User:Ohiostandard/Dose-response

( The following was copy-pasted from "Cannabinoids & Acetylcholine" on Alfie66's talk page, then refactored here to clarify it and remove off-topic content. - OhioStandard )

Hi, Alfie! I wonder if you would mind briefly responding to a question about how cannabinoids affect the acetylcholine system? My curiosity was prompted by these two quotations:

• "Cannabinoids inhibit the release of several neurotransmitters in the hippocampus, like acetylcholine, norepinephrine, and glutamate, resulting in a major decrease in neuronal activity in that region. This decrease in activity resembles a 'temporary hippocampal lesion.'" from http://en.wikipedia.org/wiki/Effects_of_cannabis#Neurological_effects.

• "Cannabinoids, depending on the dose, inhibit the transmission of neural signals through the basal ganglia and cerebellum." from http://en.wikipedia.org/wiki/Short-term_effects_of_cannabis#Neurological_effects , which also includes the previous passage.

As you may know, my understanding of pharmacology is very limited, just that of a mildly-informed layman, but I thought cannabis acted as an acetylcholinesterase inhibitor, which would tend to cause an increase in intra-synaptic availability of acetylcholine, yes? And that this higher level of acetylcholine would tend to up-regulate neuronal sensitivity and firing? Or is that a simplistic understanding; perhaps its affects differ in that way by brain region? ( The source cited to support the hippocampus statement, btw, is J.E. Joy, S. J. Watson, Jr., and J.A. Benson, Jr, (1999). Marijuana and Medicine: Assessing The Science Base. Washington D.C: National Academy of Sciences Press. ) I've tried to research this myself, via Medline, etc, but any brief comment you might have time to provide would be most helpful, I'm sure. Thanks in advance, Ohiostandard (talk) 23:32, 21 May 2010 (UTC)

You are right, that if cannabis would act as an acetylcholinesterase inhibitor, ACh–levels would increase. But this is not the case; ACh–levels are down–regulated. See the reference you quoted, Domino 1981, Gessa et al. 1998, and Grotenhermen 2004. Another source (sorry, not online): EF Domino; Cannabinoids and the cholinergic system. in: Nahas G, Sutin KM, Harvey DJ, and S Agurell (eds): Marihuana and Medicine. Totowa, NJ, Humana Press, 223–6 (1999). Therefore the statement in the article seems to be justified. 12:52, 22 May 2010 (UTC)

So papers ( like this and this one ) a few years back about the possible prevention of Alheimers's via cannabinoids as acetylcholinesterase inhibitors were based on unrealistically high concentrations of cannabinoids?

This dose-dependent response thing is confusing to me; a clue re the phytocannabinoids seems to offer when one examines the corresponding puzzle concerning the synthetic cannabinoid WIN55,212-2. Perhaps the discrepancy arises because previous researchers were using such massive doses of WIN 55,212-2, e.g. 5 or 10 mg/kg versus 0.01 to 0.15 mg/kg? Please see Acquas et al. in "Cannabinoid CB1 receptor agonists increase rat cortical and hippocampal acetylcholine release in vivo" ( European Journal of Pharmacology 401 (2000) 179–185, free full-text, here). May I quote briefly from that paper's discussion section?

The present study shows that low, intravenous doses of cannabinoids stimulate acetylcholine release in the prefrontal cortex and hippocampus. As our conditions are more likely to mimic those of cannabinoid exposure through smoke in humans than those utilized in previous studies where high doses of cannabinoids were given i.p. (Carta et al., 1998; Gessa et al., 1998a), it is suggested that the changes in acetylcholine release observed here might reflect the changes taking place in humans smoking cannabis derivatives (marijuana and hashish). If this argument is correct, one would predict that exposure to cannabis in humans is associated to an increase rather than a decrease in brain acetylcholine release.

( Emphais mine. ) Thanks for the generosity of your reply; no demand for further assistance trying to understand this, but I'd of course be grateful. Ohiostandard (talk) 19:14, 23 May 2010 (UTC)

( ← outdenting ) I think I understand this a little better after learning a bit more about pharmacodynamics, the nature of the dose-response relationship and about the concept of the therapeutic window. As is mentioned in the dose-response article, "Endocrine disruptors have also been cited with producing one effect at high dose and a different effect at low doses." That may be true of phytocannabinoids too, as it appears to be of the synthetic, WIN 55,212-2. Phytocannabinoids might increase acetylcholine levels above normal baseline at the range of plasma concentrations likely to result from inhaling cannabis smoke, but ultimately decrease them below baseline with much higher doses, e.g. at concentrations hundreds to thousands of times higher and which may correspond to Gessa's findings and to those of many of the in vitro protocols and results that have been reported.

