Witness says he inadvertently filmed Michael Schumacher's accident

Formula One legend Michael Schumacher remained in critical condition on Sunday a week after his skiing accident in the French Alps, which a German eyewitness said he inadvertently caught on his smartphone.

Investigators are focusing on the retired racer's speed when he fell and slammed his head on a rock on a small off-piste section of the Meribel ski resort, prompting his evacuation by helicopter to the Alpine city of Grenoble.

They are hoping that a helmet-mounted camera Schumacher was wearing will provide some clues, as will footage by a 35-year-old German steward who says he was filming his girlfriend on the slopes when by chance he captured the moment when the driver fell.

In the background, a skier is seen descending an unmarked run between two groomed pistes before falling, news magazine Der Spiegel reported.

According to the witness, who spoke to the magazine, the seven-time world champion was descending the slope at a "leisurely" pace - "a maximum speed of 20 kilometres an hour". He plans to hand over the footage to French investigators.

This would corroborate claims by Schumacher's spokeswoman Sabine Kehm, who said he could not have been going fast "because it appears he helped a friend who had just fallen".

But in a press conference last week, doctors who treated Schumacher said he had been skiing at great speed when he fell on December 29.

Edouard Bourgin, a specialist on accident claims, said there could have been "a catapult effect that explains the violence of the shock, even in the absence of excessive speed."

Prosecutors are also looking at whether the limits of the ski runs next to the accident site were correctly marked and whether the rock in question was lying close enough to the piste to require some kind of protection or signage.

In addition, they are examining whether the safety releases on Schumacher's skis operated properly in a probe aimed at determining responsibility for the accident.

Schumacher turned 45 on Friday, and fans marked the birthday with a silent vigil outside the facility, part of which was organised by Ferrari, Schumacher's former team.

His wife Corinna and two teenage children have been at his bedside throughout, and other family members have come to visit, including his father Rolf and his brother Ralph, who is also a racing driver.

Kehm said Schumacher remains in a "critical but stable" condition after he underwent two surgeries earlier in the week to ease pressure and bleeding. No further press conferences are scheduled before Monday.

'Don't try to beat the clock'

The accident has shocked legions of fans and racing stars used to seeing Schumacher cheat death on the track.

Mika Hakkinen, the double Formula One world champion who suffered a near fatal crash during a practice session for the 1995 Australian Grand Prix, wrote to his former rival wishing him a quick recovery, the Bild am Sonntag newspaper reported.

"Your accident is now just another challenge. You have to fight hard again, just like we both used to do on the track," the Finnish driver said.

"Do me a favour: just this once don't try to beat the clock. You don't have to post your best time in this race. You have to take all the time you need."

It is not known whether the GoPro miniature camera Schumacher had strapped onto his helmet filmed the accident, or whether images have been damaged by the impact of his fall, which was so hard it split the helmet in two.

Any usable images should shed light on the circumstances of the accident on the small, seemingly innocuous off-piste section of Meribel located between two ski slopes - one classed as easy and the other as intermediate.

Police have also obtained eyewitness testimony from Schumacher's 14-year-old son Mick, who was skiing with his father at the time, as well as a friend.

Schumacher, who made his debut in 1991, dominated Formula One during his career, winning more world titles and races than any other driver. He retired in 2012.