Circulation and Biophysics Notes

Overview of Circulation and Biophysics

The circulatory system's primary function is to serve the body's tissues by:

• Transporting nutrients to tissues.

• Removing cell excreta (waste products.)

• Transporting hormones.

• Maintaining an appropriate environment in tissue fluids for cell function.

Blood flow is mainly controlled in response to tissue nutrient needs, with some organs like the kidneys having additional functions that require high blood flow for excretion.

The heart and blood vessels are controlled to provide the necessary cardiac output and arterial pressure to ensure adequate tissue blood flow.

The systemic circulation supplies blood to all body tissues except the lungs and is also known as the greater or peripheral circulation. The circulation consists of the systemic and pulmonary circulations.

Functional Parts of the Circulation:

• Arteries: Transport blood under high pressure to tissues, possessing strong vascular walls for high-velocity blood flow.

• Arterioles: Control conduits that release blood into capillaries, with muscular walls that can completely close or dilate to alter blood flow in response to tissue needs.

• Capillaries: Exchange fluid, nutrients, electrolytes, hormones, and other substances between blood and interstitial fluid. Their walls are thin with numerous small pores.

• Venules: Collect blood from capillaries and merge into larger veins.

• Veins: Transport blood from venules back to the heart and serve as a major blood reservoir. Venous walls are thin but muscular enough to contract or expand to control the amount of extra blood.

Distribution of Blood Volume:

• Systemic circulation: 84% (64% in veins, 13% in arteries, 7% in arterioles and capillaries)

• Heart: 7%

• Pulmonary vessels: 9%

The capillaries have a low blood volume despite their critical role in substance diffusion between blood and tissues.

Vascular Cross-Sectional Areas:

• Aorta: $2.5 cm^2$

• Small arteries: $20 cm^2$

• Arterioles: $40 cm^2$

• Capillaries: $2500 cm^2$

• Venules: $250 cm^2$

• Small veins: $80 cm^2$

• Venae cavae: $8 cm^2$

Veins have approximately four times the cross-sectional area of arteries, contributing to their large blood storage capacity.

Blood Flow Velocity:

• Velocity is inversely proportional to vascular cross-sectional area: $v = F/A$, where $v$ is velocity, $F$ is blood flow, and $A$ is cross-sectional area.

• Aorta: $33 cm/sec$

• Capillaries: $0.3 mm/sec$

Blood remains in capillaries for only 1 to 3 seconds, during which diffusion of substances occurs.

Pressures in Circulation:

• Aorta: Mean pressure of $100 mm Hg$, oscillating between systolic pressure of $120 mm Hg$ and diastolic pressure of $80 mm Hg$.

• Systemic capillaries: Pressure varies from $35 mm Hg$ (arteriolar ends) to $10 mm Hg$ (venous ends), with an average functional pressure of $17 mm Hg$.

• Pulmonary arteries: Systolic pressure of $25 mm Hg$, diastolic pressure of $8 mm Hg$, and mean arterial pressure of $16 mm Hg$.

• Pulmonary capillaries: Mean pressure of $7 mm Hg$.

Despite low pressures, total blood flow through the lungs equals that of the systemic circulation because the lungs only need to expose blood to oxygen and other gases.

Basic Principles of Circulatory Function

The circulatory system operates under three basic principles:

1. Tissue Blood Flow Control: Blood flow to tissues is controlled based on tissue needs. Tissues continuously monitor nutrient availability and waste accumulation, adjusting local blood vessel diameter to regulate blood flow accordingly. Nervous control and hormones assist in this process.

2. Cardiac Output: Cardiac output is the sum of all local tissue flows. The heart responds automatically to increased blood inflow by pumping it back into the arteries. Nerve signals often assist the heart in pumping required blood flow amounts.

3. Arterial Pressure Regulation: Arterial pressure regulation is independent of local blood flow and cardiac output control. The body uses reflexes to increase heart pumping force, contract venous reservoirs, and constrict arterioles to maintain pressure. Long-term pressure control involves the kidneys, which secrete pressure-controlling hormones and regulate blood volume.

These mechanisms combined, serve the specific needs of individual tissues.

Interrelationships of Pressure, Flow, and Resistance

Blood flow is determined by:

1. Pressure difference between vessel ends.

2. Vascular resistance.

Ohm's Law: $F = \frac{\Delta P}{R}$, where $F$ is blood flow, $\Delta P$ is pressure difference, and $R$ is resistance.

This formula can be rearranged to: $\Delta P = F \times R$ and $R = \frac{\Delta P}{F}$.

Blood flow is directly proportional to pressure difference and inversely proportional to resistance.

