BLOOD PRESSURE

From Big Medical Encyclopedia

BLOOD PRESSURE — pressure of blood upon walls of blood vessels and cameras of heart; the most important power parameter of the blood circulatory system providing a continuity of a blood-groove in blood vessels.

Physiology

the Energy source for creation To. serve in cardiovascular system reductions of muscles of the ventricles of heart which are carrying out a role of the force pump. The supporting role is played by reductions of skeletal muscles, the pulsation of arteries which is transferred to nearby veins, periodic wavy reductions of veins (see. Blood circulation ).

During a ventricular systole of heart the blood which is in their cavity is exposed to volume compression, force to-rogo is counterbalanced with forces of mutual pushing away between molecules of blood. In process of reduction of muscles of ventricles when valves of heart are closed, in blood a special stressed state increases: blood is under pressure, a cut is evenly transferred extensively, including and to valves. When pressure of blood in a left ventricle becomes higher than pressure in an aorta, the portion of blood comes to an aorta (see. Arterial pressure ).

Total energy of the moving blood carried to unit volume is defined by the equation:

where h — height over the so-called flebostatichesky level of pressure in the right auricle (the size close to atmospheric pressure), P — the static pressure of blood in an aorta, ρ — density of blood, g — acceleration of gravity, v — peripheral speed of blood in an aorta.

If to consider the blood circulatory system closed and to neglect losses of total energy of a blood-groove on friction in vascular system and the work spent for filtering of liquid in capillaries, then with certain reservations it is possible to apply Bernoulli's equation to the description of the blood circulatory system, on Krom at a stationary current of true liquid the total pressure (Rp) remains a constant in any cross-section of a flow:

where RUTI — static, Rdin — Dynamic, Rg — the hydrostatic pressure, other designations same, as well as in the previous formula.

Fig. 1. Ways of a complete measurement (1) and static (2) pressure of blood (the arrow designates the direction of the movement of blood).

Total pressure can be determined by a manometrical tube, the opening a cut is directed towards to a blood flow, and static or side pressure — at the parallel direction of the plane of an opening to the movement of blood (fig. 1). Dynamic pressure represents a difference of full and static pressure.

During a ventricular systole the portion of blood is thrown out an aorta and a pulmonary artery. Owing to inertia and because of peripheric resistance this portion of blood cannot move on vessels at once, there is an increase in pressure upon elastic walls of vessels owing to what they will extend. Pressure is compensated by a tension of walls. Tensile force in proximal sites will be more, than in distal. Therefore the arising force moves blood from the first site to the second. The front of change of pressure in a wave mode extends with a certain speed along an aorta and arteries (see. Pulse ). Force necessary for advance of parts of blood arises at the expense of a difference of pressure along a blood vessel.

The aorta and large arteries stretched during a systole during a diastole are reduced, supporting by that a continuous blood flow. The pulsation of blood pressure in an aorta gradually decreases to the periphery, providing rather uniform motion of blood in capillaries.

Energy of continuous motion of blood is characterized by the size of an average To., edges would give the same hemodynamic effect on condition of lack of pulse fluctuations of pressure of blood. As the diastole is more long, the size of average pressure is closer to the size of minimal pressure.

Energy To., created by cardiac performance, is spent for advance of blood on big and small circles of blood circulation, overcoming resistance to a blood flow in vascular system (see. Hemodynamics ).

In the simplified «pump — a rigid tube» model volumetric flow rate of liquid is defined by Poiseuille's equation:

Q = (P1 - P2) / R,

where P1 - P2 — swing pressure at the beginning and at the end of a tube, R — the hydraulic resistance of this site.

In turn, resistance of R can be calculated by a formula:

R = (8ηl) / (πr 4 ),

where η — liquid viscosity, l — length of a tube, r — the radius of a vessel. It is visible that resistance with reduction of radius of a vessel increases in proportion to its fourth degree. Of an arterial part of a vascular bed it is the share apprx. 66% of the general peripheric resistance, of capillaries — apprx. 27%, and of a venous part — apprx. 7%.

Rate of volume flow of current of liquid (Q) is defined by Gagen's law — Poiseuille:

Q = (πr 4 /8η) * (P1 - P2) / l

that allows to estimate as a first approximation the movement of blood in a separate vessel on condition of constancy of its radius.

In the blood circulatory system rate of volume flow of fluid movement does not depend on the total area of cross-section of a vascular bed. Therefore in spite of the fact that the total gleam of a vascular bed changes from an aorta to veins, rate of volume flow of a blood-groove is a constant in the closed circulatory system. This pattern is broken at change of delivery function of heart, at change of a gleam of vessels on certain sites of a vascular bed, at change of the volume of the circulating blood (VCB).

On the basis of Gagen's equation — Poiseuille it is possible to estimate influence of the certain site of vascular system on the size of the general resistance of all system, having presented the equation in the following form:

P1 - P2 = (8l/πr^4) *Qη

where the so-called factor of the size (8l/πr^4) is connected with the size of a blood vessel, and a factor of viscosity (Qη) — with a speed of a volume blood-groove and viscosity. Then the general resistance to a blood-groove defining falling To., it will be equal to the work of these two factors.

Friction force on a surface unit (t) is determined by Newton's formula:

τ = F/S = η(dv/dx),

where F — friction force, S a plane surface parallel to a flow, η — viscosity of blood. Friction force is as a first approximation proportional to a gradient of the speed (dv/dx).

In the real blood circulatory system the largest total resistance to a blood-groove takes place in arterioles where flow rate of blood is rather big. In capillaries pressure drop will be less since length of capillaries is less, than length of arterioles, and the speed of the movement of blood is lower.

Falling To. usually estimate on resistance to a blood flow for a total gleam or on certain sites of circulatory system. Blood supply of separate bodies and fabrics can be considered as parallel inclusion of various sites of resistance. If the gleam of vessels increases, then resistance in this site will go down, rate of volume flow will increase, blood supply will improve.

The size of resistance to a blood flow is influenced by branchings of vessels and increase of pristenochny friction. At rather small increase in a total gleam of arterioles their quantity increases in hundreds of times in comparison with large arteries. Therefore falling To. from pristenochny friction on this site as much as possible. The number of capillaries are more, than number of arterioles, but their insignificant length and low speed of the movement of blood them brings, though to essential, but rather smaller falling To., than in arterioles. Small falling To. in veins is explained by increase in a total gleam of veins in comparison with arteries almost twice.

