Ninety minutes into his shift, Dr. Gerard B. Hayes has visited six intensive care unit patients, conferred with nurses about 12, and reviewed the records of dozens more.

“Dottie, how are you?” he asks a woman in a purple robe who is suffering from obstructive lung disease. “I’m taking a look at your X-ray right now, and it looks pretty good.” She sits up in her bed, breathing through a tracheostomy tube. “I’ll check in with you later,” he promises.

Hayes’s pace might be called breakneck if he was moving from bed to bed. But he’s remotely monitoring patients at several hospitals from an “e-ICU’’ outpost in Westwood operated by Steward Health Care System. Caregivers at the site watch video screens showing patients in hospital ICUs from Methuen to Fall River. It brings extra sets of eyes to intensive care while letting Steward keep its staffing lean.

Like everything else about for-profit Steward — robotic surgery, fixed-rate insurance contracts, managers working with patients to prevent hospital readmissions — the e-ICU is focused on innovation, efficiency, and finding ways to save money.