Vascular impedance to the blood flow of the circulatory system

2021-05-31 04:34 PM

Impedance is an obstruction to the flow of blood in a vessel, which cannot be measured by direct means, only calculated from formulas, measurements of blood flow and the difference in pressure between two points on the pulse.

The function of the circulatory system is to supply blood needed for tissues - transport nutrients to organ tissues, and transport substances and hormones from some organs in the body to other places. The concentration of substances in the homeostasis in the body helps cells survive and perform their functions well.

Unit of impedance

Impedance is an obstruction to the flow of blood in a vessel, but it cannot be measured by any direct means. Instead, impedance is only calculated from formulas, measurements of blood flow and the difference in pressure between two points on the pulse. If the pressure difference between the two points is 1 mmHg and the flow rate is 1 ml/s, the impedance is 1 unit of peripheral resistance, commonly abbreviated as PRU.

Expression of impedance in CGS . units

Occasionally, a basic physical unit called the CGS unit (cm, grams, second) is used to specify impedance. This unit is dyne second/cm5. Impedance in these units can be calculated by the formula:

R[in (dyne sec/cm3)]=(1333 x mmHg)/(ml/sec)

Total peripheral vascular resistance and total pulmonary artery resistance

The rate of blood flow through the circulatory system is equal to the rate of blood by the heartbeat - that is, the amount of blood the heart pushes out. In adults, this rate is about 100ml/s. The pressure difference from the arterial system to the venous system is about 100 mmHg. Therefore, the impedance of the entire circulatory system is called the total peripheral impedance, about 100/100 or 1 PRU.

In conditions where the entire body's blood vessels become constricted, the total peripheral impedance sometimes becomes excessively high as 4 PRU. Conversely, when the lumen becomes conductive, resistance can drop as low as 0.2 PRU.

In the respiratory system, mean pulmonary artery pressure is 16 mmHg and left atrial pressure is about 2 mmHg, resulting in a pressure difference of 14mm. Therefore, when the heart ejects normally about 100 ml/s, the total pulmonary blood pressure is about 0.14 PRU (about 1/7 of that of the macrovascular system).

The 'conductivity' of the blood in the vessel is the inverse of the impedance

Conductivity is a measure of blood flow through a vessel when pressure changes. The measurement is usually expressed in ml/s or mm of the manometer, but it can be expressed in l/s or mmHg per unit of flow and pressure.

Conductivity is inversely proportional to impedance according to the following formula:

Conductance = 1/ Impedance

Figure. A: Shows the effect of vessel diameter on blood flow. B: Concentric rings of blood flowing at different velocities; The further away from the vessel wall, the faster the flow. d, diameter; P, the pressure difference between the two ends of the tank.

Miniature circuit diameter affects conductivity

Small changes in the diameter of a vessel cause huge changes in the vessel's ability to conduct blood when blood flow is normal. This phenomenon is demonstrated in the experiment shown in Figure A, with 3 vessels having 3 diameters proportional to each other 1,2 and 4 but the same pressure of 100 mmHg between the two ends of the vessels, even though the diameters of the vessels are equal. this circuit is increased by 4 times, the currents are 1, 16, 256 respectively, which is 256 times increase of the flow. Thus, the conductivity of the blood flow increases proportionally to the 4th power of the vessel diameter, according to the formula:

Conductivity = Diameter4

Poiseuille's Law

The cause of the large increase in conductivity when the diameter increases can be explained as shown in Figure A, showing the cross-sections of large and small circuits. The inner concentric circles show that the flow rates in each circle are different because of laminar flow, as noted in the previous chapters. The blood in the ring touching the vessel wall barely flows because it is attached to the endothelium of the blood vessel. The next circle points towards the centre of the blood vessel through the first circle and so the flow is faster. The flow of subsequent circles also increases. Therefore, blood near the vessel wall has a slow speed, the further away from the vessel wall, the faster the speed.

