17 Cardiovascular System Organization

Functions of Circulatory Systems

Circulatory systems play a crucial role in the transport processes required for the survival of all but the smallest animals. Notably, all animals larger than 1 mm in diameter require a circulatory system for respiratory gas transport. The primary functions of circulatory systems include:

1. Transport of Nutrients: Nutrients are carried from the digestive tract to tissues and storage organs.

2. Transport of Metabolites: This includes substances like lactic acid that move from muscle tissues to the liver.

3. Transport of Excretory Products: These substances are transferred from tissues to excretory organs for removal.

4. Transport of Gases: Circulatory systems facilitate the movement of respiratory gases between the respiratory organs and tissues.

5. Transport of Hormones: Hormonal signals are distributed through the circulatory system to various parts of the body.

6. Transport of Cells: It includes the movement of various cells, such as leukocytes in vertebrates and different cell types in invertebrates.

7. Transport of Heat: The circulatory system helps in the regulation of body temperature by distributing heat.

8. Transmission of Force: This function is seen in locomotion for species like earthworms and spiders, as well as in the erection of the penis.

9. Coagulation: The circulatory system also is involved in blood clotting to prevent excessive bleeding.

10. Maintenance of Internal Milieu: Other functions support the overall homeostasis within the body.

Elements of the Circulatory System

The circulatory system comprises three fundamental components:

1. Liquid (Blood): The essential fluid that is circulated throughout the system.

2. Vessels: Tubes or containers through which blood is transported.

3. Pump (Heart): The organ that circulates blood through the vessels, ensuring proper flow and distribution.

In reptiles, birds, and mammals, the heart consists of two synchronized pumps: one high-pressure pump driving blood through the systemic circuit and a low-pressure pump that entails the pulmonary circuit.

Hydrodynamics of Flow through a Tube

Understanding blood flow is facilitated by examining the hydrodynamics of steady (non-pulsatile) fluid flow through rigid tubes. The behavior of blood flow can be modeled using classical hydrodynamics principles similar to Ohm's law in electricity:

• Equation: ΔP = F × R, where ΔP signifies the pressure difference between two points, F denotes the flow rate, and R represents the resistance to flow.

Blood Pressure

Blood pressure is described as the pressure difference (ΔP) between two points along a vascular tube:

1. Driving Pressure: The ΔP experienced between specific positions within the vessel (axial ΔP).

2. Transmural Pressure: The pressure difference between the interior and exterior of the vessel (radial ΔP), representing the variant between intravascular and surrounding tissue pressures.

3. Hydrostatic Pressure: Calculated as ΔPhyd = -ρg(h₁ - h₂), where ρ is blood density, g is gravitational acceleration, and h represents height differences.

Typically, blood pressure is quantified by the height it can raise a column of fluid, expressed in mm Hg or cm H₂O (1 mm Hg = 0.133 kPa).

Circulatory System Paths

Blood can traverse multiple parallel pathways from the left heart to the right heart, conceptualized through an “equivalent circuit”:

• Batteries: Represent the left and right heart.

• Resistors: Represent vascular beds of the circulatory system.

Vascular Resistance

Within the circulatory system, resistance can be analyzed similarly to electrical circuits:

• Resistances in series accumulate: R_total = R₁ + R₂ + R₃ + ...

• Resistances in parallel combine reciprocally: (R_total)⁻¹ = (R₁)⁻¹ + (R₂)⁻¹ + (R₃)⁻¹ ...

The systemic vascular resistance (SVR) embodies the total resistance faced from the left ventricle to the right atrium.

Cardiac Output, Flow, and Current

Cardiac output (CO) quantifies the volume of blood pumped by the heart per unit time, typically measured in liters per minute (approximately 5 L/min for a resting 70 kg individual). The formula presented is:

• CO = SV × HR where stroke volume (SV) refers to the amount of blood pumped per beat, and heart rate (HR) is the number of beats per minute.

In the context of Ohm's law, CO corresponds to current:

• CO = ΔP/R where ΔP is the pressure differential across the circulatory system, relating to systemic (left ventricle to right atrium) and pulmonic (right ventricle to left ventricle) circulations. In steady-state conditions, the CO is identical in both the right and left hearts.

Hagen-Poiseuille Equation

The Hagen-Poiseuille equation models flow (F) as the volume displacement (ΔV) over time (Δt):

• Equation: F = ΔV / Δt = ΔP × (πr⁴ / 8Lη) This equation indicates that flow is directly proportional to the pressure difference (ΔP) and the fourth power of the radius (r), while being inversely proportional to tube length (L) and fluid viscosity (η). The term relating to conductance illustrates resistance calculated based on the tube's dimensions and the fluid's viscosity.

Viscous Resistance and Laminar Flow

Upon applying pressure, fluids commence movement through a tube:

• The outer layer of fluid interacts with the tube wall, achieving near-zero velocity, while the inner concentric layers travel faster, resulting in a parabola indicating flow dynamics.

• Viscosity (η) refers to a fluid's internal friction; increased viscosity heightens resistance against flow.

Laminar vs. Turbulent Blood Flow

At elevated flow rates, blood flow may transition from laminar to turbulent patterns, which exhibit lower energy efficiency due to kinetic losses. Such transitions are dictated by the Reynolds number (Re), which considers diameter and viscosity; increases in velocity or decreases in viscosity uplift Re. Generally, laminar flow predominate in blood vessels, however, exceptions arise during high cardiac output situations (e.g., extreme exercise), vessel occlusions, or significantly reduced blood viscosity (e.g., anemia).