Cardiac output, the total blood flow in the circulation, is normally $5000 ml/min$ in an adult at rest.

Measuring Blood Flow

Blood flow is measured as the quantity of blood passing a point in the circulation per unit time, typically in $ml/min$.

Methods for measuring blood flow include:

• Electromagnetic Flowmeter: Measures blood flow without opening the vessel by generating an electromotive force proportional to blood flow when blood moves through a magnetic field.

• Ultrasonic Doppler Flowmeter: Measures blood flow by transmitting ultrasound downstream and analyzing the frequency shift of reflected waves, which is proportional to blood flow velocity. This is based upon the Doppler Effect.

Both methods can record rapid, pulsatile changes in flow.

Laminar and Turbulent Blood Flow

• Laminar Flow: Blood flows in streamlines, with each layer at a constant distance from the vessel wall. The central portion flows faster than the outer edges, creating a parabolic velocity profile.

• Turbulent Flow: Blood flows in all directions, creating eddy currents. It occurs at high flow rates, obstructions, sharp turns, or rough surfaces. Turbulent flow increases resistance due to increased friction.

The tendency for turbulent flow is quantified by Reynolds' number ($R<em>e$): $R</em>e = \frac{\nu \cdot d \cdot \rho}{\eta}$, where $\nu$ is blood flow velocity, $d$ is vessel diameter, $\rho$ is density, and $\eta$ is viscosity.

Turbulence occurs when $R<em>e$ exceeds 2000, or at branches when $R</em>e$ reaches 200-400. It is common in the aorta and pulmonary artery due to high velocity and pulsatile flow. Small vessels rarely experience turbulence.

Blood Pressure

Blood pressure is measured in millimeters of mercury ($mm Hg$), representing force exerted by blood against vessel walls.

High-fidelity methods for measuring blood pressure involve electronic transducers:

These transducers use a thin, stretched membrane that bulges with pressure changes. The movement of the membrane is converted into electrical signals using:

• Capacitance changes

• Inductance changes

• Resistance changes

These systems can accurately record rapid pressure changes up to 500 cycles per second.

Resistance to Blood Flow

Resistance (R) is calculated as: $R = \frac{\Delta P}{F}$, where $\Delta P$ is the pressure difference and $F$ is flow.

A peripheral resistance unit (PRU) is defined as $1 mm Hg$ pressure difference per $1 ml/sec$ flow.

In CGS units, resistance is expressed as $dyne \cdot sec/cm^5$, calculated as: $R = 1333 \times \frac{mm Hg}{ml/sec}$.

Total peripheral resistance (systemic) is normally about 1 PRU, while total pulmonary vascular resistance is about 0.14 PRU.

Conductance (C), the reciprocal of resistance, is expressed as $ml/sec/mm Hg$ and quantifies blood flow for a given pressure difference: $C = \frac{1}{R}$.

Small changes in vessel diameter significantly alter conductance. Conductance is proportional to the fourth power of the diameter: $Conductance \propto Diameter^4$

Poiseuille's Law: $F = \frac{\pi \Delta P r^4}{8 \eta l}$, where $F$ is blood flow, $\Delta P$ is pressure difference, $r$ is vessel radius, $l$ is vessel length, and $\eta$ is viscosity.

This law emphasizes the significant impact of vessel diameter on blood flow.

Arteriolar resistance accounts for about two-thirds of total systemic resistance. Arterioles' ability to change diameter allows them to control blood flow effectively.

Resistance in Series and Parallel Vascular Circuits

In series arrangements, total resistance is the sum of individual resistances: $R<em>{total} = R</em>1 + R<em>2 + R</em>3 + R_4 + …$

In parallel arrangements, total resistance is calculated as: $\frac{1}{R<em>{total}} = \frac{1}{R</em>1} + \frac{1}{R<em>2} + \frac{1}{R</em>3} + \frac{1}{R_4} + …$

Parallel circuits permit independent blood flow regulation to different tissues. Total conductance in parallel circuits is the sum of individual conductances: $C<em>{total} = C</em>1 + C<em>2 + C</em>3 + C_4 + …$

Effects of Hematocrit and Viscosity

Blood viscosity is primarily determined by hematocrit, the proportion of blood volume composed of red blood cells. Normal hematocrit is about 42 for men and 38 for women.

Increased hematocrit raises blood viscosity, reducing blood flow. Blood viscosity is normally three to four times greater than water viscosity.

Effects of Pressure on Vascular Resistance and Tissue Blood Flow

Autoregulation maintains constant blood flow despite changes in arterial pressure. Tissues adjust vascular resistance to maintain normal blood flow between approximately $70$ and $175 mm Hg$.

