Principles of Hemodynamics

Introduction

Hemodynamics explains the physical principles governing blood flow through the cardiovascular system. Blood flow is profoundly influenced by vessel diameter, pressure gradients, and blood viscosity. Understanding these factors is essential for interpreting normal circulatory function and the pathophysiology of cardiovascular disorders.

Application of Physical Principles

• Hemodynamics refers to the application of physical principles to the movement of blood through the cardiovascular system.
• The cardiovascular system consists of the heart and blood vessels, which function together to ensure adequate tissue perfusion.
• The heart acts as a mechanical pump that generates the pressure required for forward blood flow.
• Blood vessels transport blood between the heart and tissues and provide resistance, capacitance, and distribution functions.
• The structure of blood vessels varies throughout the circulation. Differences in vessel diameter, wall thickness, and elasticity significantly influence blood flow.
• Blood flow is also affected by the physical and rheological properties of blood, including viscosity, hematocrit, and plasma protein concentration.
• The two principal determinants of blood flow are the properties of blood and the diameter of blood vessels.
• Because resistance varies inversely with the fourth power of vessel radius, small changes in vascular diameter produce large changes in blood flow.
• Vascular smooth muscle is continuously influenced by neural, hormonal, and local metabolic factors.
• Therefore, vessel diameter represents the integrated response to autonomic, humoral, and local regulatory mechanisms.
• Blood is a complex fluid rather than a simple liquid. It consists of erythrocytes, leukocytes, platelets, and lipids suspended in plasma, which is a colloidal solution containing proteins and other solutes.
• Despite the complexity of blood and the dynamic nature of blood vessels, circulation remains highly coordinated because of fundamental hemodynamic principles.
• Understanding these principles is essential for interpreting normal cardiovascular physiology and circulatory disorders.

Velocity-Flow-Pressure Relationship

Velocity vs Blood Flow

• Velocity is the distance traveled by blood per unit time and is commonly expressed in centimeters per second.
• Blood flow is the volume of blood passing through a vessel per unit time and is expressed in milliliters or cubic centimeters per second.
• Blood flow depends on the pressure gradient across the vascular bed, vascular resistance, vessel dimensions, and blood viscosity.
• Average blood velocity is determined by the equation: velocity = flow ÷ total cross-sectional area.
• Thus, blood velocity is directly proportional to flow and inversely proportional to the total cross-sectional area of the vascular segment.
• The aorta has the highest blood velocity because it possesses a relatively small total cross-sectional area.
• As blood moves through arteries and arterioles into capillaries, total cross-sectional area progressively increases.
• Consequently, blood velocity falls markedly and reaches its lowest value in the capillaries, facilitating efficient exchange of gases, nutrients, and metabolites.
• Blood velocity gradually increases again in venules and veins as total cross-sectional area decreases toward the venae cavae.

Velocity vs Pressure

• Changes in pressure within a hydraulic system influence the velocity of fluid movement.
• In the cardiovascular system, pressure has two major components: static (lateral) pressure and dynamic pressure.
• Static or lateral pressure is the force exerted by blood perpendicular to the vessel wall. This pressure distends the vessel and drives blood into smaller branches.
• Dynamic pressure represents the kinetic energy associated with moving blood and increases as blood velocity rises.
• The sum of static and dynamic pressures constitutes the total energy of flowing blood.
• According to Bernoulli’s principle, in an ideal fluid system, an increase in fluid velocity is accompanied by a decrease in lateral pressure, provided total energy remains constant.
• In the circulation, when blood passes through a narrowed segment of a vessel, its velocity increases because of the reduced cross-sectional area.
• The rise in velocity increases the dynamic component of pressure.
• Consequently, lateral pressure within the narrowed region decreases.
• Reduced lateral pressure lowers the amount of blood entering side branches arising near the constricted segment.
• Therefore, tissue perfusion distal to or adjacent to a vascular narrowing may decrease.
• This principle has important clinical implications because arterial stenosis can reduce blood supply to tissues despite preservation of overall blood flow.
• Understanding the relationship between velocity and pressure helps explain the hemodynamic consequences of vascular obstruction and stenotic lesions.

Flow, Pressure and Resistance

• Blood flow through a vessel is primarily determined by the pressure gradient and vascular resistance.
• Flow increases when the pressure gradient between the arterial and venous ends rises.
• Conversely, a reduction in pressure gradient decreases blood flow.
• The relationship among flow, pressure, and resistance is analogous to Ohm’s law in electrical circuits.
• In the circulation, blood flow is directly proportional to the effective perfusion pressure and inversely proportional to peripheral resistance.
• Effective perfusion pressure is the difference between mean arterial pressure and mean venous pressure.
• Therefore, an increase in peripheral resistance reduces blood flow if the pressure gradient remains constant.
• Arterioles are the major determinants of peripheral resistance and tissue perfusion.

