Information you will never need

Health care in Ukraine is free by the constitution.  It is illegal to pay a doctor or nurse at a state hospital or clinic.  However the state then steals all the money and pays them at Soviet rates of less than $70 per month, which of course they cannot live on.  So they require 'gifts' in appreciation for their services, which is only fair.  Some angry young doctor is taking the state to court to force them to either change the law or pay proper wages.

There are also private clinics with well trained specialists and modern equipment, for which you pay. Last week, I went to see my heart specialist at ProfiMed Clinic.  Not sure if the profi is profit or professional, not that it matters.  ProfiMed have a number of specialists on staff, do blood work and also some out-patient stuff.

Tanya comes in with me and since she knows me better than I know myself, converses with the doctor and fills me in after.  My blood pressure was 150/80 or something.  Not good enough so I am on one more pill of some kind, come back in a month.  My heart rate however surprised her.  "How can you have high blood pressure with a heat rate about 45-55?" "Elephants have much lower heart rates than smaller mammals" which made them laugh.

And which brings me to today's lecture, boys and girls. How do you compare the heart rates of mice and elephants? The answer is a variant of Kleiber's Law on the relationship between body mass and metabolic rate.

Metabolic rate is, in simple terms, measurable in calories (or joules*), the amount of heat lost per unit of time by the body of an animal. We know that large animals need more energy to survive than small animals but how much more?  A 4 tonne elephant is 160,000 times larger than a 25 gram mouse.  But it does not need 160,000 time more food in a day.  Bigger animals use food more efficiently than small animals.

Heat loss is a function of surface area. Heat production is a function of body mass.  Thing of an animal as a sphere.  Surface area is a function of the radius squared (r²).  Body mass, on the other hand is the volume of the sphere which is a function of the radius cubed (r³).  So there is some argument that Metabolic Rate varies with Body Mass to the two-thirds power (MR∝W_kg^2/3).  But 2/3 is not quite right.  

Max Kleiber, sometime in the 1930's, determined that a more accurate formula was Metabolic Rate varies with Body Mass to the three-quarter power (MR∝W_kg^¾).  This is simple.  Multiply the body weight in kg (or lb) by itself three times, then take the square root twice.  Any calculator can do it. 

The formula for heart rate** or pulse (P or bpm) is a little trickier to understand but simpler to do. P≈186*W^-1/4.  An easier way to write it so it can actually be calculated is P≈ 186*(1/W^1/4). Something to the ¼ power just means take the square root twice.

Mouse – 25 grams – calculated heart rate 465

Cat – 2.5 kg – calculated heart rate 148

Human – 100 kg – calculated heart rate 59

Elephant – 4000 kg – calculated heart rate 23

Obviously these are ballpark as individual heart rates vary widely, even in an acceptable range but it does illustrate my point.  Elephants have lower heart rates than smaller mammals.

Thus endeth today’s lesson.  

*Would you refer to the week's groceries as the 'family joules'?
**My thanks to my friend and mentor, Professor Emeritus Dr D.A. Christensen, U of S, for sending me photocopies of pages from Kleiber's timeless book, "The Fire of Life"