Apologies in advance, but in the least to play a little devils advocate, actually anapana doesn't mean "mindfulness of breath" it literally means something like yes/no prana, with sati meaning awareness. The natural fluctuation, pulsation and movement of prana is most grossly seen in the breath mechanism. However all high level teachers I know teach that this is kindergarten in the bigger picture, ie only an intial step.   "Today there is much confusion surrounding the practice of anapana meditation. The problems stem from the misconception of the word 息 xi or hsi. Many cultivation sects, the Japanese Zen schools included, confuse the in-and-out breathing for xi. Therefore when they teach the students to meditate by counting the xi they are simply counting the breathing, not the xi that stands for the source of life without the movements of inhaling and exhaling...   ...life is sustained by a continuous movement of expansion and contraction, or how energy functions. The goal of anapana meditation is to cultivate that “movement,” not to cultivate the in-and-out of the respiratory breathing. This has to be clear from the outset.” Nan Huai Jin   “the meditation on breathing, on the basic dharma of prana or energy flow. Anapanasati is not, in fact, a meditation on breath, but on in/out prana. That is what this meditation is for – awareness of energy flow.   And if you were to examine the word anapana quite closely, taking it back to it’s Sanskrit roots, you really end up with “yes/no energy”. Actually, it could be “no/no energy,” because literally the word could be understood as follows: a + na and a + pana, which makes two negations...   This meditation is enumerated as the way to develop awareness of the energy feeds. You start with the breath because it is the most crude, the most obvious energy flow. The meditation naturally unfolds from there. Maybe the awareness of breathing might cease, but the awareness of energy flows, of the ana-pana-sati, should not." Namgyal Rinpoche   This is also why in Daoist xian-tian practice the "breath" is not considered a primary mechanism for the method, is it involved? Of course, the same as many physiological functions are. But it is not the focus of practice. This is why I stated the difference between hou-tian and xian-tian dantian gong earlier. All schools Hindu, Buddhist, and Daoist recognise this distinction.   Learning to feel the pulsation of the "energy"-body as related but distinct from the physical breath is not as difficult as some may have you believe.   Best,