If oxygen consumption rate increases 8x, how much do you think the cardiac output will increase?
a) 8x
b) More than 8x
c) Less than 8x
d) Not at all
Answer (2)
The Fick principle relates oxygen consumption, cardiac output, and oxygen content: V O 2 = CO × ( C a O 2 − C v O 2 ) .
If oxygen consumption increases 8x, then 8 V O 2 1 = C O 2 × ( C a O 2 − C v O 2 ′ ) .
The ratio of new to old cardiac output is C O 1 C O 2 = 8 × ( C a O 2 − C v O 2 ′ ) ( C a O 2 − C v O 2 ) .
Since venous oxygen content decreases with increased oxygen consumption, the cardiac output increases by less than 8x, so the answer is Less than 8x .
Explanation
Understanding the Fick Principle When the oxygen consumption rate increases, the cardiac output also needs to increase to meet the body's demands. The relationship between oxygen consumption ( V O 2 ), cardiac output ( CO ), arterial oxygen content ( C a O 2 ), and venous oxygen content ( C v O 2 ) is described by the Fick principle:
Applying the Fick Principle to the Problem V O 2 = CO × ( C a O 2 − C v O 2 )
If V O 2 increases by a factor of 8, we can write:
8 V O 2 1 = C O 2 × ( C a O 2 − C v O 2 ′ )
where V O 2 1 is the initial oxygen consumption, C O 2 is the new cardiac output, C a O 2 is the arterial oxygen content (assumed constant), and C v O 2 ′ is the new venous oxygen content.
Deriving the Relationship We want to find the factor by which the cardiac output increases, i.e., C O 2 / C O 1 , where C O 1 is the initial cardiac output. We have:
V O 2 1 = C O 1 × ( C a O 2 − C v O 2 )
8 V O 2 1 = C O 2 × ( C a O 2 − C v O 2 ′ )
Dividing the second equation by the first, we get:
8 = C O 1 C O 2 × ( C a O 2 − C v O 2 ) ( C a O 2 − C v O 2 ′ )
Analyzing the Venous Oxygen Content C O 1 C O 2 = 8 × ( C a O 2 − C v O 2 ′ ) ( C a O 2 − C v O 2 )
Now, consider the term ( C a O 2 − C v O 2 ′ ) ( C a O 2 − C v O 2 ) . When oxygen consumption increases, the body extracts more oxygen from the blood. This means that the venous oxygen content ( C v O 2 ′ ) will decrease. Therefore, ( C a O 2 − C v O 2 ′ ) will be greater than ( C a O 2 − C v O 2 ) .
Determining the Cardiac Output Increase Since (CaO_2 - CvO_2)"> ( C a O 2 − C v O 2 ′ ) > ( C a O 2 − C v O 2 ) , the fraction ( C a O 2 − C v O 2 ′ ) ( C a O 2 − C v O 2 ) will be less than 1. Therefore:
C O 1 C O 2 = 8 × a number less than 1
This implies that the cardiac output will increase by a factor less than 8.
Final Answer and Conclusion Therefore, the cardiac output will increase by less than 8x.
Examples
When you exercise, your muscles need more oxygen. If your oxygen consumption increases significantly, your heart pumps more blood to deliver that oxygen. This problem illustrates how the body adjusts cardiac output based on oxygen demand, showing the heart's efficiency in responding to physiological needs during physical activity.
As oxygen consumption increases by 8x, cardiac output will also increase, but not by the same factor due to physiological changes in the body. The increase in venous oxygen content means that the actual increase in cardiac output will be less than 8x. Therefore, the answer is c) Less than 8x.
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