There are a few scenes of the surgery of Kaori between the scenes of Kousei's performance which I think implies how Kaori truly died. Just throwing this in here and hoping someone interested would join the discussion.
I think Kaori has Friedreich's Ataxia which causes heart disorder, that means the surgery performed is most probaly a heart surgery. This also explains the difficulty of the surgery and the following scenes of the surgery.
In the last scene of episode 21, Kousei's performance was represented by an image of cherry blossom. Cherry blossom and Spring represents Kaori as it was the scene when Kousei first saw Kaori. This implies that Kaori exists inside Kousei and is shown when he's playing the piano. There is also a scene was Kaori's heartbeat rate at around 80 bpm, and the nurse stated that her heartbeat is stable.
In episode 22, the scene of Kaori's surgery was briefly shown again, stating that Kaori's heartbeat rate is around 90 bpm. Then, the next scene is a pair of scissors with blood stains. This suggests that the doctor accidentally cut a crucial blood vessel from near the heart, leading to fatal blood loss and hypovolemic shock, thus explaining the rise in heartbeat rate. Later, Kousei's performance suddenly turned from cherry blossoms to snow. This can mean 'the end of spring' or 'withering of cherry blossom', implying that Kaori is dying. The next scene from the surgery shows that the heartbeat rate of Kaori fell to around 80 bpm, which is probably due to the fatal blood loss. Last scene of Kaori, is that she leaned back and having cherry blossoms rushing out of her chest. This scene looked like Kaori is laying on a bed with blood rushing out of her chest. Kaori then died due to blood loss.
When I first watched episode 22, I thought the scenes of Kousei's performance are just showing his emotions, but the more I think about it, some scenes are somewhat out of place. I then rewatched the anime again and realized these scenes just aren't that simple. This is what I think after I rewatched the anime as there are a lot of implication throughout the series and this explaination makes a lot of sense to me.