Gasses are measured by volume (at STP), using the SI unit of cubic meters. The concentration of oxygen that's part of the air we breathe, a mixture containing other gasses, is measured in parts-per-X.
E.g., Earth's atmosphere contains 209,460 parts-per-million of oxygen by volume, or roughly 20%.
Of note for respiration, the partial pressure of oxygen is more important than its PPM (ehstoday.com: Confined Spaces).
I'd use, "...until the last drop of oxygenated blood reaches the brain" and "that same drop of blood..." for the other sentence. Blood does a lot of stuff.
Also note: the human body will stop working way1 before its last vestiges of oxygen are depleted.
1: to be read with echo, reverb and chorus.