Which PDEs Are Most Commonly Used in Cancer Modeling?

[Domenico94]

Which are the most frequently used PDEs in cancer modelling? Are navier-stokes' equations and fluidodynamics equations used there?

 

[S.G. Janssens]

You have become quite a PDE enthusiast, haven't you?

A few years ago I attended a course in which participated as a lecturer Luigi Preziosi. There appear two papers in my notes:

• Astanin and Preziosi, Mathematical modelling of the Warburg effect in tumour cords, J. Theoretical Biology, 2009
• Astanin and Preziosi, Multiphase models of Tumour Growth, undated?

Specially since he is also Italian, you might have a look at his page or contact him directly for some inspiration.

 

[Domenico94]

I'm not a PDE enthusiast :D It's just that I've seen many people dying of cancer last year, and I would like to, for what I can, contribute to solving these equations, which can give you detailed information about the growth of tumor and, possibly using circuit theory to solve them ( I study EE), that's why I'm looking for information about them.
Anyway, thank you for your advice..I've just sent an e-mail to this lecturer..Let's see what he has to say :)

 

[S.G. Janssens]

I'm not a PDE enthusiast :D

Yes you are, at least a little, there is no denying:
https://www.physicsforums.com/threads/a-holder-space-is-a-banach-space.848529/

It's just that I've seen many people dying of cancer last year

I'm very sorry to hear that.

and I would like to, for what I can, contribute to solving these equations, which can give you detailed information about the growth of tumor and, possibly using circuit theory to solve them ( I study EE), that's why I'm looking for information about them.

That's a good personal motivation.

Anyway, thank you for your advice..I've just sent an e-mail to this lecturer..Let's see what he has to say :)

Good, if you have anything interesting to report, maybe write some of it here. I think it could be interesting for others, too.

 

[Domenico94]

Yes he answered me and said that there are very different kinds of differential equations in this field, including fluidodinamics as well.
Then I asked him how much important stochastic models can be, he told me that they shouldn't be ignored in biological modelling, so from what I understood, there s no kind of equations prevailing on the others.
P.s.What s your field of research? I be read you re a mathematician, but what do you study precisely?

 

[S.G. Janssens]

Yes he answered me and said that there are very different kinds of differential equations in this field, including fluidodinamics as well.
Then I asked him how much important stochastic models can be, he told me that they shouldn't be ignored in biological modelling, so from what I understood, there s no kind of equations prevailing on the others.

Nice that he replied already. Did he suggest something to read to you?

P.s.What s your field of research? I be read you re a mathematician, but what do you study precisely?

Thank you for the question. My field of research is analysis and its applications. I'm often drawn towards functional analytic aspects. More in particular, I study properties of certain linear and nonlinear integral equations (so far mostly of evolutionary type, i.e. Volterra equations), as well as various classes of differential problems that can be cast into this form, sometimes after some effort. I have become particularly interested in the analysis of numerical approximation methods as well as in examples from engineering (mechanics and control). However, I still have a lot to learn about these areas of application.

I don't think I will write more here, because it is off-topic and probably not very interesting for others.

 

[Domenico94]

Hi krylov. No, he didn't suggest anything to read in particular, but he told that there's a lot of material on the internet talking about this. But I guess every kind of equation is as important as the other ones, in that field-

 

[Andy Resnick]

Which are the most frequently used PDEs in cancer modelling? Are navier-stokes' equations and fluidodynamics equations used there?

Some places to start:

https://www.birs.ca/workshops/2015/15w5072/report15w5072.pdf
http://www.worldscientific.com/doi/abs/10.1142/S0218202508002796
http://www.sciencedirect.com/science/article/pii/S0009898105001944

 

[Domenico94]

HI resnick, thanks for the answer. Just going to read the article :)