Vincent's NT Word Studies
14. Luke - Demas. See on Philemon 24.The beloved physician. See Introduction to Luke.
Robertson's NT Word Studies
4:14 {Luke, the beloved physician} (loukas ho iatros ho agapetos). Mentioned also in #Phm 1:24; 2Ti 4:11. The author of the Gospel and the Acts. Both Mark and Luke are with Paul at this time, possibly also with copies of their Gospels with them. The article here (repeated) may mean "my beloved physician." It would seem certain that Luke looked after Paul's health and that Paul loved him. Paul was Luke's hero, but it was not a one-sided affection. It is beautiful to see preacher and physician warm friends in the community. {Demas} (demas). Just his name here (a contraction of Demetrius), but in #2Ti 4:10 he is mentioned as one who deserted Paul.