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 4^th 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 4^th 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”.

In larger vessels –

– Rise in hematocrit → Increases viscosity.

In smaller vessels

– Changes less compared to larger vessels.

Fahreus – Lindqvist effect:

Viscosity of flowing blood reduces as blood vessel diameter reduces.

At low flow rate:

Increased interaction time between RBCs & adjacent lamina.

Results in erythrocyte adherence increasing blood viscosity.

Causes “Rouleaux formation” –

RBC sticking together forming chains of several cells.

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 Important

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.

3. FLOW CHARACTERISTICS (LAMINAR vs TURBULENT FLOW):

“Critical velocity” –

– Limit beyond which flow velocity exceeds resulting in turbulent flow instead laminar.

– Most important determinant of blood flow turbulence.

Velocity is inversely proportional to total cross-sectional area.

– Thus, smaller vessels have laminar flow.

– Due to low velocity & large total cross-sectional area.

Reynold’s number(R):

Determines if tubular blood flow is laminar/turbulent.

Calculated by R=SDV/η.

– S – Fluid density.

– D – Tube diameter.

– V – Fluid velocity.

– η – Fluid viscosity.

If R exceeds 2000 – Turbulent flow.

Factors favoring turbulence (increasing R):

Increased blood density (S).

Increased vessel diameter (D).

Increased blood velocity (V).

4. BLOOD FLOW & VELOCITY:

Constant flow (Q) –

– Blood flow velocity is inversely related to vessels area/square of vessel radius.

– As area =2Πr2.

– where r is radius.

5. Axial Streaming:

At high flow rate/high shear rate,