Vessel fluid dynamics

Permeability

[box type=”download”]  Its relation to membrane characteristics and diffusion coefficients  Note: knowledge of the detail of Fick’s law is NOT required [/box]

Bulk flow simply means transport with the carrying medium (blood, air).
Passive diffusion refers to movement down a concentration gradient.
The rate of diffusion in a solution is described by Fick’s law:
Directly proportional to the difference in concentration and surface area.
Inversely proportional to the distance.
Diffusion coefficient, a measure of how easy it is for the substance to diffuse (related to temperature, solvent viscosity and the size of the molecule).
The permeability (p) is related to the membrane thickness and composition, and the diffusion coefficient of the substance.

Tube flow

[box type=”download”]  Its relation to pressure differences, tube length and radius, and substance viscosity  Implication of small changes in radius upon flow rate  Laminar vs turbulent flow and the clinical implications of turbulence within a vessel  Note: knowledge of the detail of Poiseuille’s law is NOT required[/box]

Flow through a tube is dependent on the pressure difference across the ends and the resistance to flow.
Resistance is inversely proportional to diameter of the tube and directly proportional viscosity of the fluid and Length of tube:
This is Poiseuille’s law.
To sumarise, flow ∝ (radius)4: Therefore, small changes in radius have a large effect on flow (constriction of an
artery by 20% will decrease the flow by ∼60%.)

Viscosity.

Plasma has a similar viscosity to water, but blood contains cells (mostly RBCs) which increase the viscosity. Changes in cell number, e.g. polycythaemia (increased RBC), can affect the blood flow.

Laminar and turbulent flow.

Frictional forces at the sides of a tube cause drag on the fluid touching them.
So, the flow is greatest at the centre. This is termed laminar flow.
The blood cells tend to accumulate towards the centre (axial streaming).
In small vessels, this effectively reduces the blood viscosity and minimizes the resistance (the Fåhraeus–Lindqvist effect).
At high velocities, especially in large arteries and branches, the flow may become turbulent, increasing the resistance. Turbulence is heard as lung sounds (e.g. wheezing in asthma), cardiac murmurs and when measuring blood pressure (Korotkoff sounds).
Flow through a series of tubes is restricted by the resistance of each tube and the total resistance is the sum of the resistances.
In a parallel circuit, the addition of extra paths reduces the total resistance.
Although the resistance of individual capillaries or terminal bronchioles is high (small radius, Poiseuille’s law), the huge number of them in parallel means that their contribution to the total resistance of the cardiovascular and respiratory systems is comparatively small.

Wall tension

[box type=”download”]  Its relation to tubal wall thickness and radius  Clinical implications of disruption to this relationship e.g. dilated cardiomyopathy[/box]

Pressure across the wall of a flexible tube (transmural pressure) tends to extend it, and increases wall
tension.
This can be described by Laplace’s law: Pt =Tw/r
where Pt is the transmural pressure, T is the wall tension, w is the wall thickness and r is the radius.
Thus, a small bubble with the same wall tension as a larger bubble will contain a greater pressure, and will collapse into the larger bubble if they are joined.
Laplace’s law also means that a large dilated heart (e.g. heart failure) has to develop more wall tension (contractile force) in order to obtain the same ventricular pressure, making it less efficient.

 

Lesson tags: axial streaming, diffusion coefficient, Fick's law, korotkoff sounds, laminar flow, Laplace law, parallel, permeability, poiseulle's law, series, transmural pressure, turbulent flow, viscosity, wall tension
Back to: Physiology > Basic cellular physiology