NHM
Multiscale model of tumor-derived capillary-like network formation
Marco Scianna Luca Munaron
Networks & Heterogeneous Media 2011, 6(4): 597-624 doi: 10.3934/nhm.2011.6.597
Solid tumors recruit and form blood vessels, used for maintenance and growth as well as for formation and spread of metastases. Vascularization is therefore a pivotal switch in cancer malignancy: an accurate analysis of its driving processes is a big issue for the development of treatments. In vitro experiments have demonstrated that cultured tumor-derived endothelial cells (TECs) are able to organize in a connected network, which mimics an in vivo capillary-plexus. The process, called tubulogenesis, is promoted by the activity of soluble peptides (such as VEGFs), as well as by the following intracellular calcium signals. We here propose a multilevel approach, reproducing selected features of the experimental system: it incorporates a continuous model of microscopic VEGF-induced events in a discrete mesoscopic Cellular Potts Model (CPM). The two components are interfaced, producing a multiscale framework characterized by a constant flux of information from finer to coarser levels. The simulation results, in agreement with experimental analysis, allow to identify the key mechanisms of network formation. In particular, we provide evidence that the nascent pattern is characterized by precise topological properties, regulated by the initial cell density in conjunction with the degree of the chemotactic response and the directional persistence of cell migration.
keywords: in vitro tubulogenesis Cellular potts model proangiogenic calcium signals. vascular endothelial growth factor
MBE
A Cellular Potts model simulating cell migration on and in matrix environments
Marco Scianna Luigi Preziosi Katarina Wolf
Mathematical Biosciences & Engineering 2013, 10(1): 235-261 doi: 10.3934/mbe.2013.10.235
Cell migration on and through extracellular matrix is fundamental in a wide variety of physiological and pathological phenomena, and is exploited in scaffold-based tissue engineering. Migration is regulated by a number of extracellular matrix- or cell-derived biophysical parameters, such as matrix fiber orientation, pore size, and elasticity, or cell deformation, proteolysis, and adhesion. We here present an extended Cellular Potts Model (CPM) able to qualitatively and quantitatively describe cell migration efficiencies and phenotypes both on two-dimensional substrates and within three-dimensional matrices, close to experimental evidence. As distinct features of our approach, cells are modeled as compartmentalized discrete objects, differentiated into nucleus and cytosolic region, while the extracellular matrix is composed of a fibrous mesh and a homogeneous fluid. Our model provides a strong correlation of the directionality of migration with the topological extracellular matrix distribution and a biphasic dependence of migration on the matrix structure, density, adhesion, and stiffness, and, moreover, simulates that cell locomotion in highly constrained fibrillar obstacles requires the deformation of the cell's nucleus and/or the activity of cell-derived proteolysis. In conclusion, we here propose a mathematical modeling approach that serves to characterize cell migration as a biological phenomenon in healthy and diseased tissues and in engineering applications.
keywords: Cellular Potts model extracellular matrix cell migration.

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