Is the female physician required to pay expiation (kaffarah) or blood money (diyyah) for the death of the patient, given that she initially did not notice the blood and delayed administering the blood transfusion?

There is no sin upon you for not seeing the blood initially, nor for your swift action after becoming aware of the patient's condition. However, if doctors prove that you were the cause of her death, her blood money (diyah) becomes obligatory upon your 'Aqilah (male relatives responsible for paying blood money).