Particles of Miswaak entering throat whilst fasting

If a food particle (smaller than a lentil) was stuck in between the teeth and swallowed, it does not invalidate one’s fast as it is difficult to prevent it from entering the stomach. Similarly, it is difficult to prevent particles of the Miswaak from entering the throat whilst using the Miswaak, thus in this case too, the fast will not be nullified. Both Masaa’il share a common factor, hence, the ruling will also be the same.