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LD 50 calculation help (math help)

eunectes4 May 01, 2006 11:50 PM

Putting all varied factors aside and assuming testing with rodents is an accurate means of determining lethality of snake bites in humans...I am having trouble figuring this out.

I always looked through LD 50 tests and never gave them much thought as to the calculation.

Taking the LD 50 of a subcutaneous bite of a coral snake (Micrurus fulvius) I have 1.3 mg/kg according to Dr. Fry's site. Taking the venom yield of the snake as 4.5 mg I am getting that it would take 20 full dose bites from this animal to kill a 155 lb man.

Where am I going wrong?

Replies (17)

LarryF May 02, 2006 12:27 AM

I don't think you're doing anything "wrong", but there are a few things you need to consider.

Since coral venom has evolved for killing snakes, not rodents, mouse LD50 may be a less useful gauge than with rodent eating snakes.

LD50 is the amount needed to kill 50% of mice in 24 hours, and actually says nothing about what is requred to kill "some" mice or to kill them after longer than 24 hours.

I've never seen a published table of venom yields that is any more specific than "average yield". It could well be that a large specimen could have a yield of several times the "average".

Human deaths from corals are rare even without antivenom.

While you will hear quite often that the coral snake is the "most dangerous" or "most venomous" snake in the U.S., it simply isn't true and probably originated from people who heard they had "the same kind of venom as a cobra" and didn't consider that it might be a bit more complex than that.

eunectes4 May 02, 2006 01:17 AM

Thanks Larry. I am well aware of all the other varying factors and that play in to lethality. I just wanted to make sure I was doing the math correctly.

According to the way I was doing the math it would also take around 36 full yielding (50 mg) bites from a copper head to kill the same person and only about 0.7 mg of venom via IV from an eastern brown snake.

My understanding of 0.7 mg is that it is about the same size as a small plant seed. But this is just a guess because I do not weigh objects this small. I do not think I ever have actually.

But I figured you would be the one to ask about this. It isn't like this is as difficult as figuring the volume of a b. arientis fang...or even the PSI of a rattlesnake bite.

But this is my first attempt at trying to mathmatically reason my understanding of LD 50 charts.

LarryF May 02, 2006 10:18 AM

Oops, yes, your math was correct...although I alsost told you it was wrong before I realized my mistake.

(And also remember that LD50 is in dry weight, not liquid volume. I have no idea what percentage of venom are solids or what the densitys of those solids are like.)

BGF May 02, 2006 06:25 PM

Another thing to keep in mind is that the tests favour more rapidly acting venoms. There is an arbitrary cut-off (usually 24 hours). However, some snake venoms can take much longer than that to kill. We had one death here in Australia from a Tropidechis carinatus (Rough-scaled Snake) where the poor bastard took nine weeks to finally die! Not a nice way to go.

Cheers
B
-----
Dr. Bryan Grieg Fry
~~~~~~~~~~~~~~~~~~~~~~
Australian Venom Research Unit,
University of Melbourne
~~~~~~~~~~~~~~~~~~~~~~
Population and Evolutionary Genetics Unit,
Museum Victoria
~~~~~~~~~~~~~~~~~~~~~~
http://www.venomdoc.com

yoyoing May 03, 2006 11:12 AM

I would like to read that autopsy. There must have been a predisposition for death.

BGF May 03, 2006 06:15 PM

>>I would like to read that autopsy. There must have been a predisposition for death.

I was mistaken, it was a Cryptophis nigrescens (Small-eyed snake) that caused the coma then death over the nine week period. The cause of death was due to severe myotoxicity. That particular venom can cause some very nasty effects that way. The person was not predisposed, being otherwise healthy prior to the snake bite.

Cheers
Bryan
-----
Dr. Bryan Grieg Fry
~~~~~~~~~~~~~~~~~~~~~~
Australian Venom Research Unit,
University of Melbourne
~~~~~~~~~~~~~~~~~~~~~~
Population and Evolutionary Genetics Unit,
Museum Victoria
~~~~~~~~~~~~~~~~~~~~~~
http://www.venomdoc.com

yoyoing May 02, 2006 08:41 PM

Maybe you shouldn't use a linear relationship for the mg/kg between the mass of a mouse and the mass of a human.

eunectes4 May 02, 2006 11:33 PM

The post was not asking about the relationship between rodents and mice...it was checking to make sure the calculation was correct and I was not missing anything on the math side.

