Question 2. Tumor Control Probability Calculation
Cytotoxic chemotherapy for cancer is usually given as a course of several separate cycles, while radiation therapy is usually given as a course of 5-40 separate daily exposures called fractions. If there is no immune response to a tumor, it is widely accepted that the cancer will relapse if even one cell can prollferate via mitosis after these therapies.
Let the letter A represent the average number of cells that can still proliferate after a course of therapy. According to Poisson statistics, the probability that zero cells can proliferate is given by this formula:
TCP (tumor control probability) = exp (-A) = e-A
Imagine a homogeneous tumor of 5.005 billion (5.005E9) identical cells. Assume that only 1 % of these cells survive one cycle of chemotherapy. Now imagine a heterogeneous tumor composed of 5.000 billion of the same cells plus 5 million cells that are resistant enough to the chemotherapy that 10% of those cells survive each cycle of chemotherapy. Note that the starting number of homogeneous and heterogeneous cancer cells is equal.
Make an Excel spreadsheet that calculates how many cycles of chemotherapy are needed for the homogeneous tumor to have TCP > 50%. How many cycles of chemotherapy are needed so that the heterogeneous tumor has a TCP > 50%?
If you were told that you must find a second drug that kills only the resistant cell population, and that the two combined drugs need only one more cycle than the first drug to achieve TCP >50%, what fraction of the resistant cells must be killed by each cycle of the second drug?
It is true that this is only a mathematics problem—but the numerical values are realistic.
I will grade your actual Excel spreadsheets, not merely their printouts, to verify that you have done the calculation correctly. It is important to know how to use Excel in this manner.
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