In small vessels, essentially all blood flow is near the vessel wall, so the rapid flow in the centre of the vessel is almost non-existent. By summing the velocities of all concentric circles of the flow and multiplying them by the area of ​​the circle, we get a formula, which is Poiseuille's law:

 F -> π∆Pr4/8rl η

Where: F is health speed

          ∆P is the pressure difference.

          r is the radius of the circuit

          l is the length of the circuit

          η is the viscosity of blood

Especially from this formula, we see that the blood flow rate is proportional to the 4th power of the pulse radius. It is proved that the diameter of blood vessels is a very important factor that greatly affects the speed of blood flow through the vessels.

Importance of 'Law of 4' Circuit Diameters

In the circulatory system, about two-thirds of the total resistance of the blood is resistance in the small arteries. The diameter of the artery ranges from 4 µm to 25 µm. However, the strong vessel wall allows the diameter to be variable, often up to fourfold. From the 4th power-law stated earlier, which is directly related to the diameter of the blood vessel when the diameter is increased by 4 times the blood flow rate increases by 256 times. Thus, the fourth power law enables small arteries to respond to small changes in diameter from nerve impulses or chemical signals from adjacent tissues, or to almost completely shut down. whole blood flow to tissues or in a response causing a large increase inflow.

Resistance of blood flow in series and parallel vessels

Blood is pumped by the heart from the high pressure of the circulatory system (ventricles) to the low pressure (atria) through many meters of blood vessels in series and parallel vessels. Large arteries, small arteries, capillaries, venules, and veins arranged in series, when blood vessels are arranged in series, the flow carrying blood and the total resistance of the blood flow (total R) is the sum of the total resistance in the circuit:

R  =R1 + R2 + R3 + R4+….

Figure. Circuit impedance (R): A in series and B in parallel

The total resistance of the peripheral blood vessels is equal to the sum of the resistance in the great arteries, small arteries, capillaries, venules, and veins. As shown in Figure A, the total resistance is equal to the sum of R1 and R2

The wide branch of blood vessels divides in a parallel fashion to supply blood to many organs and tissues of the body. Parallel blood vessels allow the tissue to regulate its own blood flow to a large extent, independent of the flow to other tissues.

The blood vessels branch in parallel, the total blood flow resistance is as follows:

1/R  = 1/R1 + 1/R2 + 1/R3 + 1/R4

It is consistent with the pressure gradient trend, that a large amount of blood will flow through the parallel vascular system, not through any other individual blood vessels. Thus, the total resistance is smaller than the resistance of the vascular system alone. Flow-through the parallel vessel in Figure B is determined by the pressure gradient and specific resistance, not the resistance of other parallel vessels. However, any increase in vascular resistance increases the total vascular resistance.

It is the opposite when adding blood vessels to one vessel reduces total resistance. Multiple parallel vessels allow blood to flow easily through the vasculature because parallel vessels also provide many small passages or conductivity, for blood flow The total conductivity of the blood flow (C sum) is equal to the sum of the conductivity of the parallel vessels. Other songs:

C sum = C1 + C2 + C3 + C4 ...

For example, the brain, kidneys, muscles, intestines, skin, and coronary circulation are arranged in parallel circuits, and tissues contribute to the conductivity of the circulatory system. Tissue blood flow is a fraction of total blood flow (cardiac collecting) and is determined by the resistance (inverse of conductivity) of blood flow to the tissue, as well as the pressure gradient. Thus, rapid resection or resection of one kidney will destroy the parallel vasculature and decrease the total vascular conductivity and total blood flow, while the peripheral resistance increases.

Figure. Haematocrits in a healthy (normal) person and in patients with anaemia and polycythaemia. The numbers refer to the percentage of blood that consists of red blood cells.

Effect of blood haematocrit and blood viscosity on vascular resistance and blood flow

Another important note of the Poiseuille formula is the viscosity of blood. High viscosity, slow blood flow if all other parameters are constant. Furthermore, the viscosity of blood is 3 times that of water.

Does it cause the blood to stick? It is mainly red blood cells floating in the blood, causing increased frictional force against phosphate cells and against the walls of blood vessels.

Haematocrit - red blood cell component of blood

If a person has a haematocrit of 40, that means 40% of the blood volume is cells and the rest is plasma. Haematocrit of adult men is about 42, women is 38. This value varies greatly, depending on whether the patient is normal or anaemic, and is elevated during sports activities. The haematocrit changes in question are red blood cells, which carry oxygen.

