This invention uses “targeted apheresis” to treat pregnant women who are at risk of developing eclampsia. “Targeted Apheresis” is a process whereby certain growth factor receptors (sFlt-1) circulating in the blood of a pregnant woman at risk of developing pre-eclampsia are selectively removed by passing the blood through a cartridge containing immobilized anti-sFlt-1 aptamers. The circulating sFlt-1 is bound out by the immobilized anti-sFlt-1 aptamers and the cleaned blood is returned to the patient. Removal of circulating sFlt-1 will diminish the risk of developing eclampsia during pregnancy.