## Blood flow through a vessel

The flow of blood through a vessel is determined by two factors:

• Vascular resistance

The relationship among blood flow (Q, ml/min), the pressure gradient (DP, mmHg), and vascular resistance (R, mmHg/ml/min) is described by Ohm's law:

The pressure gradient is the difference between the pressure at the beginning of a blood vessel and the pressure at the end. The inflow pressure is always greater than the outflow pressure because substances, including blood and air, must flow "down" their pressure gradients; in other words, from an area of higher pressure to an area of lower pressure. The inflow pressure is initially generated by the contraction of the heart. As discussed previously, blood pressure falls continuously as the blood flows through the circulatory system. This loss of driving pressure is due to the friction generated as the components of the flowing blood come into contact with the vessel wall as well as each other. Blood flow through a vessel is directly proportional to the pressure gradient; in other words, the greater the difference between inflow pressure and outflow pressure is, the greater the flow of blood through the vessel.

The second factor that determines the flow of blood through a vessel is resistance. In contrast to the pressure gradient, blood flow through a vessel is indirectly proportional to the resistance. In other words, resistance impedes or opposes blood flow. Three factors affect vascular resistance:

• Blood viscosity

• Vessel length

Viscosity describes the friction developed between the molecules of a fluid as they interact with each other during flow. More simply put, the "thicker" the fluid, then the greater its viscosity. Viscosity and resistance are directly proportional so that, as the viscosity of the fluid increases, the resistance to flow increases. In the case of blood flow through the circulatory system, erythrocytes, or red blood cells, suspended in the blood are the primary factor determining viscosity. Hematocrit, the percentage of the blood that consists of red blood cells, is 40 to 54% (average = 47%) for an adult male and 37 to 47% (average = 43%) for an adult female. Under normal physiological conditions, hematocrit and blood viscosity do not vary considerably within an individual. Only pathological conditions, such as chronic hypoxia, sickle cell anemia, and excess blood fibrinogen, may result in hyperviscosity and, consequently, impaired blood flow.

Friction also develops as blood contacts the vessel wall while flowing through it. Therefore, the greater the vessel surface area in contact with the blood, the greater the amount of friction developed and the greater is the resistance to blood flow. Two factors determine the vessel surface area: length of the vessel and vessel radius.

The longer the vessel, the more the blood comes into contact with the vessel wall and the greater the resistance is. However, vessel length in the body remains constant. Therefore, as with blood viscosity, it is not a variable factor causing changes in resistance.

The most important physiological variable determining the resistance to blood flow is vessel radius. A given volume of blood comes into less contact with the wall of a vessel with a large radius compared to a vessel with a small radius. Therefore, as the radius of a vessel increases, the resistance to blood flow decreases. In other words, blood flows more readily through a larger vessel than it does through a smaller vessel.

Small changes in vessel radius result in significant changes in vascular resistance and in blood flow because the resistance is inversely proportional to the fourth power of the radius:

If this equation is substituted into Ohm's law, then blood flow may be calculated as follows:

Assume two blood vessels of equal length, each has a pressure gradient of 1 mmHg. However, blood vessel A has a radius of 1 mm and blood vessel B has a radius of 2 mm. The flow of blood through vessel A is 1 ml/min and the flow of blood through vessel B is 16 ml/min. Simply doubling vessel radius causes a 16-fold increase in blood flow.

As mentioned previously, the arterioles are the major resistance vessels in the circulatory system. Because the walls of these vessels contain primarily smooth muscle, they are capable of significant changes in their radius. Therefore, regulation of blood flow to the tissues is carried out by the arterioles.

Ohm's law may be rewritten to include the three factors that affect vascular resistance: blood viscosity (h), vessel length (L), and vessel radius (r). The following equation is known as Poiseuille's law:

## Essentials of Human Physiology

This ebook provides an introductory explanation of the workings of the human body, with an effort to draw connections between the body systems and explain their interdependencies. A framework for the book is homeostasis and how the body maintains balance within each system. This is intended as a first introduction to physiology for a college-level course.

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