Also, can you easily point me to any reference that documents the range of plasma concentrations for the more prominent cannabinoids that typically results from smoking and/or vaporizing and/or ingesting any given strain of cannabis? I suppose it's reasonable to assume that they're on the order of magnitude of those produced by Sativex and Marinol, whatever that may be? Sounds like a lazy question, I know, but 20 - 30 minutes of searching didn't bring me to anything that directly or concisely addresses even its simpler forms. I did see a paper that said THC concentrations in heavy cannabis users over a seven-day abstinence regimen range between 1 ng/mL and 5.5 ng/mL, but that wasn't exactly what I was looking for. Any other clarifications would be most welcome, too, of course. Cheers, Ohiostandard (talk) 21:28, 27 May 2010 (UTC)

Hi Ohiostandard! Sorry that I didn't respond to you previous messages, but I'm drowning in work… Just a few brief comments:

• Concerning the dose-response curve you are on the right track. At least for natural cannabinoids the dose-response curve is flat (= high therapeutic index); but there are cases, where the sigmoidal curve at very high doses may lead to a lower effect (so-called "hockeystick phenomenon"). Science is a cruel mistress. I once made a comment about the crazy levels reported in some in vitro studies and I received a very harsh response. It's a sad story that the article still gets lengthier almost every day – whereas on the contrary a close shave would be a good idea, IMHO.
• Concentrations after oral administration (e.g., Marinol – or cookies, if you like) are significant lower than after pulmonary administration. Reasons are the presystemic metabolization in the gut-wall (P-Glycoprotein MDR1) and a predominant first-pass metabolization in the liver (enzymes CYP2C9, CYP2C19, CYP3A5, UGT1A1). Therefore the oral bioavailability is only ~10 %. Concentrations are highly variable between patients, as well as within patients. If I had to choose between routes of administration, I would definitely go for inhalation. Oral formulations were developed for political reasons, not pharmacological ones.
• Literature on plasma concentrations is sparse and based on analytical methods lacking sensitivity and/or selectivity (³H labelled THC with TLC,...). Recent methods (GC/MS with stable isotope internal standardization) are able to measure ⁹Δ-THC and the main active metabolite 11-OH-⁹Δ-THC to a lower limit of quantification of 50 pg/ml. The maximum concentration after 4 mg p.o. is ~1 ng/ml and after 10 mg p.o. ~4 ng/ml.
• I know references on smoked cannabis, but ASFAIK no data specific for a given strain of cannabis. 01:14, 28 May 2010 (UTC)

Hi, Alfie! Thank you for your response. But never is any rush needed, please; still less should you feel the least obligation to help me learn the basic principles of pharmacology. I do greatly appreciate your help, but it's not your obligation to act as unpaid tutor. So if you need a long delay before responding, or simply can't make time to respond at all to any post that's basically an instructional request, I will not misinterpret that as any kind of personal sleight. Nor will I do so in response to very brief replies: anything, however abbreviated, to point me in the right direction will always be most welcome.

Hi Ohiostandard! I don't feel pushed. ;-) I'm running the world's largest forum on Bioavailability and Bioequivalence (you find a link at the bottom of my User page) – doing a lot of tutoring there. If some spare time is left, I'm willing to continue here in WP...

If you do have some reference easily available about the plasma or blood concentration levels of cannabinoids that result from smoking cannabis, though, as I think you're saying, that would be very helpful to me.

But ( LOL! ) I wasn't asking "Which strain will get someone the highest, dude!", as it may have appeared. I should have written "...from smoking and/or vaporizing and/or ingesting some standardized sample of cannabis." I was just trying to acknowledge that in any meaningful comparison among smoking, vaporizing, and oral administration, the strain would need to be held constant ( along with the quantity, too, I suppose ). That's what comes from trying to talk that official science-man talk when I don't got no book-learnin' for it. ;-)

Maybe I should just explain my goal in making the request, and let you figure out what data I'm actually looking for? My ultimate goal is that I want to be able to determine when a research study has used a reasonable versus an unreasonable "dose" or "stimulus amount" of cannabinoids to obtain the dependent–variable results it reports. Reasonable or unreasonable in comparison to the affect that smoking cannabis typically has on blood or plasma concentrations, you understand.

