For six of their daughter Kate's nine years of life, Paula and Hugh Murphy have made the trip down I-95 from Columbia to Children's Hospital in Washington at least weekly to see the squadron of doctors who battle against Kate's brain tumor.

At Children's, Kate is in the care of oncologists, a urologist, a psychologist, a neurologist, a neurosurgeon, an ophthalmologist and an endocrinologist. She went through chemotherapy when she was in kindergarten and first grade. She's now in fourth grade; her prospects are good, but her battles are not over.

The Murphys' insurance company, CareFirst BlueCross BlueShield, has to date paid $768,000 for Kate's care at Children's. Come the end of this month, because Children's and CareFirst are playing a very public game of chicken, Kate Murphy's care at Children's will likely end.

"We're being put out, left in the cold," says Paula Murphy, who teaches retarded and autistic children in the Howard County schools. "Her doctors want to keep caring for her, but Children's business office says we're no longer welcome."

Children's announced last month that starting Jan. 1, it will no longer accept patients from the area's largest insurer, CareFirst, which covers 3.2 million people in this region. CareFirst customers could still go to Children's, but only by paying exorbitant out-of-network rates.

Children's says CareFirst is uniquely stingy in its reimbursements, paying far less than the cost of care. CareFirst says it pays Children's as much as it pays any other hospital and calls the facility's claims unreasonably high. Children's agrees that it costs more to care for children than for adults; children need more supervision.

Children's has launched a huge PR offensive to show that this is no little contract dispute. It's a major battle in the war over health care and who's going to pay for it.

The Murphys and other families tend to blame Children's, because after all, it's the hospital that cut them off. Paula Murphy's supreme concern is that her child will be barred from seeing the doctors she knows, the pros who've plotted her care for years.

Peter Holbrook, chief medical officer at Children's, seems pained by the prospects for the 5,000 long-term CareFirst patients like Kate. "These parents entered into the relationship with Children's with the expectation that we would always be there," he says. "We should make an exception for every one of these families." Holbrook hopes to win that concession from CareFirst at a meeting today.

He shouldn't hold his breath. Dan Winn, senior medical director of CareFirst, says he'll look at each case individually but sees no reason why anyone should expect his company to continue full coverage at Children's. CareFirst says it will find specialists at other hospitals who can take over for Children's. "You never say never, but I haven't found anything yet that can't be done in another hospital in the Washington area -- and can't be done as well," Winn says.

Any parent whose child has had a serious ailment knows that is poppycock. In many specialties, the doctors at Children's are foremost in their fields; often, they're the only doctors in the region with experience handling certain procedures.

Winn portrays this as a matter of irrational parents. "Some of the parents are going to have emotional attachments, and we understand that," he says. When I ask whether patients benefit from long-term relationships with doctors, Winn first says, "That's something that can't be measured," then concedes, "There is some benefit." There certainly is.

If CareFirst lives up to the health insurance industry's well-earned image of uncaring greed, Children's may absorb the cost of care for some long-term patients. "We're obligated morally to make sure these patients are not going to receive lower quality care," Holbrook says. "If CareFirst is unwilling to accept that, we'll have to figure out what we can do."

Children's says it lost $9 million on CareFirst patients last year, using charity dollars to cover those costs. Meanwhile, CareFirst lobbies to become a for-profit company, thereby enriching its executives.

There is no white knight here; Children's must account for its own eye-popping executive salaries. Still, Children's is right to demand that insurers pay hospitals' reasonable costs, rather than simply gaming the system for ever-higher profits.