Abbie Dorn lies in a hospital bed in her parents’ home on the South Carolina coast. A halo of dark curls frames her pale face. The pump for her feeding tube clicks softly in the quiet room.

Yaakov Cohen, her older brother, settles into a folding chair by her side and begins to read. The subject is accounting. Interest payable. Bonds issued at a discount. Five-year amortization schedules.

Abbie begins to cry. Yaakov smooths her forehead, “I know this is a little boring, Abs.” She calms. He reads. Yaakov is working toward an accounting degree. Abbie once kept the books for her in-laws’ Los Angeles real estate business.

That was before she checked into Cedars-Sinai Medical Center nearly four years ago to deliver triplets -- a procedure so fraught with medical error that she is no longer able to move or speak.

A digital frame across from her bed flashes pictures of her smiling, healthy children: Esti, pretty in pink. Yossi eating dry cereal with a spoon. Reuvi on his maternal grandfather’s lap, roughhousing.

Abbie and their father, Dan Dorn, have divorced, and Dan is raising the children in a modest Beverlywood bungalow. Abbie, 34, held her babies only once, the day of their birth. She has not seen them in nearly 2 1/2 years.

Abbie’s parents have been named conservators of her estate, which includes a multimillion-dollar malpractice settlement, and are asking a Los Angeles County Superior Court judge to order Dan to let Abbie see her children. Dan has refused all requests, arguing that visitation would be too traumatic at their young age.

The bitter dispute raises questions both legal and profoundly human. What is a parent? What constitutes a parent-child relationship? How do you show children that they are loved? And can Abbie Dorn ever be a mother to her children?

In court papers, Dan, 33, describes the woman he once loved as “in a vegetative state with virtually no hope for recovery.” His attorney, Vicki Greene, says, “As far as we know, Abbie is incompetent,” that the case is all about her parents’ wishes, that “we don’t know what Abbie wants, because Abbie can’t speak for herself.”

Abbie’s mother argues vehemently otherwise. Her daughter, Susan Cohen says, has improved markedly since “the event.” She gets hours of therapy each day. She can read. She is capable of complex thought.

And she can communicate. With her smile. Her tears. And, most of all, her eyes.

“I ask her, ‘Do you want to see your children?’ ” Susan says. “And she gives me a long blink.”

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Abbie’s face is alight with joy and promise, head tossed back, her veil a gauzy cloud. Her smile could not be wider. The moment is frozen in a black-and-white photograph in her parents’ living room. It was taken Aug. 18, 2002, Abbie and Dan’s wedding day.

She had just finished chiropractic school in Atlanta. He hoped to expand the family business, which his grandfather launched during the Great Depression. They wanted children right away and dreamed of raising their Orthodox Jewish family in the tight-knit Los Angeles Lubavitcher community.

After two years, they began fertility treatments. Abbie eventually became pregnant and spent the last half of her pregnancy in bed on doctor’s orders.

Dan, recalls Susan, “was devoted. He was very protective about her not overdoing when she was on bed rest. He would dress her every morning, picked her clothes out.”

At 8 a.m. on June 20, 2006, the couple raced the short distance to Cedars-Sinai Medical Center. Esti and Reuvi were born without incident. But Yossi was positioned awkwardly, and while delivering him, Abbie’s doctor nicked her uterus, according to the malpractice attorney.

She subsequently lost a massive amount of blood. By 2:30 a.m., she was in shock, her arms and legs cold and clammy. By around 6 a.m., she had stopped breathing. Then she went into cardiac arrest. The defibrillator did not work properly. Her brain was starved for oxygen.

Susan and Paul, Abbie’s physician father, were still in South Carolina when Dan called to break the news. Susan answered the phone, listened briefly, then screamed.

“Is she dead?”

The Cohens flew to Los Angeles right away. They found Abbie on a respirator in intensive care after an emergency hysterectomy.

“When her mother came in, [Abbie’s] eyes bugged out,” Paul recalls. “She was awake. And she became very agitated. Obviously she recognized [Susan], so her brain was working at the time. They gave her more sedation to help her relax. She was fighting the respirator.”

