The job of the kidney (you should all have two, but you can get by with just one if you have to) is to filter the blood, removing toxins and waste products, and adjusting the balance of various electrolytes such as Na+

, K+

, Cl−

, H+

, and HCO−

3

. Kidneys also ensure that your body retains the correct amount of water.

The nephron is the functional unit of the kidney, and there are around 1 million nephrons in a human kidney. Each nephron is basically a collection of tubes, along which fluid flows, and these tubes are arranged in a very clever manner to allow the kidney to do its job.

One of these tubes in the nephron is the proximal tubule. The fluid pressure inside this tube is controlled by a complex feedback system called tubuloglomerular feedback, or TGF. As is often the case with feedback systems, this can result in oscillations in fluid pressure in the proximal tubule; an example of such oscillations is shown in Fig. 5.26.

a. By measuring the period, amplitude and midpoint of the oscillations, write a sine function that approximates the experimental data in Fig. 5.26. (For now, just assume that the midpoint is constant.)

b. Now notice that the midpoint of the oscillations is slowly moving up, while the amplitude first increases, then decreases, then increases again. How would you incorporate these features into the sine function you used for part a? As always, plot your function to make sure it agrees (at least approximately) with the data.
It might be helpful first to do Exercises 5.17 and 5.18 which are similar to this one, but more hints are given.