Brain and Heart are two vital organs. They keep you alive and coordinate all other organs in a symphony. This symphony can produce a wonderful music when your breathing harmonize them both. We can then say, breathing is the coordinator or the synchronization of the brain and the heart.
SYNCing Brain and Heart with breathing can be done consciously and overwrite the automatic function of the breathing brain centers that keep your breathing going on when you are asleep for example.
When breathing is smooth and relaxed, the mind get relaxed and vice versa. All in all, breathing connects the mind to all your body organs, tissues and cells.
The heart rhythm is smooth rising up and down as you inhale and exhale. This wave gets bigger when you breathe slowly and deeply. This has been long known by yogis of all traditions. The slow and deep breathing relaxes the body tissues, brings oxygen to the organs in a more efficient way and therefore, increase your vitality.
Scientific research is studying the connection between these three, brain-heart-breathing, and ceaselessly discover amazing communication pathways between them including the emotional and cognitive aspects.
By SYNCing your breath with your mind, the heart responds with certain rhythms which indicates the level of SYNC. The result of a good SYNC level are quantified by the Qi flow which is further translated into a balance of energy.
Life is a constant search for balance: professional and private, tension and relaxation, excitement and repose, day activity and sleep. The world is a constant oscillation between war and peace. What keeps the life in a healthy state is a fluid transition between these two complimentary opposites of Yang and Yin.