In 1628, William Harvey published this quote in his book De Motu Cordis (On the Circulation of Blood)

Let us therefore take it that in a man the amount of blood pushed forward in the individual heartbeats is half an ounce, or three drams, or one dram, this being hindered by valves from re-entering the heart. In half an hour the heart makes more than a thousand beats, indeed in some people and on occasion, two, three or four thousand. Now multiply the drams and you will see that in one half hour a thousand times three drams or two drams, or five hundred ounces, or else some such similar quantity of blood, is transfused through the heart into the arteries – always a greater quantity than is to be found in the whole of the body. But indeed, if even the smallest amounts of blood pass through the lungs and heart, far more is distributed to the arteries and whole body than can possibly be supplied by the ingestion of food, or generally, unless it returns around a circuit.

(translated from Latin, as quoted in Physiology By Numbers by Richard Burton)

Although Harvey wasn't the first person to suggest that blood flows in a circuit, in his time most physicians believed that the blood in our veins is generated by the liver. That is, they thought that each bit of blood that flows through your veins was created shortly before inside your liver; they did not have a modern understanding of the circulatory system and did not know that arteries and veins are connected via capillaries. In this problem, we'll work on understanding what Harvey was saying, how his reasoning worked, and how his quantitative argument informed his basic scientific position on blood circulation.

A - Your heart rate

1. Measure how many times your heart beats in ten seconds. What did you get?
2. Use your answer to A1 to figure out how many times your heart would beat in half an hour. (As always with homework, please show your work.)
3. How much error do you expect your measurement to have? You do not need to use a formula to calculate this, just give an estimate based on your judgment and the circumstances under which you took the measurement in A1.
4. How does your answer compare to Harvey's numbers?

B - Total blood pumped

Harvey identifies half an ounce with three drams. (It is actually four drams, but Harvey was approximating). Harvey also says that the amount of blood that circulates per heartbeat is one dram (today we call this the stroke volume). Cardiac physiologists often assume a stroke volume of 70 ml for 70 kg man. One ounce is approximately 30 ml (you can use this number as if it were exact for this problem).

1. How many drams is the stroke volume of the "70 kg man"? (Use the more-accurate 4 drams = .5 oz, even though Harvey used 3 drams.)
2. Using this as your own stroke volume, how many drams of blood does your heart pump in half an hour?
3. How many ounces of blood does your heart pump in half an hour?

C - Stroke Volume - Individual

Different size people have different stroke volumes, but roughly speaking, stroke volume is proportional to your height squared. (This is based on an empirical rule used in medicine, not a result derived from basic physics principles.) Assume the 70-kg man from before is 180 cm tall and has a stroke volume of 70 ml. (Note: the actual quantity used in physiology is "stroke index", or stroke volume divided by body surface area. Saying that stroke volume is proportional to height squared is similar but not precisely the same thing, but we will use height squared for this question.)

1. Write an equation, defining appropriate variables, for the stroke volume of a person as a function of height.
2. Estimate your own stroke volume using this model
3. What are some plausible reasons there would be variation in actual stroke volumes, even of people of the same height? (You do not need to know exactly; just brainstorming a few ideas is okay.)

D - Ingestion

1. Give an estimate for the total volume of food and water you've ingested in the last day, in milliliters.
2. How many times larger is the amount of blood your heart has pumped in the last day than the amount of food and drink you took in?
3. How much error do you expect in your answer to 4b? You should give an quantitative response to this, but not one generated by a formula. Instead, estimate the error by examining how closely you think you know the values you estimated for food intake and blood flow. You don't need to use advanced error propagation; an approximate response is fine.
4. What is the relevance of this calculation to the theory that all the blood that flows through your veins is generated in the liver?

E - Creating an equation

Define variables for each of the quantities Harvey described in his passage. Write an equation to relate the variables in a way that summarizes Harvey's calculation in symbols rather than numbers.

F - Compare to known formulas

There is an equation for "cardiac output" in Wikipedia here. The equation is:

How does it compare to your equation? If they are different, why?

Mark Eichenlaub 9/1/17