The ATS journal, American Journal of Respiratory and Critical Care Medicine, has published a research that says "Humming Greatly Increases Nasal Nitric Oxide" (Weitzberg, Lundberg Am J Respir Crit Care Med). Results show: "Humming (low pitch Bhramari) caused a 15-fold increase (range, 8–21) in nasal Nitric Oxide compared with quiet exhalation".
According to Nature Publishing Group Nitric Oxide has been recognized as the most versatile players in the immune system The most important thing about being healthy is Nose breathing which increases nitric oxide in the blood stream. According to Nobel prize winning paper titled “Nitric Oxide as a Unique Signaling Molecule in the Cardiovascular System”, nitric oxide is incredibly important in cardiovascular signaling and health. Today, it is recognized that nitric oxide is a widespread signaling molecule in all organs of the body, not only in the cardiovascular system. Nitric oxide (NO) production happens in the paranasal sinuses. As a vasodilator, NO decreases blood pressure and improves blood flow to the organs, causes anti-inflammatory action in the arteries, boosts immune defense, and aids in the destruction of viruses and parasitic organisms. The only organ that helps us breathe efficiently is our nose. When we breathe through our mouths it can lead to chronic hyperventilation, reduced blood circulation, lowering of carbon dioxide levels, and vasoconstriction of our airways. Chronic mouth breathing would have detrimental effects on our overall health such as sleep apnea, high blood pressure, heart disease, asthma, allergies, and more.
There is less delivery of O2 in mouth-breathing. When we breathe through our nose, nasal resistance increases by approximately 200% and helps in the release of Oxygen. Close to 80% of the population breathes ineffectively. They may breathe through their mouths, or have shallow breathing; they may not breathe using their diaphragmatic muscles and lower lung lobes, and they might breathe heavy, in a physically audible fashion.
CO2 is an important element that is necessary in the bloodstream. Carbon dioxide (CO2) has a profound and reversible effect on cerebral blood flow where it causes marked dilation of cerebral arteries and arterioles and increases blood flow. Each hemoglobin molecule carries four atoms of oxygen (hemoglobin). And since we know that oxygen is released by the presence of carbon dioxide, the harder you breathe, the less carbon dioxide there is within your blood stream, and less oxygen is utilized efficiently. You may have blood that has high oxygen saturation, but the oxygen delivery to organs would be less because it is not being released by the hemoglobin. This is the problem with most people who are under stress, hyperventilate, or breathe shallow and fast and at chest level.
Sources:
Nitric Oxide and Mouth Breathing - https://www.lviglobal.com/wp-content/uploads/2017/06/NitricOxideMouthBreathing.pdf
Humming (low pitch Bhramari) Greatly Increases Nasal Nitric Oxide - https://www.atsjournals.org/doi/full/10.1164/rccm.200202-138BC
Nose Breathing - https://www.lviglobal.com/wp-content/uploads/2017/06/NitricOxideMouthBreathing.pdf