Terephthalic Pterodactyl's picture
Terephthalic Pt...
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+ 3 What in all holy hell is a half-life exactly?

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So I recently was asked to explain half-lives since most members seem to have a misconceived view of what they are exactly. Now I'm going to be laying down some fairly advanced math here so if you don’t understand I’m sorry, but I really tried to make it as basic as I possibly could.

So to start with half-lives do not mean that there is a linear decay. However the RATE at which steroids decay is linear. What do I mean by this? Take a look at this graph.

http://www.mathexpression.com/images/graph-of-y-neg-x-4.png

This is a linear graph. This is what you guys are trying to interpret steroid half-life to be like in terms of how much testosterone you have in your body as a function of time. This is not the case. What a half-life saying is the rate of change of testosterone per half-life time is linear or decays at a standard non-exponential rate.

In mathematical differential equation terms this can be represented as dY/dT=-kY (where Y is the amount of testosterone in your body and T is time. k is our decay constant. This basically factors in how fast the material decays. Smaller half-life would have a larger decay constant.

Those d’s stand for differentials. This is basically saying an infinitesimally small slice of something. dT would represent an extremely small amount of time passing. Like .00000000000000001 half-life times. This allows us to take measurements of things that don’t have linear changes.

Anyway with our expression which we just derived (dY/dT=-kY) we can separate our variables and integrate. This is basically what a differential equation is (although this is extremely basic and the easiest form of differential equations).

Separating our variables we get

Dy/Y= (-k)dT

Now that our variables are separated we can integrate to find the amount of testosterone per unit half life. If you don’t know how to integrate from calculus I can’t really help you. It would take too long to explain. You’ll just have to trust me that I am integrating properly.

Ln(Y)=-kT+C

C is our constant of integration. It allows us to plug in different conditions without having to completely change our equation. It just represents a number that we can calculate. In this equation C will turn out to be the initial amount of testosterone injected (although this will only solve for the half life decay of a single injection, trying to explain a system of differential equations would be complex so after I finish showing half life of a single injection I’ll move onto excel and you’ll just have to trust my numbers)
Now to solve for Y (amount of testosterone in your body at any time T). To get rid of a natural log you must e both sides. e is Euler’s number (pronounced oiler) and is roughly 2.71828.

After we e both sides we get

Y=e^(-kT)+e^C

We can simplify this to

Y=C’e^(-kt)

Now we can solve for C using the initial values we were given. Say we injected ourselves with 500mg of testosterone enanthate, that would mean at time t=0 the amount of testosterone enanthate in our system would be 500mg. So

500=C’e^(-k(0))

-k times zero is zero and any exponent to the 0 power is equal to 1 so this simplifies to
500=C’

Which makes our function

Y=500e^(-kT)

With this we can solve for the amount of testosterone we have in our system as long as we have our k (which is our rate of decay constant which would vary depending on the half-life).
Knowing the half-lives we can even solve for our decay constants. If we know that test E has a half life of 10.5 days we can solve for our k by

250=500e^(-k(10.5))

Solving for k we get .066014 which makes our equation

Y=500e^(-.066014*T)

With this we can plug in any amount of time and know how much test E there is in our body after injecting 500mg of testosterone enanthate into our bodies.

So say I wanted to know how much test E was in my body after 5.25 days. That’s half the half life. So I should have ¾ of the test E still in my body right? Wrong. This is exponential decay. The greater the amount of testosterone the faster it leaves your body. Meaning the rate at which testosterone is leaving your body is constantly changing. We can find out exactly how much testosterone is in our body with our derived expression though.

Y=500e^(-.066014*5.25)

Y=353.553mg of test E which is not ¾ of 500 (which would be 375)

Anyway I don’t know if any of you will be able to understand what I just did but hopefully you can follow it enough to understand that first of all testosterone esters are constantly decaying in your body and also that it does not decay linearly over time.

cry_havoc's picture

The graph you just sourced in your response to Tread is mine. It is a front loaded 20 week Sust 250 cycle. This is almost poetic!

http://i1326.photobucket.com/albums/u656/mritchie74/Front250_zpse3b4c7b4...