So the natural starting place, I thought, would be for me to learn what blood or plasma concentration of cannabinoids a typical person would be likely to experience after smoking, say, two average-volume "inhalations" of some average strain of cannabis, holding each "inhalation" in his lungs for an average length of time. ( You get the picture. ) Did I understand you to say that you know of a published resource that documents that, or something close to that? Such a reference would be a great help to me, most welcome, if you can easily direct me to it.

I suppose the strictly-correct thing to hope for would be access to a three-dimensional graph with an axis for each of amount-smoked, plasma-concentration, and time, using a typical healthy subject, with data drawn from multiple, widely-separated smoking sessions at different dosage/intake levels for the same individual. But I can do without that "amount-smoked" dimension, and the "time" dimension also, since I just want to know the possible range that smoking can produce. In other words, I guess I'm looking for a paper about the typical and the maximum amounts of cannabinoids a person can push into his blood or plasma by smoking cannabis...

Don't be disappointed, but I don't think that this is possible. It would need:

• A clearly defined dose-response relationship – which is wishful thinking, because the curve is very flat.
• Low intra-subject variability.

The former does not exist (clinical studies e.g. for the treatment of neuropathic pain include a run-in period, where volunteers were uptitrated to get a reasonable response). The latter is not the case - on the contrary, concentrations after repeated administration of the same dose were highly variable. If you would draw a plot you suggested, you would end up with a cluster of datapoints in three dimensions, with no meaningful relationship. Meaningful in this context would be the ability to fit a function with some acceptable confidence to make predictions.

( Sigh; now that I think more about this, I suppose I shouldn't really be asking about blood or plasma, but about the levels of cannabinoids that occur in cerebrospinal fluid after smoking? But I'll leave that nice distinction alone until I learn a little more about pharmacodynamics. )

You don't have to worry about that. Due to the high lipophilicity a (pseudo-)equilibrium between plasma and CSF is reached within seconds... The high lipophilicity explains also the ability to cross the Blood-brain barrier and the flash experienced after inhalation. Therefore plasma concentrations are sufficient as an entry-point describing pharmacological effects.

In the absence of such a paper or reference, am I safe to assume that the (plasma?) concentration range of ~1 ng/ml to ~4 ng/ml that you mention as resulting from the p.o. administration of 4 – 10 mg of ⁹Δ-THC at least roughly approximates the range that typically results from smoking cannabis? ( In asking that question I take note of your mention that swallowing cannabis or cannabinoids is much less efficient than using inhalation methods; thanks for that. )

Not quite. As I said above, plasma concentrations after oral administrations are much lower than after inhalation. My reference-database crashed yesterday – I don't have time right now to go through my paper references to give you numbers; for the same dose concentrations should be 5-10 times higher after inhalation.

Some examples.

• Ohlsson A, Lindgren JE, Wahlen A, Agurell S, Hollister LE, Gillespie HK; Plasma delta-9 tetrahydrocannabinol concentrations and clinical effects after oral and intravenous administration and smoking. Clin Pharmacol Ther 28(3):409-16 (1980). PubMed. Eleven volunteers, 13.0 mg smoked (average), peak concentrations 77 ng/mL (range: 33-118) three minutes after begin of smoking. 5 mg as a two-minute rapid infusion resulted in 219 ng/ml (161-316) three minutes after end of administration. 20 mg in a chocolate cookie gave 4.4-11 ng/mL; t_max at 60-90 min, but in two subjects as late as four and six hours.
• Barnett G, Chiang CW, Perez-Reyes M, Owens SM; Kinetic Study of Mmoking Marijuana. J Pharmacokinet Biopharm 10(5), 495-506 (1982). PubMed. Six subjects, 894 mg cigarette (1% delta-9-THC), (cave: data obtained by radioimmunassay). Peak concentrations 90.4±49.6 ng/mL after 11 min.
• Naef M, Russmann S, Petersen-Felix S, Brenneisen R; Development and Pharmacokinetic Characterization of Pulmonal and Intravenous Delta-9-tetrahydrocannabinol (THC) in Humans. J Pharm Sci 93(5), 1176-84 (2004) PubMed. Eight volunteers (four males, four females), dose 0.053 mg/kg body weight (average dose 3.71 mg). Mean pulmonal bioavailability (%) was 28.5±23.1. There were two volunteers with a relative bioavailability of ~60%, but also one with only 3.7% and another one with even only 0.4%. This might give you an impression on the high variability. Mean peak plasma levels were observed 20 minutes after start of inhalation and were reported with 18.9±5.0 ng/mL. Plasma levels 5 minutes after the i.v. dose were 271.5±61.1 ng/mL (range: 81.6 ng/mL to 640.6 ng/mL).

