A model* of the cardiovascular system relates the stroke volume V(t) of blood in the aorta at time t during systole (the contraction phase) to the pressure P(t) in the aorta at the same time by the equation

where C₁ and C₂ are positive constants and T is the period of the systolic phase (a fixed time). Assume that aortic pressure P(t) rises at a constant rate from P₀ when t = 0 to P₁ when t = T.

a. Show that

b. Find the average volume of blood in the aorta during the systolic phase (0 ≤ t ≤ T).

Transcribed Image Text:

31² 21³ -C₂Pun(-/-) T² T3 V(t) = [C₁ C₂P(t)] +