Haematocrit is determined by centrifugation of the blood in a standard tube, as shown in the figure. The calibration allows the percentage of cells.

Figure. Effect of haematocrit on blood viscosity (water viscosity = 1).

An increase in haematocrit causes an increase in blood viscosity

Blood viscosity increased sharply as did haematocrit, as shown. The viscosity of whole blood in a normal haematocrit is about 3-4, that is, 3-4 times the pressure required for whole blood to force water through the blood vessel. When the haematocrit rises to 60 or 70 it is usually polycythaemia vera in humans, the viscosity of the blood can be 10 times that of water, and the flow through the blood vessels is very slow.

Another factor affecting blood viscosity is plasma protein concentration and plasma protein type, but these effects are smaller than the effect of haematocrit, and they are not significant in hemodynamic studies.  The viscosity of plasma is about 1.5 times that of water.

Effect of pressure on vascular resistance and blood flow. 'Self-regulating' reduces the effect of the vascular pressure in circulating blood tissue

From the previous discussion, it is certain that additional arterial blood pressure increases blood flow through various tissues of the body. However, the effect of arterial pressure on blood flow in many tissues is always less than the expected force, as shown. The reason for this is that an increase in arterial pressure not only increases the force of blood pushing through the vessels but also compensating increases vascular resistance within seconds through the activation of control mechanisms. In contrast, with reduced pressure, vascular resistance rapidly decreases in tissues and blood flow helps to maintain a constant flow rate. The ability of each tissue to modulate vascular resistance and maintain normal blood volume during changes in arterial pressure between 70-175 mmHg is known as autoregulatory blood flow.


Figure. Effect of changes in arterial pressure over a period of several minutes on blood flow in tissues such as skeletal muscle.

Note that between pressure 70- and 175-mm Hg, blood flow is "automatically regulated." The blue line shows the effect of sympathetic nerve stimulation or vasoconstriction by hormones such as norepinephrine, angiotensin II, vasopressin, or endothelin on this relationship. Decreased tissue blood flow is rarely maintained for more than a few hours because of the activation of local autoregulatory mechanisms that eventually return blood flow to normal.

Note above that changes in blood flow can be caused by stimulation of the sympathetic nervous system, which remodels blood vessels. Likewise, vasoconstrictor hormones, such as norepinephrine, angiotensin II, vasopressin or endothelin, can temporarily reduce blood flow.

Altered blood flow rarely persists for more than a few hours in most operations, even with sustained arterial pressure or increased vasoconstrictor levels. The reason for the relative variation in blood flow is the self-regulating mechanism of the tissues to counteract the effects of vasoconstrictors to provide an appropriate blood structure to the tissue needs.

The relationship of blood pressure in passive vessels

In isolated vasculature or in tissue without evidence of autoregulation, changes in arterial blood pressure can have a significant effect on blood flow. In fact, the effect of blood pressure is predictable according to the Poiseuille formula. The reason for this is that additional arterial pressure not only increases the force of blood pushing through the vessel but also inflates the vessel, reducing resistance. Conversely, a decrease in pressure in the passive vessel increases resistance as the vessel collapses due to a decrease in pressure. When the pressure drops below a limit, called the upper limit of blood pressure, the flow stops and the blood in the vessel completely stops flowing.

The sympathetic nervous system and vasoconstrictors can indirectly influence the blood pressure on the image. Thus, inhibition of sympathetic activity causes dilation of blood vessels and an increase in blood flow. In contrast, vasoconstrictor sympathetic stimulation causes blood flow to drop to zero within a few seconds even though arterial blood pressure remains high.


Figure. Effect of arterial pressure on passive vascular blood flow at different degrees of vascular tone due to increased or decreased sympathetic stimulation of the vessel.

In practice, there are very few physiological conditions in which the tissue appears to be co-optimal with the flow pressure in the figure. Even in tissues without the effect of autoregulatory mechanisms during acute changes in arterial blood pressure, blood flow is altered according to tissue demand during pressure changes.