|www . Science-Projects . com|
SURVIVAL CURVES and MINIMUM LETHAL HITS
| go to previous page on how to use semilog graph paper |
This collection of "dose plots" or "survival curves" starts with it origin at the red "1". From it arise three plots, a, b, and c. Plot "a" is of the most sensitive critter, while that of "c" is of the least sensitive critter.
Game theorists have proven that if you extend asymptotes from the straight portions of the curves back to the vertical axis, where that line crosses indicates the minimum number of lethal hits.
Let's discuss the meaning of that for a moment. It has been shown in battle scenarios that the average soldier is usually shot several times and still doesn't die - although it is plausible that one bullet in just the right place - brain, heart, can kill. Thus the minimum number of hits to be lethal for a soldier is one. On the other hand, if we talk not about bullets but gamma rays, then the minimum number of lethal hits in a human must be much larger for immediate death. Perhaps there are a critical 1,000 cells in the body such that if ALL of them are knocked out - each by a single gamma ray, then the minimum number of lethal hits is 1,000. Thus if you were to irradiate a large population of people with gamma rays and make your dose plot, you would find the extrapolated asymptote crossing the vertical axis at 1,000. (Again, remember that most people will be hit with millions of gamma rays - but most of them would be in inconsequential places.)
Thus when you look at this figure, you see that both "a" and "b" are critters for which the minimum number of lethal hits is one. But for "c" the line extrapolates to "2", and so that critter requires at least two hits to kill it.
Another consideration that you can derive from these plots is the LD50 ("lethal dose for 50%"; the dose that kills 50% of the critters). For "a" the LD50 is about 5. You find this by moving down the red line to where it crosses the horizontal 0.5 line and at that point look down at the bottom to see how many hits that indicates.
For "b" LD50 is about 10, but you run into a problem with "c" because its curve doesn't start declining immediately. So, for "c", you must go to a straight portion and then determine how many hits it takes to decrease the number to a half. So go down the blue line where it is straight to some convenient place and then measure off how many more hits it takes to drop in half. You should get something like 16 hits.
| Site's Table of Contents | Site's Index |