Westhauser suffered the traumatic head injury in a rock fall last weekend while exploring the huge Riesending cave complex, the deepest in Germany. In normal conditions, he would be in an intensive care unit.
Instead he is strapped into a special stretcher, wrapped in a sleeping bag and layers of styrofoam to keep him warm. One of the biggest dangers for a man with his injuries is cold, medics say, and the temperature in the cave is 3C.
A doctor travelling with the rescue party is carrying a skull drill: Westhauser is at constant risk of bleeding in the brain, and if the pressure becomes too great, the doctor will have to relieve it by drilling through his skull in an emergency procedure.
So arduous is the journey ahead that different teams of rescuers will work in relay stages to bring the victim to the surface.
Cave rescue is highly specialised, and teams have converged across the Alps from Switzerland, Austria and Italy to help.
The entrance to the cave complex lies more than 1830m up in the Bavarian Alps, and can usually only be reached by a gruelling climb. Now a helicopter is ferrying supplies in.
The Bavarian authorities are refusing to comment on the cost of all this, but German newspapers are already predicting it will be the most expensive rescue operation in German history, and could run to millions of euros.
The rescue
14 rescuers and a doctor.
5km, 7 days to get to the surface.