Sometimes a promising new fiction writer stumbles in the early portions of a first book, improving as the pages and confidence mount. Once in a while, a writer emerges with an idiosyncratic gift that challenges readers to learn in the reading how to enjoy it.

Kirsten Menger-Anderson seems to be a bit of each. A touted young short-story writer, trailing important awards, she has delivered a bold first collection chronicling a family of eccentric physicians, “Doctor Olaf van Schuler’s Brain” (Algonguin, $22.95). It is at once striking in conception and yet occasionally fussy and awkward.

The title story introduces the unfortunate Dr. Olaf van Schuler, a visionary young Dutch doctor who immigrates to New Amsterdam in 1664. With the zeal of a mad scientist, he conducts furtive dissections of animal brains, certain he is on the path to curing his mother’s deranged melancholy.

Olaf’s colleagues are unready to see the brain as the seat of the human soul, but his descendants fare better. One after another takes up once prominent medical oddities: mesmerism, female hysteria, electrical stimulation, phrenology, lobotomy, irradiated drinking water. Most are prosperous at the expense of a gullible public.

These stories yield their pleasures diffidently. Menger-Anderson practices an indirect narrative, inviting the reader to figure out the import of each plot, the nature of each character. Sometimes she presses too hard, resulting in needlessly obtuse sentences: “Richard might have forgotten that he sat accused of murder had not distress commanded his thoughts.”

That Menger-Anderson’s missteps come in the early going augers well. Soon enough she is offering one nuanced and finely morbid story after another, the patly ironic endings giving way to something more substantial. It may or may not be relevant that the stories seem to gain in power as the focus moves away from the doctors to their patients/victims.

“Hysteria tells of Edith,” a principled young woman with a gift for rehabilitating the criminals in a women’s prison. But her doctor father diagnoses her as a hysteric – social work is unfit for young women! – and she sickens when forbidden to follow her calling.

In “Reading Grandpa’s Head,” Edith gets revenge, albeit unintentionally, when, leading the life of a chastened 19th century matron, her keen intelligence falls under the influence of a phrenologist. She subjects her now-elderly father to a phrenological examination, displaying the depth of her self-delusion as her certainty grows.

These tales, droll and tragic in equal measure, are replete with vivid period characters: Edwin, a shy Macy’s clerk, seeks relief through electrical stimulation; Lillian fails to protect a feeble-minded sister from their brother’s mania for lobotomy; Quimbly, a pubescent thief, finds a way out of poverty as assistant to a mesmerist.

Through it all, “Doctor Olaf van Schuler’s Brain” presents a subtle and affectionate portrait of New York City, its horrors and glories, as it changes through the centuries. Despite some minor problems, Menger-Anderson has made an impressive debut.