Cardiovascular System Overview

Focus on Mechanical Work Done by the Heart

Date: January 2025Instructor: Kevin McGuigan

Recap of CVS5

Purpose: Ensure understanding of previous material covered in CVS5.

Viscosity of Fluids

Definition: Resistance to flow of a fluid.SI Units: Pascal-seconds (Pa.s), commonly referred to as Poise.Conversion: 1 Pa.s = 10 Poise.Typical viscosity at 20 degrees Celsius: ~10^-3 Pa.s.

Haematocrit Impact

Higher viscosity is directly proportional to Haematocrit ratio, meaning that as the proportion of red blood cells in the blood increases, the resistance to flow also increases, which can affect overall blood circulation and heart workload.

Blood Flow Dynamics

Blood near the vessel wall remains at rest (v = 0 m/s) due to frictional forces (viscosity). This stagnation can lead to turbulence in the central flow, impacting the efficiency of nutrient and oxygen delivery throughout the body.

Fluid Velocity Calculation

Average velocity (v) of fluid is half the maximum velocity in ideal flow conditions. Flow rate (Q) is derived from the Continuity Principle, stating that the product of the cross-sectional area and velocity at any point in a closed system remains constant (A1v1 = A2v2).

Poiseuille’s Equation

Q varies with the fourth power of the radius (r). If the radius is reduced by half, the flow rate decreases significantly (to one-sixteenth). This equation highlights the sensitivity of blood flow to vessel diameter.Q is inversely related to fluid viscosity and pipe length, emphasizing the role of both viscous drag and vessel dimensions in determining blood flow rates.

Impact of Deposits on Artery Radius

If the radius is reduced to one-third, the heart has to work 81 times harder to maintain blood flow, risking heart failure. This underscores the impact of conditions like atherosclerosis on cardiovascular health.

Blood Vessel Example Calculation

Given a blood vessel of length 0.1 m and radius 1.5x10^-3 m with a flow rate of 1.0 x 10^-7 m³/s, calculate pressure difference.Result: Pressure difference = 3 x 10^-3 N.s/m², which is crucial for understanding the driving forces behind circulation.

Mechanical Work Done by the Heart

Focus on work and energy expended in heart contractions.Instructor: Prof. Kevin McGuigan.

Learning Outcomes

• Define work by a mechanical pump.

• Calculate work done per cardiac contraction.

• Compare left and right ventricular work in cardiac cycle.

• State and apply Laplace’s Law to cardiovascular system.

Types of Pumps

• Vacuum Pump: Reduces pressure in a vessel.

• Force (Centrifugal) Pump: Increases pressure, used in infusions and closed circulation systems.

• Heart functions as a force pump, generating pressure to propel blood forward.

Heart Contraction Work

Each heartbeat pumps ~80 ml of blood.Work = Force x Distance = Pressure x Volume Pumped.This means that the efficiency of the heart is closely linked to the pressure it generates against the resistance of blood vessels.

Average Pressure in Ventricles

Left ventricle average pressure calculation: (120 + 80)/2 = 100 mm Hg.Right ventricle pressures: Systolic 25 mmHg and Diastolic 5 mmHg.

Cycle Timing and Power Calculation

Average pulse rate: 70 beats/minute.Time for one cycle: 60/70 seconds = 0.86 seconds.Understanding the timing of these cycles is essential for assessing heart function during stress testing and exercise.

Work and Power Output per Beat

Left ventricle expends ~1.1 joules of energy per cycle.Power output: Work done per cycle / Time.Result: ~1.28 W. This power output reflects the heart's efficiency in energy use during different activities.

Heart Efficiency

Average work done and power output are considered, noting that the heart only contracts for about one-third of the cycle.Peak power output is ~three times the average due to contraction timing, which indicates the heart’s ability to respond to increased demands for blood flow during physical activity.

Consequences of Hypertension

Heart must pump harder and faster, increasing power output while reducing energy for wall tension.Risk of heart enlargement and potential heart failure: Hypertension can cause the heart muscle to thicken, leading to a greater risk of cardiac events.

Hypertension Impact Summary

Increased heart workload leads to higher heart output, decreasing available energy for maintaining wall tension, risking heart failure. Maintaining optimal blood pressure is crucial for heart health.

Circulatory System Dynamics

Total flow rate can reach 4.0 liters/min.Calculation of pressure power output for hypertensive left ventricle: Result is ~1.33 W.

Laplace’s Law Overview

Discusses fluid dynamics in relation to pressure differences and flow rates, emphasizing the relationship between pressure, wall tension, and radius in cylindrical structures like blood vessels.

Pressure Gradient in Blood Vessels

Fluid flows from areas of higher pressure (P1) to lower pressure (P2), illustrating the fundamental principle of circulation as pressure gradients drive blood flow.

Transmural Pressure

Difference between inside (Pi) and outside (Po) pressures of blood vessels, which affects their structural integrity and ability to withstand internal pressures without collapsing.

Transmural Pressure Effect

Affects vessel bulging and is crucial for understanding vessel wall tension. High transmural pressure can lead to increased stress on vessel walls.

Laplace’s Law Application

For cylindrical membranes (blood vessels), how surface tension correlates with vessel radius.This relationship is important for understanding aneurysm formation and treatment.

Transmural Pressure in Blood Vessels

Comparison between aorta and capillary transmural pressures and corresponding tension requirements.

Capillary vs. Aorta Pressure

Aorta transmural pressure ~13,000 Pa vs capillary ~4,000 Pa; highlights differences due to vessel thickness and diameter, crucial for understanding systemic and microcirculatory pressures.

Tension Calculation Examples

Aorta: Tension required ~156 N/m; capillary tension required is much smaller at ~0.024 N/m due to size difference, underscoring the varied mechanical demands placed on different types of blood vessels.

Supporting Transmural Pressure

Capillaries do not require high surface tension to withstand pressure gradients, contrasting with the aorta and alveoli, indicating their role in efficient nutrient exchange without excessive pressure.

Contact Information

For more information, contact Prof. Kevin McGuigan via email.