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**Physiology of blood flow, resistance and velocity:** Blood flow, resistance and velocity and the factors affecting them are interrelated to each other. Changes are seen with physiological and pathological conditions and aging. It is important to understand the relationships between various factors rather than memorising the formulas per se.

Velocity of blood flow means how fast the blood is flowing through the circulatory system. Velocity is expressed as distance per unit time e.g. cm/sec. It has the following formula:

**Velocity of blood flow** = Flow/cross-sectional area

Flow simply means how much blood is flowing per unit time like e.g. ml/sec. Blood vessels are circular in cross-section so area can be calculated by PiR2. Since capillaries are widely distributed, they have the largest area of all blood vessel types in the circulatory system. According to the equation, increasing the area reduces the velocity. As capillaries have the biggest surface area, blood flows through the capillaries at the lowest velocity in the CVS. Aorta has the highest velocity of flow.

Flow is affected by multiple factors, mainly pressure gradient and resistance. Pressure gradient is simply the difference in pressure between the starting and endpoints of the system. Higher the gradient more is the flow and vice versa. Blood flows from high to low pressure.

An analogous form of Ohm’s law applied to the CVS is as follows:

**Delta P** **= Q X R**

where delta P is the pressure gradient, Q is the blood flow and R is the resistance in the system. In other words, if we are looking at the average blood pressure it can be determined as a product of cardiac output and total peripheral resistance or TPR or systemic vascular resistance (SVR). TPR is determined mainly by the arterioles. Constricted arterioles equals increased TPR and dilated arterioles equals decreased TPR.

Resistance to blood flow and its relation to length, radius and viscosity is stated by the Poiseuille’s equation as follows:

**R = 8nl/pi r4.**

Where R is the resistance , n is the viscosity, l is the length of the blood vessel and r is the radius of the blood vessel. Radius will correspond to the diameter as diameter = 2 x radius. Resistance is directly proportional to the viscosity and length and indirectly proportional to radius/ diameter. The most powerful factor here is the radius as it affects the resistance by a factor raised to four! In other words, reducing the radius by ¼ will increase the resistance by 256 times!

**Series and parallel resistance:** Major blood vessels branching out from the aorta are arranged in a parallel network to each other whereas within an organ, the blood vessels and their branches are arranged in-series plus in-parallel. For example, renal artery will divide into 4-5 branches which will branch out further into segmental and interlobar branches. Each of the segmental branches will be in-parallel, while an individual segmental artery will be in series with it’s branch interlobar artery.

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 system’s resistance as a whole will increase. By contrast, the total resistance in a parallel system is less than any of the individual resistances. In nature, it helps maintain blood flow across all the major blood vessels with no pressure loss.

Adding a new segment to a parallel system, despite technically being considered as adding a new individual resistance, will decrease the total resistance in the system as 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 the total resistance also increases because there is less volume.

Notably, large blood vessels have less impact on the 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 laminar, meaning the blood in the center of the blood vessel flows at a higher velocity than the blood close to the vessel wall. This gives rise to a parabolic profile. When, for any reason, laminar flow is disrupted, then the flow becomes turbulent, e.g., over atherosclerotic plaques, over valves, etc. The Reynolds number gives the degree of turbulence. A Reynolds number less than 2000 is seen in laminar flow; greater than 3000 indicates turbulent flow.

Turbulence is increased when the blood is thinner, like in any cause of reduced hematocrit or anemia. This is why functional murmurs can be heard in anemic patients. Stenosis caused by atherosclerosis or thromi leads to turbulent flow as the local velocity is increased, e.g., bruit in renal or carotid artery stenosis.

**Compliance and capacitance of blood vessels:** Compliance or capacitance is stated as the change in the volume of a blood vessel divided by change in pressure within the vessel. If a vessel has greater compliance then it can hold comparatively larger volumes of blood without increasing it’s pressure significantly. It is given by the formula C = V/P, where C is the compliance, V is the volume of blood in the blood vessel while P is the pressure in the vessel. In CVS, veins are also called capacitance vessels as they can hold a greater volume of blood at lower pressures. If we plot a graph of V on the Y axis and P on the X axis, then the slope is compliance. Steeper the slope, higher is the compliance. With aging, blood vessels become less compliant.

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