Roger Cole’s reply:
The dizziness that comes with deep breathing is usually caused by breathing out carbon dioxide faster than the body produces it. This makes the blood less acidic, which apparently causes a chemical alteration in nerve function that makes you feel light-headed. The cure is to breathe more slowly and/or less deeply.
Holding the breath during asana practice is not a good idea. Asanas require free circulation of the blood and plenty of oxygen to the muscles and organs. Holding the breath lowers oxygen levels. Although it raises carbon dioxide levels, it can increase pressure in the chest so much that it is difficult for blood to return from the body to the heart. Too little blood goes in, so the heart pumps too little blood out. Dizziness may result when blood pressure sensors in the heart, upper chest, and neck detect too little blood volume within the heart, or too little pressure being pumped up toward the head.
Similarly, standing up suddenly from Uttanasana (Standing Forward Bend) can cause so much blood to flow downhill into the legs and abdomen that too little blood fills the heart. Normally, reflexes quickly compensate for this by raising the heart rate and constricting blood vessels to raise pressure. However, if the reflexes are too sluggish, pressure will fall in the heart, chest, neck, and head, and you will feel dizzy.
To prevent this, do three things when coming out of Uttanasana. (1) Contract the calf and thigh muscles strongly to squeeze blood from leg veins toward the heart. Start this action before you start to come up and continue it while coming up and after you are upright. (2) Come up slowly to give reflexes time to respond. (3) Inhale while coming up. This lowers pressure in the chest, thereby helping blood flow into the heart.
The breathing pattern you describe probably contributes to your dizziness in backbends, but excess back bending of the neck might also cause this. Blood flows to your brain by four arteries: two carotid arteries in your frontal neck and two vertebral arteries that are threaded through holes in the vertebrae of the neck. Extreme back bending of the neck might theoretically constrict the vertebral arteries. If this occurred, and the carotid arteries were unable to compensate for any reason (for example, if they suffered from narrowing, or stenosis), you would experience reduced blood flow to your head. You can often avoid excess bending of the neck in backbends by learning to lift your chest more, so you bend more from the uppermost part of your back instead of your neck.