Week 7 Haemodynamic Principles Lecture Notes

Haemodynamic Principles

Volumetric Flow Rate (Q)

• Volume of blood passing a point per unit of time, expressed in milliliters per minute or per second.

• Q is affected by:

  1. Difference in pressure

  2. Resistance to flow

• Formula: Q = \frac{\text{Pressure difference}}{\text{Resistance to flow}}

Pressure Difference

• A pressure difference is required for flow to occur.

• Fluids flow from areas of higher-pressure to lower-pressure; this is also called a pressure gradient.

• In the body, the heart creates the pressure difference (gradient).

• The greater the difference in pressure, the greater the flow rate (Q).

• Example: Pressure drops from 100 mmHg in the aorta to almost 0 mmHg in the right atrium.

Resistance to Flow

• Three main factors affect resistance to blood flow in a long, straight vessel:

  1. Viscosity of blood (\eta)

  2. Radius (r)

  3. Length (l)

• Poiseuille’s Formula: R = \frac{8l\eta}{\pi r^4}

Fluids and Viscosity (\eta)

• Viscosity: The resistance to flow in liquids due to the friction forces between the molecules.

• Highly temperature dependent.

• The viscosity of normal blood at 37°C is approximately 5 times that of water.

• Factors affecting the viscosity of blood include:

  • Temperature, such as hypothermia.

  • Pathologies, e.g., Polycythemia, Anemia, and plasma protein changes.

Poiseuille’s Law

• Assumes steady flow in long, straight tubes.

• Pressure difference is directly proportional to flow rate.

• Diameter is directly proportional to flow rate. (diameter increases, flow rate increases)

• Length is inversely proportional to flow rate. (length increases, flow rate decreases)

• Viscosity is inversely proportional to flow rate. (viscosity increases, flow rate decreases)

• Poiseuille Equation:

• 

Types of Flow

• Laminar Flow - Parabolic

  • Parallel, forward, streamlined blood flow. (Laminar=layer in Latin)

  • Parabolic flow: Faster in the center and slower toward the periphery.

  • Boundary layer: Blood adjacent to the vessel wall has frictional interaction with the wall, thus slowing velocity.

  • 

• Laminar Flow - Plug

  • Constant speed across the vessel.

  • Seen at entrance to a vessel but returns to parabolic flow.

  • 

• Laminar Flow - Disturbed

  • Blood flow still in a uniform direction but parallel streamlines are altered from their straight lines.

  • Boundary layer separation.

  • Plaque in a vessel or bifurcation

    

• Turbulent Flow

  • Disorganized blood flow.

  • No longer uniform direction.

  • Random and chaotic direction and velocity.

  • Usually caused by stenosis

    

Continuity Rule

• Volumetric flow rate must be constant before, within, and distal to a stenosis.

• Velocity has to increase if cross-sectional area decreases.

• Volumetric flow rate is equal to the average flow speed across the vessel, multiplied by the cross-sectional area of the vessel.

• Continuity Equation: Q = \overline{v} \times \text{area}

The Bernoulli Effect

• A pressure decrease due to high velocity at a stenosis.

• If velocity increases, pressure decreases.

• This pressure decrease allows the fluid to accelerate into the stenosis and decelerate out of it.

• As flow energy increases, pressure energy decreases.

• 

Pulsatile Flow

• In the heart and arterial circulation, pressure and flow velocity are constantly varied by the cardiac cycle.

• Pulsatile variations increase and decrease pressure and velocity.

• Vessels expand and contract with each cardiac cycle, constantly changing vessel radius.

In Summary

• A pressure difference is required for flow to occur.

• Poiseuille's law: The volumetric flow rate (mL/min) in a long straight tube is determined by the pressure difference (\DeltaP) and the resistance (R) to flow.

• Flow can be in the forms of plug, laminar, disturbed, or turbulent.

• Continuity rule: Volumetric flow rate must be constant before, within, and distal to a stenosis.

• The Bernoulli Effect states that pressure is lower at an area of increased velocity.