Alexandria Hospital has been given approval to open an eight-unit dialysis center next year. The approval came early this month from Northern Virginia's health planning agency, which last month delayed a decision after it was unable to break a tie vote on the issue.

The need for dialysis centers, where persons with malfunctioning kidneys go three times a week to have their blood cleansed of wastes, has increased in recent years, according to health officials, and so has competition among hospitals and clinics to operate them. Federal funds pay for most of the treatments and medical fees, which can total $20,000 to $25,000 a year for one patient.

At its August meeting, the Health Systems Agency of Northern Virginia, which determines the need for additional health services, denied an expansion request submitted by a Fairfax dialysis center, Bio-Medical Applications of Arlington, but took no position on the Alexandria request because the 18 HSA board members present were split evenly on the question.

The planning agency's staff had urged approval of the $350,000 center for Alexandria Hospital, saying the area could expect an increase in the number of local residents who need dialysis. About 200 persons now use the dialysis center yearly, the staff reported.

In denying Bio-Medical's request, the HSA cited its controversial policy of "closed staffing," which requires patients to see clinic doctors rather than their own private physicians.

The approval of the Alexandria Hospital center, by a vote of 15 to 2 with two abstentions, came after the board received additional information from its staff, outlining the growing need for dialysis facilities.

The final decisions are made by Virgina's commissioner of health, but the commissioner rarely overrules recommendations from the regional health planning agency.

Alexandria Hospital hopes to open its new unit in the fall of 1981.