9_ Continuity Principle in the CVS

Learning Outcomes

  • Understand the main constituents of blood, their functions, and how they interact with each other.

  • Define and discuss haematocrit ratio, its significance in clinical settings, and variations based on demographics and conditions.

  • Basic anatomy of the heart and generalized blood circulation, including the role of major blood vessels.

  • Compare the heart's function to mechanical pumps, emphasizing the differences in operational principles.

  • Explain the Continuity Principle and apply its equation to non-viscous fluids, including practical applications in biomedical contexts.

  • Calculate flow rates for non-viscous fluids and apply this knowledge to understand cardiovascular health.

  • Examine variations in blood velocity with vessel area and the effects of vessel diameter changes on blood flow dynamics.

  • Differentiate between laminar and turbulent flow, including defining critical flow speed and its implications for cardiovascular diseases.

Blood Constituents

1. Plasma

Definition: The liquid component of blood in which the RBC’s, WBC’s, and platelets are suspended.

Characteristics:

  • Accounts for over half of blood volume (approximately 55%).

  • Primarily consists of 90% water, with the remaining 10% made up of dissolved salts (electrolytes), proteins (such as albumin, globulins, and fibrinogen), nutrients, hormones, and waste products.

2. Red Blood Cells (RBCs)

Definition: Also known as erythrocytes.

Volume Proportion: Comprises approximately 40-45% of blood volume.

Function:

  • Contains haemoglobin, a protein that chemically binds to oxygen in the lungs and releases it in tissues.

  • Gives RBC’s its red colour

  • Plays a role in carbon dioxide transport back to the lungs.

  • Key indicator of overall health; anemia (low RBCs) or polycythemia (high RBCs) can signal underlying conditions.

3. White Blood Cells (WBCs)

Definition: Known as leukocytes.

Volume Proportion: Roughly 1 WBC for every 660 RBCs, making up about 1% of blood volume.

Function:

  • Vital component of the immune system, defending the body against infections and foreign pathogens.

4. Platelets

Definition: Also termed thrombocytes; these are cell fragments smaller than RBCs and WBCs.

Volume Proportion: Approximately 1 platelet for every 20 RBCs.

Function:

  • Crucial for hemostasis; involved in blood clotting by forming plugs at injury sites and releasing chemicals that promote clotting and healing.

  • Reduced platelet count can lead to excessive bleeding (thrombocytopenia), while an increased count may contribute to thrombosis.

Haematocrit

Definition: The ratio of the volume of red blood cells to the total volume of blood. Hematocrit is the percentage of red cells in your blood. 

Measurement: Typically obtained through centrifugation, allowing separation of blood components.

Haematocrit Ratio is defined as the ratio of red blood cell (rbc) volume to the total blood volume, i.e. % rbc volume.

Variability:

  • Influenced by factors such as hydration, altitude, and diseases (e.g., dehydration increases haematocrit).

  • Hematocrit is important bc it determines the viscosity of the blood

  • In a 70 kg male, total blood volume represents ~7% of body mass (~5 liters), where the average haematocrit is roughly 45%.

  • Heart pumps ~80 ml of blood per contraction; a typical red blood cell completes a full cycle through the body in about 1 minute.

Heart Pumps

Types of Pumps

  • Vacuum Pumps: Reduce pressure (e.g., diaphragm type used in various machines).

  • Forced Pumps: Increase pressure, such as the heart, which ensures continuous blood flow despite varying vascular resistance.

Heart Functioning

Diastole Phase:

  • Heart chambers expand, lowering pressure to draw blood into the atria from the veins (venous return).

    Systole Phase:

  • Heart contracts, increasing pressure to pump blood out of the heart into the arteries (ventricular ejection).

    Valves:

  • Ensure unidirectional blood flow; include the right atrioventricular (tricuspid) valve, left atrioventricular (mitral) valve, aortic valve, and pulmonary valve.

Comparative Mechanics

  • Functions similarly to Boyle’s Law: Volume x Pressure = Constant, demonstrating the interdependence of these two factors in cardiovascular function.

  • Phases:

    • Diastole: Relaxation and filling of the heart, requiring optimal venous return and low vascular resistance.

    • Systole: Pumping of blood into systemic and pulmonary circulation, requiring sufficient myocardial contractility.

Blood Flow Dynamics

Fluid Dynamics Principles

Fluid in motion: Studied under fluid dynamics, focusing on pressure, flow rate, and fluid velocity.

Types of flow:

  • Streamline (Laminar) Flow: Characterized by smooth, non-crossing paths of fluid particles, minimal energy loss, and silent flow in blood vessels.

  • Turbulent Flow: Chaotic, irregular flow with significant energy loss; characterized by eddies, often seen in areas of arterial stenosis or high flow rates.

Equation of Continuity

Overview:

  • The principle states that for incompressible fluids, inflow equals outflow.

  • Continuity Equation:

    Q = ΔV / Δt, where Q is flow rate, A is cross-sectional area, and v is fluid velocity.

  • Derivation:

    A1v1 = A2v2; flow rates remain constant across varying vessel areas, demonstrating a key principle of hemodynamics.

Velocity and Vessel Area

Principle:

  • Decreased area = Increased velocity and vice versa; this is critical in understanding circulatory dynamics.Example:

  • Aorta: ~30 cm/s vs capillaries: ~1 mm/s; the capillary network's total area (~900 cm²) results in slower blood flow, facilitating optimal gas and nutrient exchange with tissues.

Effects of Atherosclerosis

Mechanism:

  • Narrowing of arteries by plaque build-up increases flow speed according to the Continuity Principle, which can increase the risk of turbulence and complications like thrombosis.Example Calculation:

  • For varying diameters and blood velocity:

    • Plaque-free artery: d1 = 1.1 cm -> v1 = 15 cm/s

    • Narrowed artery: d2 = 0.75 cm -> v2 calculated as 32 cm/s, showing how significant narrowing increases velocity and turbulence.

Turbulent Flow Criteria

Critical Speed:

  • Vcrit = (Constant) x (Viscosity) x (Density) x (Radius), a critical threshold beyond which laminar flow becomes turbulent, often linked to cardiovascular disorders.Reynolds Number:

  • For blood ~1000 indicates turbulence risk; monitoring flow speeds can help assess cardiovascular health and risks.Hemodynamic Changes:

  • Flow speed varies with the cardiac cycle, causing turbulence during phases like rapid ventricular ejection.

Conclusion

The cardiovascular system is an interconnected network relying on fluid dynamics principles to ensure effective blood circulation throughout the body, playing a critical role in overall health and response to various stresses.