Explore BrainMass

Explore BrainMass

    Modeling of tumor's growth

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    2. The Gompertz equation
    y'(t) = y[a-b*ln(y)]

    is an important model for avascular tumor growth. In the avascular growth phase, tumor cells obtain nutrients directly from the surrounding tissue. (The transition from avascular to vascular growth is marked by the onset of angiogenesis, the formation of blood vessels, which are used to bring nutrients to the tumor.) In this model, y(t) represents the number of cells in the tumor and a and b are constants related to the tumor's growth rate.

    Assume b>0. Determine the range of y over which the function y[a-b*ln(y)] is positive or negative (indicating increasing or decreasing tumor size).
    Based on this information, what is the value of y(t) as t ---> infinity if we start with a positive number of tumor cells?

    Repeat the qualitative analysis for b<0. Whet is the biological significance of y=exp(b/a)

    c. Find the analytic solution to the equation subject to an initial condition y(0) = y0. To do this use z = ln(y) and solve for z

    © BrainMass Inc. brainmass.com March 6, 2023, 1:28 pm ad1c9bdddf


    Solution Preview

    Hi there!

    Here is the solution for this very interesting problem, ...

    Solution Summary

    Th 5 page long solution shows how to analyze the equation in order to gain some insight into the behavior of the solution undere different conditions and then solves the equation completely.