Tissue Engineering Problem - Find minimum starting cell population

In summary, when creating a tissue engineered blood vessel using smooth muscle cells, it is important to start with a large enough cell population. If the desired number of cells is 5 trillion in four weeks and the cells have a doubling time of 15 hours, the minimum starting cell population needed would be 1e12 (.5)^44.8.
  • #1
bmed90
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0

Homework Statement




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?

Homework Equations





The Attempt at a Solution

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

 
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  • #2
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.
 
  • #3
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?
 
  • #4
epenguin said:
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?

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
 
  • #5
bmed90 said:
So your saying the answer is 1e12(.5)^44

44.8 to be precise.
 
  • #6
bmed90 said:
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

Yes. Which is...?
 
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1. What is tissue engineering?

Tissue engineering is a multidisciplinary field that combines principles of biology, engineering, and medicine to create functional tissues and organs using living cells, biomaterials, and biochemical factors.

2. Why is finding the minimum starting cell population important in tissue engineering?

The minimum starting cell population is important in tissue engineering because it determines the success of tissue regeneration. Too few cells may not be enough to form a functional tissue, while too many cells can lead to overcrowding and hinder proper tissue development.

3. How is the minimum starting cell population determined?

The minimum starting cell population is determined through experimental and computational methods. Experimentally, different cell numbers are tested in tissue culture to determine the minimum number needed for tissue formation. Computationally, mathematical models can be used to predict the minimum cell number based on factors such as cell type, tissue type, and growth conditions.

4. What are the challenges in determining the minimum starting cell population?

One of the main challenges in determining the minimum starting cell population is the complexity of tissue development. Tissue formation involves multiple cellular processes, and the exact number of cells needed for successful tissue growth may vary depending on factors such as cell type, tissue type, and growth conditions. This makes it difficult to establish a universal minimum starting cell population for all tissue engineering applications.

5. How can the minimum starting cell population be optimized for tissue engineering?

The minimum starting cell population can be optimized by using advanced techniques such as cell patterning, cell sheet engineering, and biomimetic scaffolds. These methods allow for precise control of cell placement and distribution, which can improve tissue formation with a smaller number of cells. Additionally, the use of growth factors and other biochemical cues can also enhance tissue development and reduce the required cell population.

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