Half of the film is based around the current events, following the police questioning of Alex, while the other half studies the relationship that Alex and Milena had leading up to the overdose. Their background shows a very checkered path, so the police must deduce exactly what part, if any, the secluded professor played.
This could cause confusion between the events - it is a little bit off-putting at the beginning - but Garfunkel displays that he is not just a musical talent by showing off his range of acting. While Flaherty just has to lie down in the hospital, she makes up for it in her interpretation of a woman falling slowly in and out of madness and is impressive.
It should noted that this film doesn't really tell much of a story and primarily focuses on the personalities of the characters. That's not to say it's a bad film, but more one that can be open to various interpretations. If film was art, this would certainly be a Picasso.