Physiology of blood flow, resistance and velocity: Blood flow, resistance, and velocity are closely linked. They change with normal physiology, disease, and aging. It’s more useful to understand how these factors relate to each other than to memorize formulas.
Velocity of blood flow means how fast blood moves through the circulatory system. Velocity is expressed as distance per unit time (e.g., cm/sec). It can be described by:
Velocity of blood flow = Flow/cross-sectional area
Flow means the volume of blood moving per unit time (e.g., ml/sec). Blood vessels are circular in cross-section, so area can be calculated as PiR2. Because capillaries are widely distributed, they have the largest total cross-sectional area of all blood vessel types in the circulatory system. From the equation, increasing cross-sectional area decreases velocity. Since capillaries have the greatest total area, blood flows through capillaries at the lowest velocity in the CVS. The aorta has the highest velocity of flow.
Flow is affected by multiple factors, mainly the pressure gradient and resistance. The pressure gradient is the difference in pressure between the start and end points of the system. The higher the gradient, the greater the flow (and vice versa). Blood flows from high pressure to low pressure.
An analogous form of Ohm’s law applied to the CVS is:
Delta P = Q X R
where delta P is the pressure gradient, Q is blood flow, and R is resistance in the system. In other words, average blood pressure can be described as the product of cardiac output and total peripheral resistance (TPR), also called systemic vascular resistance (SVR). TPR is determined mainly by the arterioles:
Resistance to blood flow, and its relationship to length, radius, and viscosity, is described by Poiseuille’s equation:
R = 8nl/pi r4.
Where R is resistance, n is viscosity, l is the length of the blood vessel, and r is the radius of the blood vessel. Radius relates to diameter as diameter = 2 x radius. Resistance is:
The most powerful factor here is radius, because it affects resistance to the fourth power. In other words, reducing the radius by ¼ increases resistance by 256 times.
Series and parallel resistance: Major blood vessels branching from the aorta are arranged in a parallel network, whereas within an organ, blood vessels and their branches are arranged in-series plus in-parallel. For example, the renal artery divides into 4-5 branches, which branch further into segmental and interlobar branches. Each segmental branch is in-parallel with the others, while an individual segmental artery is in series with its interlobar branch.
The total resistance in a series system is the sum of the individual resistances. So, if you increase the resistance of any one segment, the total system resistance increases. By contrast, the total resistance in a parallel system is less than any of the individual resistances. In nature, this helps maintain blood flow across all the major blood vessels with no pressure loss.
Adding a new segment to a parallel system (even though it adds a new individual resistance) decreases the total resistance in the system because there is more total volume for blood flow. Similarly, in a parallel system, if the resistance of an individual vessel increases (e.g., plaques narrow a vessel) or if a segment is removed, then total resistance increases because there is less volume.
Notably, large blood vessels have less impact on total resistance compared to arterioles. [Co-relate that with the protocol of invasive interventions only when coronary stenosis (big vessel) is above 70%.]
Turbulence: Blood flow is normally laminar, meaning blood in the center of the vessel flows at a higher velocity than blood near the vessel wall. This produces a parabolic velocity profile. If laminar flow is disrupted, flow becomes turbulent (e.g., over atherosclerotic plaques, across valves, etc.). The Reynolds number indicates the degree of turbulence:
Turbulence increases when blood is thinner, such as with reduced hematocrit or anemia. This is why functional murmurs can be heard in anemic patients. Stenosis caused by atherosclerosis or thromi also leads to turbulent flow because local velocity increases (e.g., a bruit in renal or carotid artery stenosis).
Compliance and capacitance of blood vessels: Compliance (capacitance) is the change in vessel volume divided by the change in pressure within the vessel. A vessel with greater compliance can hold a larger volume of blood with a smaller rise in pressure. It is given by C = V/P, where C is compliance, V is the volume of blood in the vessel, and P is the pressure in the vessel.
In the CVS, veins are called capacitance vessels because they can hold a greater volume of blood at lower pressures. If you plot V on the Y axis and P on the X axis, the slope of the graph represents compliance: the steeper the slope, the higher the compliance. With aging, blood vessels become less compliant.
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