Amoytrophic should be broken down into its three Greek root words: a-myo-trophic.
· ‘a’ is similar to saying “not” or “absent”, or “un-“
· ‘myo’ refers to muscle cells (e.g. myocardium – the “muscle of the heart”)
· ‘trophic’ means something close to “nourishing”, although in medical terminology it is often taken to mean something nearer to “growing”.
For instance, if you don’t use your muscles they may waste away. The medical term for this would be “atrophy”, as in “a-trophy” – “not grow”. Thus “amyotrophic” means (loosely) “wasting away of the muscles”. This is a distinct clinical feature of ALS, and is due to the denervation of muscle fibres that occurs as the motor neurones die away.
Then there’s the “lateral sclerosis bit”. ALS affects both upper and motor neurones; the former causes a thinning of the descending white matter tracts travelling from the brain down the spinal cord. These tracts happen to be located largely in the lateral portion (and, to a slightly lesser degree, anterior portion) of the spinal cord. As the tracts degenerate, they are replaced by the nervous system’s equivalent of fibrosis – gliosis. And this of course gives the lateral (and anterior) portion of the spinal cord a particular firmness, with the attractive pathological term for hardening being “sclerosis”.
There you go!
Edit: Sorry, Stephen Hawking almost certainly does not have ALS. This disease typically kills in 3-5 years; he's been going for about 10 times as long. It is thought that he may have a variant form, or more probably one of the spinal muscular atrophies.