The person narrating has committed a murder and shoved the corpse under his floorboards. As some time passes the heart beat is a glimpse into his insanity, and how he is delusional over hearing non existent sounds. He believes he hears the heart of the person he murdered under the floorboards, which is a delusion, most likely made out of paranoia. When the police come to ask about the victim, the man almost fools them until he breaks down and confesses. He expressed annoyance at the victim earlier, saying that he could not get away from their eye, I believe. He tried to solve this by killing them, but his mind would not let him do so by making up false realities.
In my opinion, out of the sentences offered here the one which best
shows how Dr Heidegger's character represents wisdom is D - 'If the
fountain gushed at my very doorstep, I would not stoop to bathe my lips I
it; no, though its delirium were for years instead of moments.' Here Dr
Heidegger is discussing the fountain of youth and how, although he can
admit he is tempted by it, he would be able to resist due to his wisdom
and powers of reasoning.
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your answer is Simile I do believe