Alberto Contador has tested positive for the banned substance clenbuterol. Contador claims that the positive test result was a result of food contamination and that he did not deliberately take the drug.

In this blogpost I do the pharmacokinetics calculation to see if Contador’s claim is feasible. My calculation is limited to this specific test result.

Here are some facts relevant to the case:

• Contador tested positive for clenbuterol on the 21st July, with a urine concentration of 50 picograms per millilitre (see UCI press release)
• A picogram is a very small amount, a millionth of a millionth of a gram.
• The UCI has said further scientific investigation is required before any conclusion could be drawn.
• Tests on July 19th and 20th showed no traces of the drug. After finding 50pg/ml on the 21st, Contador’s sample from the next day showed 20pg/ml and then only traces on the following two days.
• In the European Union, it is illegal to use clenbuterol in animal feed.
• Nevertheless some farmers use clenbuterol, since it increases the lean yield of livestock
• There have been of cases of human clenbuterol poisoning from contaminated meat. These have occurred in both pork and beef and in various countries including Spain, France, Ireland, Mexico, and China. The European cases occurred in the 1990s. (see Tainted Meat: Clenbuterol use in the meat industry)
• There have been no recent cases of human clenbuterol poisoning in the European Union.
• In the European Union it is legal to use clenbuterol as a tocalytic (that is to surpress premature labour) in cattle.

So could Contador’s test result be due to contaminated food? We can do a calculation to find out. Given the concentration of clenbuterol in Contador’s urine we make an estimate of how clenbuterol much was ingested. We can then compare this estimate with the residue levels of clenbuterol in contaminated meat and the therapeutic dosages of clenbuterol and thus decide which is more likely: cheat or bad meat.

According to “Clenbuterol Residues in Bovine Feed and Meat” (see reference 1) clenbuterol levels in contaminated beef (in Mexico) have values in the range 0.1 to 2.3 micrograms of clenbuterol per kilogram of meat. So a 100g piece of steak could contain between 0.01 and 0.23 micrograms, that is between 10 and 230 nanograms, of clenbuterol. Contamination levels may of course differ in European meat.

The European Union Maximum Residue Limit (MRL) for clenbuterol is 0.1 microgram per kilogram for bovine muscle and 0.05 microgram per kilogram for bovine milk. So a 100g piece of steak could legally contain up to 0.01 micrograms, that is 10 nanograms, of clenbuterol.

Therapeutic dosages of clenbuterol are in the range of 20 to 80 micrograms per day (that is 20,000 to 80,000 nanograms).

According to my calculation (full workings at end of blogpost), Contador ingested approximately 540 nanograms of clenbuterol. This is slightly higher than expected if Contador ate contaminated meat, but much much less than if Contador had taken a therapeutic dose of clenbuterol. This dosage is much higher than could be obtained from meat that complied with EU regulations.

### Conclusions

The amount of clenbuterol ingested by Contador (540 nanograms) is consistent with his assertion that he ate contaminated meat.

This amount is only 1/40th of the theraputic dose, and so seems unlikely to have resulted in any performance benefit.

On this occasion, I am inclined to believe Contador’s story.

There have been suggestions in the press that Contador’s positive test is the result of an autologous blood transfusion (blood doping) – that is he re-infused so of his own blood that was collected earlier in the year – and that this blood contained clenbuterol. This is indeed possible, but autologous blood transfusions can be detected in a blood test, and, as winner of the Tour de France, Contador would undoubtably have been subjected to a blood test. My assumption is that if the UCI had detected blood doping, then they would have already released the test results. To clarify this matter, the UCI should make a formal statement and publish the results of any such blood tests.

### Update – Sunday 3rd October 2010

There are currently three proposed explanations for Contador’s positive drug test:

2. Contador inadvertently took clenbuterol as a result of eating contaminated meat.
3. Contador had a blood transfusion and the clenbuterol was in the tranfused blood.

The calculations in this blog post show that it is unlikely that Contador deliberately took clenbuterol, and that it is feasible that eating contaminated meat could have resulted in his test result (namely urine with a concentration of 50 picograms/millilitre).

