Questions about the Circulatory section please help!

[happily123]

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1. I have in my notes that if you increase the diameter of an artery by a factor of 4, then peripheral resistance should decrease by a factor of 4- I don't understand this. Can someone clarify please?

2. What is the difference between cardiac AP and auto rhythmic cells?

Thank you!

 

[Cawolf]

1. Resistance is proportional to 1/r^4 (Poiseuille's law).

So if you increase the diameter (radius) by 4 one could set a ratio.

Resistance'/Resistance = R'/R

R'/R = (1/r'^4)/(1/r^4)

=r^4/r'^4

=r^4/(4r)^4 = 1/256

The resistance would actually only be 1/256 of the original resistance with an increase in diameter of 4x.

2. I don't understand your question.

Action potential vs auto-rhythmicity? ?

 

[happily123]

1. Resistance is proportional to 1/r^4 (Poiseuille's law).

So if you increase the diameter (radius) by 4 one could set a ratio.

Resistance'/Resistance = R'/R

R'/R = (1/r'^4)/(1/r^4)

=r^4/r'^4

=r^4/(4r)^4 = 1/256

The resistance would actually only be 1/256 of the original resistance with an increase in diameter of 4x.

2. I don't understand your question.

Action potential vs auto-rhythmicity? ?

1. So when they ask questions about the effect of diameter on resistance, the formula is know is R=1/r^4?
2. I got it thank you!

 

[Cawolf]

Poiseuille's law is specifically for flow through a closed tube and is the best approximation for quantitative values.

I suggest looking up the entire formula and understanding the overall effects of radius, length, viscosity, and pressure differential - but I do not believe memorizing the formula is important.

In general you are right, but it is not equal to 1/r^4, simply proportional to.

R ∝ 1/r^4

 

[erythrocyte666]

1. I have in my notes that if you increase the diameter of an artery by a factor of 4, then peripheral resistance should decrease by a factor of 4- I don't understand this. Can someone clarify please?

2. What is the difference between cardiac AP and auto rhythmic cells?

Thank you!

As for # 2, cardiac AP is distinct from auto rhythmic cells b/c they have a plateau phase where Ca influx is balanced momentarily K efflux whereas auto rhythmic cells lack the plateau. Also, I believe auto rhythmic cells have a lot of Na leak channels for spontaneous depolarization and probably have a resting potential close to or above the threshold potential, which is why they can fire by themselves.