General literature

Blood pressure: models

Principle

Blood pressure (BP) is the pressure exerted by the blood at right angles to the walls of the blood vessels P_i minus the environmental or ambient pressure P_a, so:

BP = P_i – P_a.

Unless indicated otherwise, BP refers to systemic arterial BP, i.e. the pressure in the large arteries delivering blood to body parts other than the lungs, such as the brachial artery (in the arm). The pressure of the blood in other vessels is lower than the arterial pressure. BP values are generally stated in mmHg, but can be converted to an SI-unit, i.e. in Pascals. The conversion is:

P = ρ_Hggh, (Pa)

where ρ_Hg is the specific density of Hg (kg/m³), g the gravitational acceleration (m/s²) and h the value of BP, but now expressed in mHg (not mm).

The mean arterial pressure (MAP) is defined as the average arterial pressure during a single cardiac cycle. It is a result of the heart pumping blood from the veins back into the arteries. MAP can be calculated by:

MAP = (stroke volume x systemic resistance) + CVP,

where CVP is central venous pressure (see Blood pressure: (Central) venous). Mostly, CVP can be neglected. The first term at the right is the heamodynamic analog of Ohm’s law for an electric cirquit (V=iR). The up and down fluctuation of the arterial BP results from the pulsatile nature of the cardiac output. The pulse pressure is determined by the interaction of the stroke volume versus the volume and elasticity of the major arteries.

Cardiac output is heart rate times stroke volume. It represents the efficiency with which the heart circulates blood throughout the body.

Factors influencing BP

The physics of the circulatory system, as of any fluid system, are very complex. Many physical and physiological factors influence BP. Some physical factors are:

Heart rate The higher the heart rate, the higher BP (assuming no change in stroke volume).

Blood volume The higher the blood volume, the higher the cardiac output.

Resistance The higher the resistance, the higher the BP. Resistance is related to size (the larger the blood vessel, the lower the resistance), as well as the smoothness of the blood vessel walls. Smoothness is reduced by the buildup of fatty deposits on the arterial walls. Deposits can affect the laminar character of the flow (see Poiseuille’s law and Reynolds number). Various substances (vasoconstrictors and vasodilators change vessel diameter, thereby changing BP.

Viscosity or thickness of the fluid. Increase of viscosity results in increase of resistance and so of BP. anemia reduces viscosity, whereas hyperemia increases viscosity. Viscosity also increases with blood sugar concentration.

More Info

Usually, the systolic pressure P_sys amounts to 120 mmHg, or about 16 kPa. At this P_sys and an air pressure P_a of 1 atm, about 100 kPa, the total, absolute pressure in the blood vessel P_i is:

P_i = P_sys+ P_a = 116 kPa.

16 kPa is equivalent to a the pressure of a column of water with a height of 1.63 m.

The flow speed of blood in the body is 10 up to 100 cm/s (respectively during diastole and systole) in the aorta, approximately 10 cm/s in the arteries and approximately 0.1 cm/s in capillares. According to the law of Bernoulli (see Bernoulli's and Pascal’s Law)it holds that:

P_i+ ρgh + ½ρv² = c,

where c is a constant. This means that: P_sys + ρgh + ½ρv² = c - P_a. Since the ambient pressure is the same in all tissues, it holds that:

P_sys+ ρgh + ½ρv² = constant.

At a flow speed v = 50 cm/s (the largest flow speeds in the blood vessels are of this order of size) it holds that ½ρv² = 0.13 kPa. Since P_sysis 16 kPa, the term ½ρv² in the law of Bernoulli, which we may call the flow-pressure, is negligible with respect to the blood pressure P_sys. However, the term ρgh is not negligible as is explained in Blood pressure: body posture.