There remains the question of the blood transfusion. Nowadays it is possible to detect if someone has had a blood transfusion, whether that transfusion is autologous (from one’s own blood) or homologous (from someone else’s blood). We know that cyclists are tested to see if they have had blood transfusions – Alexander Vinokourov was tested positive in 2007. I see four possibilities:

1. Contador was tested for blood doping and the result was positive.
2. Contador was tested for blood doping and the result was negative.
3. Contador was tested for blood doping and the result was inconclusive.
4. Contador was not tested for blood doping.

Contador himself has denied receiving blood transfusions

The UCI and the World Anti-Doping Agency have refused to comment on L’Équipe’s story that raises the possibility of blood doping.

In my view the UCI’s reticence on the blood doping issue is inexcusable. Both in fairness to Contador and for their own credibility they must release the results of any blood doping tests they have made on Contador.

### References

1. Clenbuterol Residues in Bovine Feed and Meat (Research Journal of Biological Sciences)
2. Pharmacokinetics of plasma and urine clenbuterol in man, rat, and rabbit (PubMed)
3. Tainted Meat: Clenbuterol use in the meat industry (Serendip)
4. Press release – Adverse analytical finding for Alberto Contador (UCI press release)
5. Contador maintains innocence (The Press Association)
6. Maximum Residue Limits, Clenbuterol (European Agency for the Evaluation of Medicinal Products)
7. Contador’s scientific expert De Boer details defense (Cycling News)

### Calculation

From reference [2] we know that after ingesting clenbuterol reach a maximum level after 2.5 hours, remain at this level until 6 hours after ingestion. From this, and assuming that the rate of drug removal by the kidneys is proportional to its plasma concentration, we can model the concentration C of clenbuterol at time t (given in hours) in the urine as:

$C(t) = \left\{ \begin{array}{l l l} mt & \quad \mbox{0} \le {t} \le {2.5} \\ 2.5m & \quad \mbox{2.5} \le {t} \le {6.0} \\ 2.5me^{-k(t-6)} & \quad \mbox{t} \ge {6.0} \end{array} \right.$

The half life of clenbuterol in blood plasma is approximately 35 hours, so:

$k = \frac{ln(2)}{35} = 0.01980$

The cumulative urinary excretion is 20% of the dose, D after 72 hours, so:

$\int_{0}^{72} C(t)\: \mathrm{d}t = 0.2D$

that is

$D = {5}\left(\int_{0}^{2.5} mt\: \mathrm{d}t + \int_{2.5}^{6} {2.5}m\: \mathrm{d}t +\int_{6}^{72} {2.5}me^{-k(t-6)}\: \mathrm{d}t\right)$

$\quad = {5}\left[{0.5}mt^{2}\right]_{0}^{2.5} + {5}\left[{2.5}mt\right]_{2.5}^{6} + {5}\left[\frac{-2.5m}{k}e^{-k(t-6)}\right]_{6}^{35}$

so

$D = 378.63m \quad (equation 1)$

Let’s assume Contador’s urine sample was taken 24 hours after ingestion of the clenbuterol and consists of the urine produced in the previous hour. Then, assuming a typical urine production rate of 50ml/hour, the quantity of clenbuterol excreted, per ml of sample, E is given by:

$E = \frac{1}{50}\int_{23}^{24}C(t)\: \mathrm{d}t$

$\qquad = \frac{1}{50}\int_{23}^{24} {2.5}me^{-k(t-6)}\: \mathrm{d}t$

$\qquad = \left[\frac{-m}{20k}e^{-k(t-6)}\right]_{23}^{24}$

so

$E = 0.03536m \quad (equation 2)$

We know Contator’s test result – his urine sample contained 50 picograms per ml, this allows us to solve equation 2 for m and feed the result back into equation 1 to obtain the approximate dose of clenbuterol ingested by Contador. This gives an approximate dosage of 535,400 picograms, that is 540 nanograms (rounded).

Disclaimer: I’m a mathematician, not a medic or a pharmacologist. The above calculations have not been independently reviewed, so there may be errors in the model or the calculations. If you find any errors, please let me know and I will correct them.

1. Oct 1, 2010 at 14:38

it appears the test was some time after dinner the night of the rest day, so wouldn’t that lower the max amount he would have to ingest to produce that sample?

