Fighting Cancer with Math

zoloback writes "A group of scientists have developed a mathematical method to fight certain forms of cancer. The study has taken the team several years, but the first trial on a human has been successful. You can read the actual paper. It looks like a huge advancement in science, because there's a possibility to extrapolate the method to other types of cancer" From the article: "The researchers have evidence to show that all tumors grow in the same way, irrespective of the tissue or species in which they develop. In a previous paper, these researchers reported that tumor growth, rather than being exponential as commonly believed, is a much slower "linear" process similar to the growth of certain crystals and other natural phenomena."

Not really

[fgl]

Im very Impressed Im sure. But its not really fighting cancer with math, just creating a good model on how to repond with the treatments we have.

Re:Could they elaborate a bit?

[zoloback]

The breakthrough lies in the connection between the variables that allow a tumor to grow and the control that can be put over those variables, a lot of these were never considered before (such as barometric pressure inside the mass, and blood vessel proliferation).
This are easily controllable factors, so instead of treating the tumor by trying to kill the cells via radio or chemical therapy, they attack the factors that (in a mathematical model) determine the growth of the tumor, turning them into negative variables and therefore extinguishing the mass

Re:If this is true

[greenskyx]

I thought I'd send a quick response to this. You can't get a nobel prize in Mathematics [mathforum.org]. I'm not sure if they could get one with this research for medicine though. I'm guessing it's that possible. Peace.

Re:Not really

[Anonymous Coward]

The paper is actually describing a model for how tumors grow and doesn't really have anything to do with treatments. But in designing such a model, one needs to identify the mechanisms responsible for the majority of the growth. The growth of tumors wasn't very well understood up to this point. The new model nails the growth correctly and all one needs do is look at what physical processes were represented in the model to determine what the driver for tumor growth is in patients. Then you simply design treatments that will attack those processes. Takes the guesswork out of tumor-fighting.

Re:Nature is nothing if not clever

[bersl2]

how much are we tempting Nature to change the formula

Cancer is an anomaly of mitosis; it is not an organism and therefore does not evolve. The body regularly squashes cells which go into a sort-of mitotic infinite loop, and that's the end of that. It's the ones that the immune system does not recognize that grow into tumors.

Still early days.

[scottZed]

There is a follow-up article criticizing the original article: abstract [nih.gov]

And a response by the original authors: abstract [nih.gov]

In any event, it's a little premature to celebrate. Their follow-up work in mice (abstract [nih.gov]) used implanted tumours. It is already known that tumours have the capacity to evade immune response, and we should not be surprised that implanting a foreign tumour mass into a host and stimulating the immune system will provoke a favourable response. The situation is more complicated when trying to raise the immune system to attack a tumour comprised of one's own cells. It seems to me that, at this point, they are trying to prove their particular growth model, not developing a de facto cure.

That their devised strategy worked on a single human subject is cause for optimism, and nothing more. That work has not been published (that I could find), so there is no way to properly assess the result. At this point, they are more than likely drumming up press to ensure continued funding for their research... not that there's anything wrong with that ;).

Some Background...

[KrackHouse]

This is from an old article describing the results on mice...
Link [about.com]

"In 16 mice with a tumor mass in the muscle, the researchers induced neutrophil production by administering an immune system booster known as GM-CSF over two months. In a short time, they observed that GM-CSF altered the growth dynamics of the cells. The tumors of two mice regressed completely and 80-90% tumor-cell death was seen in the rest. If the growth dynamics of tumors are universal, there is every reason to be hopeful the same result could be obtained in humans."

And some detail on how it works...

"Tumor cells, they have found, grow through the diffusion or migration of cancer cells at the tumor's outer edges. Only the cells close to the edge of the tumor proliferate--those inside the tumor do not, contrary to previous assumptions. According to the researchers' observations, cells formed at the edge of the tumor diffuse at the border of the tumor mass until they settle in curved depressions where the competition for space is lowest and where they are best protected from the immune system. In their new paper, Bru and co-workers show that the mechanical pressure exerted by immune-system cells known as "neutrophils" around mouse tumors can prevent the diffusion of these cells and thus prevent tumor growth."