Ultimately, of course, if some study reports that its researchers injected mice with some fixed amount of a standardized cannabinoid extract, I'd like to know or be able to reasonably estimate the blood or plasma concentrations that would result, and then see whether they're in or out of the range that cannabis smokers typically experience. I accept and appreciate your caveat about blood and plasma "concentrations of cannabinoids data" being sparse and often poorly-measured, btw. Still, knowing typical concentrations that result from smoking and then ( ultimately ) being able to accurately predict even the order-of-magnitude of the plasma concentrations that a given study protocol is likely to generate would be a very happy outcome for me.

Of course I understand that's a tall order: I understand that it may take some investigation and additional study on my part to approach even that fairly modest goal. So I won't ( anytime soon ;-) go from asking you for a smoking/concentrations reference to asking you something like, "What plasma concentration is the paper by Schmirkenfiffer where he injected 2 mg/kg i.p. of ⁹Δ-THC probably reporting results for?"... I'd like to ask, of course ... but I'll do my own "homework" to try to get to that point. :-)

LOL – Schmirkenfiffer: How did you manage to come up with a name giving zero google-hits? BTW, the second part of the name for a native speaker of German sounds like kiffer, which means pothead. ;-) I'm not sure whether you should even try to do some homework in this case.

• Intravenous administration bypasses first-pass metabolization and presystemic metabolization in the gut wall. So far so good. Concentrations therefore are closer to ones obtained after inhalation.
• But: elimination is not comparable between species, because enzymes are different. That's the reason why allometric scaling (the prediction of concentrations in species A from species X-Z) fails if (any) drug is excreted mainly after metabolization.

That's the reason why I'm always weary in drawing conclusion from animal models.

On a separate topic, you mentioned the reactions you encountered last year ( around August, 2009 ) when you pointed out that some studies being cited were using in vitro "doses" that were so high as to be unreachable in vivo, at least by the usual routes of administration. ( Yes, I know that "dose" is the wrong word for use with in vitro studies, but I don't know the right word. ) That whole kerfuffle was really unfortunate; thanks for dealing with it all so patiently. It was a real loss to everyone, and to the article, that the discussion became so contentious.

My current project: I'm looking up all the references I can from page 53 of Marijuana and Medicine ( ed. Joy, Watson, and Benson, 1999 ) that the chapter's authors cite in their "Memory Effects" section to support their statements that acetylcholine levels in the hippocampus and elsewhere are decreased by exposure to cannabinoids. I had to suspend that effort about half-way through those refs, but all the references I have looked at so far are to studies which seem to have used "doses" that I suspect (?) might be ten, one-hundred, or even one-thousand times higher than those that can be obtained by inhalation or swallowing.

If it turns out that the rest of the studies cited on page 53 also used such high "doses" then perhaps we might consider editing some of the Wikipedia pages that rely on that page of the book for information about the relationship between cannabis use and acetylcholine levels. We might want to disclose the very high "doses" used, at least. There's much to be done before such a step would be justified, though, I know. For example, I'd like to post a table of the "doses" used in each of the studies somewhere on Wikipedia, although not in mainspace, of course.

100% agree.

I'd probably post that table here, on your talk page, by default, as a continuation of this thread if that's acceptable to you. But I know that some editors find long discussions on their talk page a bit intrusive; they like to keep their talk pages tidy. If that's a concern for you please say so, and we'll find a better "home" for this.

I wouldn't post it here, because old threads will be archived here. Maybe we can open a subpage here or at your talkpage.

Thank you once again, and please don't feel pressured to respond quickly, at length, or even at all if you find you just cant afford the time. Best regards, Ohiostandard (talk) 07:02, 1 June 2010 (UTC)

I don't feel pressured and appreciate your efforts getting a clearer view. Hopefully once we will be able to shift the article to a higher level.

