The Shunt equation quantifies the extent to which

venous blood Venous blood is deoxygenated blood which travels from the peripheral blood vessels, through the venous system into the right atrium of the heart. Deoxygenated blood is then pumped by the right ventricle to the lungs via the pulmonary artery whic ...

bypasses

oxygenation Oxygenation may refer to: * Oxygenation (environmental), a measurement of dissolved oxygen concentration in soil or water * Oxygen saturation (medicine), the process by which concentrations of oxygen increase within a tissue * Water oxygenation, t ...

in the

capillaries A capillary is a small blood vessel from 5 to 10 micrometres (μm) in diameter. Capillaries are composed of only the tunica intima, consisting of a thin wall of simple squamous endothelial cells. They are the smallest blood vessels in the body: ...

of the

lung The lungs are the primary organs of the respiratory system in humans and most other animals, including some snails and a small number of fish. In mammals and most other vertebrates, two lungs are located near the backbone on either side of t ...

. “Shunt” and “

dead space ''Dead Space'' is a science fiction/horror fiction, horror media franchise created by Glen Schofield and Michael Condrey, developed by Visceral Games, and published and owned by Electronic Arts. The franchise's chronology is not presented in a lin ...

“ are terms used to describe conditions where either blood flow or ventilation do not interact with each other in the lung, as they should for efficient gas exchange to take place. These terms can also be used to describe areas or effects where blood flow and ventilation are not properly matched, though both may be present to varying degrees. Some references refer to “shunt-effect” or “dead space-effect” to designate the ventilation/perfusion mismatch states that are less extreme than absolute shunt or dead space. The following equation relates the percentage of blood flow that is not exposed to inhaled gas, called the shunt fraction

Q_s/Q_t

, to the content of oxygen in venous, arterial, and pulmonary capillary blood. :

Q_s/Q_t = (Cc_ - Ca_) / (Cc_ - Cv_)

:Where: :''Q_s'' = Pulmonary Physiologic Shunt (mL/min) :''Q_t'' = Cardiac Output (mL/min) :''C_CO2'' = End-pulmonary-capillary Oxygen Content :''C_aO2'' = Arterial oxygen content :C_VO2 = Mixed Venous Oxygen Content

Derivation

The blood entering the pulmonary system will have oxygen flux

Q_t \cdot Cv_

, where

Cv_

oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as wel ...

content of the venous blood and

Q_t

is the total

cardiac output In cardiac physiology, cardiac output (CO), also known as heart output and often denoted by the symbols Q, \dot Q, or \dot Q_ , edited by Catherine E. Williamson, Phillip Bennett is the volumetric flow rate of the heart's pumping output: t ...

. Similarly, the blood emerging from the pulmonary system will have oxygen flux

Q_t \cdot Ca_

, where

Ca_

content of the arterial blood. This will be made up of blood that bypassed the lungs (

Q_s

) and that which went through the pulmonary capillaries (

Q_c

). We can express this as

Q_t = Q_s + Q_c

. We can solve for

Q_c

Q_c = Q_t - Q_s

. If we add the oxygen content of Qs to Qc we get the oxygen content of Qt:

Q_t \cdot Ca_ = Q_s \cdot Cv_ + (Q_t - Q_s) \cdot Cc_

Substitute Qc as above, CcO2 is the oxygen content of pulmonary (alveolar) capillary blood.

Q_t \cdot Ca_ = Qs \cdot Cv_ + Q_t \cdot Cc_ - Qs \cdot Cc_

Multiply out the brackets.

Q_s \cdot Cc_ - Qs \cdot Cv_ = Q_t \cdot Cc_ - Qt \cdot Ca_

Get the Qs terms and the Qt terms on the same side.

Q_s \cdot (Cc_ - Cv_) = Q_t \cdot (Cc_ - Ca_)

Factor out the Q terms.

\dfrac   = \dfrac

Divide by Qt and by (CcO2 - CvO2).

References

{{DEFAULTSORT:Shunt Equation Physiology

Derivation

See also

References