Examples of calculus use in medicine?

I got a question,
"I am supposed to teach my calculus class one lesson.
That lesson has to be on something that can be applied
to whatever I am hoping to major in. I am planning on
studying pre-med to become a doctor. Could you tell
me how doctors apply math learned in calculus 1?"

I suspect doctors don't actually use any calculus in their daily work with people. BUT, it is used in medical research and analysis.

For example, calculus concepts are applied in studying how medicines act in the body. I found an article called Half-life and Steady State that talks about how the patient might be taking a medication and all the same time the body is clearing the previous doses... Eventually there comes a "steady state" where the amount of "the amount of drug going in is the same as the amount of drug getting taken out."

Many drug effects occur primarily when the blood level of the drug is either going up or going down. When the drug reaches steady state, these effects can be either attenuated or completely absent. For those of you who are familiar with calculus, one way to understand this is that these effects only take place if there is a first derivative other than zero.

Or, from www.math.gatech.edu/~bourbaki/MapleProjects.html
we find that calculus is used to find out the rate of change of the surface area for a rapidly growing adolescent. This ties in with medicine in the fact that sometimes the drug dosage depends on the size of the individual, and the surface area is one way to measure the size of a person.
"This worksheet, provides a correlation between height, weight, and surface area
for humans as determined by the commonly used West Nomogram. Additionally, partial derivatives (and the chain-rule) are used to find the rate of change of the
surface area for a rapidly growing adolescent."

BIOLOGY and MEDICINE research abound with mathematical models, and calculus is an essential tool for analyzing those models. I personally have not studied these in-depth, but taking a peek in a Calculus for Biology and Medicine course syllabus from a certain community college we find that on that course the students;

1. Analyze allometric models.
2. Analyze models in cell diffusion.
3. Analyze models in population growth models.
4. Analyze models in population biology for interacting species.
5. Analyze models for respiration and control of respiration.
6. Analyze models for cardiac dynamics and control of heart rhythms.
7. Analyze models for neuron dynamics.
8. Analyze models in pharmacology.
9. Utilize a computer-algebra system in a model's analysis.

Calculus is simply an indispesable tool for modern science.

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A said…
I found your article very useful in helping me compose a paper related to the uses of calculus in Medcine. Thank you for your time.
Anonymous said…
I dunno if you've already done your project (probably so) but I know of one specific example using a concept from calculus called related rates.

Say your an Oncologist and you suspect a patient has a tumor. Say you know the the rate of change of the radius or the rate of change of the volume (with respect to time of course). Also we will assume the tumor is spherical.

equation of a sphere is v= 4/3 pi*r^2

You can find dv/dt (change in volume with respect to t) if you have dr/dt (change in radius with respect to time)

Taking the derivate you find your answer. It may be a little far fetched but it is sort of applicable.

Cheers bud!
Anonymous said…
your article is very useful to me. i'm taking some info in it for my assignment related to the application of calculus. i hope u dont mind.btw, tanx a lot for writing such a good article
LuciferAmadeus said…
I have a question. What about integration? Most of the students that looks for medical course are not mathematics-oriented students (at least here). They really struggle with understanding integration by parts and whatnot. Even in research, I don't see where integration applies in medical school.

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