Additional Math Pages & Resources

Thursday, October 28, 2010

Not So Loud, or so seldom

Yesterday I mentioned a common personal health-related condition - a very unpopular practice that disturbs other people in your house.

But sometimes I snore, and so it's an appropriate topic for this blog (if I can discover some math about snoring). How about some numbers about the frequency of this irritating habit?

Perhaps 30-50% of middle-aged or older people snore, compared to about 5-6% of children.

The most reliable methods to control snoring are lose weight, stop smoking, breathe through the nose, and sleep on your side. I have taken the last two of these as my preferred approach. Even though you are asleep most of the night I can tell you from personal experience that it is possible to train yourself to stop snoring by sleeping only on your side, and to keep your mouth shut to breathe through your nose.

Other approaches you might consider include:
  • Chin straps to keep your mouth closed
  • Nasal strips and nose clips
  • Mouth guards
  • Fancy pillows
  • Surgery
  • Drugs
  • Ear plugs (not for you but for your family!
A related condition is called sleep apnea. You stop breathing for a long time (at least 10 seconds),  oxygen levels drop 3-4%, carbon dioxide levels rise, then the "stay alive" reflex kicks in and the body gasps for air to catch up.

People with sleep apnea rarely get enough quality sleep at night, so they are liable to fall asleep in the daytime, even while driving or talking. I have at least 6 friends who have been diagnosed with serious sleep apnea -- it was terrifying to be with them in the car.

The "Medical World" has only known of this condition for about 40 years. About 9-10% of men are thought to have have sleep apnea, compared to about 4% of women. Only 10% of sufferers have been diagnosed. Sleep clinics identify the condition by having you come in and sleep in their observation rooms, or by giving you a recording device to wear while sleeping.

This condition is taken very seriously by doctors, because sleep apnea sufferers have as much as 30% higher risk of heat attacks and a 240% increased risk of congestive heart failure. One study suggested that medical costs for undiagnosed sufferers of sleep apnea might cost twice as much on average (per year) than the cost of a non-sufferer.

The Continuous Positive Air Pressure (CPAP) machine is nearly 100% effective in reducing sleep apnea. The CPAP machine was invented about 30 years ago. ResMed, one of the world's largest suppliers of CPAP machines, is located just a few miles from our offices. I saw an article that stated they probably supply 30% of the machines in the US, and perhaps 50% of those around the rest of the world. It's more than a one billion dollar business for ResMed alone!

Although it works to reduce the effects and dangers of sleep apnea, the CPAP machine isn't a cure, and it's a nuisance. It's certainly not attractive to wear the face mask. At least 25-50% of the people who get the machines stop using them.

Note: If you fall asleep while reading this abstract, you don't necessarily have sleep apnea, you are just normal:

"Recent studies have uncovered high prevalence of undiagnosed sleep-disordered breathing, and its linkage to metabolic or cardiovascular disorders which represent increasing health hazard. However, the mechanistic links behind these disorders as well as their contribution to the experimental observations and treatment responses remain poorly understood. Therefore, the screening of clinical measurements still relies upon relatively simple diagnostic features, such as signal averages or event frequencies, which may represent suboptimal or surrogate markers of the underlying abnormality. Consequently, most patients are being treated with general therapies regardless of the cause of their key dysfunction. Combining experimental measurements with mathematical modelling has the potential to provide mechanistic insights into the individual factors underlying the disease progression, which may finally enable tailored treatment alternatives for each patient. This review depicts a number of modelling approaches to elucidate sleep-related dysfunctions of the human respiratory system, and how these models are being used to translate the measurements first into new ideas and then into testable hypotheses. Such model-based investigations can provide systematic strategies towards better understanding, predicting or even preventing these dysfunctions. Along with the brief description of the modelling approaches, we discuss their relative merits and potential implications especially for clinical research."

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