Exploring the Role of PDEs in Cancer Modeling: A Comprehensive Overview

In summary, the most frequently used PDEs in cancer modelling are Navier-Stokes' equations and fluidodynamics equations.
  • #1
Domenico94
130
6
Which are the most frequently used PDEs in cancer modelling? Are navier-stokes' equations and fluidodynamics equations used there?
 
Biology news on Phys.org
  • #2
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.
 
  • #3
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 :)
 
  • #4
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.
 
Last edited:
  • #5
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?
 
  • #6
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.
 
Last edited:
  • #7
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-
 
  • #9
HI resnick, thanks for the answer. Just going to read the article :)
 

1. What are PDEs and how are they used in cancer modeling?

PDEs (partial differential equations) are mathematical equations that involve multiple independent variables and their corresponding partial derivatives. They are used in cancer modeling to describe the behavior and growth of cancer cells over time.

2. What factors are typically included in PDE models for cancer?

PDE models for cancer often include factors such as cell proliferation, cell death, nutrient diffusion, and interactions with the surrounding tissue. These factors are important in understanding the dynamics of cancer growth and spread.

3. How do PDE models help in predicting the effectiveness of cancer treatments?

PDE models allow scientists to simulate the effects of different treatments on cancer cells and their surrounding environment. This can help in predicting which treatments will be most effective in stopping or slowing tumor growth.

4. Can PDE models be used to study different types of cancer?

Yes, PDE models can be applied to study various types of cancer, as long as the model is specific to the characteristics of that particular cancer. Different types of cancer may require different variables and parameters in the PDE model.

5. What are the limitations of PDE models in cancer research?

While PDE models are a valuable tool in cancer research, they have some limitations. These models may oversimplify the complex processes involved in cancer development and may not accurately reflect the behavior of cancer cells in a real-life situation. Additionally, PDE models require accurate and specific data to be effective, which may be difficult to obtain in some cases.

Similar threads

  • Differential Equations
Replies
2
Views
1K
  • Mechanical Engineering
Replies
14
Views
6K
  • Differential Equations
Replies
3
Views
171
Replies
2
Views
8K
Replies
2
Views
1K
Replies
18
Views
921
  • Other Physics Topics
Replies
2
Views
1K
Replies
1
Views
1K
Replies
4
Views
1K
  • Biology and Medical
Replies
10
Views
7K
Back
Top