In physical. - the chemical relation blood is suspension of high concentration since apprx. 36 — 48% of its volume make uniform elements.

About moving blood it is possible to speak as about two-phase system, in axial current a cut there are erythrocytes, and in a peripheral (wall) layer the plasma having smaller viscosity moves. The current of blood in vessels normal has generally laminar character.

Valves of heart, aorta, pulmonary artery and veins perform only one function: provide the unilateral direction of the movement of blood on vessels, i.e. exclude a countercurrent.

According to anatomo-fiziol, a structure cardiovascular system (see) distinguish endocardiac, arterial, venous and capillary To., measured or in mm w.g. (pressure in veins), or in mm of mercury. (pressure on other sites of vascular system).

Intracardiac pressure (see) unequally in different cameras of heart and sharply differs in phases of a systole and a diastole, i.e. depends on the power of cordial reduction. In addition to the power of cordial reduction at a size K. in ventricles of heart influences a shape of a cavity of ventricles and its change in process of exile of blood. In a cavity of a left ventricle at healthy adults size K. averages 120 mm of mercury in the period of a systole., in the period of a diastole — 4 mm of mercury.; in a right ventricle — 25 and 2 mm of mercury. respectively. Distinctions of sizes K. in ventricles of heart at a small difference of volumes of their filling corresponds bigger (approximately by 5 — 6 times) to the power of a left ventricle in comparison with right.

In auricles size K. fluctuates not only on phases of a cardial cycle, but also in connection with respiratory fluctuations of intrathoracic pressure. Average values To. for a cardial cycle make 8 — 9 mm of mercury in the left auricle., in right — 3 mm of mercury., reaching sometimes negative values. Size K. in the right auricle is accepted to so-called flebostatichesky level, in relation to Krom estimate height To. in different sites of system of a big circle of blood circulation. Due to the development of technology of sounding of cardial cavities measurement in them To. is more and more widely used with the diagnostic purpose.

Arterial pressure (see) in the central arteries has phase fluctuations with the maximum values during exile of blood from ventricles (systolic pressure) and minimum — at the end of a diastole (diastolic pressure). In large arteries of a big circle at adults of value systolic To. normal are in limits of 100 — 140 mm of mercury., diastolic — 70 — 80 mm of mercury.; in a pulmonary trunk these sizes make respectively 16 — 30 and 5 — 14 mm of mercury. Arterial To. changes with age, has daily fluctuations, depends on level physical. loading and other factors.

Rather high value K. in the period of a diastole is supported thanks to compression function of the central arteries. Stretching of walls of vessels the additional volume of blood in the period of a systole as if accumulates a part of systolic energy of a blood-groove in the form of energy of tension of walls. It provides gradual and uniform decrease To. in the vascular camera after a systole, proportional to reduction of tension of walls of the camera in process of decrease of blood from it during a diastole. Therefore, size diastolic To. to in the arterial camera it is directly proportional to a systolic volumetric gain of blood in it, to the size of peripheric resistance to a blood-groove and it is inversely proportional duration of a diastole. A role of a compression chamber in a big circle of blood circulation carry out an aorta (especially its most extensible chest department) and large arteries of muscular and elastic and muscular type.

It should be noted that sports doctors the interesting phenomenon accompanying activity of cardiovascular system at big physical is revealed. loadings and the received name of infinite tone. Its essence consists that lack of measurable values of diastolic pressure is found in athletes of youthful age at a maximum load. Fiziol, origins of infinite tone and its value are not clear for life activity yet.

Difference between sizes systolic and diastolic To. call pulse pressure, and pulse fluctuations To. call sometimes waves of the I order, unlike respiratory fluctuations To. (waves of the II order) and slower, not strictly periodic vibrations (waves of the III order) which connect with changes of activity of a vasomotor center. Pulse fluctuations To. smooth out in vessels of resistance (small arteries, arterioles) and are almost not defined in capillaries. Waves of the II order are more expressed in veins.

For a hemodynamics the size of average pressure has crucial importance, edges in arteries is defined by the relation of the sum of all changes of pressure for a cardial cycle by the time of this cycle. An average To. in arteries it is much steadier, than sizes of systolic and diastolic pressure, and less than the last changes on length of arterial vessels.

Capillary pressure (see) differs normal in sufficient constancy, making 30 — 50 mm of mercury on an arterial piece of a capillary of a big circle of blood circulation., on venous — 15 — 25 mm of mercury. at horizontal position of a body. Size K. in capillaries of a small circle — apprx. 10 mm of mercury. To the most important factors determining size capillary To., belong active changes of resistance to a blood-groove in precapillaries, number of capillaries and change of venous pressure.

Venous pressure (see) — the lowest To. in vascular system. In this regard postural changes of a body significantly affect size K. in the veins which are located above or below flebostatichesky level. At horizontal position of a body size K. in peripheral veins makes 60 — 100 mm w.g. also depends on energy of inflow of blood from capillaries, resistance to outflow of blood from the central veins (pressure in a chest cavity, in the right auricle) and the tone of venous walls determining the total capacity of a venous bed. In portal system size K. is 2 — 3 times higher, than in the lower vena cava, and is depending on the size of intra belly pressure (see. Portal blood circulation ). Fluctuations of intrathoracic pressure affect size K. in all veins, but most they are shown in the veins located in a chest cavity.

For the characteristic of some important parameters of a hemodynamics (e.g., for calculation of a full pressure gradient) it is accepted to measure so-called central venous pressure in vascular system — i.e. pressure in top and bottom venas cava.

Value of blood pressure for life activity of an organism is defined by its role as power factor of providing a blood-groove, processes of exchange between blood and body tissues and mocheobrazovatelny function of kidneys and also as the factor which is supporting or including many reflex reactions homeostasis (see).

In a big circle of blood circulation of the person the share of a motive energy in rest is insignificant therefore for a blood-groove the difference of sizes K has crucial importance. in an aorta and venas cava, or a full pressure gradient. In a small circle of blood circulation where resistance to a blood-groove is small, and also in a big circle at physical. to loading the share of a motive energy is much higher, but existence of a pressure gradient keeps the leading value.

The pressure gradient determines not only the speed, but also the direction of a blood-groove (always from area high to the area low To.). In patol. conditions the pressure gradient can change in the opposite direction and in vessels the reversed current of blood is observed.

