## Mathematics and cancer research ?

What are applications of mathematics in cancer research ?

Unfortunately I heard quite small about math, but I heard something about applications of physics. And let me put this story here, it might be useful to be aware. There is well-known radiation therapy. But less well-known is proton therapy http://en.wikipedia.org/wiki/Proton_therapy It is much more rare and based on protons accelerators used in particle physics. "The chief advantage of proton therapy is the ability to more precisely localize the radiation dosage when compared with other types of external beam radiotherapy." As far as I know it is only practiced in physics research centers which have proton accelarators. It is highly useful for cancer of sensitive tissues when it is dangerous to use other radiation therapy cause it will destroy everything surrounding.

A colleague of mine told me this really helped his father with the eye cancer. Moreover this method is so rare, that the leading experts in cancer were NOT aware of it and he become known of it only through friends.

PS

The research institute where it happend is leading Russian research center ITEP (Institute for Theoretical and Experimental Physics). Note this: http://saveitep.org/

PSPS

If one is aware of new (may be on trial) methods for pancreatic cancer, please let me know: al dot chervov dog gmail dot com

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Fractal theory is a branch of mathematics that is very helpful in cancers detection. It is possible that, we model the cancer growth by some fractal structure. – Shahrooz Feb 5 2012 at 18:49

My colleague Emmanuel Grenier (École Normale Supérieure de Lyon) leads a research group on mathematics in medical sciences, in collaboration with surgeons and pharmacologists. One of their tasks concerns the control of angiogenesis, which is the way a cancer gets food and blood supply.

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The Centre for Mathematical Biology in Oxford does a great deal of work on cancer modelling. To quote their webpage "We are interested in modelling the dynamics of cancer progression and treatment from a number of different view points and on various spatial and temporal scales."

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A lot of maths (and related stats) goes into the development of techniques for screening in the detection of breast cancer using mamography. (I know of this from work by Reyer Zwiggelaar in Aberystwyth. He is in a computer science department but uses a lot of deep maths.)

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A variety of medical image reconstruction methods are very relevant to cancer research and diagnosis.

Prime examples are: Positron Emission Tomography (PET), CT, MRI, etc.; In particular, all of these famous and successful technologies depend on solutions to inverse problems where one must reconstruct an image from a set of noisy measurements.

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You can find some information here: Mathematical Biosciences Institute

For example these... 1 2

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One can find some lecture on modern development of pharma-drugs (lecture was at public lectorium so it is quite understandable and interesting (imho)):

http://polit.ru/article/2011/03/22/cancercure/

Let me try to sketch a part and mention what is math-related. (Sorry, lecture is in Russian (try google.translate), but there are some slides inside in English, see also link to "Novartis" below).

## Drug development process

Math can be used at step 3 (as far as I understood). Let me first give all steps.

1) Target discovery (find a protein or cascade or smth which are critical for cancer development)

2) Hit discovery (by brute force test 50.000-1.000.000 molecules whether they can kill target or not)

3) Lead-optimization - (assume on previous step you find "something" which can hit cancer, but you must care about that this "something" will not kill person also or it is stable enough to work in real life. At this stage one looks for certain modifications which can preserve the positive features and dismiss negative).

4) Trials on animals

5) Phase 1 trials (10-50 people just to test that they will not be killed by side effects)

6) Phase 2 trials (100-300 people determine dosation, effectiveness, safety)

7) Phase 3 trial (1000-3000 people determine: side effects, interaction and comparing with other drugs,

8) Registration

9) Post launch studies

This is based on presentation from "Novartis", part can be found at:

"Novartis" is in particular famous for recent innovation of "Gleevec"(=Imatinib)

which is one of rare successes in the field of cancer drugs.)

So, (as far as I understood) at step 3 - "lead optimization" certain mathemaical modelling is sometimes possible. There is certain mathematical-based software which can try to predict some properties of moleculas based on their structure - so when people try to modify hiting molecula they sometimes use it.

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I attended a talk by Heiko Enderling on modeling cancer growth as a spatial process.

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