In the practice of yoga, pranayama is the ancient art and formal practice of controlling the breath.
The basic technique includes settling the body and the mind in a quiet place and in a position of rest (either sitting, lying down, or even standing). The idea is to take a full 6-7 seconds to breathe in and a full 6-7 seconds to breathe out. During this time, it is recommended that the participant clear his thoughts by focusing on mentally following the breath to certain areas of the body. Spiritually or emotionally speaking, it is the same thing as meditation. This calming of the heart, mind, and spirit lowers the heart rate, provides "active rest," and is said, if practiced with regularity, to provide a host of health benefits.
Scientifically speaking, this makes sense. Consider the body's process of removing waste from the system. The digestive system is not doing all the work. Many people forget that carbon dioxide is also waste in the human body. Inhaling deeply increases the flow of oxygen to all of the organs (including digestive organs) and exhaling "deeply" removes waste. Controlled breathing has been linked to increased respiratory and cardiovascular vitality, decreased nervous activity, and overall improvement in physical and mental health.
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The first step to breathing your troubles away is to clear your mind. Imagine that all your thoughts are clouds. Whenever an intruding thought comes into your mind, let that cloud float away. Visualizing your unwanted thoughts as clouds and letting them float away helps clear your mind. Once your mind is calm and empty, breathe deliberately and focus on your inhales and exhales. It will take some practice but meditation has great benefits.