# Universal Dynamics of Tumor Growth: A Breakthrough

1. May 31, 2005

### Clausius2

A work of an spanish applied mathematician, Antonio Brú, has caused a shock here. Spain has a large tradition in the fight against Cancer, and has great sciencists working in this topic.

http://www.biophysj.org/cgi/content/full/85/5/2948 [Broken]
(The Biophysical Society).

I have got surprised how one can apply mathematics to this subject. In particular, if h(x,t) is the position on the tumor or colony border, then there is an equation such as:

$$\frac{\partial h(x,t)}{\partial t}=-K\frac{\partial^4 h(x,t)}{\partial x^4}+F+\eta(x,t)$$

which describes the tumor motion, and receives the name "Universal Dynamics of Tumor Growth".

I like very much this stuff about expanding physics and mathematics to other places traditionally dominated by other knowledges. Such a sinergy could cause great advances. As far as news I heard, there have been a proof on a terminal patient, who has recovered sucessfully from a Cancer. He seems to know the exact rate to administrate some inmunizing substance to the patient.

This come to demonstrate in our country there is little money for great laboratories, but there remains great brains who are very useful with pen and paper aside.

Last edited by a moderator: May 2, 2017
2. May 31, 2005

### Clausius2

By the way:

The true purpose was to share my astonishment about the power of Physics and Mathematics Sciences when they are applied to another non traditional fields of science. I thought it was worth to mention.

3. Jun 1, 2005

### PerennialII

... read the article and although have to say can't really present any sort of critique, was extremely interesting ... fractal description, growth via 'surface diffusion' etc. enabling analysis of a really 'biological' process. Nice to see quantitative aspects in this kind of study, impressive !

4. Jun 1, 2005

### Spin_Network

One has to determine that the Culture Medium in experimental growths, has a 'non-influential' result of the Tumour?

If the Tumour follows the dynamics of Fractal patterning, then there could be an obvious starting point at the Medium interface?..the surface tension of the Culture Medium would be 'naturally' re-produced by the Tumour, following the Fixed locations, or specifically geometric 'anchor points' cloned by the Tumour Cells from the Culture Cells?

This is interesting for many aspects, local domains for manifold interactions, the dynamical evolution of Structured Growth ie..dependant and non-dependancy for surface to surface reproduction techniques.

P.S.
I should really stipulate that my knowledge is based on very-little experience in this field of research, but purely out of amazement.

No doubt the researchers have performed some varying calibration techniques, I would like to know if they have performed a 'thin-film' or constraining Trapped Surface (between to near perfect plates), to observe if the Tumour evolves into a 2-D spiral pattern?..rather than an open-medium 3-D culture.

The Tumour would follow a fractal 'spiral path' linearly between two glass slides?

Last edited: Jun 1, 2005
5. Jun 1, 2005

### skeptic

Why is the OP surprised that mathematics can be applied to this? Mathematics can be applied to anything (but with varying degrees of success).

6. Jun 1, 2005

### Clausius2

Maybe the OP is surprised because he is young .

Maybe if the OP was a scientist he wouldn't get surprised, but he is not one.

Maybe the OP gets surprised from his point of view (some ignorant student).

Maybe when the OP will learn more about Physics & Mathematics he will see this stuff as some kid game, but nowadays he is instaured in the ignorance world.

Maybe the OP wanted to share another different vision of Physics not usually underlined here.

Maybe....

7. Jun 1, 2005

### arildno

Maybe the OP expressed a well-founded sense of wonder (which I share) that a seemingly intractably difficult physical phenomenon can be adequately described by a mathematically startlingly simple equation.

Last edited: Jun 1, 2005
8. Jun 1, 2005

### Clausius2

Thanks Arildno. By the way your superiority when expressing ideas with English is admirable. I think I'll never reach your level of english.

You know, it seems there are such a wisdom people who don't get surprised about anything....Fortunately I have not reached such grade of wisdom...

BY THE WAY: you have a great knowledge in mathematics, could you describe to a layman how the posted equation works and which are the physical meaning of the terms in your opinion?

Last edited: Jun 1, 2005
9. Jun 1, 2005

### arildno

Ah well, I'll never reach your level in expressing ideas adequately in Spanish, so we call that even..
(Norwegian is such a crude language of grunts and whistles, so it doesn't count to my advantage..)

10. Jun 2, 2005

### Clausius2

Today this guy has been on TV, talking about the discover. He has tried to explain it to layman people, but I have not understood it.

He has said the external boundary of the tumor has a "fractal curve behavior" (I don't know what does it mean). While comparing the mathematical model (which it seems belongs to MBE theory, I don't know what does it mean also)with experimental data, it can be shown that the main tumor growth is concentrated just at the boundary.

"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. "

The mathematical explanation about how the tumor growths has enhanced him and his co-workers to know how to administrate "neutrophils" (which are currently medically substances used) more accurately and effectively.

Some curiosity: he has had to spent 90000€ of his proper bank account to fund the experiments, because Spain government has no actual interest on research issues. Dramatic.

11. Jul 12, 2005

### saltydog

The figure below is a Koch Curve. Note how at each iteration, the perimeter "replicates" the overall geometry but on a smaller scale. This is a fractal curve.

Edit: Rather, the curve becomes a fractal at the limit as the number of iterations reach infinity.

Edit: One more. I realize this thread is probably already dead but I'll say so anyway. I noticed the following in the article describing the tumor boundary:

"and scale invariance of the colony contour"

That reflects nicely the geometry of the fractal curve below. Notice how as one magnifies the Koch curve, the geometry of the boundary looks the same. Really, there's lots of fractal dynamics in living tissues. A number of books have been published on the subject so I'm really not surprised that tumors would have a fractal component.

Thanks for the reference. Personally, wouldn't mind moving the PDE into DE and solving it in general terms but that's just me.

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Last edited: Jul 12, 2005
12. Jul 12, 2005

### Clausius2

Thanks for sharing your thoughts, Saltydog!!

Yeah, I've understood where you're getting at in your example.

Have you seen the PDE I have written some posts above from the original article?. If so, have you understood it?. Could you explain us what mechanism is it being representing?

13. Jul 12, 2005

### Spin_Network

There is recent paper I came across, I have not read it thoroughly though, so if it not of relevance sorry:http://arxiv.org/abs/physics/0507070