Over the next 48 hours, Abbie slowly improved. Her blood was clotting. Her kidneys were working. Family members allowed themselves a sliver of hope.

Then, early in the evening on June 23, Abbie became very still. The Cohens crowded around her bed along with Roz Dorn, Dan’s mother.

“Wiggle your toes,” the two women urged Abbie. “Wiggle your fingers.”

Abbie did not respond. Paul leaned over his gravely ill daughter and gently lifted her eyelids. Her right pupil was dilated, indicating increased pressure to the brain.

“I knew at the time,” Paul recounts, “that things had gone from bad to worse.”

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Three months at Cedars-Sinai were followed by seven months in an Oxnard skilled nursing center. When Abbie’s insurance coverage ran out, her parents moved her to the $1,650-a-day Centre for Neuro Skills in Bakersfield, cashing in their retirement funds and selling their boat to pay for it.

Abbie’s progress was slow and painful.

Strokes often affect specific parts of the brain, but when Abbie’s brain was deprived of oxygen, it damaged the entire organ. In addition to being unable to move or speak, she could no longer eat or drink. She was incontinent.

Her hands and arms curled tight against her torso. Her feet were permanently extended, like a ballerina’s feet en pointe. Muscle spasms made her cry.

Paul quit his job so he and Abbie’s mother could move to California, where they rented to be near their daughter. Susan spent her days at Abbie’s side. Paul found work at a community clinic in Watts and commuted daily.

At first, Dan visited regularly, sometimes bringing their babies for his wife to see. But as the months passed, the visits tapered off.

Exactly a year after “the event,” Paul was stuck in rush-hour traffic when his cellphone rang. It was Dan.

“I want to move on,” Paul recalls his son-in-law telling him. “I want to get married again.”

Dan declined to be interviewed. Through his attorney, he answered four brief questions about his understanding of Abbie’s prognosis and his decision to divorce. He was briefly engaged but that relationship was broken off.

After the botched delivery, “I was hopeful until 11 or 12 months, because all studies show that your chances of recovery or getting better are slim to none after that point,” he says.

But when a year had passed, the neurosurgeon told him that Abbie “has not ‘been there’ since Day One,” Dan says. “I was 31 years of age, with three 1-year-olds, and I wanted to start rebuilding my life.”

It was time to take Abbie home to South Carolina.

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Abbie saw her children for the last time on a Sunday in October 2007. They were 17 months old, cavorting on playground equipment at Westwold Park, across the street from Abbie’s apartment at the Centre for Neuro Skills.

Abbie sat in a wheelchair with an extra high back to support her head. As she watched her children play, her body seized with muscle spasms. She cried out. After a couple of hours, Dan scooped up the children and drove them home. “That was the last time Dan saw her too,” Susan recalls. “That’s probably the memory he has of her -- someone in constant pain.”

Abbie was flown east two weeks later, to her parents’ sprawling home. Her hospital bed stands in the center of a sea-foam green first-floor suite with a kitchenette.

An intricate calendar is pinned to one wall, a color-coded guide to Abbie’s busy, hopeful schedule: Hot pink for occupational therapy. Aqua for massage. Dark green, neuro-feedback. Chartreuse is for acutonics, a doubly alternative regimen of acupuncture that uses tuning forks instead of needles.

Abbie spends several hours every day strapped snugly onto a tilting table that allows her to stand nearly upright and helps to strengthen her legs.

Across from her bed hangs a group portrait Susan commissioned in Oxnard: Abbie striding across the dunes with three laughing toddlers toward a kneeling man, his arms outstretched.

“It was important to me for Abbie to see herself well and walking,” Susan said. “And she does look at that picture, all the time.”

Susan, a former medical social worker specializing in neurosurgery patients, designed her daughter’s rehab program, which is funded by a nearly $8-million malpractice settlement and costs about $33,000 a month.

In a 2007 medical report filed during court proceedings to name the Cohens as Abbie’s conservators, neurologist Richard Helvie described her condition as “permanent.” The report contained a long catalog of mental functions; Helvie described Abbie as “so impaired as to be incapable of being assessed” for most of them.

But Abbie’s therapists swear otherwise in letters contained in the growing court file.

