The air we breathe normally contains 20.9% oxygen by volume. When liquid nitrogen boils or frozen carbon dioxide sublimes, the increase in the concentration of these gases will reduce the concentration of oxygen in the air. In a confined space, it is this fact which is often the major hazard when dealing with these materials. There is a simple formula for calculating the oxygen concentration in a confined space during a worst-case spillage scenario.

At the Kennedy Space Center in Florida, an oxygen-deficiency monitoring system (ODMS) has been developed for a ten-room facility. Liquid nitrogen and helium are used here such that if a leak occured, it would present a hazard to personnel. The ODMS consists of three subsystems, of which two monitor three rooms each, and one monitors four rooms. The ODMS generates alarms when the oxygen content of the air in a room falls below 19.5 mole percent. Each subsystem includes transport pumps that draw air continuously from each room through two tubes. Each subsystem uses two oxygen analyzers equipped with sampling pumps, as well as two programmable-logic controllers (PLCs) and associated hardware that control solenoid valves that admit a portion of the flows to the oxygen analyzers. The PLCs cause the valves to connect the two oxygen analyzers to two different sampling tubes, and then to switch the connections to a different pair of sampling tubes after an interval of about 10 seconds, and so forth until the air from all sampling points has been monitored, and then the sequence repeats. If one sampling tube, oxygen analyzer, pump, or PLC fails, it can be repaired while the system continues to operate, albeit at a reduced rate.

In October 1999 a lab technician died in an Edinburgh laboratory apparently as a result of oxygen deprivation. You can find the BBC news report of the incident.
As later reported in Laboratory News, August 2000;

"MRC fined £25,000 in LN2 death.
   The MRC has been fined £25,000 after admitting responsibility for the death of an experienced laboratory worker. Mr James Graham had been using liquid nitrogen to freeze biological samples. Seven hundred litres leaked into the laboratory and evaporated, asphyxiating him. 
   The MRC admitted that there was inadequate ventilation, that there was no safety device on the storage tank and that a warning alarm was not switched on. Ms Suffolk, a colleague, told Edinburgh Sheriff Court that she had gone into the room and heard a hissing noise. Mr Graham was collapsed on the floor, unconscious and frozen. Liquid nitrogen was streaming from a hose attached to the wall. She was able to turn off the supply and summon help before she too was overcome.

In September 1992 a barge operator died in an Alaska barge from asphyxiation. You can find the Alaska Fatality Assessment and Control Evaluation report of the incident.

   A 59-year old male barge operator (the victim) lost consciousness and fell into one of the holds of a barge used in ice-making operations. The first would-be rescuer also lost consciousness upon entering the compartment. Both were removed by fire/rescue personnel. The first rescuer recovered, but the barge operator did not. A low level of oxygen (6 percent) was subsequently determined to be the culprit. No leaks in the refrigeration system were found, and the cause of the lowered O2 level was suspected to be internal rust that depleted the oxygen if the sealed compartment.

Effects and symptoms of oxygen depletion.
In general, oxygen deficiency leads to a loss of mental alertness and a distortion of judgement and performance. This happens within a relatively short time, without the person's knowledge and without prior warning.

21 to 14%

Increasing pulse rate, tiredness

14 to 11%

Physical movement and intellectual performance becomes difficult

11 to 8%

Possibility of headaches, dizziness and fainting after a fairly short period of time

8 to 6%

Fainting within a few minutes, resuscitation possible if carried out immediately

6 to 0%

Fainting almost immediate, death or severe brain damage

Effects and symptoms of carbon dioxide enrichment.
Carbon dioxide vapor is not truly inert. It is mildly toxic.

1%

Slight, and un-noticeable, increase in breathing rate

2%

Breathing becomes deeper, rate increase to 50% above normal. Prolonged exposure (several hours) may cause headache and a feeling of exhaustion

3%

Breathing becomes laboured, rate increases to 100% normal. Hearing ability reduced, headache experienced with increase in blood pressure and pulse rate

4 to 5%

Symptoms as above, with signs of intoxication after 30 minute exposure and slight choking feeling

5 to 10%

Characteristic pungent smell noticeable. Breathing very labored, leading to physical exhaustion. Headache, visual disturbance, ringing in the ears, confusion probably leading to loss of consciousness within minutes

12%

Characteristic taste

10 to 100%

Loss of consciousness more rapid, with risk of death from respiratory failure. Hazard to life increased with concentration, even if no oxygen depletion. Concentrations of 20-30% and above are immediately hazardous to life.

The gasping reflex is triggered by excess carbon dioxide and not by shortage of oxygen.

Oxygen depletion calculation for a typical spillage scenario

1. Calculate the volume (V_r m³) of the confined space
2. Calculate the volume of the released gas (V_g m³) by multiplying the volume of the liquid nitrogen (in m³) or weight of solid carbon dioxide (in Kg) by the expansion ratio (682 for LN and .552 for CO₂). (1,000 liters = 1 m³)
3. Calculate the volume of available oxygen (V_o m³) as 0.2095*(V_r-V_g)
4. Calculate the % oxygen available to breathe as 100*V_o/V_r

The above calculation assumes good mixing so that the oxygen concentration is uniform throughout the room. This may well be the case in a room where the air is vigorously mixed, such as our cold rooms. However, where the oxygen deficiency comes from displacement by evaporated cryogenic materials in a room where air mixing is less vigorous there might be quite a marked vertical concentration gradient due to the temperature gradient (and the gas density in the case of CO₂).
If someone collapses, for whatever reason, there could be a much higher concentration of the (colder) nitrogen or (colder and denser) carbon dioxide near the floor, meaning a lower oxygen concentration, and, therefore anyone unconscious on the floor could rapidly asphyxiate.