In passive vascular beds (without autoregulation), increased arterial pressure distends vessels, reducing resistance:

Pressure-Flow Relationship Example:

• Normal blood flow: Tissue vasoconstriction

Hormonal vasoconstrictors or sympathetic stimulation can transiently reduce blood flow.

Vascular Distensibility and Compliance

Vascular distensibility is the fractional increase in volume per $mm Hg$ pressure rise: $Vascular \ Distensibility = \frac{Increase \ in \ Volume}{Original \ Volume \times Increase \ in \ Pressure}$.

Vascular compliance (capacitance) is the total quantity of blood stored per $mm Hg$ pressure rise: $Vascular \ Compliance = \frac{Increase \ in \ Volume}{Increase \ in \ Pressure}$.

The veins are more distensible and compliant than arteries. Systemic veins are approximately 24 times more compliant than corresponding arteries.

Volume-Pressure Curves of Arterial and Venous Circulations

Volume-pressure curves illustrate the relationship between pressure and volume in vessels:

• The arterial system, with about $700 ml$ of blood, maintains a mean arterial pressure of $100 mm Hg$.

• The venous system, with volume ranging from $2000 ml$ to $3500 ml$, requires a large volume change to cause a small pressure change.

Sympathetic stimulation increases vessel pressure for a given volume, while sympathetic inhibition decreases it.

Delayed compliance (stress-relaxation) allows vessels exposed to increased volume to initially exhibit a pressure increase, followed by a gradual return to normal as smooth muscle stretches. This effect helps accommodate extra blood volume.

Arterial Pressure Pulsations

The systolic pressure is about $120 mm Hg$, the diastolic pressure is about $80 mm Hg$, and the pulse pressure (difference between systolic and diastolic) is around $40 mm Hg$.

Factors Affecting Pulse Pressure:

• Stroke volume output of the heart

• Compliance of the arterial tree

Pulse pressure is approximately: $Pulse \ Pressure \approx \frac{Stroke \ Volume}{Arterial \ Compliance}$.

Abnormal pressure pulse contours can indicate conditions like aortic stenosis, patent ductus arteriosus, or aortic regurgitation.

Pressure pulses are transmitted through the arteries at varying velocities, with slower transmission in more compliant vessels like the aorta and faster transmission in less compliant small arteries.

In the smaller arteries, arterioles, and capillaries, the pressure pulses are progressively damped due to resistance and compliance of the vessels.

The auscultatory method is used to clinically measure pressures through listening to Korotkoff sounds, which are produced when blood flow is constricted. Normal arterial pressures increase with age due to aging of blood pressure control mechanisms.

Mean arterial pressure is approximately determined as: $MAP = (2 \times Diastolic \ Pressure + Systolic \ Pressure)/3$, or about 60% diastolic and 40% systolic pressure.

Veins and Their Functions

Veins function in blood return, storage, and cardiac output regulation. Venous pressures are influenced by:

• Right atrial pressure (central venous pressure)

• Peripheral venous pressures

Right atrial pressure is regulated by the heart's pumping ability and blood flow from peripheral veins. Normal right atrial pressure is about $0 mm Hg$ but can vary between $-3$ to $30 mm Hg$, depending on conditions.

Large veins offer little resistance when fully distended. Peripheral venous pressure is normally $+4$ to $+6 mm Hg$ greater than right atrial pressure. Factors Influencing Venous Pressure:

• Intra-abdominal pressure can increase venous pressures in the legs.

• Gravitational pressure increases venous pressure in dependent body parts (e.g., feet).

Venous valves and the venous pump (muscle pump) counteract gravitational effects. Standing still causes venous and capillary pressures to increase, leading to fluid leakage and potential fainting. Venous valve incompetence leads to varicose veins, edema, and potential skin ulceration.

Venous pressure can be estimated by observing neck vein distention.

The tricuspid valve level is the reference point for pressure measurements.

Blood Reservoir Function of Veins

Veins act as a blood reservoir due to their compliance, holding over 60% of blood volume. During blood loss, sympathetic constriction of veins maintains arterial pressure.

Specific Blood Reservoirs:

• Spleen: Can release up to $100 ml$ of blood.

• Liver: Sinuses can release several hundred milliliters.

• Large abdominal veins: Can contribute about $300 ml$.

• Venous plexus beneath the skin: Can contribute several hundred milliliters.

• The heart can contribute some 50 to 100 milliliters of blood, and the lungs can provide another 100 to 200 milliliters of blood when the pulmonary pressures decrease to low normal values.

The spleen has venous sinuses and red pulp for blood storage, releasing concentrated red blood cells during sympathetic activation. It also filters blood and removes old or damaged cells and infectious agents.