Table 92.1: Differences between laminar flow and turbulent flow.

Feature	Laminar Flow	Turbulent Flow
Flow pattern	Blood moves in parallel, orderly layers with minimal mixing.	Blood moves irregularly with eddies and multidirectional mixing.
Velocity	Occurs at relatively low velocities.	Develops when flow velocity exceeds a critical level.
Reynolds number	Usually < 2000	Usually > 3000
Sound production	Normally silent.	Commonly generates audible sounds, such as murmurs or bruits.

Types of Blood Flow

• Blood flow within the cardiovascular system occurs in two principal patterns: laminar flow and turbulent flow.
• Under normal physiological conditions, blood flow in most vessels is laminar.

Laminar Flow

• Laminar flow refers to orderly movement of blood in parallel layers with minimal mixing between adjacent layers.
• It is also termed streamline flow because blood particles follow smooth, regular pathways.
• The layer of blood immediately adjacent to the vessel wall is essentially stationary because of frictional interaction with the endothelium.
• Successive layers located progressively toward the center move at increasingly higher velocities.
• Consequently, blood velocity is lowest near the vessel wall and highest at the center of the vessel lumen.
• This velocity profile produces a parabolic distribution of flow across the vessel cross-section.
• Laminar flow is energy efficient and usually occurs at relatively low velocities.
• Efficient exchange of gases and nutrients in the microcirculation depends largely on maintenance of laminar flow.
• Laminar flow persists only up to a certain velocity, known as the critical velocity.
• When blood velocity exceeds this threshold, flow becomes turbulent.

Turbulent Flow

• Turbulent flow is characterized by chaotic movement of blood with eddies and multidirectional mixing.
• Turbulence increases energy loss and raises resistance to blood flow.
• The likelihood of turbulence depends on blood velocity, vessel diameter, blood density, and blood viscosity.
• The tendency for turbulence is expressed by the Reynolds number, calculated as: Re = (density × diameter × velocity) ÷ viscosity.
• A Reynolds number below approximately 2000 generally indicates laminar flow.
• Values exceeding approximately 3000 usually indicate turbulent flow, whereas intermediate values represent transitional flow.
• Turbulence is promoted by increased blood velocity, increased vessel diameter, decreased blood viscosity, and irregular vessel surfaces.
• Anemia predisposes to turbulent flow because reduced hematocrit lowers blood viscosity.
• In the cardiovascular system, blood flow frequently becomes turbulent at sites of vascular narrowing or valvular stenosis because velocity rises markedly in these regions.
• Turbulent flow generates audible vibrations.
• A murmur is heard when turbulence occurs across abnormal cardiac valves.
• A bruit is heard over a stenosed artery.
• The Korotkoff sounds heard during indirect blood pressure measurement arise from turbulent flow in the partially compressed brachial artery.

Poiseuille-Hagen Formula

• Poiseuille’s law describes the relationship among blood flow, pressure gradient, vessel radius, blood viscosity, and vessel length.
• Blood flow is directly proportional to the pressure difference across a vessel and to the fourth power of the vessel radius.
• Blood flow is inversely proportional to blood viscosity and vessel length.
• Because flow varies with the fourth power of radius, even small changes in vessel diameter produce large changes in blood flow.
• For example, increasing vessel radius by approximately 20% nearly doubles blood flow if other factors remain constant.
• Conversely, slight vasoconstriction markedly reduces blood flow.
• Vascular resistance varies inversely with the fourth power of vessel radius.
• Therefore, arteriolar vasoconstriction increases resistance and arterial pressure, whereas vasodilation decreases resistance and arterial pressure.

Peripheral Resistance

Peripheral resistance is the opposition encountered by blood as it flows through the systemic circulation.

Factors Affecting Peripheral Resistance

• It is determined primarily by vessel diameter and blood viscosity.
• Arteriolar caliber is the most important determinant because small changes in arteriolar radius produce large alterations in resistance and tissue perfusion.

Radius of Blood Vessel

• The radius of blood vessels is the most important determinant of peripheral resistance and is often referred to as vascular resistance.
• Vasoconstriction decreases vessel radius and markedly increases peripheral resistance, whereas vasodilation lowers resistance.
• According to Poiseuille’s law, resistance is inversely proportional to the fourth power of vessel radius.
• Therefore, reducing the vessel radius by one-half increases resistance approximately sixteen-fold.
• As a consequence, blood flow through that vessel decreases markedly if the pressure gradient remains unchanged.
• Conversely, doubling the vessel radius reduces resistance to one-sixteenth of its original value, greatly enhancing blood flow.

