You may find this article from Liberty Voice helpful in explaining to your patients the link between sleeping and eating.
One study found that rats deprived of food spend an increasing number of hours awake. Even when they sleep, such rats experience a steady decrease in slow wave sleep (deep, non-dreaming sleep) and an even more precipitous decrease in their amounts of REM sleep. After about six to 11 days of starvation conditions, the rats no longer slept. After all sleep behaviors had disappeared the researchers re-introduced food to the rats and let them eat as they wanted. The rats that did not spontaneously eat this food died within 24 hours.
