This is totally different from the sort of books I normally read (SF/F, detective stories and mysteries, historicals) but I picked it up in a sale on my way to a job interview because it looked intriguing. I'd heard of the film, but I haven't seen it, and I really enjoyed the book, which I finished unusually quickly. Spoilers follow.
My Sister's Keeper is about a court case to determine whether Anna, a 13-year-old who was genetically engineered specifically to be a perfect donor for her older sister Kate, who suffers from leukemia, should be medically emancipated from her parents so that she can choose whether or not to donate a kidney to her sister. I was mildly annoyed at the blurb and general packaging of the book, which implied that the story was told from the mother Sara's point of view in a pathetically obvious bid to appeal to women in their 30s and above (apparently it was a Richard and Judy Best Read, but I won't hold that against it). In fact, the story is told from multiple points of view, the most sympathetic being Anna's and as the title implies, it is the relationship between the sisters that is at the heart of the story (though not in the way you might think, as it turns out).
'Anna' is short for Andromeda, named by her father Brian, whose hobby is astronomy and who deliebrately named her after the Greek princess. Andromeda was left as a sacrifice to a sea monster because her mother Cassiopeia had compared her own beauty (or sometimes Andromeda's) to the Nereids (goddesses of the sea). Perseus saved her and married her. There are obvious parallels to the novel's plot, in which the mother Sara's conviction that she can somehow save her older daughter leads her to such a proud, brooks-no-arguments attitude that she forgets to ask what either of her daughters actually want, while Anna is left out as, potentially, a sacrifice for her sister and for her mother's refusal to back down (the removal of a kidney being pretty serious surgery). The ending, however, strays away from the myth and Perseus is nowhere to be seen (though in the film version Anna's lawyer might be a Perseus of sorts).
The most interesting thing about the use of Greek mythology in this novel is that it comes mostly via an interest in astromony. Apart from the fish Kate names Hercules (the strongest of heroes - pretty obvious symbolism going on there) all the mythological references are there because Brian is interested in astronomy, and that has led him to an interest in the myths behind the constellations. This is partly because fire is another theme of the book - Brian is a firefighter and one of the book's subplots concerns an arsonist - so Brian spending his time gazing up at flaming balls of gas drives home that theme. The characters, especially Brian, show a genuine interest in the mythical stories and Brian has certainly done his homework on them, but only as far as they relate to the stars; little interest is shown in myth independent of astromony. This is because the stars are something tangible, that we can see for ourselves in the night sky (though Brian does ponder the issues around the movement of stars and the differences between the ancient night sky and our own at one point). Brian enjoys mythology because he can, in a sense, see it up above him at night (not the actual Andromeda, of course, she doesn't exist, but the constellation named for the story by actual Greeks). Since death is also one of the themes of the book, it also relates to the popular idea of the dead being among the stars, giving a tangible point of reference for a bereaved family.
The ending of the book is quite different from the film - the film has the ending you expect this story to have, the book goes in a different direction and has the sort of highly manufactured ending you rarely find outside of fiction, though it is a satisfying ending nevertheless. It drives home some of the book's themes and works well enough if you like that sort of thing, and makes Anna's full name and the position of Andromeda, described as spread-eagled out across the sky ready to be sacrificed, especially relevant and poignant. I did like the way it made the reader re-think the title and prologue as well, though I think I shall return to something a bit nicer and more cheerful for my next read!