Reference: http://www.alfawzan.af.org.sa/node/15745
Question: How should the one who is ill purify himself if he is unable to use water on some or all the required parts of the body for wudhoo?
Response: Yes, if he is unable to use water on all the parts of the body required for wudhoo, then he should do tayammum – by striking the clean earth with his hands, and then wipe his face and both hands – this is for the one who is unable to wash [all the required parts of the body for wudhoo]. As for the one who is able to wash some of the parts of the body [required for wudhoo], then he should wash what he is able, and then do tayammum over those parts [of the body] he is unable to use water on – in this manner he combines the use of water and tayammum.