Mathematical Model Of SIDS
Every infant has their own set of particular capabilities that vary
greatly over the period of concern (ages 2 to 4 months). The geometry of
each particular case of stagnant air is also dependent on a host of
variables. Therefore, this model will use a theoretical infant breathing
oxygen from a specific stagnant volume without any mixing of the oxygen
and carbon dioxide. The results are then analyzed with respect to the
various parameters to see how they affect the results. This is called a
sensitivity analysis.
Theoretical Conditions:
A theoretical infant with a lung capacity of 5 cubic inches and a
breathing rate of 20 breaths per minute is placed so that it is inhaling
and exhaling into a 12"x12"x4" stagnant volume. The lung
conversion efficiency for oxygen to carbon dioxide is 3%.
The Problem:
How long does it take this infant to convert all of the oxygen to carbon
dioxide?
Solution:
|
Time |
= Breathing Volume / Conversion Rate |
|
Conversion Rate |
= Breathing Rate x Volume per Breath x Conversion
Efficiency |
|
= 20 breaths/min. x 5 cu. in./breath x 0.03 |
|
= 3 cu. in./min. |
| Time |
= (12x12x4) cu. in. / (3 cu. in./min) |
|
= 576 cu. in. / (3 cu. in./min) |
|
= 192 min. or 3.2 hours |
Sensitivity Analysis:
- Breathing Volume - the larger the volume that the infant is breathing
from the longer it takes to convert that volume of oxygen into carbon
dioxide.
- Respiration Rate - if this rate changes (either between individuals,
with age, or over the event) then the time is inversely proportional;
i.e. an increase produces a decrease in time; and a decrease produces an
increase in time.
- Respiration Volume - as this increases the time decreases (as the
infant grows over this period of time a safe situation can worsen by
having a reduction in time).
- Conversion Efficiency - as this increases the time decreases (the
physical health of the infant and the growth over time can cause this to
change).
What does all this mean?
It means that in a very short period of time the theoretical infant
consumed all of the oxygen in the volume it was breathing out of. It
also means that over time conditions with the infant can change. If they
happen to change in the wrong direction a tragedy could be the outcome.
Never assume that things are totally safe because nothing has happened
yet.
What happens in real life?
In real life nothing is constant and pure. Here are some examples:
- The air we breathe is mostly nitrogen.
- Respiration and breathing volumes are not constant.
- Conversion efficiency can vary as the amount of oxygen is decreasing
in the breathing volume.
- The exhaled air mixes with the breathing volume so that each breath
inhaled has less oxygen in it.
- As the oxygen level in the inhaled volume decreases the respiration
rate and volume may increase for a period of time, then they may slow
down as the body tries to conserve oxygen.
This analysis simply shows that the oxygen level in the air being
breathed by an infant trapped in a stagnant air pool can quickly drop to
fatal levels. Every effort must be made to recognize and dismantle any
stagnant pools before placing an infant in one.
There are enough tragedies in the world. This is one that is easily
avoidable simply by education and a cheap fan. Insuring that the infant
always has an adequate supply of fresh air is all that is needed to
prevent the tragedy of SIDS.
Note: A "groggy" baby that was just awakened may actually
be one that is simply recovering from a near-SIDS event. Such a baby may
even be suffering some brain damage due to that event.
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