Fixed Boundary PDE Model Formulation
Fixed Boundary PDE Model Implementation
Fixed Boundary PDE Model Output
Moving Boundary PDE Model Implementation
Moving Boundary PDE Model Output
The focus of this book is a detailed discussion of a dual cancer vaccine (CV)-immune checkpoint inhibitor (ICI) mathematical model formulated as a system of partial differential equations (PDEs) defining the spatiotemporal distribution of cells and biochemicals during tumor growth.
A computer implementation of the model is discussed in detail for the quantitative evaluation of CV-ICI therapy. The coding (programming) consists of a series of routines in R, a quality, open-source scientific computing system that is readily available from the internet. The routines are based on the method of lines (MOL), a general PDE algorithm that can be executed on modest computers within the basic R system. The reader can download and use the routines to confirm the model solutions reported in the book, then experiment with the model by varying the parameters and modifying/extending the equations, and even studying alternative models with the PDE methodology demonstrated by the CV-ICI model.
Spatiotemporal Modeling of Cancer Immunotherapy: Partial Differential Equation Analysis in Rfacilitates the use of the model, and more generally, computer- based analysis of cancer immunotherapy mathematical models, as a step toward the development and quantitative evaluation of the immunotherapy approach to the treatment of cancer.
• Facilitates computer-based analysis of CV-ICI mathematical models as a step toward the development and quantitative evaluation of the immunotherapy approach to the treatment of cancer
• Provides detailed discussion of a dual cancer vaccine (CV) - immune checkpoint inhibitor (ICI) mathematical model
• Routines are programmed in R, a quality open-source computing system that is readily available as a download from the internet
William E. Schiesser is Emeritus McCann Professor of Computational Biomedical Engineering, Biomolecular and Chemical Engineering, and Professor of Mathematics at Lehigh University.