Hemodynamics is the sum of forces that govern blood flow. In the last post, we saw how pressure and resistance could affect blood flow through the blood vessels. The Ohm’s law helped us see how a change in pressure difference and low resistance power blood flow.
In this post, we will see how turbulent flow, Poiseuille’s law and the arrangement of the blood vessels affect vascular supply.
Reynolds Number
Blood flow may turn from linear to turbulent when it passes through obstruction on its path. Regardless of the change of type of flow, the primary aim is to ensure blood, nutrient and oxygen are supplied to the target tissue. In turbulent flow, the flow is no long streamlined and eddy currents may form. Due to the presence of eddy currents, turbulent flow has more friction, reducing the rate of blood supply to a tissue compared to a linear flow.
The following factors affect Reynolds Number.
Re= (v×d×ρ)⁄η
Where Re= Reynolds number
V= velocity
d= diameter of the blood vessel
ρ= density
η= viscosity of the blood.
- When the velocity of blood flow is high, the velocity of blood flow will be high leading to a higher Reynold number.
- When the diameter of the blood vessel is high as in large arteries, it contributes to a higher Reynolds number.
- When the density of the blood vessel is high, the Reynold number will also be high.
- The blood viscosity is inversely proportional to the Reynolds number. A high blood viscosity contributes to a low Reynolds number and a laminar flow. A low viscosity leads to a high Reynolds number leads to a high Reynolds number because there’s no impediment to blood flow that a high hematocrit would have posed.
At low Reynold numbers blood flow is linear while at high Reynold numbers, blood flow is turbulent with greater resistance to flow.
Conductance and Resistance
Conductance is the blood flow through a blood vessel at a given pressure difference. This value is inversely proportional to the resistance of the blood vessel.
Conductance = 1⁄resistance
When the resistance of the blood vessel is high, conductance or blood flow through the blood vessel will be reduced.
The change of conductance relating to the diameter of the blood vessel is also an important factor. When the blood vessel is dilated, blood flow is increased. When the blood vessel is constricted, blood flow is reduced. This relationship is expressed as:
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Small changes in vascular diameter leads to a tremendous increase or decrease to blood flow
conductance α diameter 4
This relationship shows how a small change in the diameter of a blood vessel leads to an increase in blood conductance.
For example, any increase in blood vessel diameter leads to a proportional fourth power of an increase in conductance even if the pressure difference stays the same. Using this hemodynamic principle the blood vessels are able to constrict and dilate in response to nervous system stimulation to control blood flow and blood pressure to a high degree.
Poiseuille’s law
Poiseuille’s law is an important hemodynamic factor that explains further the relationship between blood vessel diameter change and conductance.
F= ΔP r4⁄8ηl
Where F= this is the rate of blood flow through a blood vessel.
ΔP is the change in pressure at both ends of a blood vessel.
r is the radius of the blood vessel
l= this is the length of the blood vessel
η= this is the blood viscosity
In this equation, the relationship between blood flow and the fourth power of the radius of a blood vessel again shows how much a little increase in radius causes a corresponding fourth power increase in conductance.
The length of the blood vessels is inversely proportional to the blood flow. A longer blood vessel leads to a slower rate of flow and vice versa.
A high viscosity has the propensity to also slow down blood flow considerably while a change in pressure increases blood flow.
Vascular circuits and their effect on blood flow.
When blood is pumped out of the the heart to the aorta, it enters through the systemic circulation to blood vessels arranged in series or parallel.when blood flows through the arteries→arterioles→capillaries→venules→veins, it is almost always in series. Just like in physics parallel and series circuits, blood flow through a serially arranged vascular circuit is the same in all vessels.
Blood flow in series and in parallel through the systemic and pulmonary circulation
The total resistance is also a sum of all the resistance in each vessel.
Rtotal= R1+R2+R3
But for vessels arranged in parallel, it is different.
The advantage of a parallel arrangement means that the blood vessels are extensively distributed to supply each tissue, and each tissue can control the blood supply to it.
Due to the ‘individual’ nature of a parallel connection, it’s resistance, and blood flow to each vessel are calculated individually rather than in summation like in series.
1⁄Rtotal= 1⁄R1+ 1⁄R2+ 1⁄R3
Ohm’s law, Poiseuille’s law, Reynolds Law and the others discussed are just some of the guiding principles explaining how blood flow and subsequently oxygen and nutrient supply to a tissue is affected.
References
Guyton, Arthur C, and John Hall, Textbook of Medical Physiology. Elsevier, 2000.
Hemodynamics
Reynolds number