Value K. for processes of a metabolism at the level of capillary membranes very significantly and ambiguously. First, in the presence of perikapillyarny pressure in fabrics preservation of a gleam of a capillary is possible only with a positive transmural pressure — a difference between To. in a capillary and external fabric pressure. Secondly, total quantity of open capillaries depends on pressure of blood in precapillaries that along with influence To. on their gleam determines the total area of capillary membranes via which there is an exchange. Thirdly, for the substances passing through a membrane by diffusion, a role To. by it is indirectly connected with the size of rate of volume flow of a blood-groove, from a cut concentration of the diffusing substances on a membrane and, therefore, the speed of their diffusion depends. At last, size intra capillary To. has crucial importance for straining actions of solutions through a membrane. On an osmotic state the blood plasma differs from intercellular liquid in higher concentration of the colloids creating kolloidnoosmotichesky or oncotic, pressure interfering filtering of a liquid part of blood in intercellular space (see. Blood ). Speed and the direction of filtering is defined by a difference between transmural and oncotic pressure by the capillary membrane, to-ruyu call filtrational pressure. The size of oncotic pressure of a blood plasma in a capillary makes from 20 to 30 mm of mercury., what is commensurable with intra capillary To. On the standard representations of E. Starlinga, filtering of solutions from blood in fabric on an arterial piece of a capillary is provided with size K., creating positive filtrational pressure; on length of a capillary To. decreases, and oncotic pressure grows (because of losses of the filtered water), and on a venous piece of a capillary it exceeds transmural pressure owing to what solutions are filtered on this piece from intercellular space in blood. Normal ratios of straining actions on length of capillaries can significantly be broken at patol, changes To. Also change of position of a body since in the vessels lying below or above flebostatichesky level To plays a role. respectively raises or goes down. The pressure gradient at the same time does not change (at the expense of an identical gain of pressure in arteries and veins), and the blood stream is not broken, but the transmural pressure and, therefore, filtrational pressure in capillaries change depending on extent of change To. in relation to flebostatichesky level. To. is important also for mocheobrazovatelny function kidneys (see).

Mechanisms of regulation of blood pressure

Are normal To. at the healthy person is characterized by a certain stability in various sites of a vascular bed. Constancy of level K. is the vital need connected with ensuring optimum blood supply of bodies and body tissues.

Stability To. in an organism is provided functional systems (see), supporting the level of arterial pressure, optimum for metabolism of fabrics. Osnovnm the principle of activity funkts, systems is the principle of self-control, thanks to Krom in a healthy organism any incidental fluctuations of the ABP caused by action physical. or emotional factors, through certain time stop and the ABP is returned to initial level. At emotional reactions and physical. loadings there is a change of the set level K. and funkts, systems carry out under the law of self-control keeping track of new, raised in comparison with rest and the ABP level, more adequate for this adaptive activity of an organism. The positive and negative emotional reactions having various biol the importance, are followed by cardiovascular reactions, characteristic of them. Negative emotions, as a rule, are followed by hypertensive dynamics of arterial pressure, and positive reactions — two-phase hyper - and hypotensive dynamics of the ABP. Thus, at negative emotional states in connection with dominance hypertensive influence the best conditions for summation of pressor hemodynamic reactions are created, than at positive emotional states.

In animal experiments it is shown that at the negative emotional retension caused by a long conflict situation (e.g., owing to a 30-hour immobilization rats), have characteristic hemodynamic reactions. The groups of rats showing either stability of the ABP, or long hours-long hyper - and hypotensive reactions of the ABP were found. One group of animals was predisposed to an emotional stress. These animals could not adapt and perished against the background of hyper - and hypotensive dynamics of the ABP, hypertensive crises leading to increase in the ABP to 180 — 200 mm of mercury. At the long emotional stress caused by a months-long periodic immobilization the tendency to development of persistent arterial hypertension is found, and also the increased emotional reactivity which is characterized by stronger hemodynamic reactions arising in response to emotionally significant incentive comes to light.

Fig. 2. The schedule characterizing change of size of blood pressure in various sites of a vascular bed; on ordinate axis — the size of blood pressure in mm of mercury.; on abscissa axis — sites of a vascular bed according to the course of the movement of blood: 1 — an aorta; 2 — large arteries; 3 — arterioles; 4 — capillaries; 5 — veins; 6 — a vena cava (at heart); it is visible that pulse fluctuations (a difference between systolic and diastolic pressure), maximum in an aorta, gradually decrease, reaching a minimum in arterioles.

Size ABP directly is defined by the following effector mechanisms. First, action of the heart, performing delivery function, from a cut depend the systolic and minute volume of a blood-groove. Secondly, the peripheric hemodynamic resistance depending on a tone and a gleam of vessels, especially arterioles and also from viscosity and mass of the circulating blood. Thanks to frequency of delivery function of heart and elasticity of vessels pressure in an aorta and arteries fluctuates. Fluctuation band (pulse pressure) depends on systolic emission of blood and elasticity of vessels. In process of the movement of blood pulse fluctuations decrease and, since arterioles, blood flows in vessels almost under constant pressure (fig. 2). Minimal pressure of blood — in large veins (at the mouth of venas cava is lower than atmospheric).

Mechanisms of self-control of the ABP in an organism assume dynamic interaction of two opposite tendencies: pressor and depressor, exerting the corresponding impacts on action of the heart, hemodynamic resistance of a peripheral vascular bed and a regional blood stream.

Pressor reactions (see) are characterized by increase in minute volume of a blood-groove due to increase of systolic volume or increase of cordial reductions at the invariable systolic volume, increase in peripheric resistance as a result of narrowing of vessels, increase of viscosity and volume of the circulating blood and so forth.

Depressory reactions (see) are characterized by reduction of minute and systolic volumes, decrease in peripheric hemodynamic resistance due to expansion of arterioles and reduction of viscosity of blood.

A peculiar form of regulation To. is redistribution of a regional blood-groove, at Krom increase in the ABP and rate of volume flow of blood in separate vitals (heart, a brain) is reached due to short-term reduction of these indicators in others, less significant bodies for existence of an organism.

Between sizes K. in various sites of a vascular bed exists a certain interrelation. First of all size K. is defined by the ABP level in the initial site of an aorta. To. depends also on a tone of vessels and their peripheric resistance to a blood-groove. Regulation of a regional blood-groove and redistribution of blood between bodies are based on it. Increase in hemodynamic resistance in separate bodies leads to decrease in a blood-groove in them and to simultaneous increase in the ABP in the main vessels that promotes strengthening of blood circulation in other bodies.

