The Gompertz growth model is commonly used to model tumor cell growth. Let v(t) be the tumor’s volume, then
where λ and α are two appropriate constants (Edelstein- Keshet, 2005).
a. Verify that the solution to this equation is given by v(t) = v0eλ/α(1 -e-αt), where v0 is the initial tumor volume.
b. This model takes into account the fact that when nutrients and oxygen are scarce at the tumor’s core, its growth is impaired. Find the final predicted tumor volume (let t→∞).
c. For a specific mouse tumor, it was experimentally found that λ = 2:5 days; α = 0:1 days with v0 = 50 × 10-3 mm3 (Chignola, 2005). Use any method available to make a plot of v(t) vs. t.
d. Check the result obtained in Part b with the results from the graph found in Part c.
