Bill, honest question here. What exactly do you mean when you say "re-distribution"? Are you talking about esterfied steroid being "re-distributed" from the injection site throughout the body, or the base steroid? Perhaps this is where we're not seeing eye to eye, if you think that the still-esterfied steroid gets distributed.
I believe if you read the Chaudry and James reference that I've listed twice as having the information you need, though you've chosen to falsely claim that I provided no references, that then, well, you'd have the information you need.
I appreciate that the reference is not accessible on-line, but it would take me two hours' round trip to go get it, not to mention however much time it might take to type the relevant parts of the article (I don't have a scanner.) It might take you no longer a period of time to obtain it yourself, if desired.
If not doing that, and I can see why it may be infeasible for you as well, then you could consider this:
1) Why would it take two days or more for peak blood levels to appear if the esterified steroid all remains at the injection site? Why would the rate of delivery increase if there is no redistribution of the esterified steroid?
This is readily explainable however with redistribution, as the exposure to aqueous phase and the bloodstream would increase.
It doesn't have to be the case and I wasn't saying it was the case that ALL of the esterified steroid redistributes. I'm sure that that is not the case except, for close enough purposes, after considerable time. But there is redistribution and it is very important to the pharmacokinetics.
2) On a possible area of miscommunication: You made the statement that to me appeared insane that there was very little steroid ever in the body. This could have been sane although incorrect if you meant the body other than the injection site, but you said plainly that you were including the injection site. I replied that after one injects a gram of esterified steroid, there may well be 900 mg remaining the next day and so it is obviously untrue that there is very little steroid in the body.
It occurs to me that you may have meant unesterified steroid.
Yes, that amount is always rather little, relative to the amount of esterified steroid.
3) It is correct to refer to deesterification as "metabolism" where it occurs enzymatically, which is by far the prevalent mode.
4) It is correct to state that this is the controlling step in rate of elimination from the body and duration of action. If this rate is very slow, as with a pivalate ester, then the duration of action will be quite long regardless that the partition coefficient may be lower than (less disfavoring water) or the same as some straight chain ester, e.g. perhaps enanthate. If it is fast, as with an acetate ester, excretion can be rapid regardless that partitioning -- absorption into aqueous phase -- is not greatly more rapid than with moderately longer esters. So with esters longer than acetate, partitioning into aqueous phase cannot be the rate-liming factor. (Not that it must be limiting for acetate, either, but the above point proves nothing with regard to acetates.)
Really.
Just give it some thought. If the esterified steroid leaves a lipid phase (is absorbed) but does not become de-esterified, after an extremely short while it partitions back into lipid phase. Absorption or transfer to aqueous phase is not the rate limiting factor. Rate of deesterification is, which is metabolism.
Absorption to aqueous phase -- generally called partitioning to aqueous phase -- when having a close interface with large surface area is a fast process, not one requiring a week (for example) to achieve mass transfer of half the material. You can try it sometime by dissolving a compound that has some solubility in both an organic solvent and in water in one of these phases, then give it a quite modest amount of time, a matter of minutes, with moderate stirring and you will find that the other phase now is equally saturated (approximately speaking: actually with equal chemical potential and in accordance with the partition coefficient.) It's not a slow process.
Or consider this, as you may say that there is no stirring in the body: Diffusion of a molecule through the skin takes a matter of hours, typically. So short distances don't even require stirring for relatively fast mass transfer compared to the durations of action being considered.
5) Rate of diffusion is not markedly different between different steroid esters of fairly similar chain length: therefore, considering that a single added carbon can add a day to the half-life, it doesn't follow that different speed of diffusion from lipid phase to aqueous phase is the responsible factor, does it?
Rather, driving of the equilibrium (mass transfer) is effected by the substance being consumed in the phase receiving the net transfer of mass. In this instance, de-esterification is what drives the mass transfer. Slow de-esterification for reasons of low water solubility and hence little availability to enzyme, or for reason of structure, with the first factor being usually by far the predominant one, results in long duration of action, as the rate of mass transfer is thus slow as the driving of the equilibrium -- removal of product -- is slow.
(Of course, further metabolism of the free steroid followed by excretion also occurs, but is not the limiting step.)
6) While this is not as elegant a way of looking at the matter, it reinforces and supports it:
Alkyl ester hydrolysis in serum isn't an instantaneous process. It's not the case that on average, a molecule of steroid ester will, upon partitioning into serum, hydrolyze in the first second. The half-life of alkyl esters does vary according to the compound, but it's typically on the order of 1 minute as a reasonable approximation for the present purpose.
Let's say as a very rough approximation that the steroid ester has a partition coefficient of 10,000. As well as meaning that the free molar concentration will be only 1/10,000th as high in serum as in fat assuming equilibrium conditions as a simplification, it means that the time that these molecules are in aqueous phase is 1/10,000th as much time as they are in a lipid phase. And let's say our steroid ester has a half-life of 1 minute in serum.
How many minutes are in a day? 1440.
How many days then would it take for, on average, a molecule with this partition coefficient to spend a total of one minute in aqueous phase?
About 6 days.
There's your rate limiting.
If the ester hydrolysis were faster, for example due to lower partition coefficient yielding higher free concentration in serum and greater percentage time spent free in serum, the duration of action of the drug would be shorter. E.g. with an acetate or propionate. So far as partitioning (absorption from lipid phase into aqueous phase), most molecules of a longer-chain ester would have in that time shuttled back and forth between the two phases many times, certainly more times than was the case with an acetate or propionate ester. That is not the limiting step after redistribution. It is limiting however while still all at the injection site, yielding a small surface area for partitioning.
7) Which is why it takes a few days to reach peak level with a longer-chain steroid ester before transitioning to classical half-life kinetics.