Porth's Essentials of Pathophysiology, 4e

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Circulatory Function

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In segments of the circulation where blood vessels branch extensively to form parallel circuits, as in those that supply blood to the many organs and tissues of the body, greater amounts of blood will flow through parallel vessels than through any of the individual ves- sels. Thus, for any given pressure, the total resistance to blood flow will be equal to the sum of the reciprocals of the individual resistances (1/R 1 + 1/R 2 + 1/R 3 ). Velocity, Cross-Sectional Area, and Flow In addition to the amount of blood flowing through a given organ or tissue, the rate or velocity at which the blood is moving is also important. Flow is a volume measurement (milliliters [mL] per second [sec]) that is determined by the cross-sectional area of a vessel and the velocity of flow. Velocity is a distance measurement; it refers to the speed or linear movement per unit time of blood as it flows through a vessel. When the flow through a given segment of the circulatory system is constant—as it must be for continuous flow—the veloc- ity is inversely proportional to the cross-sectional area of the vessel (i.e., the smaller the cross-sectional area, the greater is the velocity of flow). The linear velocity of blood flow in the circulatory system varies widely from 30 to 35 cm/second in the aorta to 0.2 to 0.3 mm/second in the capillaries. This is because even though each individual capillary is very small, the total cross-sectional area of all the systemic capillaries greatly exceeds the cross-sectional area of other parts of the circulation. As a result of this large surface area, the slower movement of blood allows ample time for exchange of nutrients, gases, and metab- olites between the tissues and the blood. Laminar VersusTurbulent Flow Ideally, blood flow should be laminar or streamlined, with the blood components arranged in layers so that the plasma is adjacent to the smooth, slippery endothelial lining of the blood vessel, and the blood elements, includ- ing the platelets, are in the center or axis of the blood- stream. This arrangement reduces friction by allowing the blood layers to slide smoothly over one another, with the axial layer having the most rapid rate of flow. Under certain conditions, however, blood flow can switch from laminar to turbulent. In turbulent flow the laminar stream is disrupted and the flow becomes mixed, moving both radially (crosswise) and axially (lengthwise). Turbulent flow can be caused by a number of factors, including high velocity of flow, change in ves- sel diameter, and low blood viscosity. The tendency for turbulence to occur is increased in direct proportion to the velocity of flow. Because energy is used in propelling blood both radi- ally and axially, more energy (pressure) is required to drive turbulent flow than laminar flow. Turbulence is often accompanied by vibrations of the blood and sur- rounding cardiovascular structures. Some of these vibra- tions are in the audible range and can be heard using a stethoscope. For example, a heart murmur results from turbulent flow through a diseased heart valve.

Principles of Blood Flow The term hemodynamics refers to the principles that gov- ern the flow of blood in the vascular system. The physics of fluid flow through rigid tubes provides the basis for understanding the flow of blood through blood vessels, even though blood vessels are not rigid tubes (they are distensible) and blood is not a simple homogenous fluid. Pressure, Resistance, and Flow Flow through the blood vessels in the circulatory system is determined almost entirely by two factors: the pressure difference ( Δ P) between the two ends of a vessel or group of vessels and the resistance (R) that the blood must over- come as it moves through the vessel or vessels. Thus, the flow of blood through a vessel can be calculated using the equation: flow = Δ P/R. In the circulatory system, blood flow is represented by the cardiac output. Resistance is the opposition to flow caused by friction between the moving blood components and the stationary vessel wall. In the peripheral circulation, the collective resistance of all the vessels in that part of the circulation is referred to as the total peripheral vascular resistance. The relationship between pressure and resistance can be quantified by what has become known as Poiseuille’s law . In the 1840s, Louis Poiseuille determined that the flow of fluid was determined by the pressure difference between the two ends of a tube (P 1 − P 2 ), the fourth power of the radius (r 4 ) of the tube, the viscosity ( η ) of the fluid, the tube length (l), and two constants ( π and 8) using the following equation: flow = πΔ P r 4 /8 η l. Simplifying the equation (i.e., flow = Δ P r 4 / η ) by deleting the constants π and 8 along with the length, which usually does not change, makes it clear that flow will increase as the pressure gradient and vessel radius increase and decrease as the blood viscosity increases. Note particularly that the rate of flow is directly related to the fourth power of the radius, emphasizing the importance of vessel diameter in determining the rate of flow through the vessel. For example, if the pressure remains constant, the rate of flow is 16 times greater in a vessel with a radius of 2 mm (2 × 2 × 2 × 2 = 16) than in a vessel with a radius of 1 mm (1 × 1 × 1 × 1 = 1). Viscosity generates resistance to flow by producing friction between the molecules of a liquid. Unlike water that flows through plumbing pipes, blood is a nonho- mogeneous liquid. It contains blood cells, platelets, fat globules, and plasma proteins that increase its viscosity. It is mainly the hematocrit or percentage of suspended red cells in the blood that determines viscosity. Flow in Series and Parallel Vessels The interaction between pressure and resistance is deter- mined by whether blood vessels are arranged in series or in parallel. In vessels such as arteries, arterioles, capillar- ies, venules, and veins, which are collectively arranged in series, flow through each vessel at any given pressure is the same; therefore, the total resistance is equal to the sum of the resistances (R) of each vessel (R 1 + R 2 + R 3 ).