ti poiiL) Consider our simplified model for the working of the atrioventrical (A

Question

ti poiiL) Consider our simplified model for the working of the atrioventrical (AV) node. If the decay rate is C-0.4, the critical voltage is Ve = 18, and the increase in potential when the heart beats is u = 15, then we have the discrete dynamical system 0.4V, + 15, 0.41, when 0.4% 18 = t+1 1. Ir Vo 23, what will the potential be after 1 unit of time (round your answer to two decimal places)? Did the heart beat? Vi= Beat? (Y or N): 2. If Vo 47, what will the potential be after 1 unit of time (round your answer to two decimal places)? Did the heart beat? VI Beat? (Y or N) 3. Is there an equilibrium for this system? If so, compute the equilibrium value to two decimal places. If not, type NONE below Equilibrium voltage - 4 select the option which best describes the long-term behavior of the heart in this case. ) Stable Rhythm 2:1 AV Block O Wenckebach Phenomenon

Explanation / Answer

1) If V0 = 23 then 0.4V0 = 9.2 < 18

So, the potential after 1 unit time V1 = 0.4V0 + 15 = 9.2 + 15 = 24.20 , and Yes, the heart beats.

2)If V0 = 47 then 0.4V0 = 18.8 > 18

So, the potential after 1 unit time V1 = 0.4V0 = 18.8, and Yes, the heart beats.

3) There is an equilibrium for this system and the equilibrium voltage Vt =25

If Vt =25 then 0.4Vt = 10 which is less than 18 so that Vt+1 =10+15 =25. So, at this point system will be stable.

4) Stable Rhythm

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