Delivery function of heart, a tone of vessels, a condition of peripheric circulation, volume of the circulating blood are under control of century of N of page, including parasympathetic and sympathetic departments. The special role in management of activity of the specified peripheral bodies defining a hemodynamics belongs to hormonal influences from a hypophysis, adrenal glands, kidneys, a thyroid gland.,

Pressor influences on the cardiovascular device are carried out directly through a sympathetic nervous system, the cut is a neurotransmitter noradrenaline (see). Activation of the sympathoadrenal mechanisms including effect of hormones of a hypophysis on adrenal glands causes hypersecretion adrenaline (see) and corticosteroids (see). Catecholamines at the same time have a promoting effect on and - and p-adrenoceptors of heart and vessels. Involvement of pituitary hormonal mechanisms in pressor reactions also leads to increase in secretion of Aldosteronum and antidiuretic hormone which, raising a reabsorption of salts and absorption of water, increase the volume of the circulating blood (see. Vasopressin ).

Powerful pressor effect is had a renin-angiotenzinnye of system (see. Angiotenzin ). renin (see), formed in the juxtaglomerular device of kidneys, maloaktiven also carries out a starting role, defining concentration of angiotensin II in blood which is a product of interaction of a renin with angiotensinogen and has direct pressor effect. It is established that secretion of a renin also is under control of sympathoadrenal mechanisms which together with catecholamines stimulate formation of a renin. Depressory reactions of the cardiovascular device arise at decrease of the activity sympathoadrenal and a renin-angiotenzinnykh of mechanisms. One of mechanisms of regulation of the ABP level is regulation of a renal diuresis. Removal of an overflow water through kidneys causes reduction of extracellular liquid, decrease in volume of the circulating blood and reduction of cordial emission (see. Blood circulation ).

It is established that a number of humoral factors has the expressed depressor effect. Carry renal to them prostaglandins (see), and also kinina (see). These substances participate in regulation of a renal blood-groove and release of sodium salts and waters. Kinina blood possess generalized action. The bradykinin which is formed in blood has depressor effect, directly influencing a wall of small arteries. Kinin and a renin-angiotenzinnye of system are closely connected with enzymes — kininazy II and carboxycathepsines which convert transition of angiotensin I to angiotensin II and inactivate kinina.

Besides, there are mechanisms of direct influence of level K. on fiziol, activity of vasomotor centers. So, increase To. in vessels of a brain reduces a tone of its pressor centers.

The condition of the bulbar vegetative centers and a hypophysis is coordinated by the highest centers of vegetative self-control including structures of a limbiko-gipotalamoretikulyarny complex (see. Limbic system ).

In self-control of the ABP the initiative role belongs to vascular baroreceptors (see. Angiotseptora ). At increase in the ABP excitement of vascular baroreceptors, especially aortal and sinocarotid reflexogenic zones, leads to increase of frequency of impulsation in depressor and sinus nerves. Periodic phase activity at the same time is replaced by a continuous impulsation. It is characteristic that the frequency of impulsation in depressor nerves (sinus and aortal) increases depending on the steepness and the level of increase in the ABP and the fiziol, reactions baroreceptors cover all range of possible changes of the ABP. This afferent impulsation leads to activation of the central depressor mechanisms influencing on vasomotor centers (see) and reducing tonic sympathetic reactions of heart and vessels.

Neyrofiziol, researches indicate that increase in the ABP at an emotional overstrain is connected first of all with increase of tonic pressor influences of limbiko-reticular formations of a brain on bulbar sympathetic vasoconstrictive departments of a vasomotor center.

As a result hypertensive vasoconstrictive influences have more powerful effect, than depressor activity opposite to them, as provides dominance of pressor reactions over depressor.

On neurons of the emotsiogenny zones of a brain including structures of a limbiko-reticular complex, and neurons of the highest centers of vegetative regulation there is an integration of a set of the influences reflecting an emotional condition of the person and animals, behavioural reactions, muscular activity and a barorecrptor depressor impulsation. As a result of this integration to the periphery there is a complex of the neurohumoral influences defining a ratio of earlier described pressor and depressory reactions on which eventually level K depends. The optimum level is defined by interaction of these mechanisms To. of the healthy person. == Blood pressure at children ==

With age indicators To. at children raise and depend on many internal and exogenous causes.

The lowest systolic To. is observed at newborns (apprx. 70 mm of mercury.); in the next weeks it gradually raises to 80 — 90 mm of mercury. Arterial To. both at boys, and at girls accrues most quickly on the first year of life. During a second or third lives it increases to a lesser extent. During from 4 to 7 years level arterial To. changes a little. Children at the age of 7 years have a level sistolich. pressure is usually in limits of 80 — 110 mm of mercury., children have 8 — 13 years — 90 — 120 and children have 14 — 17 years — 90 — 130 mm of mercury.

Limits of fluctuations of diastolic pressure are distributed as follows: at the age of 7 years it makes 40 — 70 mm of mercury., at the age of 8 — 15 years — 50 — 80, 16 — 17 years — 60 — 80 mm of mercury. The sharpest increase in level arterial To. it is noted at girls at the age of 12 — 14 years, and at boys — by 14 — 16 years. Indicators arterial To. up to 12 years at girls and boys are identical; in 13 — 14 years at girls it is higher, than at boys. At the age of 15 — 16 years these indicators at boys are higher. Children of rural areas have indicators To. lower and fluctuate in narrower borders, than at the children living in the cities.

Size arterial To. at children can change at a postural change of a body: the maximal arterial pressure upon transition from a sitting position to horizontal increases by 10 — 20 mm of mercury. Considerably the ABP at babies raises during suction (on 4 — 20 mm of mercury.). Upon termination of the act of suction it within 3 — 4 min. is returned to norm. During the overheating of a body (in hot day) the ABP level at children decreases; during the cooling it raises. Considerable impact on size ABP is exerted by positive and negative emotions of which increase in maximal pressure, sometimes on 30 — 32 mm of mercury is result most often. The ABP changes usually by the end of school day, raising or going down within 20 mm of mercury., especially strongly it is noticeable upon termination of educational half-year. Size ABP with other things being equal depends also on a way of its definition. More often To. at children measure by Reeve-Rochchi device by Korotkov's method — Yanovsky; it is convenient for measurement To. at any age sfigmotonoostsillometr, released by the Krasnogvardeets plant, supplied with a set of age cuffs and allowing to use sound, ostsillometrichesky and oscillographic methods. In addition to indicators of the systolic and diastolic ABP levels, in pediatric practice for more detailed studying of a condition of a hemodynamics average determine pressure, side, true pulse and hemodynamic blow. This method allows to gain more complete and exact idea of indicators To. which increase with age.

