Vessel fluid dynamics

Permeability

Permeability – Its relation to membrane characteristics and diffusion coefficients (knowledge of the detail of Fick’s law is NOT required)

Curriculum

Passive diffusion – movement down a concentration gradient – Doesn’t need any transporters. So not saturable. The simple diffusion is linear, if you increase concentration on one side, the diffusion increases linearly.

Facilitated diffusion – It utilizes transport channels and gradients created by another active transport system. It does not utilize the energy directly. (Ex Sodium gradient created by Sodium pump is used by Glucose to enter into cells via facilitated diffusion). – As it uses channels, it can get saturated, unlike passive diffusion.

Active transport – Utilizes energy directly to move an ion across the cell (against the concentration gradient). – Eg: Sodium potassium ATPase.

The rate of diffusion of a substance 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 – measure of ease for a substance to diffuse.
Diffusion depends on temperature, solvent viscosity and the size of the molecule.

The permeability is related to the membrane thickness and composition, and the diffusion coefficient of the substance.

Tube flow

Tube flow – 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 (knowledge of the detail of Poiseuille’s law is NOT required)

Curriculum

Flow across a tube depends on the pressure difference across at 2 ends and the resistance to flow.
Resistance is inversely proportional to diameter of the tube and directly proportional viscosity of the fluid flowing and Length of tube:
This is Poiseuille’s law.
We do not need to know full details of the law, but to summarize, flow ∝ (radius)4.
In other words, small changes in radius will impact a large changes in flow.

Example – If we reduce the diameter from 10cm to 8cm,
Initial flow :104 = 10000;
New flow in reduced diameter tube : 84 = 4096;

So, constriction of an artery by 20% (10cm to 8cm) will decrease the flow by ∼60%!! (10000 to 4096)

Viscosity.

Plasma and water will have similar viscosity (simply speaking thickness), but as blood contains cells (mostly RBCs) the viscosity is higher. Any fluid with higher viscosity will flow slower in vessels. Imagine pouring water into one tube and honey into the other, which one flows faster? Water.
Anything that increases the cell numbers in blood, e.g. polycythaemia (increased RBC), can affect the blood flow – slowing down.
Similarly, if too much of IV fluids are given, blood gets diluted and viscosity drops.

Laminar and turbulent flow.

Laminar Vs turbulent flow

When some fluid or air is flowing through a tube, frictional forces at the periphery will exert a dragging force on them. This will result in faster flowing speeds in the center compared to the periphery. This is known as laminar flow. (In the image above, dark red lines will move faster than green lines)
The blood cells tend to accumulate around the center – this is called axial streaming.

Large arteries will have more faster flows. When flow speed increases or if there is branching (as shown in image above), the flow may become turbulent. Turbulence causes higher resistance to flow.
Turbulence is the reason we hear lung sounds (e.g. wheezing in asthma), cardiac murmurs.
Same thing applies to Korotkoff sounds heard while measuring blood pressure.

When a few tubes or arteries are connected in series, the resistance adds up, where as if they are connected in a parallel circuit, the extra paths of flow will reduce the total resistance (fetal circulation is in parallel to the maternal).

Wall tension

Wall tension – Its relation to tubal wall thickness and radius.

Clinical implications of disruption to this relationship e.g. dilated cardiomyopathy.

Curriculum

Pressure acting on the wall of a tube (transmural pressure) tries to extend it (increase the diameter), and the wall tension will increase accordingly.
Laplace’s law says Pt =Tw/r
Pt – transmural pressure
T – wall tension
w – wall thickness and r is the radius.

Based on this law, the radius is inversely proportional to wall tension (Smaller bubble will have more pressure on walls than a larger bubble and will collapse into the larger bubble if they are joined).

A dilated heart (e.g. heart failure in DCMP – dilated cardiomyopathy) needs to exert more wall tension (contractile force) to generate ventricular pressure.

Clinical pearl
Lesson tags: Fick's law, laminar flow, Laplace law, permeability, poiseulle's law, turbulent flow
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