I used it to illustrate a point in a write up I did called Maximizing Cycles. Ain't that ironic. Tread is effectively saying that his experiences are similar to the graphs. When he stops taking prop as do most of us....after several days the sides wear off such as high bp, sweats and cardio endurance. This is obviously because when you discontinue injections the quick half life he wrote about eliminates rapidly without maintenance injections to carry the steady state. He is saying the same stuff!

For the record I never said your function was incorrect....I said your graph did not mach the function you were writing about. The graph is very consistent with the numbers you charted, but those numbers are not at all accurate with a what the half life is for any test at those doses. I do know what linear interpolations is; I use it in soil mechanics all the time. You would interpolate when you have unknowns. But using a decay function you shouldn't have any unknowns between 600 and 0. What I was saying and trying to get you to discuss; was how you were using the function so that your numbers were so off? When you discuss a function or equation you should state what each variable in the function represents and what it does. This is so you can substantiate your findings and people can follow what your saying. This is normal in any engineering, scientific or medical community. You could write an awesome post on quantum mechanics or a Higgs Bozen, but if people can't follow it and then reiterate back to you then you have accomplished very little.

Greg's picture

I don’t need to understand the math behind Einstein’s theory of relativity to appreciate the sensation of motion when (in fact it’s) the object next to me that is moving.

All I need to know about a half life is to get an approximate understanding when my levels will have leveled off and why it takes that long.

To suggest that I’d be able to mathematically measure how much test I have in my system so precisely is foolhardy. The math does not take into consideration so many other variables. What muscle did I pin, what’s my body temp, activity level, diet, my ph balance, metabolism, blood pressure etc, etc..

The ONLY true measure is via a blood test.

But, if you want to solve a math problem that would be interesting for me and perhaps others as well please answer this:

If I’m 54 and my natural test level is 620 what was it when I was 30? Given a degradation of 1% per year.

cry_havoc's picture

Lol I just said roughly the same thing just a few lines below in response or agreeance rather, to tread!

porky's picture

math sucks

Greg's picture

Uummm, has anyone heard of the rule of thumb?

This is all nice and heady talk, but for my needs, is it really pertinent?

cry_havoc's picture

It depends on how you chart your cycles. The way this kid does his math (and I am betting he hasn't actually graduated yet and the calc I shit he is touting above he just learned), exponential decay function is very useful in putting together a cycle. It is a graphical and mathematical model of how your cycle will function over time. But there are different variations of it and you have to know how to use it correctly. There is a standard radioactive decay used in physics and chemistry and a variation of it used for pharmaceutical purposes. This is found in Pharmacokinetic research labs. The point I am getting at with this kid is he is giving out bad info and on here that can get someone hurt. He also is very adamant that front loading is bad and should not be done.

Check this link out and see what I mean bud. It is a simple quick read.

Maximizing Cycles

Greg's picture

All I need to know about a half life is to get an approximate understanding when my levels will have leveled off and why it takes that long. And, why front loading is beneficial in maximizing my cycle...

Greg's picture

For some reason my wife agrees. She feels term life is better -lots of it. Should I be worried?

cry_havoc's picture

I tend to agree. Term is the smarter way to go. You will never really see any returns from a whole life policy. The insurance companies are just betting on your health that way!

cry_havoc's picture

You should take a gander at this thread bud.
Try and stomach through it and read most of it if you can.

http://www.eroids.com/forum/steroids-qa/steroid-cycles/front-loading-vs....

