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| Figure 2: As modified from Laird [7], for one particular tumor Laird fit W=W0 * exp [(0.788/0.142) * (1– exp (-0.142 t))]. That Gompertzian expression reasonably well fit those data. Then expanding [1 –exp (-0.142 t)] in a Taylor series as [1 – 1 + 0.142 t –0.1422 t2/2! + …] or 0.142 t (arbitrarily taking only the first non-zero term), Laird concluded that the exponential curve to compare to the best fit Gompertzian fit is exp [0.788 t]. It is no surprise that the exponential starts at the same point as the Gompertzian but thereafter is always larger. This is a mathematical identity and has nothing to do with cancer. |