Quick addition: You mentioned "the sigmoidal curve" in your last reply, and I didn't know what that meant. But I do now! Sweet! Cheers, Ohiostandard (talk) 07:20, 1 June 2010 (UTC)

Well, I will try to link more technical terms in the future. ;-) 14:13, 3 June 2010 (UTC)

That is a very substantial reply, thank you! I'm slow to respond, but I thought I'd better at least tell you that I haven't forgotten about my small project to check on and report the "doses" ( or "concentrations", for in vitro? ) that were used in the studies that are cited on page 53 of Marijuana and Medicine. Lately it seems very easy for me to find a reason to put off the fun stuff; something always seems more urgent. I will finish that, though ... even if I probably won't be able to translate the study protocols into probable plasma concentrations.

Hi, Ohiostandard, really appreciate your efforts!

I've looked at the references you provided about plasma concentrations from smoking cannabis; thanks for including those. Those references, along with your own comments, have brought me to a much greater appreciation of the problems that arise in trying to determine whether the plasma concentrations that a given study's "dosing protocol" is likely to produce are in the range that's produced by simply smoking cannabis. I'm amazed and rather dismayed to learn that ( among other impediments ) the degree of variability between persons is so incredibly high. Do you think the results reported by Naef, et al. are reliable? ( You wrote, about those results: "There were two volunteers with a relative bioavailability of ~60%, but also one with only 3.7% and another one with even only 0.4%." ) I wonder whether any of the eight subjects might have had any other substances on-board, substances that might increase or decrease bioavailability? I'm just "thinking out loud" here, btw, because the results seem so extraordinary to me. I don't expect you to answer those questions.

I would say Naef et al.’s results are reliable indeed. The study was a randomized, placebo-controlled, double-blind, cross-over approved by the Regional Ethics Committee, the Swiss Agency for Therapeutic Products (Swissmedic), and the Swiss Federal Office for Public Health. One of the exclusion criteria (amongst others) was past or existing drug abuse; a cannabis urine test was performed before each session. The subjects were not allowed to take analgesics, alcohol, and caffeinated beverages 48 h before and during the study. The lower limit of quantification of the method (gas chromatography/mass spectrometry) was 0.4 ng/ml – which is sufficient for this administration route. Theoretically it would be possible that other drugs interacting with the CYP450-system might influence the degree of metabolization (and therefore THC-levels), but:

• In well-controlled pharmacokinetic studies this is rarely the case. I have seen just a few cases in the 500+ studies I have performed, where volunteers took other drugs. Subjects are hospitalized and under close supervision.
• In the study not only THC, but also two metabolites (11-OH-THC; active and 11-COOH-THC; inactive) were measured. If co-administered drugs would have altered the activity of CYP450, it would have been noticed in individual plasma profiles (altered parent drug / metabolite ratios). This was not the case.

Besides the three examples you provided above, I suppose you've also seen this 2008 study by Goullé, et al.? It reports rather similar results: "After smoking THC bioavailability averages 30%. With a 3.55% THC cigarette, a peak plasma level near 160 ng/mL occurs approximately 10 min after inhalation."

I don't have the original article in my files; from the abstract it's not clear what the actual dose (in mg) was. However, results look plausible – at least the order of magnitude is OK.

In contrast to that, however, I found the results from a study by Hunault, et al. interesting ... and confusing, too. If I understand their results correctly, they report serum mean maximal concentrations (Cmax) as high as 231.0 microg/L for THC when more potent cannabis was smoked. That's 231,000 nanograms/liter of serum. ( I know that you know this, of course. The conversion is for my own benefit when I read this again. ) Is it possible that so huge a difference is somehow due to the difference between serum and plasma? Since serum is plasma minus clotting proteins, I mean? I'm just speculating again; I have no expectation of a specific reply to this, truly.

Here you made a minor mistake in getting the units right. ;-) In pharmacokinetics concentrations are mainly given as mass/volume (commonly the volume in millilitres, because this is the volume bioanalysts deal with) or amount of substance/volume (commonly in moles/litre]. µg/L is quite uncommon. 231 µg/L equals 231 ng/mL (just divide both units by 1000: µg→ng and L→mL or divide your 231,000 ng/L by 1000 to get also 231 ng/mL). Therefore their value is high, but given the dose of 70 mg and the variability between subjects not impossible. BTW, serum and plasma shouldn't make a difference.

