Creating A Formula for Cell Growth

[elgg]

• Hello,
  I am junior and at my high school I am a part of a program called Sci - Tech that focuses on STEM (science, technology, engineering, and math). For the program, as juniors, we are required to complete an innovative project. For my project I am using stem cells for breast reconstruction in breast cancer patients. I am currently stuck on the math and have heard multiple things in reaction to what I currently have come up with. I need a solid response to whether my formula works or not and what I can do to make it better if it doesn't.
  
  We know cells usually grow exponentially unless limited resources reduce growth. For example, some bacteria cells divide every 30 minutes so 1,2,4 etc can be computed and then a carrying capacity can be estimated resulting in a J curve that stabilizes when resources and predation limit growth. Some cells, including a type of stem cell reproduce at a rate of 12.5 times the original amount per 48 hour period. There is no expected predation in stem cells as stem cells are grown initially in labs to then specialize into specific cells to replace sick/damaged cells. Recently, a group of scientists have grown a partial esophagus in the lab and installed into a person who had esophageal cancer. How realistic would I be to use exponential growth with the premise:
  
  [list]y = the area within the implant
  a= the number of stem cells initially transplanted
  b = the growth rate of stem cells
  c = the number of stem cells after growth
  d = the death rate of stem cells
  
  therefore: y = ae^bx - ce^dx
  
  I had also thought about y = ae^(b-d)x

• • All help is greatly appreciated.
    • Thank you.

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[deleted-63393]

What is the variable you are trying to solve for? What is X?

[elgg]

• I will be solving for y when I set up my examples. x represents time like exponential growth.

[deleted-63393]

Well this is certainly a complex equation.
I'm assuming you are using this as a hypothetical equation since it really depends on the density and health of the stem cells implanted. I guess I'm just trying to understand what you will be using this equation for. Are you just going to list it to show how you could predict the time it would take to regrow a certain type of tissue, in your example...breast tissue? Or, are you actually going to grow cells?

[elgg]

It's hypothetical for my project and I have to give examples. It proof that my innovative idea will work. I've just been moved toward logistics though. Those, I unfortunately know nothing about. So help with that would be really nice

[LeungWilley]

Hi Elgg,
This looks like a very interesting project.
Just out of curiosity, have you tried using the search term "Stem cell growth rate model" in google? There appears to be a few article with details on the growth rate of stem cell that looks to be relevant to your research. The URL of one of these article is as follows: http://onlinelibrary.wiley.com/doi/10.1 ... -5-536/pdf

Good Luck!
Willey

[elgg]

[list]Thank you!

I was about to finalize with the math that I wasn't very clear on, but this all makes so much more sense and will legitamitely help me so much! I can finally say I am done with my project!

Thank you again! (: [/list]