• Oct 1, 2010 at 17:54

The UCI statement says the sample was “taken during an in competition test on 21st July 2010 on the second rest day of the Tour de France”. Contador’s statement says “on the afternoon of the 20th, a day before our rest day, the meat was cooked”. I don’t know the exact times that the sample was taken or the meat was eaten, so I made a conservative estimate that 24 hours elapsed between the two events.

But you are correct in your statement that if there was a shorter interval between the two events, then a smaller amount of clenbuterol would need to have been ingested to produce the given result. So, for example, if the test was administered on the morning of the rest day then the amount of clenbuterol calculated to be in the meat would be smaller, lending further credence to the contamination theory.

2. Oct 1, 2010 at 16:31

I would not be inclined to believe Contador but as it stands, should not result in his facing serious sanctions.

3. Oct 1, 2010 at 17:44

Really interesting and thorough analysis. Thanks!

There have been allegations both on German TV and in L’Equipe that a separate test has found the presence of plasticizers used in blood bags in Contador’s sample. This certainly suggests the possibility of autologous blood doping. However, the test has not been ratified by WADA.

The biggest question for me remains the timing of yesterday’s announcement. Neither early enough to be fully transparent nor late enough to provide conclusive investigation results. Were Contador and the UCI’s hands forced by the realisation that the aforementioned third parties were about to leak the story? If so, the implications for the sport are potentially disastrous.

4. Oct 3, 2010 at 01:33

He said that he ate the meat twice, two days in a row. How is this compatible to the levels found?

• Oct 3, 2010 at 08:35

It would depend when he ate the meat the second time. If it was after his urine sample was taken, it would make no difference to the analysis. If it was before the urine sample was taken, then it would mean that the meat would have had a lower level of clenbuterol. My analysis showed the meat had slightly higher levels of clenbuterol than is expected in contaminated meat, if Contador ate the meat twice it would bring the level of contamination into the expected range.

5. Oct 4, 2010 at 14:15

It’s interesting to see the numbers crunched to indicate that contador’s story may be true.

However you are incorrect in asserting that autologous blood transfusions can be detected, it is my understanding that at the moment they can’t.

• Oct 4, 2010 at 17:32

Blood doping (be it doping by transfusion or by use of a banned substance such as EPO) may be detected in two ways: indirect and direct. In indirect detection the althetes blood is sampled over time and doping is inferred from an abnormal variation in the blood composition – one of the reasons for the introduction of the “blood passport” was to allow indirect detection of blood doping. In the case of an autologous blood transfusion there will be two abnormal variations in the blood composition – a decrease in red blood cell count immediately after the althete’s blood is harvested, and an increase in red blood cell count immediately after the transfusion. Whether these changes are detected depends on the timing of the samples taken for the blood passport.

In direct detection the doping agent is directly detected in the blood sample. Homologolous blood transfusions may be detected because red blood cells have markers (antigens) specific to the individual, simplistically if more than one type of marker is present then the individual has had a blood transfusion from someone else.

Autologous blood transfusions can be detected by the age profile of the red blood cells – simplistically the blood cells from the transfusion are older than the althetes normal blood cells. So if the blood contains older cells a transfusions must have occured. This autologous transfusion test is still in development, and does not yet have ‘official’ status.

So the short answer to your question is: autologous blood transfusions can be detected, but there is, at present, no officially approved direct test for them.

6. Oct 5, 2010 at 15:52

It appears in an article in today’s New York Times (http://nyti.ms/d0X78C), that the IV bag plasticizer was already detected the day before the first clenbuterol traces were detected.

As a side comment to your calculations (which I repect):
(1) half-time values for clenbuterol according to Clin.Toxicol. 2001, 39:339344 range between 25 and 39 hours, so this would give your calculation a range of plausibility rather than 2 significant digits;
(2) the values of 50 and 20 pg/ml reported are not clear; I haven’t seen the official report, but the letter by Dr Douwe de Boer states that “the methods were not quantitative, but it may be estimated that the concentration was in the range of XX pg/mL”; I imagine this to mean that the Dr gleaned that amount out of his experience with such tests; my guess is that the de Boer’s guesses are +/- 10 pg/mL.

• Oct 8, 2010 at 19:35

Thanks for the link to the New York Times article.

