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Cardiac output

Cardiac output is the measurement of blood flow from the heart through the ventricles, and is usually measured in liters per minute. Any factor that causes cardiac output to increase, by elevating heart rate or stroke volume or both, will elevate blood pressure and promote blood flow. These factors include sympathetic stimulation, the catecholamines epinephrine and norepinephrine, thyroid hormones, and increased calcium ion levels. Conversely, any factor that decreases cardiac output, by decreasing heart rate or stroke volume or both, will decrease arterial pressure and blood flow. These factors include parasympathetic stimulation, elevated or decreased potassium ion levels, decreased calcium levels, anoxia, and acidosis.

Compliance

Compliance is the ability of any compartment to expand to accommodate increased content. A metal pipe, for example, is not compliant, whereas a balloon is. The greater the compliance of an artery, the more effectively it is able to expand to accommodate surges in blood flow without increased resistance or blood pressure. Veins are more compliant than arteries and can expand to hold more blood. When vascular disease causes stiffening of arteries, compliance is reduced and resistance to blood flow is increased. The result is more turbulence, higher pressure within the vessel, and reduced blood flow. This increases the work of the heart.

A mathematical approach to factors affecting blood flow

Jean Louis Marie Poiseuille was a French physician and physiologist who devised a mathematical equation describing blood flow and its relationship to known parameters. The same equation also applies to engineering studies of the flow of fluids. Although understanding the math behind the relationships among the factors affecting blood flow is not necessary to understand blood flow, it can help solidify an understanding of their relationships. Please note that even if the equation looks intimidating, breaking it down into its components and following the relationships will make these relationships clearer, even if you are weak in math. Focus on the three critical variables: radius (r), vessel length (λ), and viscosity (η).

Poiseuille’s equation:

Blood flow =  π ΔP r 4 8ηλ MathType@MTEF@5@5@+=feaagyart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOqaiaabYgacaqGVbGaae4BaiaabsgacaqGGaGaaeOzaiaabYgacaqGVbGaae4DaiaabccacaqG9aGaaeiiamaalaaabaGaaeiWdiaabccacaqGuoGaaeiuaiaabccacaqGYbWaaWbaaSqabeaacaqG0aaaaaGcbaGaaeioaiaabE7acaqG7oaaaaaa@4A84@
  • π is the Greek letter pi, used to represent the mathematical constant that is the ratio of a circle’s circumference to its diameter. It may commonly be represented as 3.14, although the actual number extends to infinity.
  • ΔP represents the difference in pressure.
  • r 4 is the radius (one-half of the diameter) of the vessel to the fourth power.
  • η is the Greek letter eta and represents the viscosity of the blood.
  • λ is the Greek letter lambda and represents the length of a blood vessel.

One of several things this equation allows us to do is calculate the resistance in the vascular system. Normally this value is extremely difficult to measure, but it can be calculated from this known relationship:

Blood flow =  ΔP Resistance MathType@MTEF@5@5@+=feaagyart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOqaiaabYgacaqGVbGaae4BaiaabsgacaqGGaGaaeOzaiaabYgacaqGVbGaae4DaiaabccacaqG9aGaaeiiamaalaaabaGaaeiLdiaabcfaaeaacaqGsbGaaeyzaiaabohacaqGPbGaae4CaiaabshacaqGHbGaaeOBaiaabogacaqGLbaaaaaa@4C0B@

If we rearrange this slightly,

Resistance =  ΔP Blood flow MathType@MTEF@5@5@+=feaagyart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOuaiaabwgacaqGZbGaaeyAaiaabohacaqG0bGaaeyyaiaab6gacaqGJbGaaeyzaiaabccacaqG9aGaaeiiamaalaaabaGaaeiLdiaabcfaaeaacaqGcbGaaeiBaiaab+gacaqGVbGaaeizaiaabccacaqGMbGaaeiBaiaab+gacaqG3baaaaaa@4C0B@

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Source:  OpenStax, Anatomy & Physiology. OpenStax CNX. Feb 04, 2016 Download for free at http://legacy.cnx.org/content/col11496/1.8
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