1.3 Biophysics of pressure, flow and resistance

Basic principles of circulatory function

  • Primary function: Deliver oxygen and nutrients, remove waste

  • Driving force: Circulatory flow is driven by a pressure gradient generated by the heart.

Flow patterns

Laminar Flow

  • Definition

    • Blood flows in parallel layers (streamlines) with no mixing between layers

  • Velocity profile

    • Highest in the centre of vessel

    • Zero at vessel wall (due to friction)

  • Normal

    • Occurs in most of the circulatory system under physiological conditions

  • Efficient

    • Low resistance, low energy cost

    • Predictable flow

  • Clinical importance

    • Maintains quiet, smooth blood movement

Turbulent flow

  • Definition

    • Disordered, swirling flow with cross-stream mixing of layers

  • Occurs when

    • Flow velocity is too high

    • Blood passes through obstructions, sharp bends, or narrowings

    • Surface is rough (e.g. atherosclerosis plaques)

  • Increased energy demand

    • Turbulence = ↑ Resistance = ↑ work for the heart

  • Can cause murmurs

    • Turbulent flow is audible on auscultation (e.g. valvular stenosis)

Interrelationship between pressure, flow and resistance

  • Ohm’s law for circulation:

    • Flow (Q) = Change in pressure (P) / Resistance (R)

    • Flow is directly proportional to the pressure gradient

    • Flow is inversely proportional to resistance

Vascular resistance and conductance

Vascular resistance (R)

  • Defined as the impediment to blood flow within vessels

  • Factors influencing resistance:

    1. Vessel diameter (most significant; smaller radius → higher R)

    2. Vessel length (longer → higher R)

    3. Blood viscocity

    4. Network organisation (e.g. serial vs parallel)

    5. External compression forces (e.g. muscle contraction)

Vascular conductance (G)

  • Defined as the ease of blood flow through a vessel at a given pressure

  • It is the inverse of resistance:

    • Conductance (G) = 1/R

  • Highly sensitive to vessel radius:

    • Conductance ∝ diameter4

Fluid dynamic applied: Poiseuille’s law

  • flow=π×ΔP×r48×η×lflow=\frac{\pi\times\Delta P\times r4}{8\times\eta\times l}

  • Where

    • ΔP = Pressure difference

    • r = Radius of vessel

    • η = Viscosity of blood

    • l = Length of vessel

Reynolds number and turbulence

  • Reynolds number (Re) = v⋅d⋅ρη\frac{v\cdot d\cdot\rho}{\eta}

  • Describes the likelihood of turbulent flow:

    • High Re → more likely turbulent

    • Turbulence ↑ resistance and energy demands