### Archive

Posts Tagged ‘Science’

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.

## Popular science on TV – call for a scientist’s cut

Apr 25, 2010 1 comment

Films are sometimes re-released as a director’s cut – a version that more closely reflects the director’s vision for the film, free from the commercial pressures of the studio.

Science programme makers could take a cue from filmmakers and produce two cuts: one for the general public and one for enthusiasts.

Take Wonders of the Solar System. This has all the makings of a great science programme: an enthusiastic and knowledgable presenter in Professor Brian Cox, great pictures of space and the earth, travel to interesting locations, interviews with scientific experts and fantastic computer simulations. Yet the programme is hard to watch – it’s like eating cabbage: I do it because I know I ought to, not because I want to. And it’s not just me. A friend of mine, who is also a science and technology enthusiast, said he fell asleep during the programme.

The main problem is that the programme is constrained to a 1-hour slot, and is edited to fit that slot. This means there is a lot of filler to sit through. Shots of Brian Cox walking up to a telescope, unnecessary shots of him driving in his car (and, of all forms of filler, presenters driving in their car is the most clichéd and overused), scenes that are portmanteaux of earlier scenes, and so on.

The second problem is that the programme, by necessity, targets a wide audience: since there are relatively few science programmes on television, such programmes have to target both the general public and those who have a deeper understanding of science. This means these programmes generally need to include explanations of the basics, and even when these explanations are good, they are not that interesting to people who already understand what is being explained. A good example is when Brian Cox explained the size of the solar system, by placing planets in their relative positions on a table, and then driving to the position of the Oort cloud. This was a dramatic illustration of the solar system’s size (and, incidentally, appropriate use of a shot of him driving), but not that interesting to someone who understands the vastness of space.

Both these problems could be solved by having two cuts of the programme – a standard version and a scientist’s cut. The scientist’s cut would differ from the standard cut in that it would not include the filler and the basic explanations. But it might include more detail in other areas.

Programme lengths no longer have to be totally dictated by the TV schedule. Perhaps the main showing needs to fit a one-hour slot, but repeats on BBC iPlayer certainly do not. There is no reason why two cuts of “Wonders of the Solar System” should not be available on iPlayer – the full version and the scientist’s cut. The programme is repeated on BBC1 and BBC4, often in the middle of the night – there is no reason why one of these repeats should not be a scientist’s cut. The programme is to be sold on DVD – there is no reason why there should not be a DVD scientist’s cut.

Despite the fact that it contains some wonderful material, I won’t be buying the DVD of Wonders of the Solar System. But if Professor Brian Cox was given full editorial control and was allowed to make a scientist’s cut of the programme, I would buy that.

Film enthusiasts get a special cut, science enthusiasts should get one too.

## One in 10 UK children thinks Queen invented telephone – NOT

According to an article on BBC News one in ten UK children thinks the Queen invented the telephone. One in twenty think that Luke Skywalker was the first man to set foot on the moon. And an amazing 60% of nine and ten year olds think that Sir Isaac Newton invented fire.

I think not.

What this survey shows is that children have a sense of humour. What it shows is that, when presented with a bunch of boring questions, the average 10 year old will have a laugh and choose the stupidest answer. I probably would too.

The real story here is the poor quality of the BBC reporting. Without even considering the plausibility of the results the reporter presented the results of an online survey as fact.

May I suggest an alternative story:

### Gullible BBC reporter outsmarted by a bunch of 10 year olds

When presented with a survey showing that “60% of nine and ten year olds thought that Sir Isaac Newton invented fire” a gullible BBC reporter naively presented this story at face value. The reporter did not consider the plausibility of this factoid, nor did they seek a second source to verify the factoids.

Which is more likely: the ten year olds were having a laugh by giving stupid answers to a boring survey, or the ten year olds were genuinely ignorant? I think the children proved themselves smarter than at least on BBC reporter.

Tags: , ,