An Algorithm for Partial Functional Differential Equations Modeling Tumor Growth
We introduce a parallel algorithm for the numerical simulation of the growth of human tumor cells in time-varying environments and their response to therapy. The behavior of the cell populations is described by a system of delay partial differential equations with time-dependent coefficients. We construct the new algorithm by developing a time-splitting technique in which the entire problem is split into independent tasks assigned to arbitrary numbers of processors chosen in light of available resources. We present the results of a series of numerical experiments, which confirm the efficiency of the algorithm and exhibit a substantial decrease in computational time thus providing an effective means for fast clinical, case-by-case applications of tumor invasion simulations and possible treatment.
Zubik-Kowal, B. (2018). "An Algorithm for Partial Functional Differential Equations Modeling Tumor Growth". Applied Mathematics and Computation, 321,85-92. http://dx.doi.org/10.1016/j.amc.2017.09.028