A High-Performance Cellular Automaton Model of Tumor Growth with Dynamically Growing Domains

Jan Poleszczuk, Heiko Enderling

(Submitted on 24 Sep 2013)

Tumor growth from a single transformed cancer cell up to a clinically apparent mass spans many spatial and temporal orders of magnitude. Implementation of cellular automata simulations of such tumor growth can be straightforward but computing performance often counterbalances simplicity. Computationally convenient simulation times can be achieved by choosing appropriate data structures, memory and cell handling as well as domain setup. We propose a cellular automaton model of tumor growth with a domain that expands dynamically as the tumor population increases. We discuss memory access, data structures and implementation techniques that yield high-performance multi-scale Monte Carlo simulations of tumor growth. We present simulation results of the tumor growth model and discuss tumor properties that favor the proposed high-performance design.

link: http://arxiv.org/abs/1309.6015

A filter-flow perspective of hematogenous metastasis offers a non-genetic paradigm for personalized cancer therapy

This is a rather short paper authored by some of us who maintain Warburg's Lens. The focus is on metastatic spread and how it can be understood from a filter-flow perspective, i.e. how the blood flow and filtration that occurs in capillary beds affects the efficiency of the process. This method builds on the work of Leonard Weiss, who was a leading figure in research into metastatic spread for many years.

Jacob G. Scott, Alexander G. Fletcher, Philip K. Maini, Alexander R. A. Anderson, Philip Gerlee

Research into mechanisms of hematogenous metastasis has largely become genetic in focus, attempting to understand the molecular basis of `seed-soil' relationships. Preceding this biological mechanism is the physical process of dissemination of circulating tumour cells (CTCs). We utilize a `filter-flow' paradigm to show that assumptions about CTC dynamics strongly affect metastatic efficiency: without data on CTC dynamics, any attempt to predict metastatic spread in individual patients is impossible.

link: http://arxiv.org/abs/1309.5078

A general framework for modeling tumor-immune system competition and immunotherapy: mathematical analysis and biomedical inferences

Alberto d'Onofrio

(Submitted on 13 Sep 2013)

In this work we propose and investigate a family of models, which admits as particular cases some well known mathematical models of tumor-immune system interaction, with the additional assumption that the influx of immune system cells may be a function of the number of cancer cells. Constant, periodic and impulsive therapies (as well as the non-perturbed system) are investigated both analytically for the general family and, by using the model by Kuznetsov et al. (V. A. Kuznetsov, I. A. Makalkin, M. A. Taylor and A. S. Perelson. Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis. Bulletin of Mathematical Biology 56(2): 295-321, (1994)), via numerical simulations. Simulations seem to show that the shape of the function modeling the therapy is a crucial factor only for very high values of the therapy period $T$, whereas for realistic values of $T$, the eradication of the cancer cells depends on the mean values of the therapy term. Finally, some medical inferences are proposed.

link: http://arxiv.org/abs/1309.3337