The venous pressure determined by usually direct method by a flebotonometr (see. Flebotonometriya ), depending on age fluctuates between 40 and 100 mm w.g. and it is identical on both hands. At irritable children as a result of shout, crying and concern venous pressure can rise to 120 mm w.g. Therefore the norms relating to younger age cannot be considered reliable. For judgment of height of venous pressure it is possible to use method of straight vision behind a vascular tone, loading of vascular system is the basis to-rogo funkts. Height of venous pressure is defined twice: at the time of compression of veins and at discovery of stagnation, their after education. By data A. P. Belova, at healthy children at the age of 7 — 10 years the first pressure fluctuates from 15 to 30 mm of mercury., and the second — from 35 to 50 mm of mercury. At children at the age of 10 — 15 years the corresponding figures make 18 — 34 mm of mercury. and 40 — 55 mm of mercury. The main advantage of this method is its beskrovnost and ease of technical performance.

Pressure in heart cameras is defined at catheterizations of heart (see). In cardial cavities pressure fluctuates in the following limits: in the right auricle — from 2 to 5 mm of mercury., in a right ventricle — from 20 to 30 mm of mercury., in the left auricle — from 4 to 6 mm of mercury., in a left ventricle — from 70 to 110 mm of mercury.

Pulmonary pressure makes: maximum — 20 — 30, minimum — 7 — 9, an average of 12 — 13 mm of mercury. Pressure in pulmonary capillaries makes 6 — 7 mm of mercury., in pulmonary veins — 4 — 6 mm of mercury.

Changes of blood pressure in advanced and senile age

With age the ABP raises. However even at long-livers the average level of the ABP does not exceed 150/90 mm of mercury. The main reason for increase in the ABP, and first of all his systolic level, decrease in elastic properties of large arterial trunks, in particular aortas, as a result of sclerous changes is. Sharp increase in the ABP is interfered by increase in volume of an aorta and decrease in cordial emission. Changes To. in various vascular zones are uneven.

With age decreases venous To. that is connected with expansion of a venous bed, decrease in a tone and elasticity of a venous wall, and also decrease in the general muscle tone. Capillary pressure of blood does not change practically with age.

At advanced and senile age neuroreflex mechanisms weaken and value of humoral mechanisms of regulation of level K increases.

Recovery of size K. to initial level at funkts, loadings occurs in a slowed-up way. Sizes of pressure of blood in a pulmonary artery and intracardiac pressure in cavities of the right department of heart in the period of a systole and a diastole practically do not differ from similar indicators for persons of younger age. At the same time pressure in a left ventricle is higher, than at young people. It is connected with increase in residual volume of blood owing to increase in the general peripheric resistance in a big circle of blood circulation. Because of easing of sokratitelny ability of a myocardium also the speed of rise in chamber pressure of blood decreases.

Pathological changes of blood pressure

Changes To. are symptoms of pathology of the blood circulatory system or systems of its regulation. The expressed changes To. in itself become a pathogenetic factor in development of disturbances of general circulation and regional blood-groove.

Changes To. in cardial cavities are observed at damages of a myocardium, considerable deviations of sizes K. in the central arteries and veins, and also at the disturbances of an endocardiac hemodynamics caused by the inborn or acquired heart diseases and large vessels (see. Intracardiac pressure ).

Patol, increase To. in the main arteries can be caused by increase in shock and minute volumes of heart, increase in kinetics of cordial reduction, growth of peripheric resistance to a blood-groove and rigidity of walls of an arterial compression chamber (see. arterial hypertension ). As regulation To. is carried out by difficult neurohumoral mechanisms, arterial hypertension can be a symptom: diseases of kidneys — glomerulonephritis (see), pyelonephritis (see), nephrolithiasis (see); hormonal and active tumors — aldosteroma (see), Itsenko-Cushing disease (see), kortikosteroma (see), paraganglioma (see), pheochromocytoma (see); thyrotoxicosis (see), organic diseases of c. N of page, idiopathic hypertensia (see). The reason of increase To. in vessels of a small circle of blood circulation (see. Hypertensia of a small circle of blood circulation ) there can be diseases of easy and pulmonary vessels, pleurae, a thorax, and also pathology of heart. Steady arterial hypertension leads to a hypertrophy of heart, development of dystrophy of a myocardium and can be the cause heart failure (see).

Patol, decrease arterial To. can be a consequence of damage of a myocardium, including acute (e.g., cardiogenic shock), decrease in peripheric resistance to a blood-groove, blood losses, sequestration of blood in capacity vessels at insufficiency of a venous tone (a collapse, blood loss, orthostatic circulatory disturbances). Steady arterial hypotension (see. Hypotension arterial ) it is observed at the diseases which are followed by insufficiency of a hypophysis, adrenal glands. At occlusion of arterial trunks To. decreases only distalny places of occlusion. Considerable decrease To. in the central arteries owing to a hypovolemia turns on adaptable mechanisms of so-called centralization of blood circulation — redistribution of blood preferential in vessels. a brain and heart at sharp increase in a tone of vessels on the periphery. At insufficiency of these compensatory mechanisms are possible syncope (see), ischemic injuries of a brain (see. Stroke , Crises ) and a myocardium (see. Coronary heart disease ).

Increase in venous pressure is observed or in the presence of arteriovenous shunts, or at disturbances of outflow of blood from veins, napr, as a result of their squeezing. At cirrhoses of a liver develops portal hypertensia (see); increase To. in the right or left auricles (at heart diseases, heart failure) leads to system build-up of pressure in veins of a big or small circle of blood circulation.

Changes of capillary pressure usually are a consequence of primary changes To. in arteries or veins are also followed by disturbances of a blood-groove in capillaries, and also processes of diffusion and filtering on capillary membranes (see. Mikrotsirkulyation ). Hypertensia in a venous part of capillaries leads to development of hypostases (see. Swelled ) — the general (at system venous hypertensia) or local that is observed at phlebothrombosis (see), prelum of veins (e.g., Stokes collar). Increase capillary To. in a small circle of blood circulation is the cornerstone of development fluid lungs (see).