Viscosity of Blood

• Blood viscosity also contributes significantly to peripheral resistance and represents a hematological factor influencing flow.
• Viscosity depends mainly on hematocrit, plasma protein concentration, erythrocyte deformability, and temperature.

Hematocrit

• Hematocrit is the principal determinant of blood viscosity because it reflects the proportion of red blood cells in blood.
• Increased hematocrit, as occurs in polycythemia, raises viscosity and peripheral resistance.
• Decreased hematocrit, as seen in anemia, lowers viscosity and contributes to a hyperdynamic circulation.
• The effect of viscosity on resistance is less pronounced in very small vessels because erythrocytes align and deform while traversing the microcirculation.
• Plasma proteins, particularly immunoglobulins and fibrinogen, also influence viscosity.
• Blood viscosity increases in disorders associated with excessive plasma proteins, such as multiple myeloma and other paraproteinemias.

Composition of Plasma

• Plasma proteins, particularly immunoglobulins and fibrinogen, also influence viscosity.
• Blood viscosity increases in disorders associated with excessive plasma proteins, such as multiple myeloma and other paraproteinemias.
• Reduced plasma protein concentration decreases viscosity.
• The ability of erythrocytes to deform is essential for smooth microvascular flow.

Resistance of Red Cells to Deformation

Reduced erythrocyte deformability, as observed in hereditary spherocytosis and sickle cell disease, increases blood viscosity and impedes circulation.

Temperature

Temperature affects viscosity inversely. Increased body temperature lowers blood viscosity, whereas hypothermia increases viscosity and vascular resistance.

Plasma Skimming

• In flowing blood, erythrocytes tend to migrate toward the center of the vessel lumen, whereas plasma occupies the peripheral region near the vessel wall.
• As a result, blood entering small side branches is derived predominantly from the plasma-rich peripheral layer.
• Consequently, these smaller vessels receive blood containing relatively fewer red blood cells.
• This phenomenon is known as plasma skimming.
• Plasma skimming contributes to the lower hematocrit observed in capillary blood compared with systemic large-vessel blood.
• Capillary hematocrit is typically about 20–25% lower than whole-body hematocrit.
• Plasma skimming facilitates efficient microcirculatory flow by reducing viscosity within small vessels.
• In rigid tubes, blood flow decreases linearly as pressure falls and ceases only when the pressure gradient becomes zero.
• However, blood vessels, particularly capillaries, behave differently because they are distensible and surrounded by tissues.

Critical Closing Pressure

• Critical closing pressure is the intravascular pressure below which blood flow stops despite the presence of a positive pressure within the vessel.
• Flow ceases because a minimum pressure is required to keep small vessels open and to propel erythrocytes through narrow capillaries.
• External tissue pressure exerted on blood vessels also opposes intraluminal pressure.
• Therefore, capillary blood flow resumes only when intraluminal pressure exceeds the surrounding tissue pressure and the critical closing pressure.

Law of Laplace

• Laplace’s law describes the relationship among distending pressure, wall tension, vessel radius, and wall thickness.
• In a thin-walled cylindrical blood vessel, wall tension is directly proportional to the product of intraluminal pressure and vessel radius (T = P × r).
• Therefore, larger vessels require greater wall tension to withstand the same internal pressure.
• Small blood vessels require less wall tension and are consequently less susceptible to rupture.
• When wall thickness is considered, wall stress is directly proportional to pressure and radius but inversely proportional to wall thickness.
• Hypertrophy of arterial walls helps reduce wall stress in hypertension.

$$\mathrm= \mathrm{Wall\ tension\ (T) = P \times \frac{r}{w}}$$

Application of Laplace Law

• Laplace’s law is useful for understanding the mechanical behavior of hollow organs under physiological and pathological conditions.
• In hollow structures such as the urinary bladder, cardiac ventricles, and pulmonary alveoli, wall tension increases as intraluminal pressure or cavity radius increases.
• Therefore, progressive filling or dilation of these organs increases the force required to maintain their shape and function.
• Wall tension is inversely related to wall thickness. Consequently, thicker walls reduce wall stress, whereas thinner walls increase it.
• In ventricular hypertrophy, increased myocardial thickness lowers wall stress and helps compensate for chronic pressure overload, such as in hypertension or aortic stenosis.
• In contrast, a dilated ventricle, as seen in chronic heart failure, has increased wall tension because of its enlarged radius.
• Increased wall tension raises myocardial oxygen demand and reduces the efficiency of cardiac pumping.