I certainly "came to the right shop" for general guidance in this, though: the world's largest forum on bioavailability and bioequivalence, indeed! I looked at your site, and I am impressed. Of course I didn't understand most of what I read there, but ... well, I can at least say that I really liked the Szent-Györgyi quotation about the nature of discovery! Best,  – OhioStandard (talk) 15:34, 9 June 2010 (UTC)

Haha; this quotation was selected by a nice random number generator from my quotations database (you will see another one tomorrow). My favorite one is Karl Popper's: “Whenever a theory appears to you as the only possible one, take this as a sign that you have neither understood the theory nor the problem which it was intended to solve.” That's the one I use in my lectures; generally in the first slide after the title. ;-)

A point about comparability between studies: Whilst in noncompartmental analysis (NCA) the Area Under the Curve (AUC) reflecting the extent of absorption is relatively robust to suboptimal blood sampling schemes, C_max is not. The peak concentration is a single point metric, and it is quite improbable that a blood sample was taken at exactly the time point of C_max (=t_max). The same sampling schedule is valid for all volunteers in a study. Therefore the measured maximum concentration is likely to underestimate the true C_max (the sample was taken too early or too late). Now for the nasty part: THC follows a multi-compartmental model, where after both i.v. and pulmonary administration the first distribution phase is very fast (with a half-life of a couple of minutes). Different sampling schedules were used in these studies, making a comparison even more difficult. Only a few groups tried to fit a pharmacokinetic model to the data (which would allow to estimate the C_max). 09:39, 10 June 2010 (UTC)

Thanks once again for your generosity in providing answers like this, and for your encouragement to continue learning the basics. I can't understand how I made so careless a mistake with units re the Hunault paper. I'd noticed that the "numerator" units had changed from nanograms to micrograms, of course, but I somehow failed to notice the "denominator" units had likewise changed, from milliliters to liters. Thanks for setting me right.

I should mention that I'll be away for the next two weeks, and that I may be offline during some or all of that time. I don't know whether the (wireless) internet modem I use will be able to connect from the rural location where I'll be staying. I hope it will: I'd like to be able to take at least some of the time I'll be away to revisit what you've written here, to more closely examine some of the references we've discussed, and perhaps to write a concise summary of what I've learned thus far about the pharmacodynamics of cannabis, just for my own future reference. It's a fascinating area to learn about, and you know I'm grateful for the opportunity. But I'll admit that I also feel some desire to consolidate what I've learned, even though it's not very much. Each time I've gone back to review what we've discussed here more closely I keep being surprised by important things I'd forgotten, or by important facts that I barely noticed when I read them the first time, and I keep finding new information that contradicts or at least significantly modifies my understanding of what I thought I'd learned. Many thanks,  – OhioStandard (talk) 02:37, 13 June 2010 (UTC)

Hi Alfie! A difficulty arose for me while I was away that has proved very time-consuming. I'm sorry to have left this discussion incomplete for so long, though, and I hope to have the opportunity to review the above and respond within the next week. Best regards,  – OhioStandard (talk) 06:07, 15 July 2010 (UTC)

Hi Ohiostandard! Nothing to worry about; I'm used to the unexpected as well. I started to gather data in the meantime to come up with some kind of a dose-resonse relationship (pharmacokinetics - not pharmacodynamics!). It didn't look that bad - with the exception of Barnett et al. (1982). As I already stated above, concentrations were measured by a radioimmunoassay - due to cross-reactivity they probably have measured not only ⁹∆-THC, but metabolite(s) also. Once I have finished that, I will post results here for our fun - can't go to the article, because it will be 100% original research. ;-) Well, I can't publish it also, because the only scientifically accepted method to assess dose proportionality would be a crossover study of different dose levels - all peer-reviewed journals would reject it. Different subjects (parallel study) and different bioanalytical methods give us just a hint. In the meantime have a look here. I definitely appreciate your linguistic/philosophical remarks also! 15:55, 15 July 2010 (UTC)

Thanks for understanding. And I appreciate your intention as well to look into this further since I'm rather out of my depth here, as you know very well, despite your very helpful hints, information, and direction. I greatly appreciate the opportunity to learn about this your area of expertise, however, and I do aspire to one day rise to the dignity of error. ;-) I'm going to have a look at articles related to pharmacokinetics, for example; that may help.

