In the body, liver cells (hepatocytes) are able to regenerate many times (each c

Question

In the body, liver cells (hepatocytes) are able to regenerate many times (each cell can undergo 34 cell divisions). However, researchers have not yet found a way to culture hepatocytes so that they proliferate in vitro. Suppose that someone were to discover a growth medium that would allow hepatocytes to proliferate in culture. How long would it take to generate 10% of a human liver mass (a therapeutically sufficient amount) starting with cells taken from a liver biopsy? A typical liver biopsy involves a portion of the tissue removed that fills 5 cm of a syringe of approximately 1 cm in diameter. Assume that hepatocytes are 20 mu m in diameter and that 70% of the biopsy cells survive. You may assume that a typical human liver has approximately 250 billion cells and that the doubling time of hepatocytes is 12 hrs. What is the minimum number of hepatocytes that you would need to be able to generate a cell mass the size of a whole human liver, assuming that 70% of your biopsy cells survive? How long would it take to produce the needed number of cells, starting with your calculated minimum starting population?

Explanation / Answer

Solution a) we know this equation, N = Noe[(ln2/td)t] this equation can be rewritten as t = td[ln(N/No)]/0.69 ----- (Equation 1)

We have information provided in questiont, d = 12 hours,

N = 10% of 250 billion = 25 billion = 2.5 ×1010

No = number of viable cells which were taken from liver biopsy.

To solve for the value of No first, we have to assume that the shape of a barrel of the syringe is perfectly cylindrical.

and the volume which can be enclosed in the 5 cm of the syringe with diameter = 1 cm ( r= 0.5 cm) V = ?r2h;

V = ?(0.5)25 = 3.927 cm3

the diameter of a hepatocyte = 20 ?m;

so the volume of one hepatocyte = (4/3)?r3 = 4189 ?m3

Number of hepatocytes can be calculated as = 3.927 cm3/4189 ?m3 = 937455240 cells

but, those cells which will remain viable are only 70% ;

so, No = 70% of (937455240) = 656218668 cells

Put this value in the Equation 1 deduced earlier:

t = 12[ln(2.5 ×1010/656218668)]/0.69 = 63.30 hours ---- (take this as Equation 2)

b) In this equation 2, [ln(2.5 ×1010/656218668)]/0.69 is similar to the number of divisions the cells might undergo.

it means that the cells might be undergoing 5.275 divisions.

but hepatocytes may divide as many as 34 times.

N = 2.5 ×1011

No = ?

so, the equation, 34 = [ln(2.5 ×1011/No)]/0.69

Or, ln(No) = ln(2.5 ×1011) - (34 × 0.69)

Or, No = e[ln(2.5 ×1011) - (34 × 0.69)]

or No = 16.19

so, (16.19/70%) = 23.13 (~ 23 cells) will be minimally required to generate the complete liver. and the time required for this, 12 × 34 = 408 hours

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