Moving Boundary PDE Model Output

  • William E. Schiesser


The output from the moving boundary partial differential equation (MBPDE) algorithm discussed in Chap.  4 is presented in this chapter. First, the velocity and position of the tumor outer boundary are confirmed for the two test cases explained in Chap.  4 (zero and constant boundary velocities). Then the velocity and position of the boundary are presented for the third case of the velocity proportional to the boundary cancer cell density. In particular, the effect of the proportionality constant in the velocity equation of the third case is demonstrated. As in case (5) of Chap.  3, a cancer-free condition evolves for increasing time, thus indicating that increasing the CV-ICI dosages gives an effective cancer therapy.


Moving boundary partial differential equation (MBPDE) Boundary velocity equation Boundary cancer cell density CV-ICI therapy effectiveness 

Supplementary material


  1. 1.
    Soetaert, K., J. Cash, and F. Mazzia. 2012. Solving differential equations in R. Heidelberg: Springer.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • William E. Schiesser
    • 1
  1. 1.Department of Chemical and Biomolecular EngineeringLehigh UniversityBethlehemUSA

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