Smaller mammals and birds have faster heart rates than larger ones. It would be useful to have a model that might explain this variation in heart rates. A warm-blooded animal uses large quantities of energy in order to maintain body temperature, because of heat loss through its body surface. Since cold-blooded animals require very little energy when they are resting, the major energy drain on a resting warm blooded animal seems to be maintenance of body temperature. Letâs explore a model based on this idea. The amount of energy available is roughly proportional to blood flow through the heart to the lungs â the source of oxygen. At rest, the amount of energy available is proportional to the amount of heat lost, which is proportional to body surface area. (a) Show that the basal (resting) blood flow f is related to the body weight w by (approximately) f â w 2/3 . Define all the variables that you use. (b) Derive a model that relates basal pulse rate p to body weight w as (approximately) p â w â1/3 . What assumption(s) did you make about hearts?
Smaller mammals and birds have faster heart rates than larger ones. It would be useful to have a model that might explain this variation in heart rates. A warm-blooded animal uses large quantities of energy in order to maintain body temperature, because of heat loss through its body surface. Since cold-blooded animals require very little energy when they are resting, the major energy drain on a resting warm blooded animal seems to be maintenance of body temperature. Letâs explore a model based on this idea. The amount of energy available is roughly proportional to blood flow through the heart to the lungs â the source of oxygen. At rest, the amount of energy available is proportional to the amount of heat lost, which is proportional to body surface area. (a) Show that the basal (resting) blood flow f is related to the body weight w by (approximately) f â w 2/3 . Define all the variables that you use. (b) Derive a model that relates basal pulse rate p to body weight w as (approximately) p â w â1/3 . What assumption(s) did you make about hearts?
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