Methods and devices for a hemodynamometry

in practice a wedge, and fiziol, researches developed and methods of measurement of arterial, venous and capillary pressure in a big circle of blood circulation, in the central vessels of a small circle, in vessels of separate bodies and parts of a body are widely used.

To. represents the dynamic size changing during a cardial cycle and from a cycle to a cycle. Exact information about To. is represented the continuous sequence of its instantaneous values. For the characteristic To. can be used as well discrete indicators — extreme, average or other its values.

All types of measurements To. can be carried to three classes: a) measurements at which the measured size is transferred directly to the measuring device; b) measurements, at which the measured size K. is actively counterbalanced with the external pressure (counter-pressure) and it is transferred to the measuring device; c) measurements at which the measured size is it is settlement or indirectly — according to measurement of sizes, excellent from measured. These measuring principles can be designated respectively as direct, indirect and indirect.

Direct measurement of blood pressure (a direct manometriya) is carried out directly in a vessel or a cardial cavity where the catheter filled with isotonic solution transferring pressure upon the external measuring device, or the probe with the measuring converter on the entered end (is entered see. Catheterization ).

For the first time direct measurement To. (at a horse) carried out S. Hales in 1733. In 1831 J. Poiseuille offered the special device for measurement of the ABP who represented the U-shaped tube filled with mercury. In 1847 K. Ludvig added a mercury manometer with the float supplied with a feather thanks to what graphic registration was created To. In 1861 E. Marey offered membrane recorders for record various mechanical fiziol, the phenomena, including. To. in cardial cavities and vessels. More perfect diaphragm gage for registration To. was created in 1888 Mr. of K. Hurthle.

Philosophy of direct manometrical measurement To. are formulated by Frank (O. Frank) in 1903 who showed that the main characteristic defining dynamic qualities of the manometer is own frequency of fluctuations of a fluid column in system of hydraulic transmission (f0) expressed by dependence:

f0 = d / (4πρLC)

where d — diameter of the channel of a catheter, ρ — density of fluid medium in a catheter, L — length of a catheter, With — the volume shift of the metering device which is expressed the relation of volume movement of a fluid column in a catheter to the operating pressure characterizes softness, a pliability of system.

It is necessary for high-quality record that the size f0 considerably surpassed the frequency of the most high-frequency components of the studied process. Performance of this condition at escalating requirements to the boundary registered frequency of process is the main direction of improvement of Manometers for direct measurement To. As diameter and length of catheters are defined by conditions of their introduction to this or that vessel and cannot strongly change, the only parameter, for the account to-rogo dynamic properties of measuring system increase, the volume shift of a membrane of the manometer is. For optical manometers it was at the level of 1 mm 3 /100 mm of mercury., for electronic manometers — 0,05 mm 3 /100 mm of mercury., reaching 0,01 mm 3 /100 mm of mercury. at the best devices. On set of characteristics of static and dynamic accuracy modern electromanometers for tonometry are in heart and vessels at the level of the unique gages of pressure which do not have analogs among devices of all-technical appointment.

In 50 — the 60th began to combine a direct manometriya with an angiography, an intracavitary phonocardiography, an elektrogisografiya, etc. Characteristic feature of modern development of a direct manometriya is the computerization and automation of processing of the obtained data.

Direct measurement To. is carried out practically in any sites of cardiovascular system and serves as a basic method, on Krom indirect and indirect measurements are checked To. Advantage them is the possibility of simultaneous sampling of blood for biochemical, analyses and introduction to a circulatory bed of necessary pharmaceuticals and indicators.

The main lack of direct measurements is need of carrying out in a blood channel of elements of the metering device that demands strict observance of aseptic conditions of carrying out a research, limits a possibility of repeated measurements. Some types of measurements (catheterization of cardial cavities, vessels of lungs, kidneys, a brain) actually are surgeries and are carried out only in the conditions of a hospital since demand anesthesia, can be followed by complications.

Tonometry in cardial cavities and the central vessels. A direct manometriya — the only way of measurement To. in them is also carried out by catheterization of cardial cavities and the central vessels or their puncture (see. Catheterization of heart , Heart, methods of a research ). The measured sizes are instant pressure in cavities, the average pressure and other indicators which are defined by means of the registering or showing manometers.

An entrance link of the electromanometer is the sensor. Its sensitive element — a membrane directly contacts to fluid medium, on a cut pressure is transferred. The movements of a membrane which are usually making shares of micron are perceived as the changes of electric resistance, capacity or inductance transformed to the voltage measured by the output device.

The method is a valuable source fiziol, and the wedge, information, is used for diagnosis, in particular diagnosis of heart diseases, control of efficiency of operational correction of disturbances of the central blood circulation, at long observations in the conditions of resuscitation and in many other cases.

Direct measurement of arterial pressure at the person is taken only in cases when constant and long overseeing by level K is necessary. for the purpose of timely detection of its dangerous changes. Such measurements are widely included into practice of overseeing by patients in chambers of intensive observation, blocks of resuscitation. They are carried out also to time of surgeries.

Measurement of the ABP is carried out similar to measurement of intracardiac pressure. The technical means used at the same time have much in common with those which are applied to endocardiac measurements. However at measurement of the ABP there is no need for his long registration, and automatic detection of the maximum and minimum values K is made. in each cardial cycle.

Measurement of venous pressure. Venous pressure is reliably measured only by a direct method. Pressure in a top and bottom vena cava has steady indications, srednedinamichesky value to-rogo is designated as the central venous pressure (CVP). In peripheral veins pressure differs in variability. For measurement of venous pressure

the «Device for determination of venous pressure» released by the Leningrad production association «Krasnogvardeets» is among serially made devices. The device represents the liquids which are reported among themselves system of drop intravenous injection, a manometrical tube and a rubber hose with a syringe needle on the end. The device can work in the mode of bystry flebotonometriya (see), at Krom the system of drop injection is disconnected, and in the mode of a long flebotonometriya, at Krom from system of drop injection liquid constantly comes to the measuring highway and from it to a vein. It excludes thrombosing of a needle and creates a possibility of long measurement of venous pressure.

The simplest measuring instruments of venous pressure contain only the scale and a manometrical tube from plastic material intended for disposable. In total with standard systems of hemotransfusion of one-time use measuring instruments of venous pressure of one-time use form system, essentially equivalent to the device considered above.

