Math Makes Room for More Patients


Patients who undergo a surgical procedure may move from a surgical prep area, to an operating room, to a post-anesthesia care unit and possibly an ICU bed, before settling into a regular hospital bed. Ideally, hospitals would schedule surgeries and other procedures in a way that serves as many patients as possible—i.e., keeps all of these beds full—without bottlenecks that lead to delays and long wait times. That’s where math is helping at Lucile Packard Children’s Hospital Stanford.

In 2015, Packard Children’s hired David Scheinker, who has a PhD in mathematics and directs Systems Utilization Research For Stanford (SURF). He and his team use advanced mathematical approaches to improve internal operations – including optimizing surgical scheduling. 

As I reported in Valuable Addition in a recent issue of Stanford Medicine magazine,

Bringing a mathematician on board was “a bit of an experiment,” said Kristin Petersen, vice president of operations, procedures and diagnostic services for Packard Children’s and executive sponsor and director of strategy for SURF.

That experiment is panning out in multiple projects around the hospital. For example, to help guide surgical scheduling, Scheinker’s team used historic data to determine the time it takes to perform various types of surgery; created a mathematical model of patient flow through the post-anesthesia care unit; developed a system to ensure that operating rooms are stocked with the correct surgical supplies for the scheduled surgeries; and created an electronic system for dealing with cancellations.

“It’s all about providing more access to care,” Petersen said. “By improving the efficiency of our operations, we can actually get more patients in. There are fewer barriers, and wait times go down.”  

In another example designed to provide care to more patients, Scheinker and his team used computer simulations to identify under-utilized beds in the Bass Center for Childhood Cancer and Blood Diseases outpatient treatment unit. According to their analysis, the Bass Center had extra capacity and could take on more patients—such as those who received other kinds of infusion treatments elsewhere in the hospital. But at first, the center’s staff wasn’t convinced.

Patient care manager Merian van Eijk remembers thinking, “We’re full! How can we do this?” … So she set about collecting her own data — only to discover that the analyses were right.

“My perception was that we were always busy, but the reality was that it was in a very inefficient way,” she said. “I thought, ‘Okay we’re going to do this, because we need to take care of these patients.’” 

Based on their computer simulations, members of Scheinker’s team proposed a better way to schedule Bass Center patients. Instead of letting the patients and doctors dictate their preferred appointment times, Bass Center schedulers now fill one room at a time while consistently striving to leave open the largest possible blocks of time. This strategy avoids carving the day into short, potentially unusable segments. 

“The data is so powerful. It has proven itself,” van Eijk said.

Scheinker and his team typically work on five to 15 hospital projects at a time, and not all of them relate to space and scheduling.

[O]thers have helped ensure appropriate staffing levels for the Packard Children’s Hospital’s recent expansion and will do the same for the new Stanford Hospital, opening later this year. Another project will make better use of data to identify the sickest diabetes patients and provide them with the additional attention they need. Still another will help families understand what to expect during a stay at Packard.  

Now Scheinker is working with Peterson, at the request of the hospital’s CEO Paul King, on a project intended to make an even bigger improvement in hospital operations: a detailed mathematical simulation of ideal patient flow through the hospital.

The simulation will help Packard develop a long-term strategy for more efficiently providing high-quality, predictable care for as many patients as possible. “It’s a new, big project,” she said, “and it’s a first for any hospital.” 

Scheinker hopes the simulation reveals some valuable action items. “My favorite results aren’t the ones that involve enormous complexity,” he says. “It’s the ones where you say, “oh my, that makes so much sense, why didn’t I think of it.”

Photo by John Moeses Bauan on Unsplash


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