Hemodynamics

HEMODYNAMICS (from Greek haima- blood and dynamis- force), the science of the movement of blood through vessels. In its basic principles, H. uses the laws of hydrodynamics, the science of the movement of liquids in general, but the conditions of natural blood circulation are so complex and the character of blood flow through vessels depends on such a large number of variables that the laws of hydrodynamics apply to a living organism only within certain limits, with great restrictions, and can serve only for approximate orientation. The basic law of H.-Torricelli's law, stating that the speed of liquid flowing out of a vessel through a round hole in its bottom is expressed by the formula: v=√2gH, where v is the speed, H is the pressure of the liquid column, and g is the acceleration of gravity. The amount of liquid flowing out of this vessel per unit of time depends on the size of the hole and will be equal to Q=πr²v=πr²√2gH, where r is the radius of the outflow hole. In fact, Q will always be less than what this formula would suggest, since part of the pressure H is spent on vortex movements of the liquid particles flowing out of the narrow hole. The loss of pressure force will be even greater in the case where the liquid flows out of the vessel not directly but through a tube of a certain length. In this case, part of the pressure (and a very significant part of it) will be spent on overcoming the resistance to flow. Lateral pressure, easily measurable by vertically standing tubes, piezometers, will decrease in the direction of liquid flow from the vessel with liquid, where it is maximum, along the tube to the outflow hole, where it is zero. If the tube has the same cross-section throughout its entire length, then the drop in pressure per unit length of the tube will be the same everywhere. If, however, the tube has different cross-sections, then at the larger cross-section, where resistance is less, the drop in pressure will also be less than at the smaller cross-section. Confirmation of this law is clearly seen in the distribution of pressure in the circulatory system: along the more or less wide arteries, pressure drops insignificantly; the capillary system with its enormous resistance causes a sharp drop in pressure; along the veins, the drop in pressure is again comparatively insignificant. The speed of flow is greater, the smaller the cross-section of the tube at a given place; therefore, the speed of blood flow from the aorta to the capillaries sharply decreases due to the general expansion of the channel, again increasing in the veins due to its narrowing in this part of the circulatory system. At the branching of tubes, the speed in the branch is the less, the greater the angle at which it departs from the main trunk, although this angle has no effect on the total amount of liquid flowing out. For a horizontal tube through which a liquid that wets it flows, Poiseuille established the following dependence between the amount of liquid flowing out, P pressure, and the resistance of the tube: Q = P/W, where P is the difference in pressure at the beginning and end of the tube, and W is the resistance; for resistance, Poiseuille gives the expression: W = 128μL/πD⁴, where D is the diameter of the tube, L is its length, and μ is the viscosity of the liquid expressed in absolute units. Thus, Poiseuille's formula in its final form will be: Q = πD⁴P/128μL. Poiseuille's law also holds for glass tubes only for tubes whose length and diameter are within certain limits. The speed of outflow also has its limit for the applicability of this law: at high speeds, vortex movements of liquid particles arise, at which Poiseuille's law loses its force. Reynolds gives the following expression for this critical speed: V = 26Ds cm/sec., where D is the diameter of the tube, and s is the specific weight of the liquid. As for the applicability of Poiseuille's law to the movement of blood through vessels, many studies have been conducted in this direction. Blood does not leave the heart continuously, but in spurts, due to which the movement of blood in the arteries is much more complex than would be required for Poiseuille's law; with each systole, the arteries expand in waves, therefore the movement of blood cannot be schematically conceived as consisting of sliding hollow cylinders nested within one another, as required by Poiseuille's law. But in the capillaries, blood flow becomes continuous, and for it the application of this law is possible. In the veins, the contractions of the atria, as well as the presence of valves causing vortex movements, again complicate matters. The laws of blood flow through vessels are further complicated by the fact that blood is not a homogeneous liquid, but has suspended blood cells; therefore, in vessels, as it were, two liquids with different coefficients of viscosity are formed: a wall layer of plasma and an axial layer with blood cells. It is self-evident that Poiseuille's law is not applicable in such narrow capillaries whose cross-section is equal to or slightly larger than the size of an erythrocyte. In general, according to Hess, this law holds only in the case where the pressure in relation to the width of the capillary lumen and the size of the erythrocyte exceeds a certain magnitude. Tigerstedt says that one can use Poiseuille's law insofar as there is no complete theory of blood movement through vessels, which must take into account a significantly larger number of variables than this law. But this law allows one to answer many questions, and the error in most cases is small.