M.L. Martins

Reaction-diffusion model for the growth of avascular tumor.

A nutrient-limited model for avascular cancer growth including cell proliferation, motility, and death is presented. The model qualitatively reproduces commonly observed morphologies for primary tumors, and the simulated patterns are characterized by its gyration radius, total number of cancer cells, and number of cells on tumor periphery. These very distinct morphological patterns follow Gompertz growth curves, but exhibit different scaling laws for their surfaces. Also, the simulated tumors incorporate a spatial structure composed of a central necrotic core, an inner rim of quiescent cells and a narrow outer shell of proliferating cells in agreement with biological data. Finally, our results indicate that the competition for nutrients among normal and cancer cells may be a determining factor in generating papillary tumor morphology.

Morphology transitions induced by chemotherapy in carcinomas in situ.

Recently, we have proposed a nutrient-limited model for the avascular growth of tumors including cell proliferation, motility, and death [S. C. Ferreira, Jr., M. L. Martins, and M. J. Vilela, Phys. Rev. E 65, 021907 (2002)], which qualitatively reproduces commonly observed morphologies for carcinomas in situ. In the present work, we analyze the effects of distinct chemotherapeutic strategies on the patterns, scaling, and growth laws obtained for the nutrient-limited model. Two kinds of chemotherapeutic strategies were considered, namely, those that kill cancer cells and those that block cell mitosis but allow the cell to survive for some time. Depending on the chemotherapeutic schedule used, the tumors are completely eliminated, reach a stationary size, or grow following power laws. The model suggests that the scaling properties of the tumors are not affected by the mild cytotoxic treatments, although a reduction in growth rates and an increase in invasiveness are observed. For the strategies based on antimitotic drugs, a morphological transition in which compact tumors become more fractal under aggressive treatments was seen.

A growth model for primary cancer

One of the most aggressive phenomena in biology is the growth of cancer cells. In this paper we propose a simple model to simulate the growth of carcinoma “in situ”, which includes cell proliferation, motility and death, as well as the reciprocal influence among cells. Every simulated growth pattern is characterized by its gyration radius, surface roughness, number of cells on tumour periphery and fractal dimension. Our results indicate that the patterns are compact, with gyration radius, surface roughness and number of peripherical cells scaling, in the asymptotic limit, as a square root of the total number of tumour cells. Also, a preliminary comparison between the simulated patterns and explants of primary tumours is done.

A cellular automata model for cell differentiation

Developmental processes generating spontaneously coordinated and inhomogeneous spatiotemporal patterns with differentiated cell types are one of the main problems in modern biology. In this paper a cellular automata model for cell differentiation is proposed. It takes into account the time evolution of the gene networks representing each cell, cell–cell interactions through gene couplings and cell division. Our computer simulations show that a society with differentiated cell types exhibiting the main features observed in biological morphogenesis emerges from a marginally stable regime at the edge of chaos.

Electoral surveys’ influence on the voting processes: a cellular automata model

Nowadays, in societies threatened by atomization, selfishness, short-term thinking, and alienation from political life, there is a renewed debate about classical questions concerning the quality of democratic decision making. In this work a cellular automata model for the dynamics of free elections, based on the social impact theory is proposed. By using computer simulations, power-law distributions for the size of electoral clusters and decision time have been obtained. The major role of broadcasted electoral surveys in guiding opinion formation and stabilizing the “status quo” was demonstrated. Furthermore, it was shown that in societies where these surveys are manipulated within the universally accepted statistical error bars, even a majoritary opposition could be hindered from reaching power through the electoral path.

Cluster size distribution of cell aggregates in culture

The growth patterns of established normal and cancer cell lines, cultured in monolayer and collagen gel, have been characterized using the cluster size distribution of cellular aggregates. HN-5 (cancer) cells exhibit, either in gel or in monolayer, power-law distributions at any time in culture, whereas for MDCK (“normal”) and Hep-2 (cancer) cells there is a transition from an exponential behavior to a power-law distribution after a transient time in culture. These results suggest that the transitions in growth regimes observed in MDCK and Hep-2 cell lines might be associated to changes in the control of replication or in the expression patterns of cell adhesion molecules of cell–cell and cell–matrix type related to intracellular signalling. These transitions are irreversible and seems to be an adaptative response to the growth constraints imposed by high cell population density or long permanence in culture.

One-dimensional cellular automata characterization by the roughness exponent

Cellular automata (CA) are discrete, spatially homogeneous, locally interacting dynamical systems of very simple construction, but which exhibit a rich intrinsic behavior. CA can, even starting from disordered initial configurations, evolve into ordered states with complex structures crystallized in its space-time patterns. In this paper we concentrate on the several Wolfram qualitative classes of CA behavior. In order to better characterize these classes we apply the roughness exponent method to the profiles generated by the spatiotemporal patterns of one-dimensional “elementary” CA rules. We find that this method can separate Wolfram class IV from other ones.

A growth model for primary cancer (II). New rules, progress curves and morphology transitions

In the present paper we extend the analysis of another model recently proposed to simulate the growth of carcinoma “in situ”, which includes cell proliferation, motility and death, as well as chemotactic interactions among cells. The tumour patterns generated by two distinct growth rules are characterised by its gyration radius, surface roughness, total number of cancer cells, and number of cells on tumour periphery. Our results indicate that very distinct morphological patterns follow Gompertz growth curves and their gyration radii increase linearly in time and scale, in the asymptotic limit, as a square root of the total number of tumour cells. In contrast, these distinct tumour patterns exhibit different scaling laws for their surfaces. Thus, some biological features of malignant behaviour seem to influence particularly the structure of the tumour border, while its gyration radius and progress curve are described by more robust functions. Finally, for both rules used, morphology transitions as well as a transient behaviour up to the onset of the phase of rapid growth in the Gompertz curves are observed.

Strategies for Optimize Off-Lattice Aggregate Simulations

We review some computer algorithms for the simulation of off-lattice clusters grown from a seed, with emphasis on the diffusion-limited aggregation, ballistic aggregation and Eden models. Only those methods which can be immediately extended to distinct off-lattice aggregation processes are discussed. The computer efficiencies of the distinct algorithms are compared.

Fractal patterns for dendrites and axon terminals

In the present paper we analyse the morphology of dendrites of cerebellar Purkinje cells and axon terminals in the cerebral cortex of rats. We find that these three-dimensional biostructures are fractal over at least one decade of length scales, with fractal dimension 1.68 ± 0.08 for the Purkinje cells and 1.28 ± 0.17 for the axon terminals. We also discuss the largelly unknown mechanisms underlying neurite outgrowth which frequently develops neuronal shapes with fractal dimensions very different from that predicted for diffusion-limited-aggregation model (DLA) in three dimensions.