Why are the oxygen concentration formulas 2 1 and 4?

Why is the oxygen concentration formula 2 1 and 4 as follows:

Inhaled oxygen concentration (%)=2 1+4x oxygen flow (liter/minute)

This formula only applies to nasal ducts or nasal congestion. In the chapter of respiratory failure, Internal Medicine talks about oxygen therapy, especially pointing out two kinds of oxygen inhalation devices: nasal catheter and nasal congestion. The relationship between inhaled oxygen concentration and oxygen flow rate is the above formula.

1. The derivation basis of this formula:

The ICU attending physician manual has detailed instructions. Let's briefly explain the "normal breathing mode" of "normal people". Normal people breathe tidal volume 500 ml, breathing frequency 20 times/minute, inspiratory time 1 second, expiratory time 2 seconds, oral and nasopharyngeal dead space 50 ml (this estimation is very important).

When the oxygen inhalation flow rate of nasal catheter is 6 L/min( 100 ml/ s), it is assumed that the exhalation is completed 1.5 seconds (75%) before the exhalation time, and there is almost no gas exhalation in the last 0.5 seconds. Pure oxygen from nasal catheter (the oxygen inhalation flow rate is 6 L/min, that is, 1 00 ml)

1) 50 ml of pure oxygen in the dead space of oropharynx dissection (100 ml/s x 0.5 s = 50 ml);

2) nasal catheter pure oxygen100 ml (100 ml/s x1s =100 ml);

3) Because we assume that the tidal volume is 500 ml, we need to inhale an additional 350 ml of air (the oxygen concentration is 2 1%, about 20%), so the oxygen is 350 ml x 20% = 70 ml.

It can be seen that the 500 ml inspiratory tidal volume contains 220 ml of pure oxygen (50 ml+100 ml+70 ml), and the inhaled oxygen concentration is 44%(220 ml/500 ml). That is to say, in the "ideal ventilation state", when oxygen with a flow rate of 6 L/min is inhaled through the nasal catheter, the inhaled oxygen concentration is 44%.

If the oxygen flow rate is gradually increased from 1 L/min to 6 L/min, when the oxygen flow rate changes 1L/min, the inhaled oxygen concentration will change by about 4%, which is the calculation basis of the above formula.