“Abbie has shown remarkable progress over the course of the past two years,” wrote acupuncturist Susan Swearengen. “She now clearly demonstrates a basic ability to comprehend and communicate. She no longer cries inexplicably.”

Susan has set goals for her daughter: “I want Abbie to get better. I want the children to gradually know who their mother is. . . . I eventually want them to come here.”

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The difference between Susan’s view and Dan’s -- between vital and vegetative -- is central to the battle over Esti, Reuvi and Yossi.

Abbie and Dan were divorced on Sept. 11, 2008, in a proceeding that left decisions over custody, visitation, support and property until later.

A trial is scheduled for May 13. Dan has asked that Abbie pay child support. His attorneys in the increasingly rancorous case have requested that Abbie be questioned and a videotape of the deposition shown in court.

Abbie’s attorneys have been granted an emergency order protecting her from such questioning. They have asked that the children see a psychologist to prepare them for meeting their mother. They want Paul, who flies out four times a year to visit the triplets, to be able to tell them about Abbie.

The triplets call him Saba, Hebrew for grandfather, but Paul does not believe they know what that means. He does not tell them that he is their mother’s father. He does not tell them about their mother at all. He describes Dan as the “keymaster” to his beloved grandchildren and does not want to anger him and lose all access.

On a trip last December, Paul drove with Dan to pick the triplets up from preschool. The principal approached Dan, Paul says, to report that Yossi was asking, “Why don’t I have a mommy like everybody else?”

At a recent pretrial hearing, Superior Court Judge Rudolph Diaz called the case “serious,” “complicated” and “novel for me” -- sentiments echoed by family law and child development experts.

The California Supreme Court ruled in 1979 that disabled parents cannot be denied custody simply because of their handicaps. Parenting, the justices wrote, is as much about emotion as it is about physical ability.

“A handicapped parent is a whole person to the child who needs his affection, sympathy and wisdom to deal with the problems of growing up,” the justices wrote.

But that case was about custody, not visitation, and concerned a quadriplegic parent who had raised his children alone before his injury and who could talk and drive.

Lisa Helfend Meyer, Abbie’s attorney, said, “There is no case in point that addresses Abbie’s particular circumstance, whether someone in her condition has a constitutional right to parent or visit her children.”

But as she argued in March during a pretrial hearing, “Abbie is alive and wants to see her children. . . . The children need to have a relationship with their mother. The kids need to know the truth.”

Meyer points to the California Family Code, which says that the “public policy of this state” is to make sure children have “frequent and continuing contact with both parents.” The only exception is if that contact is not “in the best interest of the child.”

To Vicki Greene, Dan’s attorney, the case boils down to who is doing the talking. Abbie’s brain injury has left her incapable of even asking to see her children, Greene says, let alone interacting with them.

“Our position is that it’s really the grandparents talking, not Abbie, it’s the grandparents’ desire, not Abbie’s,” she said, and the grandparents have no legal standing to ask for visitation.

In court documents filed Thursday, Dan charges that the Cohens are trying “to financially destroy the children’s sole means of support” by pushing costly litigation and attempting “to force visitation that the children are too young to understand and may cause more psychological long-term harm than good.”

Greene says Dan worries that the triplets would feel “terribly guilty” if they see Abbie in her current condition and “know that their childbirth put her in that position.”

“He is not opposed to them seeing her when they are older, if they want to,” Greene says. “They are too young, and there is no evidence of any ability [by Abbie] to interact with them.”

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Abbie is strapped onto her tilting table on a blustery afternoon in March. She is neatly dressed in pink sweat pants and a black, long-sleeved T-shirt.

Paul and Susan are in Virginia, where Abbie’s younger sister has just given birth to a healthy baby boy. Preparations continue in the legal battle over Esti, Reuvi and Yossi.

The parade of therapists has ended for the day, the house is quiet and caregiver Amber Morrell is explaining how to have a conversation with Abbie.

Make sure to ask simple yes-or-no questions. Give her time to think and reply. A long blink means yes. No response means no.

“Do you want to see your children again?” Abbie is asked.

She blinks, long and hard.

maria.laganga@latimes.com