the most resource-intensive patients
This is a less crass way of saying the most expensive patients, because it conjures up a mental picture of devoted people spending time with patients rather than money being spent on patients.
The result is the same, of course. All these highly skilled people must be paid for their time. Resource-intensive patients require a lot of attention from doctors, physician's assistants, nurses, technicians, therapists, nursing assistants, dieticians and aides, and also usually require many tests, high-tech monitoring and lots of medicines. All of this is expensive.
The results can be miraculous.
A resource-intensive task is one that requires a lot of resources, often but not always over a limited period of time. Resource, from Dictionary.com:
a source of supply, support, or aid, especially one that can be
readily drawn upon when needed.