Most writers struggle for their art, but Paul Kalanithi went through more than most for it.

A year before he died aged 37 on March 9 last year, the American neurosurgeon began tapping out his parting gift to his doctor wife, Lucy Goddard, and their daughter, Elizabeth "Cady" Acadia, on his silver laptop.

He wrote his memoir When Breath Becomes Air "in midnight bursts" as Goddard put it, while he lay next to her in bed, after a 16-hour day as Stanford University School of Medicine's neurosurgery chief resident.

When the flesh on his fingers began splitting from chemotherapy for Stage 4 lung cancer, she found seamless, silver-lined gloves that enabled him to continue tapping out his first, and last, book on his laptop.

He took calls from his editor as the drugs dripped into his veins.

Kalanithi was the second son of two doctors from India, who migrated to the United States. Together with his elder brother Suman and younger brother Jeevan, they survive him along with Goddard and Cady.

They had known him as "Pubby", the over-achieving wit who had won the American Academy of Neurological Surgery's highest award for research, after graduating with degrees in English literature, human biology, the history and philosophy of science and medicine and neurosurgery from the universities of Stanford and Cambridge and the Yale School of Medicine.

But seven days after he learnt he had cancer, he went from standing for 36 hours straight in a Stanford operating room to, as he recalled in his memoir, "hobbling out of hospital".

Confronted with the prospect of being paralysed, he managed through in-vitro fertilisation to father a daughter, who was born eight months before he died.

His book, which was released on Jan 12, is now an international bestseller and dubbed a must-read by, among others, The New York Times, The Boston Globe, the Guardian and The Times Of London.

Dr Goddard, who specialises in internal diseases, had to finish her husband's manuscript for publication, by contributing an epilogue, which is a telling counterfoil to his end-of-life musings. He had never smoked, preferring ice-cream sandwiches.

She is now doing the media rounds for his book and updating his readers on Twitter via her handle @rocketgirlmd.