Which PDEs Are Most Commonly Used in Cancer Modeling?

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Discussion Overview

The discussion centers on the types of partial differential equations (PDEs) commonly used in cancer modeling, exploring various mathematical approaches and their relevance to biological processes. Participants inquire about specific equations, including the Navier-Stokes equations and fluid dynamics, and discuss the importance of stochastic models in this context.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant asks about the most frequently used PDEs in cancer modeling, specifically mentioning the Navier-Stokes equations and fluid dynamics.
  • Another participant references lectures by Luigi Preziosi and mentions papers related to tumor modeling, suggesting they may provide insights into the topic.
  • A participant expresses a personal motivation to contribute to solving PDEs related to tumor growth, indicating a background in electrical engineering and interest in circuit theory.
  • Responses indicate that there are many different types of differential equations used in cancer modeling, including fluid dynamics, and that no single type of equation prevails over others.
  • Stochastic models are highlighted as important in biological modeling, suggesting a need for diverse mathematical approaches.
  • Participants share their research interests, with one focusing on functional analysis and its applications, particularly in relation to differential equations.
  • Links to external resources are provided for further reading on the topic.

Areas of Agreement / Disagreement

Participants generally agree that multiple types of equations are relevant in cancer modeling, and there is no consensus on a single prevailing model. The importance of stochastic models is acknowledged, but the discussion remains open-ended regarding specific PDEs.

Contextual Notes

Some participants note the lack of specific recommendations for reading materials on the topic, and there is an acknowledgment of the vast amount of information available online. The discussion reflects varying levels of familiarity with the subject matter among participants.

Who May Find This Useful

This discussion may be useful for researchers and students interested in mathematical modeling of biological processes, particularly those focusing on cancer research and the application of differential equations in this field.

Domenico94
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Which are the most frequently used PDEs in cancer modelling? Are navier-stokes' equations and fluidodynamics equations used there?
 
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You have become quite a PDE enthusiast, haven't you? :smile:

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.
 
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 :)
 
Domenico94 said:
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/ :wink:
Domenico94 said:
It's just that I've seen many people dying of cancer last year
I'm very sorry to hear that.
Domenico94 said:
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.
Domenico94 said:
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.
 
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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?
 
Domenico94 said:
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?
Domenico94 said:
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.
 
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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-
 
HI resnick, thanks for the answer. Just going to read the article :)
 

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