At the beginning of this chapter, on page 439, we saw the equation for measuring cardiac output by the dye-dilution method.

If an amount A of a dye is injected into the heart, and its concentration, c(t), measured in the aorta, then the cardiac output, F, is given by F =

A

∫ T 0

c(t) dt

.

T is some time when the concentration in the aorta has dropped to some small number, and thus all the dye has been pumped by the heart.

A reasonable approximation to c(t) is given by the function c(t)

cmax

= 0.33te−0.18t

(1 + 0.5 sin(2πt/20)), where cmax is the maximum value of

c. This function is plotted in Fig. 23.3. It’s not a perfect match to the experimental data

(page 440) but it’s not too bad either; it has an initial large hump as the majority of the dye goes through the aorta, followed by some smaller wiggles.a. First, check that the units all match up. (Hint: the units of F are volume/time, the units of A are amount, while the units of c are amount/volume.)

b. T = 40 s seems like a pretty good choice. Why?

c. Use a computer to calculate ∫ 40 0

c(t) dt. (According to us, it’s 11.2 cmax s. Where does the cmax come from?)

d. What difference does it make if you choose T = 30? Or T = 50?