In this paper, we introduce a three-dimensional lattice-based computational model in which every lattice point can be occupied by an agent of various types (e.g. cancer cell, blood vessel cell or extracellular matrix). The behavior of agents can be associated to different chemical compounds that obey mass-transfer laws such as diffusion and decay in the surrounding environment. Furthermore, agents are also able to produce and consume chemical compounds. After a detailed description, the capabilities of the model are demonstrated by presenting and discussing a simulation of a biological experiment available in the literature.
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 Starruß J. de Back W. Brusch L. Deutsch A. “Morpheus: a user-friendly modeling environment for multiscale and multicellular systems biology” Bioinformatics 30 9 (2014) 1331–1332.
 Ghaffarizadeh A. Heiland R. Friedman S. H. Mumenthaler S. M. Macklin P. “PhysiCell: an open source physics-based cell simulator for 3-D multicellular systems” PLoS Comput. Biol. 14 2 (2018).
 Kang S. Kahan S. McDermott J. Flann N. Shmulevich I. “Biocellion: accelerating computer simulation of multicellular biological system models” Bioinformatics 30 21 (2014) 3101–3108.
 Drasdo D. Höhme S. “Individual-Based Approaches to Birth and Death in Avascular Tumors” Mathematical and Computer Modelling 37 (2003) 1163–1175.
 Drasdo D. Hoehme S. Block M. “On the Role of Physics in the Growth and Pattern Formation of Multi-Cellular Systems: What can we Learn from Individual-Cell Based Models?” Journal of Statistical Physics 128 1 (2007) 287–345.
 Walker D. C. Southgate J. Hill G. Holcombe M. Hosea D. R. Wood S. M. Mac Neil S. Smallwood R. H. “The epitheliome: agent-based modelling of the social behaviour of cells.” BioSystems 76 (2004) 89–100.
 Cytowski M. Szymanska Z. “Large-Scale Parallel Simulations of 3D Cell Colony Dynamics” Computing in Science & Engineering 16 5 (2014) 86–95.
 Cytowski M. Szymanska Z. Uminski P. Andrejczuk G. Raszkowski K. “Implementation of an Agent-Based Parallel Tissue Modelling Framework for the Intel MIC Architecture” Scientific Programming 8721612 (2017).
 Waclaw B. Bozic I. Pittman M. E. Hruban R. H. Vogelstein B. Nowak M. A. “A spatial model predicts that dispersal and cell turnover limit intratumour heterogeneity” Nature 525 7568 (2015) 261–264.
 Summers H. D. Wills J. W. Brown M. R. Rees P. “Poisson-Event-Based Analysis of Cell Proliferation” Cytometry A. 87 5 (2015) 385–392.
 Yates C. A. Ford M. J. Mort R. L. “A Multi-Stage Representation of Cell Proliferation as a Markov Process” Bulletin of Mathematical Biology 79 12 (2017) 2905–2928.
 Ghaffarizadeh A. Friedman S. H. Macklin P. “BioFVM: an efficient parallelized diffusive transport solver for 3-D biological simulations” Bioinformatics 32 8 (2016) 1256–1258.
 Ramachandran P. Varoquaux G. “Mayavi: 3D Visualization of Scientific Data” IEEE Computing in Science & Engineering 13 2 (2011) 40–51.
 Roberts D. L. Selim M. S. “Comparative study of six explicit and two implicit finite difference schemes for solving one-dimensional parabolic partial differential equations” International Journal for Numerical Methods in Engineering 20 (1984) 817–844.
 Mombach J. Glazier J. “Single cell motion in aggregates of embryonic cells” Phys. Rev. Lett. 76 3032 (1996).
 Grimes D. R. Kelly C. Bloch K. Partridge M. “A method for estimating the oxygen consumption rate in multicellular tumour spheroids” J. R. Soc. Interface 11 20131124 (2014).
 Macklin P. Edgerton M. E. Thompson A. M. Cristini V. “Patient-calibrated agent-based modelling of ductal carcinoma in situ (DCIS): From microscopic measurements to macroscopic predictions of clinical progression” Journal of Theoretical Biology 301 (2012) 122–140.
 Kiss D. Lovrics A. “Performance analysis of a computational off-lattice tumor growth model” Proceedings of the IEEE 30th Jubilee Neumann Colloquium (2017).