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### Doctors and Math

```
Date: 10/27/98 at 16:55:08
From: SAM
Subject: How do doctors use math?

I would like to have a math problem to show my Geometry class how
doctors use math in real life. I would also like some examples of how
doctors use math.

Thanks for the help,
Sam
```

```
Date: 10/27/98 at 20:22:05
From: Doctor Tom
Subject: Re: How do doctors use math?

Here are a few examples.

1) Neurologists who take EEGs (electro-encephalograms) are measuring
brain voltages at various points in the brain to detect how the
voltages surge around. There's normal wave motion, as well as all sorts
of types of epilepsy and other problems that can be detected by this
method. Unfortunately, the data, as they come out of the machine, are
pretty noisy. Various mathematical "filters" must be applied to see the
underlying wave phenomena. This is basically Fourier analysis on wave
forms that shows how the geometry of the complex, noisy forms is
composed of stong, underlying primitive waves.

2) Sometimes you can treat a cancer by irradiating it. Now if you just
shine a powerful beam of radiation straight through the cancer, you'll
kill it, but you'll also kill everything on both sides of it that the
beam passes through. It's much better to have a bunch of beams crossing
in 3 dimensions so that the stuff in each beam isn't killed since the
beams are weak, but all the beams go through the cancer, so it really
gets "toasted."

3) PET scans and NMR scans use many 1-dimensional scans of the body to
reproduce 2-D and 3-D views. Radiologists have to do this all the time
- use math to reconstruct a 3-D view from many 1-D views.

- Doctor Tom, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 10/19/2001 at 19:06:10
From: Stephanie
Subject: How do doctors use mathematics in their practices?

Hi!  I have to write a report about how doctors use math in their
careers. It would helpful to have medicine dosage formulas or
something like how surgeons decide how big they are going to make a
cut in someone, to operate. I looked on lots of different Web sites
and none of them could tell me specific information.

Thank you for your help and your time!
```

```
Date: 10/19/2001 at 20:51:36
From: Doctor Tom
Subject: Re: How do doctors use mathematics in their practices?

Hi Stephanie,

I'll just give you a couple of ideas.

My wife is a physician, a neurologist working with patients with
epilepsy. Every day she runs EEGs on the patients, where you hook
electrodes to the heads and plot the (microscopic) voltage differences
between various parts of the brain. If there are irregularities (caused
by tumors, lesions, et cetera), there are irregularities in the
electrical signals. She needs to take sums or differences of the
voltages, and can apply various digital filters to the data to
eliminate noise, or to eliminate a known signal from the rest to see if
there are irregularities in what's left. The frequencies of the signals
are interesting, but they come in a horrible mix, so the filters
effectively do various mathematical transforms to the signals, such as
Fourier transforms and many others. It's basically digital signal
processing, but with 20 signals, all of which are related.

Radiologists use even more math in related ways, but I don't have any
direct experience, so I can't give you details, but it would be a good
lead to follow up. The only example I know of for sure in this field is
when the doctors use radiation for killing a cancerous tumor. If you
just use one beam, it'll kill everything in your body in a straight
line from the x-ray machine straight through, and that's not so good.
So multiple beams (or moving beams) are used so that a little radiation
goes through lots of paths, but it all hits the tumor, so the tumor
gets totally "fried" and the other parts get a mild "sunburn". (Of
course, I'm sure the docs don't say "fried" and "sunburn", but you get
the idea.)

Do you know any physicians? If so, ask them. Most people love
to talk about their work.

- Doctor Tom, The Math Forum
http://mathforum.org/dr.math/
```
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