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Tissue Engineering Problem - Find minimum starting cell population

  1. Feb 26, 2013 #1
    1. The problem statement, all variables and given/known data


    You want to create a tissue engineered blood vessel using smooth muscle cells. Your plan is to isolate smooth muscle cells from discarded human tissue obtained from heart surgery and grow them for a long time to create cells own ECM. Smooth muscle cells have enormous groth potential in culture and assume they have a doubling time of 15 hours. If you need at least 5 trillion cells to make the blood vessel in four weeks what minimum starting cell population would you need?

    2. Relevant equations



    3. The attempt at a solution\

    I've tried several attempts and I don't think they are even worth posting. Cant seem to get reasonable answers.

    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 27, 2013 #2

    Borek

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    Staff: Mentor

    This is about exponential growth. It will be probably easier to find information about exponential decay, but the math is the same, just works in a different direction.
     
  4. Feb 27, 2013 #3

    epenguin

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    Everyone should understand exponentials but this is a biologist in a hurry. :biggrin:

    According to Wikipedia a trillion can mean either 1012 or 1018 which is not a negligible difference. So use scientific notation please.

    The cell population doubles in 15 hours. So if it's a trillion (whatever that is) now, it was half a trillion 15 hours ago. It halves every 15h you go back in time. So how many halving times, how many 15 h are there in 4 weeks? So the number of cells you needed to start with is (a trillion) X (1/2)^ raised to the power of that number of halving times. In other words you multiply by a half for every 15 h.

    What was unreasonable about the answers you got? Was it less than one? Doesn't mean the maths was wrong. What does it mean?
     
  5. Feb 27, 2013 #4
    Well honestly I can tell you right now that whatever I got was wrong. I got like 5.6e11..... So your saying the answer is 1e12(.5)^44
     
  6. Feb 27, 2013 #5

    Borek

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    Staff: Mentor

    44.8 to be precise.
     
  7. Feb 27, 2013 #6

    epenguin

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    Yes. Which is...?
     
    Last edited: Feb 27, 2013
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