Nitti's picture

I haven't done this in a while but what a fuckin gem to do it on.....BOOM!

cry_havoc's picture

Just out of curiosity how did you find that graph?

cry_havoc's picture

I agree an have done that very thing you describe. Taking my cycle experience and comparing it to the math. I love it. But they are by no means exactly the same. More like refined ranges. I say this because all these math theories and graphical representations of a cycle are at best a Model of what it would look like. The reality is no two bodies metabolize anything at the same rate. Pharmaceutical companies develop these models long before trials and they refine them as they get empirical data which is acquired through regular blood tests. That's when ranges are compared to the theory and it is validated. In actuality these companies use very complex models comprised of 7 different compartments of the body or systems rather, that all metabolize substances at different rates. We in the bodybuilding community will never find such studies because there is no medical reason on the planet to take the doses we do. Being that there is no need for such a study an we do not have access to daily blood tests testing all 7 systems to compare data we at best can only make a mathematical model on only one compartment. That is to say we believe the entire body metabolizes gear at the same rate.
That being said I love Eroids because it is the closest thing you can get to an empirical data base being that there are so many vets who can differentiate their experiences on here and comparing my own bloods to the cycle and the math only verifies my beliefs with experience. Again the graphs only give a close approximation of the decay on a daily bases not how our bodies metabolize the juice.

In my humble opinion, If you post a graph or math theorem then you are claiming it to be fact. If you post an experience you are posting an interpretation of the facts.

cry_havoc's picture

I would love to see the study you are talking about. As far as the PHD thing goes I am not sure how any of that came into this whole thing. I know of no PHD on this site. I don't think he will last very long on here running his mouth the way he is. Take care bro.

cry_havoc's picture

The only problem Tread is, this guys math is wrong. He even posted the proof for all of Eroids to see. I hope no one takes his advice.

strongman480's picture

i say we all just let him find out the hard way. he has been talking this crap since he joined. when he comes on to someones thread and tries to sound like he know it all just say... o.k. buddy. and leave it at that. just like tread-m said he will find out after running a few cycles that the math is flawed.

strongman480's picture

so i looked because i didn't remember coming right out and saying you were wrong...well guess what i didn't find in one sentence where i said you were wrong

strongman480's picture

where did i say you were wrong? show me were i said "you are wrong."

strongman480's picture

what? Telling me something that goes against what I say and then telling me to do something differently is still telling someone they're wrong. what you say huh? like your the H.N.I.C.

strongman480's picture

i was not talking to you thank you. i was talking to cry havoc. i could care less what you think you know. it's a free web site and no i don't have to shut my mouth.

strongman480's picture

o.k i'm carefree :free of trouble and worry and care.

spartacus91's picture

-I FEEL THE HEAT OF THIS THREAD LOL EVERYONE JUST STAY CALM -

In each human coupling, a thousand million sperm vie for a single egg. Multiply those odds by countless generations, against the odds of your ancestors being alive, meeting, siring this precise son; that exact daughter...until your mother loves a man ...and of that union, of the thousand million children competing for fertilization, it was you, only you...(it's) like turning air to gold...thermodynamic miracle."

this world's smartest man means no more to me than does its smartest termite.

Giant steps, ninety feet high...A constantly changing topographical map, flowing and shifting...Tell me...would it be greatly improved by an oil pipeline ?

There is no future. There is no past....Time is simultaneous, an intricately structured jewel that humans insist on viewing one edge at a time, when the whole design is visible in every facet."

i hope this helps the angry men and woman in this post

PEACE

Doss's picture

Good post btw. IMO there is more to what we do than just pumping exogenous hormones in our bodies and hoping for the best. +1

spartacus91's picture

This is never going to help the little guys or average guys coming on here who don,t have A* in maths lol but it is some good info its got my mind ticking over.yano what would be a good idea if eroids had some sort of app well not a app like a extra add to our profile where you could type in AAS doses and find out there half lifes and amounts left in your system but get rite down to the fine lines of it not just 250mg or 187 mg and so on but 150.00516 ect and all you do is type your dose in and bobs your uncle the half life button sorts the sum for you.just an idea it would be realy hard to make and get up on the site tho haha am allways wanting more its eroids its set high standards for forums av seen no over like it now i am going off topic BYEE Smile

Doss's picture

With a general Understanding of spreadsheets, plus this equation, a person could build a spreadsheet that would calculate for him/her.

I never made it to calculus, so he lost me halfway thru this thing. I have, however, save it to come back and reference later.

spartacus91's picture

No laptop at the min bro so can't do that am just putting it in favs for a later date and use roidcalc untill laptops sorted.cheers