I'm too much of a damn pessimist to believe it's true after reading something similar to this just about every week followed by "could lead to treatments"... Here's hoping I'm wrong.

A joke and maybe more

[vashdot]

At the risk of trolling beyond my bounds...
It irks me to hear a good joke all the way to the end, only to find someone botched the punchline. Thank you fellow mathematician for enlightening us to the real deal.

Just so this isn't a pure fluff-post, here's a link to the abstract of the original paper from clinical studies in mice, published in Physical Review Letters, June 7, 2004. Mind you this has only been tested in one human case study and they make no claims to generalize this to other forms of cancer.

http://scitation.aip.org/getabs/servlet/GetabsServ let?prog=normal&id=PRLTAO000092000023238101000001& idtype=cvips&gifs=Yes [aip.org]
I will most likely download the full report tomorrow from the university.

Cancer is evolution

[Anonymous Coward]

Actually, unregulated mitosis is just one of the mutations that contributes to cancer. Some of the others include: genetic instability, resistance to apoptosis signaling (i.e. no cell suicide,) ability to recruit vasculature, ability to migrate (i.e. reduce cell-cell bonding and increased motility,) ability to survive in novel body environments. These are loosely related to the "stages" of cancer.
Each of these mutations is selected for by very stringent competition for nutrients both among cancer cells themselves and the body's normal cells. There is a very real type of evolution occuring, and as the cancer cells begin to ignore the signals coming from nearby cells and their behavior represents their own individual interests rather than the interests of the body as a whole--they have in a very literal sense become an independent organism. It is not exactly analogous to a speciation event, but it is related.
A literature search for "evolution" and "cancer" would return a number of papers that borrow models from evolutionary biology to model cancer.

Well, we'll see...

[missing_boy]

The excitement over this paper, or "treatment" is perhaps a bit premature. Scaling treatment is a common and quite popular approach in many growth phenomena, and has been investigated to death in the context of crystal growth (MBE, molecular beam epitaxy), but ironically, the equation that bears the name "MBE equation" does not actually describe MBE growth correctly (in my view). Therefore, saying that equation (2) in the original paper describes the physical process of "surface diffusion" in the case of MBE or surface cancer cells is highly suspect. The growth of the cancer cells might be well approximated by the growth MBE equation (2), but this is mere curve fitting, and a closer look at the underlying physical mechanisms is more important than getting good fits.

Re:Not as "new" or "revolutionary" as advertised

[rentedflowers]

If I've read your post correctly, you've misunderstood the article. They're arguing -- convincingly -- that the Gompertz model should be thrown out in favor of an MBE (Molecular Beam Epitaxy) model. The MBE model differs from the Gompertz model in that it has most of the growth occurring at the tumor surface, rather than uniformly throughout. It's this phenomenon that they're targeting their therapies at.

Re:Still early days.

[eledu]

There is a note (in spanish) in the Complutense web site about this. http://www.ucm.es/info/ucmp/pags.php?tp=Importante %20logro%20cient%EDfico&a=directorio&d=0003499.php [www.ucm.es]
I'll translate (freely) some points below:

Dr.Bru mentions that the article is
Regulation of neutrophilia by granulocyte colony-stimulating factor: a new cancer therapy that reversed a case of terminal hepatocarcinoma
in the Journal of Clinical Research.
He says that this kind of therapy opens very promising horizons for the treatment of all types of solid tumors in a relatively short time, since all these tumors share a common mechanism.

He also adds:

1. The proposed treatment is in an experimental phase, and much broader experimentation is necessary before validating it.
2. Therefore, at this time, there is no treatment protocol that would allow it to be used in a general way
3. Since it is impossible to answer to all the calls received at the Universidad Complutense de Madrid, and taking into account the disruption that these represent to normal teaching and research activities, please direct all enquiries to this email address (which you can find in the link at the beggining of this reply)