Calculus of the Lungs and Heart

Question 1

How do you find the amount of a component from its concentration and the total volume of gas?

Answer 1

amount = concentration * volume

Question 2

What is the general lung DTDS?

Answer 2

C(t + 1) = (1 - W/V)Ct + (W/V)CA
V = lung volume
W = breath volume
CA = ambient concentration of gas
Ct = concentration of gas in lungs after t breaths

Question 3

What is the equlibrium for gas exchange problems?

Answer 3

The ambient concentration

Question 4

In gas exchange problems, is the equilibrium stable or unstable?

Answer 4

It is always stable

Question 5

What is the sinoatrial (SA) node?

Answer 5

A node in the heart that emits electrical signals at regular time intervals

Question 6

What is the atrioventricular (AV) node?

Answer 6

A node that recieves electrical signals from the SA node and converts them to electrical potential

Question 7

What must occur to trigger a heartbeat?

Answer 7

The electrical potential must be at or below a certain threshold, Vc

Question 8

If there is a heartbeat, what subsequently happens to electrical potential in the AV node?

Answer 8

It increases by a factor of u

Question 9

What is the equation for the graph of electrical potential decay?

Answer 9

e^-ατ

Question 10

Heart: what does τ represent?

Answer 10

The time between electrical signals from the SA node

Question 11

Heart: what does α represent?

Answer 11

The rate of decay of electric potential

Question 12

Heart: what is the equation for c?

Answer 12

e^-ατ

Question 13

Heart: what does Vc represent?

Answer 13

The threshold potential in the AV node

Question 14

Heart: what does Vt represent?

Answer 14

The electrical potential in the AV node after heartbeat t.

Question 15

Heart: what does u represent?

Answer 15

The increase in electrical potential occurring after a heartbeat

Question 16

What is the general DTDS for heart dynamics when the heart beats?

Answer 16

V(t +1) = cVt + u, if cVt ≤ Vc

Question 17

What is the general DTDS for heart dynamics when the heart doesn’t beat?

Answer 17

V(t + 1) = cVt, if cVt > Vc

Question 18

Heart: when the updating function does not cross y = x, what condition is represented?

Answer 18

2:1 AV block, the heart beats once every two signals

Question 19

If the updating function does not cross y = x, what kind of equilibrium is there?

Answer 19

No equilibrium

Question 20

Heart: when the tip of the updating function touches y = x, what is the condition represented?

Answer 20

Wenckeback phenomenon: the heart mostly beats normally but skips an occasional beat

Question 21

When the heart is healthy, is there stable equilibrium?

Answer 21

Yes

Question 22

When the heart exhibits 2:1 AV block, is there stable equilibrium?

Answer 22

There is no equilibrium

Question 23

When the heart exhibits Wenckeback phenomenon, is there stable equilibrium?

Answer 23

Yes