I could have said a 155 lb rat for the example I guess.

The point was 20 full yielding intravenous bites from a coral snake seemed a bit high and I wanted to make sure I was doing the math correctly.

hence:

"putting all varied factors aside and assuming testing with rodents is an accurate means of determining snake bite lethality in humans"

Is there a better test to attempt a linear relationship? As far as I knew, rodents have been the only test subjects used : )

yoyoing May 03, 2006 08:25 AM

Your calculations are dead on. My suggestion is that being suprised by the result may be inappropriate as this is not a good check. Part of the calculation involves y=mx b (where y is dose, x is mass, m is mouse LD50, and b=0). So yes, if the validity of "m" as a constant is given, all is fine. I just wouldn't say that 20 bites are necessary to 50% kill me (if I weighed 155 pounds that is).

yoyoing May 03, 2006 09:12 AM

That should be y = mx b (missed the " " in the linear equation).

yoyoing May 03, 2006 09:18 AM

Try this: y = mx "PLUS" b. For some reason the plus sign typed as a plus sign (little perpendicular line segments that bisect each other with a north-south orientation) doesn't show up in the post. Here, I am going to type 10 of them to see what happens: .

eunectes4 May 03, 2006 01:27 PM

I figured the calculation out it appears. I was having it double checked because the number seemed high.

I do not understand what you are suggesting. LD 50 is not what it takes to kill 50% of you. It would be that would of 100 people (or rodents) weighing 155 lbs, 50 of them would die if bitten 20 times by a full yielding subcutaneous bites from M. fulvius.

Once again, this is a relative example just to get the math done. I am not extremely surprised by the results, only they seemed like I was getting some surprising numbers.

So instead of forming an opinion on how I view LD 50 tests, I wanted to make sure I was doing my math right....

Before I repeat to people that it would take around six and a quarter full yielding (411 mg) subcutanous bites from a Bushmaster (L. muta) to kill a 155 lb person (assuming a 155 lb person is equal to a 155 lb rodent).

yoyoing May 03, 2006 02:07 PM

Your math is indesputable You did ask what was wrong with the math and I suggested you are using a constant that is not appropriate. I propose that a 155 pound human and a 155 pound rat are not interchangable. Imagine the results of exchanging the LD50 of a rat dropped from a height to a human dropped from a proportionate height.
If all you want to know is whether you made an appropriate calculation, the answer is YES (A-plus (I learned not to type a "plus"). If you are searching for approval to extrapolate the data to humans my answer is NO.

eunectes4 May 03, 2006 03:11 PM

No, I am not asking for approval to interchangeably use a rodent and a human for lethality of LD 50 tests.

Most people should be well aware that humans and rats have many differences which would play into how they react to venom.

The examples were used because rodents are the only test subjects I know of which have gone through this type of testing. And I did not think it was of any relavance to try and compare the test done on a rat or mouse to a capybara...they have varying factors as well so you might as well take the next step and compare it to a human relative to assuming all other varying factors aside.

However, even after stating I was trying to put all other factors aside (we could think of hundreds), it still seems to be the topic of interest as far as responses go.

yoyoing May 03, 2006 03:52 PM

I am 110 percent wrong, and you are right. Please feel free to do the following based on your accurate calculations:
"I repeat to people that it would take around six and a quarter full yielding (411 mg) subcutanous bites from a Bushmaster (L. muta) to kill a 155 lb person (assuming a 155 lb person is equal to a 155 lb rodent)."
Again, I concede.

eunectes4 May 03, 2006 05:48 PM

LOL, conceding makes it sound like this was an argument. I never felt as though we were arguing...only trying to reason through a sequence of misunderstanding.

I have the feeling one full yielding bite from L. muta would be more than sufficient to kill you...this is not based off my calculation of the LD 50 chart...only my natural history knowledge of this animal.

Also, I bet you would have some good odds of it not being a subcutaneous bite.

TJP May 04, 2006 05:38 AM

That's why LD50's can be so misleading. A bite from a neonate bushmaster is enough to kill a human. If an adult unloads on you, you're in serious trouble. It's a snake that I would never want to get bitten by, not that I would want to get bit by any hot, but definitely not a bushmaster. Their effects on humans are quite dramatic....unconscious within 10 minutes, projectile vomiting. I'll pass. Give me an inland taipan anyday.

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