You are quite right to point out that there is considerable uncertainty in the calculations – as well those you point out there is also the stated cumulative urinary excretion of 20% after 72 hours. I don’t regard this calculation as anything more than an order of magnitude calculation, and did not mean to imply that it was accurate to 2sf.

Because the amount found in the urine was so small, even an order of magnitude calculation is enough to make a judgment as to which of the two initial proposed explanations was most likely.

7. Oct 7, 2010 at 18:02

This makes interesting reading. This is linked – but a different case. Could you advise on the conclusions you would make if the level of clenbuterolwas 40 ng/ml. Is this a significant amount or could this also have been from contaminated meat? In this case there were symptoms of severe food poisoning.

• Oct 8, 2010 at 19:57

I can’t “advise” on any specific cases – nothing in this blog constitutes advice.

To make any conclusions from the urine level you also need to know when the urine sample was taken. A clenbuterol level of 40 ng/ml is 800 times the level used in my calculations, so making the same assumptions (namely that the sample was taken 24 hours after ingestion) it would imply that the clenbuterol dosage was 800 times higher: that is 430,000 nanograms, or 430 micrograms. That is over 5 times the maximum recommended daily therapeutic dose.

8. Oct 8, 2010 at 01:54

Martin you may be interested in the following reference:
Brambilla G, Cenci T, Franconi F, et al. Clinical and pharmacological profile in a clenbuterol epidemic poisoning of contaminated beef meat in Italy. Toxicol. Lett. 2000;114(1-3):47-53.

Key sentence in the abstract:
Clenbuterol was found in the urine of all the symptomatic patients, at higher levels than pharmacokinetic computing (mean level 28 ng/ml, 36 h after ingestion), based on the levels found in the meat (1140-1480 ng/g edible tissue) …

• Oct 8, 2010 at 19:59

Yes, thank you.

9. Dec 18, 2010 at 11:48

I think there is a key data missing. The important thing is not the concentration in urine but the amount found in urine. We know the concentraiton but we don´t know (or I have not found) the amount of urine to estimate the amount of clembuerol. The second point is that elimination in urine follows first order kinetics, thus the amount excreted at earlier times is much greater than the amount excreted at later times. If the urine sample is taken later then the amount of drug will also be much, much smaller, even if the amount of drug taken in therapeutic, as most of the drug would have been eliminated earlier.
I doubt that a conclusion may be drawn with the data available at the moment.

• Jul 18, 2011 at 20:42

A person typically passes about 1.5 liters of urine a day, a point noted even by Contador’s lawyers in the RFEC hearing, though they pointed out it could be somewhat less. Contador tested positive four times over 5 days (was not tested on one of those days). From the concentrations of CB in his urine found in those tests, and assuming 1.5 l of urine a day, it can be estimated he passed about 150 ng of CB during the four days (day 1 to day 5), and about 130 ng in the first three days.

Elimination follows first order kinetics initially, but later a second, slower phase of elimination appears. In fact, in ref 2 in Martin’s blogpost, it’s noted that following a single dose of CB, only about 20% of the substance appears in the urine in the first three days. Most of the rest is excreted much more slowly. So we can estimate from this that Contador ingested about 650 ng of CB, which agrees reasonably well with Martin’s estimate.

Of course changing assumptions a little will affect calculations. The key point, though, is that Contador ingested far more CB than could be accounted for by eating meat, unless that meat had a level of contamination far above the 100 ng/kg standard allowed in Spain. So the question becomes, how likely is it that he would have eaten meat that exceeded the inspection limit? The available testing data indicate this is extremely unlikely.

10. Feb 17, 2011 at 17:40

I am an engineer and I reviewed your estimates. The published on Clenbutrol residues agrees nearly exactly if Contador ate about a 200 mg steak. This is about equivalent to a 6 oz steak, and would be in range of what a rider would consume.

So it does appears that steak with Clenbutrol is a valid hypothesis, turned more believable by having the level expected from measured meat contamination agree.

Thus, I now know that Contador must be found innocent.

What if he did microdosing – but yet he did not have 40x residue below on other test days.

So therefore, I submit that the probability of being contaminated by the meat is over 90%. Has anyone forwarded the published papers and Clenbutrol calcs to the UCI?

