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the movement of blood through the blood vessels caused by the difference in hydrostatic pressure in various parts of the vascular system. The difference in pressures is maintained by the pumping function of the heart, which ejects into the human vascular system 60-70 milliliters of blood with each contraction; this is equivalent to 4.5-5 liters per minute (l/min) at rest. This quantity is the minute volume of the heart or cardiac output, the most important parameter of cardiovascular function. During muscular exertion it can increase to 20-25 l/min.
Blood is ejected into the closed vascular system, which resists the movement of blood because of the friction of blood against the vascular wall and of the viscosity of the blood itself. In a detailed mathematical model of the movement of blood, the latter is regarded as a suspension of formed elements, that is, a non-Newtonian fluid, whereas the blood vessels are considered ductile-elastic tubes whose properties (the geometric properties, including size and branches, and the physical properties, including ductility, flexibility, and permeability) change over their length. The friction of blood against the vascular wall tends to vary with the size of the vessel, that is, with its diameter and length. Vascular resistance to the movement of blood can be expressed by Poiseuille’s law.
The vascular system is a series of tubes of different lengths and diameters connected successively and in parallel (see Figure 1). With a successive connection, the total resistance is equal to the sum of the resistances of the individual vessels:
Σ R = R1 + R2.
With a parallel connection, the total resistance is expressed by the equation
The terminal portions of the arteries, the arterioles, are the most resistant. The impedance to the outflow of blood from the arterial system creates so-called arterial pressure. Its level (P) is proportional to the vascular resistance (R) and amount of blood ejected by the heart into the vascular system per unit of time (Q), that is, P = Q x R, hence Q = P/R. This formula is used for the cardiovascular system as a whole if the pressure at the beginning of this system (that is, in the arteries) is equal to P, and at the end of the system (that is, in the orifice of the venae cavae) it is equal to zero. If it is not equal to zero, the equation acquires a somewhat different appearance:
(where P1 and P2 are the pressures at the beginning and end of the vascular system, respectively). By using this basic equation of hemodynamics one can determine the vascular, or so-called peripheral, resistance if the pressures P1 and P2 and the minute volume of the heart (Q) are known.
The amount of peripheral resistance is determined mainly by the tone of the arterioles, that is, by the degree of constant contraction of the smooth musculature of the walls of these vessels. The level of arterial pressure in the organism is regulated by change in arteriole tone. The latter alters the lumens of the arterioles and resistance of the vessels. The arteriole tone thus regulates the flow of blood through the separate vascular regions, adjusting it to the intensity of the metabolic processes in the tissues, that is, to their oxygen and nutritional requirements. (The blood flow may increase 100 times or more in vigorously functioning tissues, for example, in contracting muscle, without any significant change occurring in the general arterial pressure and minute volume of the heart.)
The amount of blood flowing through all parts of the vascular system per unit of time is constant. The linear velocity of the blood flow is inversely proportional to the total lumens in a given section of the vascular bed. The average linear velocity of the blood flow in the human aorta is 50 cm/sec; it is 0.5 mm/sec in the capillaries and 20 cm/sec in the venae cavae. The blood flow in the aorta and large arteries is pulsating; it increases during systole (contraction) and decreases almost to zero during diastole (relaxation) of the heart.
The relationship between the total lumens of the various parts of the vascular bed, level of blood pressure therein, and rate of blood flow is shown in Figure 2. Thanks to the flexibility of the arterial walls, the arterioles stretch during systole and hold additional blood, but they collapse during diastole, helping to force blood into the capillaries. This ensures a continuous flow of blood in the capillaries, which is important for the exchange of substances between the blood and the tissues.
REFERENCESChizhevskii, A. L. Strukturnyi analiz dvizhushcheisia krovi. Moscow, 1959.
Savitskii, N. N. Biofizicheskie osnovy krovoobrashcheniia i klini-cheskie metody izucheniia gemodinamiki, 2nd ed. Leningrad, 1963.
Fiziologiia cheloveka. Moscow, 1966.
Guyton, A. Fiziologiia krovoobrashcheniia: Minutnyi ob”em serdtsa i ego reguliatsiia. Moscow, 1969. (Translated from English.)
Handbook of Physiology, vols. 1-3. Washington, D.C., 1962-65.
G. I. KOSITSKII