Principles Of Blood Flow

PRINCIPLES OF BLOOD FLOW

PHYSICAL PRINCIPLES APPLICABLE TO BLOOD FLOW & RESISTANCE:
1. OHM’S LAW:

• According to Ohm’s law,
• Blood flow (Q) = Pressure gradient(ΔP) / Resistance(R).
• In exchange Ohm’s law for flow of electric current.
• Flow of current (i) = Electromotive force (E) / Electrical resistance (R).

2. POISEUILLE’S LAW:

• Also referred as “Hagen-Poiseille’s Law”.
• Poiseuille’s equation states, 
• Q = P1 – P2 * { (Π r4) / (8 η L)}
• Q – Flow rate
• (P1 – P2) – Pressure difference across vessel (provided P1 > P2).
• η – Blood viscosity.
• r – Radius.
• L – Tube length.

If parameter values remains constant, 

• Blood flow is directly proportional to 4th power of radius.
• Resistance of vessel to blood flow can be calculated by combining Ohm’s law with Poiseuille’s equation.
• By substituting values of Q from Poiseuille’s law in Ohm’s law.

Implying, resistance is mainly affected by,

• Blood vessel radius,
• Vasodilatation/vasoconstriction.
• Thus ultimately, if parameter values remain constant, 
• Resistance to blood flow is inversely proportional to 4th power of radius.

Arterioles are chief site of vascular resistance due to,

• Presence of smooth muscle
• Less elastic tissue in their walls.
• Also sympathetic innervation contracting smooth muscles.

3. FLOW CHARACTERISTICS (LAMINAR vs TURBULENT FLOW):

• Blood flow through blood vessels is mainly laminar.
• Laminar blood flow is noiseless.
• Turbulent blood flow generates vibrations.
• Can be heard over artery by stethoscope.
• E.g., Korotkoff sounds while recording BP or heart murmurs.

Reynold’s number(R):

• Determines if tubular fluid flow is laminar or turbulent 

Calculated by, 

• R=SDV/η.
• S – Fluid density.
• D – Tube diameter.
• V – Fluid velocity.
• η – Fluid viscosity.
• If R less than 2000 – Laminar flow.
• If R exceeds 2000 – Turbulent flow.

Factors favoring turbulence (increasing R):

• Increased Blood density (S).
• Increased vessel diameter (D).
• Increased blood velocity (V).
• Decreased blood viscosity (η).

“Critical velocity” – 

• Limit beyond which flow velocity exceeds resulting in turbulent flow instead laminar.
• Most important determinant of blood flow turbulence.
• Causes of increased critical velocity – 
• Artery constriction by atherosclerosis.
• External pressure application. 
• Eg: By inflatable cuff of sphygmomanometer.

Velocity is inversely proportional to total cross-sectional area.

• Hence, smaller vessels have laminar flow.
• Due to, 
• Low velocity.
• Large total cross-sectional area.

4. BLOOD FLOW & VELOCITY: 

Blood flow (Q) – 

• Volume flow per unit time (cm3/s).

Blood flow Velocity (V) – 

• Displacement of blood per unit time (cm/s).

Constant flow (Q) – 

• Blood flow velocity is inversely related to vessels area/square of vessel radius.
• As area =2Πr2, 
• Where r is radius.

5. BLOOD FLOW & VISCOSITY:

• Viscosity – 
• Internal friction or lack of slipperiness between adjacent lamina.
• Factors affecting – 
• Shear rate/Velocity gradient
• Hematocrit value 
• Temperature.

5a. Shear rate/velocity gradient:

• Increased velocity gradient – Decreased blood viscosity & vice-versa.
• At high flow rates – Lower viscosity.
• At low flow rates – Higher viscosity.

Axial Streaming:

• At high flow rate/high shear rate,
• RBCs occupy tube’s central axis.
• Also moves along blood vessel long axis with maximum velocity.
• Two important consequences of axial streaming: 
• Plasma skimming.
• Fahreus-Lindqvist effect.

Plasma skimming:

• Due to axial streaming cells occupy central axis leaving thin peripheral plasma layer.
• Hence, small branches of large vessels carry more plasma than cells.
• Because plasma’s cell-free zone lies at periphery of flowing blood→> this enters small vessels.

Forms basis for 2 important facts,

• “Hematocrit of capillary blood is about 25% lower than the whole-body hematocrit”.
• “Hematocrit changes having relatively lower effect on peripheral resistance unless changes are large”.

5b. Hematocrit value:

• Variation in hematocrit – Major factor changing blood viscosity.

5c. Temperature:

• Cooling increases blood viscosity.
• Critical closing pressure/Zero flow pressure:
• Pressure gradient at which blood flow through a vessel reduces to zero.

5d. Effect of increased viscosity:

• Decreased plasma skimming.
• Rouleaux formation.
• Increased capillary RBC count.

6. LAW OF LAPLACE:

• States that tension (T) in wall of a cylinder is equal to product of transmural pressure (P) & radius (r) divided by wall thickness (w).
• I.e., T = Pr/w.

7. Perfusion pressure:

• According to Ohm’s law, blood vessel flow depends on,
• Pressure difference/pressure gradient at two ends of vessels & vascular resistance.
• Pressure gradient – Driving force.
• Resistance – Opposing force.

Perfusion pressure – 

• Pressure difference between arterial & venous pressure.
• Perfusion – Driving force for blood flow through an organ.

Hence, 

• Blood flow through an organ is directly proportional to perfusion pressure
• Inversely proportional to resistance.

Eg: Renal blood flow – 

• Determined by renal artery pressure, renal vein pressure, & renal vascular resistance.

Exam Question

PRINCIPLES OF BLOOD FLOW

1. OHM’S LAW:

• According to Ohm’s law,
• Blood flow (Q) – Pressure gradient(ΔP) / Resistance(R).
• In exchange Ohm’s law for flow of electric current.
• Flow of current (i) – Electromotive force (E) / Electrical resistance (R).

2. POISEUILLE’S LAW/HAGEN-POISEILLE’S LAW:

• Poiseuille’s equation states,
• Q = P1 – P2 * { (Π r4) / (8 η L)}; 
• Q – Flow rate.
• If everything else remains constant,
• Blood flow is directly proportional to 4th power of radius.
• Resistance to blood flow is inversely proportional to 4th power of radius.
• Arterioles are chief site of vascular resistance.