Rand Paul's filibuster today is courageous (just like this live blog), but it has been far from a solo effort. On several occasions, Paul stopped to field questions from some of his Senate colleagues. Paul may paused to take questions from other senators while still holding the floor, and he has availed himself of this rule. In fact, it is not even necessary for Paul to be present in the chamber while other senators ask him questions.
Thus, Paul has been able to excuse himself from the chamber to do whatever it is that he's had to do that he can't do on the Senate floor without being the Senate's version of a drunk and incontinent bum on the subway.