Explain how the leaf contributes to the extended metaphor and the theme in this story

The leaf is the symbol for the fragility and the perseverance of life.

Explanation:

The leaf is the extended metaphor and the theme of the story. Not only does it represent the perseverance and the fragile nature of human life, it also represents faith as in the end a picture of it is able to keep a person alive who attaches their life to it.

The leaf is the belief in life for the patient while for the artist it is the fragility and the momentary impermanence of his own life that he confronts when he does the work of painting and getting the leaf onto the tree in the process dying himself.