### Archive

Posts Tagged ‘Tour de France’

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.

## Estimating your Etape du Tour time

The 2010 Etape du Tour is from Pau to the summit of the Tourmalet.

I’ve produced a spreadsheet that allows you to estimate your time. I’ve ridden the Etape three times myself (2003, 2004, and 2006) and used a similar spreadsheet to estimate my time. It has proven accurate to within about 10 minutes. In 2003 and 2004 I placed just outside the top 1000 riders, and was about 20 minutes short of gold standard time.

To estimate your time you need to provide 6 pieces of information:

1. Weight (rider + equipment) (kg). This is the total weight of everything, including clothes, shoes, food, water, tools etc. The easiest way to measure it is to set up the bike as you will ride it (including full waterbottles, tools, pump, food etc), put on the gear you will wear when riding the etape (including shoes and any spare clothing or food in pockets), pick up your laden bicycle and weigh yourself on the bathroom scales.
2. Power (when climbing). This the power output you can sustain over a long climb of about an hour. I’ll give you a way of estimating this later.
3. Slight incline speed (km/h). This is the speed you can sustain on a slight incline (1%-3%)
4. Flat speed (km/h). This is the speed you can sustain on the flat in a group of riders.
5. Slight descent speed (km/h). This is your speed on a slight downhill. (1%-5%)
6. Descent speed (km/h). This is your speed on a steepish (more than 5%) downhill. Note that it is not your maximum speed, it is your average speed and takes into account the corners.

As well as allowing you to estimate your time, it allows you to ask What if? questions about how you ride the course.

• What if I reduce my weight by 1kg? Depending on your power output, your time will improve by about 2 to 3 minutes for each kilogram of weight saved.
• What if I go 10km/h faster on the steep downhills? Surprisingly this only shaves about 3 minutes from your time.
• What if I go 5km/h faster on the flats? This improves your time by about 10 minutes.

### Why does the spreadsheet work?

The spreadsheet works because, for the Etape, the climbs dominate the stage. Differences in speed on the flats and on the descents make relatively little difference to your overall time, so you don’t to estimate these speeds very accurately. The climbs are steep enough that wind resistance does not really come into play, so your speed is determined pretty well by your overall weight and your sustainable power output – if you know these two things, you can make a pretty good estimate of your overall time.

### How do I estimate my climbing power output?

You can estimate your time either using an ergometer (say at a gym) or by doing a timed climb. For either method you need to warm up and then start riding at a heart rate that you can sustain comfortably for several hours – if you know what your lactate threshold rate is, it will be slightly below this rate. On an ergometer read off the power rating for this heartrate – make sure you have been riding long enough for the heartrate and power to settle. If you use a timed climb (ideally this should have a steady gradient) then ride the climb at this heartrate. Enter the total weight of you and your equipment, the length of the climb, and the altitude gained into the spreadsheet and it will give you an estimate for your power output.

### The route profile

I obtained the route profile from http://www.letour.fr/ augmented with climb profiles from http://www.climbbybike.com/

Col de Marie Blanque steep climb with over 3km at or near 11% gradient

Col du Soulor steady climb, mostly at at around 8%

Col du Tourmalet mostly at around 8% with last kilometer at 10%

### Advice on riding the Etape

Below are some words of advice. They are mainly intended for riders not experienced in riding long mountainous courses. If you know what works for you, then use that.

### What gears should I use?

The choice of gears is determined by the steepest parts of the course. You need a gear low enough to allow you to ride at a comfortable cadence on the steepest parts of the course. This year the Etape has some steep sections, so you’ll need low gears.

There is a section on the spreadsheet that calculates your cadence on the steepest part of the course. If you want to keep your cadence above 50rpm on the steepest sections, then you can see you’ll need low gears. I advise the largest possible sprocket, normally 27 or 28 teeth. This means something like an 11-28 or a 12-27 rear cassette. To go with this you’ll need either a triple chainring with a 30-tooth inner chainring or a compact chainring with a 34 tooth inner chainring. A standard chainring (with an inner chainring of 37 or 38 teeth) just won’t cut it. (For the record, I’ve always used a triple chainring when I’ve ridden the Etape, even though I hate triple chainrings.) A 30×28 gear is not overkill for this course. Every year that I did the Etape I saw riders who got off their bikes and walked. They did not have a low enough gear.

But the pros don’t use such low gears, I hear you say. That’s true, but they are pros. A top professional might weigh 65kg and have a power output of 400W while climbing. Add 10kg for bike and equipment and put the figures in the spreadsheet. You’ll see that a top pro can maintain a good cadence riding a 37×21 or a 37×23 gear.

### How should I ride the course?

Assuming you have trained well, you need to do four things to get a good time:

Climb well. This means keeping a good pace on the climbs. It also means riding on your own: unless you are experienced it’s easy to either get behind a rider who is going a bit too slow or a bit too fast. My strategy is to climb by heartrate and cadence, for me this means something like: “keep the heartrate at 145bpm and the cadence at 85rpm”. You’ll need to find the figures that work for you. The heartrate needs to be a rate that you can sustain for several hours, it will be below your lactate threshold rate. The cadence is what is comfortable for you for long climbs.

Eat and drink well. Make sure you don’t dehydrate or bonk. Talk to other riders and get experience of how much to eat and drink on long rides.

Descend well. First and foremost this means don’t crash. Don’t take risks on the descent. From the spreadsheet you can see that even going 10km/h faster on the descents won’t make much difference to your time. It also means don’t brake too much. Too much braking tires you out – you need to be reasonably relaxed on the descents. If you’ve never done long descents you need to get some practice in before the Etape.

Get into a group on the flats. On the flat parts of the course try and ride with a group. Save your energy for the climbs.

Good luck!