11. Jun 19, 2011 at 13:54

I believe the calcs.

However, assuming everybody in Spain had the same probablility of eating a piece of randomly sampled beef, then anybody in Spain could test positive too.

I suggest nobody in Spain except Alberto would actually test positive and there’s nothing wrong with Spanish beef. Evidence, Clenbuterol poising number for 2010 Mexico vs Spain. 217 vs 0.

Also checkout: Urinary di-(2-ethylhexyl)phthalate metabolites in athletes as screening measure for illicit blood doping: a comparison study with patients receiving blood transfusion. Jordi Segura

12. Jul 3, 2011 at 12:41

You should try calculating the chances of all spanish riders (and all other spanish atlethes) eating spanish meat regularly and having thousands of doping tests being done on them in de last few years and only one of them getting caught with these levels of clenbuterol.

It is also fairly ridiculous to compare to Mexican situation as the clenbuterol levels found there have not been found in the whole of europe in this century.

Contador having consumed 54 times more than what would be the legal limit for 100 grams meat would seem incredibiliy unlikely. The chances of him having eaten meat that would be tainted with amounts never found in the EU before is also extremly unlikely.

The by far most likely explanation is that he transfused blood from a high altitude traning period where he used clenbuterol.

• Jul 18, 2011 at 20:30

Rob is correct. In the RFEC hearing that exonerated Contador, WADA provided estimates of the level of contamination of the meat that ranged from 3-110 times the legal standard of 100 ng/kg. Martin’s estimate is well within that range (though Contador probably ate more than 100 g of meat, say 300 g, which would bring Martin’s estimate down to roughly 15 times the legal standard) and IMO is quite reasonable.

It’s what Martin does with that calculation that makes no sense. The testing data in Spain show that meat with CB above the 100 ng/kg standard is extremely rare. Indeed, studies have shown that even meat bought off the street in Mexico is rarely contaminated to the degree required by Martin’s calculation.

In contrast, the same study used by Martin to model the pharmacokinetics (ref. 2 in his blogpost) indicates that if an athlete took 80 ug of CB twice daily for several days, levels of this substance in his blood would plateau at about 1-1.2 ng/ml. If 500 ml of this blood were withdrawn and re-infused, the athlete would ingest 500-600 ng of CB, which is comfortably within the range of Contador’s estimated amount of ingestion. Larger amounts of CB taken would be compatible with smaller amount of blood transfused.

13. Nov 21, 2011 at 16:14

Hi Martin,
I need to admit that you have done a very good job with your calculations, but I don’t agree with one point, the 24 hours between ingestion and the test, I believe the test was done in the morning after he claimed to eat the meat, so probably only about 12 hours.
Still, I think he’s guilty and he’s lying, because a cyclist would never eat meat, and never ever in that amount, in the middle of a 3 week competition race, plus the plastics also found in his system.
Javi

14. Nov 22, 2011 at 20:47

u make quite a few assumptions in all of this
to me the most glaring is
You completely ignore the possibility of the clenbuterol being taken in conjunction with another drug/drugs which would drastically alter the levels found/ingested ratio.
For instance taken with a common diruetic what are the parameters?

15. Sep 10, 2012 at 00:00

I have to point out that just because there is a maximum allowable amount of a drug in meat doesn’t mean that any meat actually is within those tolerances. It’s certainly possible for some farmer/rancher somewhere to be cheating. After all, we know humans cheat for monetary gain and we know that no food system in any government can possibly test every animal. Not anywhere close. Some (most?) agencies don’t test meat unless there is a suspected problem.

In other words, farmers and ranchers are considered to be honest. Athletes are considered to be cheaters.

It’s also possible that an athlete could take a substance at an optimal time with the knowledge of when it would be likely to be past the point of detection. So race is at time B, and test for drugs wouldn’t be until at least time C, so therefore take it at time A.

Perhaps his math was simply off, or he ate something that extended the half life of the drug.

Personally, I think athletes who want to do whatever to themselves should be allowed, but have to run in a separate race or as a special class with awards for “clean” athletes, and another for “enhanced”.

I’m pretty sure various military organizations would be interested in sponsoring athletes under those rules.

1. Jul 4, 2011 at 23:57