December 31, 2013 - 10:36 GMT hellomagazine.com Michael Schumacher shows 'some improvement' after second operation for serious head injuries from ski accident while family keep bedside vigil Michael Schumacher's doctors say he is showing "some improvement" after undergoing a second operation for the severe head injuries he suffered in a skiing accident The retired racing driver's medical team performed the operation on Monday night which they said helped them to "control the situation". Meanwhile his family are keeping a bedside vigil at the French hospital where he is "fighting for his life" after hitting his head on a rock while skiing off-piste with his teenage son. The Formula One champion's wife Corinna, daughter Gina Maria and son Mick are in a state of shock at the Grenoble hospital. "The family is not doing very well, obviously. They are shocked," the racing driver's manager Sabine Kehm told reporters. The seven-time F1 champion was taken to the hospital on Sunday where was put in a medically-induced coma to relieve the pressure on his brain. Doctors have lowered his body temperature to 34-35C (93.2-95F) slowing his metabolism to help reduce inflammation. "We operated urgently to try to eliminate the haematoma," Jean-Francois said. "After the operation we saw that we had been able to eliminate these haematoma but also sadly the appearance of various bilateral lesions. "So therefore he was taken to intensive care to try to help. "It's too early to say what is going to happen and to have a prognosis. Taking into consideration the very violent shock, his helmet did protect him to a certain extent, of course. "Somebody who would have this kind of accident without a helmet, certainly, he would not have got to here." The German race driver, who turns 45 on 3 January, is said to be a keen skier. He was with 14-year-old Mick at the time of the accident. He retired from F1 for a second time in 2012 having won seven world championships and secured 91 race victories during his 19-year career.