F.y.i. pharmacokinetics is really poor – though one editor started in the recent past to translate parts of es:Farmacocinética, which is excellent. BTW, the article in my home-wiki de:Pharmakokinetik is only fairly better... If you are interested in mathematics, I would say articles in DE:WP generally are better than ones in EN:WP. Even if you don't speak German, just have a look at some article's versions in German. OK, to be honest I checked only a few articles in the field of mathematics, but a lot concerning statistics. 11:39, 17 July 2010 (UTC)

I also appreciated the link to your website's database of quotations; thanks! Leslie Z. Benet's words about the difference between pharmacokinetics and pharmacodynamics prompted me (along with your own remarks above) to learn enough to use the words properly - sorry I hadn't previously. The Roger Staubach quotation about the proper origin of confidence was a great one, as was the Cornelius Lanczos one saying that "filling in the details" by one's own efforts is the best way to learn mathematics - I hadn't seen that before, and it's a gem. Thank you for sharing them with me. Cheers,  – OhioStandard (talk) 19:56, 16 July 2010 (UTC)

I give Popper's quote from my talk page and Les' about applied science in all of my lectures. Les is one of the most important persons in PK (pharmacokinetics); last month he was introduced at a conference by the president of the Hungarian Academy of Sciences with 'Mr. Leslie Benet, the man with more than 15,000 citations.' I remember Les at a conference a couple of years ago, where he started his presentation (quoting from my memory) with: 'In the past 35 years I have said ... [sorry, too technical to be given here] and it's quoted in all textbooks written ever since. Today I must tell you that I was wrong and I will tell you why I was wrong.' Is Les notable for an article in WP? Yes. Is there one? No. Also, I added one quote by David Hilbert and Russell's/Whitehead's counterpart (not sure whether that's the correct term?) Kurt Gödel to my collection. 11:39, 17 July 2010 (UTC)

Dear Ohiostandard!
As promised some of my original research to satisfy our private interests. To assess dose proportionality I fitted literature data (peak concentrations) to the weighted power model Y=Ax^B, where Y is the pharmacokinetic response (here C_max), x the administered dose, and A and B are the parameters of the model. If the exponent B equals 1, the model reduces to that of dose linearity (i.e., response doubles with a doubled dose). In order to deal with heteroscedasticity the model was weighted with w=1/x. C_max is not the optimal metric to assess dose proportionality – AUC would be a much better choice. As said somewhere above values of Barnett at al. were measured by RIA and may be too high. The biggest drawback of the pooled analysis is the fact that data originate from different studies.

Here is a plot of the fit. Not so bad. B is 0.6886 (coefficient of variation 14.8%; 95% confidence interval: 0.3136 – 1.0635). Within the dose range of 3.71 mg to 69.4 mg the increase is not proportional; however, since 1 is included in the confidence interval, this deviation is not statistical significant (at α 0.05). In other words, if we double the dose (+100%) the model predicts an increase of only ≈69% in C_max. I checked also the residuals and Barnett's data do not qualify as a statistical outlier and therefore can't be removed. But since this no serious work I can do what I like, namely remove it anyhow. The fit gets better; B 0.7838 (CV 9.51%) with a tighter CI of 0.4797 – 1.0878 (plot upon request).
Now let's look at Hunault at al. – which was a cross-over study (perfect design to assess dose proportionality) in 24 subjects: plot. Within the high dose range of 29.3 mg to 69.4 mg the increase in C_max appears to be almost linear, but again B is lower than 1 with 0.6279 (CV 18.6%; 95% CI: -2.8516 – 4.1074). Since we have two parameters in the model and three data points, there is only one degree of freedom left for the calculation of the confidence interval – which does not make any sense. I included in both plots also a red line showing linear regression forced through the origin as a kind of an optical reference.

Conclusion: It might well be that C_max after pulmonal administration is lower than dose proportional, but with the given high variability (within as well as between subjects) your original question ‘Which (peak-)concentrations can I expect after an (inhaled) dose?’ remains an open one. ;-) 18:35, 3 August 2010 (UTC)

Maturity is the capacity to endure uncertainty. – John Huston Finley
12:29, 4 August 2010 (UTC)