses in terms of the integrated structural and functional properties of the circulatory system. It follows that the deformation of the object is related to the spatial derivatives of the displacement.


Veins are more compliant than arteries and expand to accommodate changing volume. Curves giving red blood cell flux fraction in one branch as a function of overall flow fraction entering that branch are derived from empirically derived relationships as described in the text, assuming a discharge hematocrit of 0.

Thus, the effects of flow pulsatility on velocity profiles in arteries vary widely within the arterial system according to vessel diameter.

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