The most common and most likely answer to this crossword clue is the 13 letter word PSYCHOSOMATIC
I've seen this crossword clue in The Daily Telegraph
P
S
Y
C
H
O
S
O
M
A
T
I
C
Buddy explains!

The straight part
We know that "Imagined" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case imagined = psychosomatic.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does PSYCHOSOMATIC mean?
PSYCHOSOMATIC adjective- Pertaining to both the mind and the body.
- Pertaining to physical diseases, symptoms etc. which have mental causes.