For measurement of venous pressure also electronic manometers are used. Their main advantage is the possibility of measurement not only TsVD, but also pressure in the right departments of heart and pulmonary artery. Measurement of TsVD is carried out through a thin polyethylene catheter which is entered or in elbow hypodermic, or into a subclavial vein. At long measurements the catheter remains attached and can be used for sampling of blood, administration of medicines. Measurement of TsVD is widely used in an intensive care, resuscitation, for the control of a state operated and for differential diagnosis of insufficiency of a right ventricle.

Measurement of capillary pressure. Direct measurement of capillary pressure is essentially carried out similar to another invasive dimensions To. However measurement is taken in a single capillary, pressure in Krom does not reflect the system-wide level of this indicator, and transfer of pressure is carried out through a microcannula with big dynamic distortions. Therefore direct measurements of capillary pressure have no wedge, values. However their performance both at experimental animals, and at the person very important for understanding of processes of microcirculation.

The first direct measurement of capillary pressure is carried out in 1923 by Karryerom and Reberg (E. V. Carrier, R. V. Rehberg). Reliable sizes of capillary pressure were received for the first time by Landis (E. M of Landis) in 1926, having measured by a micropipet average pressure in capillaries of a mesentery of a frog, and in 1930 — in capillaries of a nail bed of the person. For visualization of vessels stereoscopic and television microscopes, for tonometry — electro-manometers are used; became possible to carry out record of dynamic intra capillary pressure.

For measurement of average capillary pressure the microcannula connected to the manometer and a source of external pressure and filled fiziol, solution by means of the micromanipulator under control of a microscope is entered into a capillary or its lateral branch. Average pressure is established and about size created external (set and registered by the manometer) pressure, at Krom there is a stop of a blood-groove in a capillary. For obtaining extreme values of capillary pressure use its continuous record after introduction of a microcannula to a vessel.

The indirect hemodynamometry is carried out without disturbance of integrity of vessels and fabrics. The full atravmatichnost even at the known decrease in accuracy does these measurements very valuable, opens a possibility of their broad use, in particular for unlimited repeated researches.

Indirect measurement To. is carried out by an equilibration of pressure in a vessel by the known external pressure through its wall and soft tissues of a body. The methods based on this principle received the name of compression. All indirect methods of measurement concern to them To., except a method of measurement of venous pressure according to G. Gartner.

Compression methods differ with way of creation of the compressing pressure and the choice of criterion of identification of the moment of balance of the compressing and intravascular pressure. The compressing pressure can be created by liquid, air or a solid and to be transferred to a body surface directly or through an elastic membrane. The compression air through a soft membrane has preferential use that provides more exact transfer of external pressure. At the same time the configuration and the sizes of the compressing device, its compliance of that part of a body are of great importance, about a cut it is interfaced. The most adequate is compression by the inflatable cuff imposed around an extremity or a vessel and providing uniform circulator compression of the fabrics and vessels which are in it. For the first time the compression cuff was offered S. Riva-Rocci in 1896 for measurement of the ABP.

Changes of pressure, external in relation to a blood vessel, during measurement To. can have the nature of slow smooth build-up of pressure (compression), smooth decrease in earlier created high pressure (decompression), and also to follow changes of intravascular pressure. The first two modes are used for definition of discrete indicators To. (maximum, minimum, etc.), the third — for continuous registration To. to it is similar to a method of direct measurement.

As criteria of identification of balance of external and intravascular pressure use the sound, pulse phenomena, changes of a krovenapolneniye of fabrics and a blood-groove in them, and also other phenomena caused by compression of vessels.

Measurement of arterial pressure. The main measured sizes are systolic, or maximum, diastolic, or minimum, and average, or srednedinamichesky, pressure. Usually measure pressure in a humeral artery, in a cut it close aortal. In some cases measure pressure in arteries of fingers of hands, hips, a shin and other areas of a body.

Pulse methods are based on measurement owing to a compression of character of a pulsation of an artery in its distal part. Methods use for assessment of the systolic ABP. To protozoa the palpatorny method, the offered Riva-Rochchi in 1896 is. Measurement is carried out as follows. Put on a compression cuff a middle part of a shoulder and quickly lift in it pressure to the level which is obviously exceeding the expected systolic pressure. The artery at the same time is pressed, and the pulsation in it stops. Then, slowly letting out the air from a cuff, palpatorno define emergence of pulse in a beam artery and on the manometer note the level of pressure in a cuff at this moment. It corresponds to the systolic ABP. Tool option of this method is sfigmomanometriya (see), at a cut instead of a subjective palpation objective pulse recording in a distal piece of an artery, and also external pressure is used.

Sound, or auskultativny, the method has in the basis the phenomenon of sounding of an artery opened in 1905 by N. S. Korotkov during the squeezing it from the outside. N. S. Korotkov established that if on an artery to give the external pressure exceeding diastolic in it there are sounds (tones, noise) which stop as soon as external pressure exceeds systolic level. Listening by means of a phonendoscope to a humeral artery in an elbow bend in the course of its decompression, define the moments of emergence and termination of sounds and note the levels of external pressure corresponding to these moments on the manometer. The first level corresponds systolic, the second — to diastolic pressure.

For measurement of size K. sound or pulse use in the ways sphygmomanometers. In the USSR release two types of sphygmomanometers: PMR (with a mercury manometer), the possessing with a range of measurement of 0 — 260 mm of mercury. with a margin error measurements in limits ± 3 mm of mercury., and PMP (with the diaphragm gage) measuring pressure in range of 20 — 300 mm hg with a margin error ± 4 mm of mercury.

The sound method has tool options in which auscultation is replaced with objective perception of the sound phenomena the microphone. In such devices the signal of the microphone is visualized by the light indicator or manages the arrow or digital index of systolic and diastolic pressure.

The Volyumometrichesky method is based on change of a krovenapolneniye of the distal site of an extremity at compression of the artery feeding it. Changes of filling define ple-tizmografichesk (see. Pletizmografiya ); the method is offered by M. V. Yanovsky and A. I. Ignatovsky in 1907. During a compression of an artery register the level of pressure in a compression cuff. On the plethysmogram at first there is a rise caused by the termination of venous outflow from an extremity. When also the artery is pressed, blood ceases to come to an extremity and rise on the plethysmogram stops that corresponds to achievement of systolic pressure in an artery.

The Volyumometrichesky method is more sensitive, than sfigmograficheskiya, and is used for measurement To. it is preferential in experimental practice at small laboratory animals.

The Ostsillyatorny method is based that as a result of dynamic interaction of the pulsing vessel and the cuff compressing it in the last there are pulsations of pressure (oscillation) which character changes depending on ratios of levels of pressure in a vessel and out of it. At increase in external pressure above diastolic level growth of amplitude of oscillations takes place. Their maximum is observed when external pressure reaches srednedinamichesky value. When external pressure becomes equal systolic, oscillations practically stop. The method is offered by E. Marey in 1886, gained development in L. I. Uskov's modification (1908).

Amplitude of oscillations can visually be estimated according to indications of the differential manometer (an ostsillometrichesky method). For more exact analysis of character of oscillations their registration (an arterial oscillography) is used.

Arterial oscillography (see) it is carried out by graphic registration of two processes: level of the compressing pressure and oscillations in a cuff. N. K. Savitsky (1956) suggested to register oscillations in the form of a takhoostsillogramma by means of the mechano-cardiograph (see. Mekhanokardiografiya ). The Takhoostsillografichesky method of measurement of the ABP is of great importance in pediatrics when it is difficult to use a sound method, and also in experiments on animals. The oscillographic method is suitable for measurement of end systolic, side systolic, average and diastolic pressure.

A kind of an ostsillyatorny method is the phase method. Representation is the cornerstone of it that at compression of an artery pressure exceeding diastolic level, the pulsation in a distal part of an extremity begins to be late; the moment of emergence of delay is identified as diastolic pressure. Systolic pressure is determined by the termination of a pulsation in a distal cuff.

The method of continuous measurement of the average ABP is based on maintenance of external pressure at the level of the maximum of oscillations in a compression cuff observed at equality of pressure to an average dynamic. The method is offered by V. A. Reeben and M. A. Euler in 1963. For this purpose use two compression. the cuffs imposed on two fingers of a hand. Give pressure differing on 30 mm of mercury to them., also support at such level, at Krom of oscillation in both cuffs have identical amplitude. It means that in one of them pressure did not reach the level of the maximum oscillations yet, in another — already exceeded it. The average value is as a half-sum of two external pressure.

The offered measuring principle differs in high stability and repeatability of results. Special researches showed close coincidence of the obtained data with data of a direct manometriya. The method is technically realized in the ABP EXPERT device P made by the Leningrad production association «Krasnogvardeets». The device has the following characteristics: range of measurement is 0 — 200 mm of mercury., maximum error of measurement + 5 mm of mercury.

Measurement of venous pressure. For indirect measurement of venous pressure two groups of methods are offered: compression at which the equilibration of the measured pressure is reached by an external compression, and hydrostatic when position of a body or its parts changes so that to reduce hydrostatic pressure in the field of measurement and to bring it to level atmospheric. Compression methods were doubtful and did not receive use. Their small accuracy first of all is connected with difficulty of transfer without distortion on a vessel of pressure of such low level what is observed in veins. It is difficult as well indication of a condition of an equilibration of pressure in a vessel. Hydrostatic methods are free from the first shortcoming. Achievement of a necessary ratio of external and intravascular pressure in them does not demand imposing on a body surface and fastenings of any devices.

Most just measurement is carried out by Gertner's method: watching a dorsum of a hand at its slow raising, note at what height veins are fallen down. The distance from the level of an auricle to this point serves as an indicator of venous pressure.

The error of this method is also big in view of lack of accurate criteria of a full equilibration of external and intravascular pressure. Nevertheless simplicity and availability do it useful to approximate assessment of venous pressure.

The hydrostatic method of measurement of the central venous pressure (CVP) offered by V. A. Degtyarev and soavt is more perfect. in 1978. Inspected by means of a rotary table slowly transfer from horizontal position to vertical and watch change of character of pulsations in the cuff imposed around a neck. The size of falling of hydrostatic pressure is considered equal TsVD when in the drawing of a pulsation the component of a venous pulse disappears. Results of measurement have close values to data of direct measurements of TsVD.

Measurement of capillary pressure. The first indirect measurements of capillary pressure were carried out by N. Kries in 1875 by overseeing by discoloration of skin under the influence of pressure enclosed from the outside. The size of pressure, at a cut skin begins to turn pale, is accepted to pressure of blood in superficially located capillaries. Modern indirect methods of tonometry in capillaries are based also on the compression principle.

The compression is carried out transparent small rigid cameras of different designs or transparent elastic cuffs which impose on the explored area (skin, a nail bed, etc.). The place of compression is well lit for overseeing by vascular network and a blood-groove in it under a microscope. Capillary pressure is measured in the course of a compression or a decompression of microvessels. In the first case systolic pressure is established on compression pressure, at Krom there will be a stop of a blood-groove in the majority of visible capillaries, in the second — on the level of compression pressure, at Krom in several capillaries there will be a blood stream. Indirect methods of measurement of capillary pressure give considerable discrepancies of results.

Indirect methods of a hemodynamometry. The method of measurement of systolic pressure in a pulmonary artery is offered in 1967 by L. Burstin. It is based on measurement of duration of a cardial cycle and the period of isometric relaxation of a right ventricle which is defined from the beginning of a pulmonary component II of tone on the phonocardiogram prior to the beginning of a diastolic collapse on the phlebogram of a jugular vein. In these sizes, using the nomogram offered by the author, find required values of pulmonary pressure. During the comparison of the obtained data with results of direct measurement of pulmonary pressure rather good coincidence is noted.

E. K. Lukyanov in 1971 developed a method of a research of dynamic structure of venous return according to a flebografiya which allows to estimate degree of venous hypertensia indirectly. The method is based that the pulse volume fluctuations perceived as a venous pulse are result of a uniform venous inflow of blood from the periphery and its pulsing outflow to heart. Proceeding from it it was succeeded to spread out the phlebogram to two components, one of which represents a graphic image of volume inflow of blood to the central veins, and another — a graphic image of volume outflow of blood from them to heart. The last process is presented to the step curve reflecting the phase nature of return of blood to heart; the curve gives the chance to determine duration of phases of a venous inflow (in shares of a stroke output of heart) and relative sizes of inflow to each phase.



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V. P. Zhmurkin; O. V. Korkushko (rep.), E. K. Lukyanov, B. S. Salmanovich (mt. issl.), L. I. Studenikina (ped.), K. V. Sudakov, V. P. Shmelyov, E. A. Yumatov (physical.).

Яндекс.Метрика