A cellular automata model to investigate immune cell–tumor cell interactions in growing tumors in two spatial dimensions

We develop a hybrid cellular automata model to describe the effect of the immune system and chemokines on a growing tumor. The hybrid cellular automata model consists of partial differential equations to model chemokine concentrations, and discrete cellular automata to model cell–cell interactions and changes. The computational implementation overlays these two components on the same spatial region. We present representative simulations of the model and show that increasing the number of immature dendritic cells (DCs) in the domain causes a decrease in the number of tumor cells. This result strongly supports the hypothesis that DCs can be used as a cancer treatment. Furthermore, we also use the hybrid cellular automata model to investigate the growth of a tumor in a number of computational “cancer patients.” Using these virtual patients, the model can explain that increasing the number of DCs in the domain causes longer “survival.” Not surprisingly, the model also reflects the fact that the parameter related to tumor division rate plays an important role in tumor metastasis.

A hybrid cellular automata model of multicellular tumour spheroid growth in hypoxic microenvironment

A three-dimensional hybrid cellular automata (CA) model is developed to study the dynamic process of multicellular tumour spheroid (MTS) growth by introducing hypoxia as an important microenvironment factor which influences cell migration and cell phenotype expression. The model enables us to examine the effects of different hypoxic environments on the growth history of the MTS and to study the dynamic interactions between MTS growth and chemical environments. The results include the spatial distribution of different phenotypes of tumour cells and associated oxygen concentration distributions under hypoxic conditions. The discussion of the model system responses to the varied hypoxic conditions reveals that the improvement of the resistance of tumour cells to a hypoxic environment may be important in the tumour normalization therapy.

Cellular Automata Models of Traffic Behavior in Presence of Speed Breaking Structures

In this article, we study traffic flow in the presence of speed breaking structures. The speed breakers are typically used to reduce the local speed of vehicles near certain institutions such as schools and hospitals. Through a cellular automata model we study the impact of such structures on global traffic characteristics. The simulation results indicate that the presence of speed breakers could reduce the global flow under moderate global densities. However, under low and high global density traffic regime the presence of speed breakers does not have an impact on the global flow. Further the speed limit enforced by the speed breaker creates a phase distinction. For a given global density and slowdown probability, as the speed limit enforced by the speed breaker increases, the traffic moves from the reduced flow phase to maximum flow phase. This underlines the importance of proper design of these structures to avoid undesired flow restrictions.

Cellular automata: Simulating alpine tundra vegetation dynamics in response to global warming

This study attempts to model alpine tundra vegetation dynamics in a tundra region in the Qinghai Province of China in response to global warming. We used Raster-based cellular automata and a Geographic Information System to study the spatial and temporal vegetation dynamics. The cellular automata model is implemented with IDRISI's Multi-Criteria Evaluation functionality to simulate the spatial patterns of vegetation change assuming certain scenarios of global mean temperature increase over time. The Vegetation Dynamic Simulation Model calculates a probability surface for each vegetation type, and then combines all vegetation types into a composite map, determined by the maximum likelihood that each vegetation type should distribute to each raster unit. With scenarios of global temperature increase of I to 3 degrees C, the vegetation types such as Dry Kobresia Meadow and Dry Potentilla Shrub that are adapted to warm and dry conditions tend to become more dominant in the study area.

Cellular automata-based spatial dynamic modeling for analyzing urban land use change

This paper analyzes land use change in Rio Claro City and its surroundings, located in the southeastern state of Sao Paulo, in the period from 1988 to 1995, using air-borne digital imagery and a cellular automata model. The simulation experiment was carried out in the Dinamica EGO platform and the results revealed a constrained urban sprawl, resulting from both the densification of residential areas implemented in previous years and the economic recession that led to an internal financial crisis in Brazil during the early 1990s. The simulation outputs were validated using a multi-resolution procedure based on a fuzzy similarity index and showed a satisfactory fitness in relation to the historical reference data. © 2013 IEEE.

Chlamydial infection and spatial ascension of the female genital tract : a novel hybrid cellular automata and continuum mathematical model

Sexually transmitted chlamydial infection initially establishes in the endocervix in females, but if the infection ascends the genital tract, significant disease, including infertility, can result. Many of the mechanisms associated with chlamydial infection kinetics and disease ascension are unknown. We attempt to elucidate some of these processes by developing a novel mathematical model, using a cellular automata–partial differential equation model. We matched our model outputs to experimental data of chlamydial infection of the guinea-pig cervix and carried out sensitivity analyses to determine the relative influence of model parameters. We found that the rate of recruitment and action of innate immune cells to clear extracellular chlamydial particles and the rate of passive movement of chlamydial particles are the dominant factors in determining the early course of infection, magnitude of the peak chlamydial time course and the time of the peak. The rate of passive movement was found to be the most important factor in determining whether infection would ascend to the upper genital tract. This study highlights the importance of early innate immunity in the control of chlamydial infection and the significance of motility-diffusive properties and the adaptive immune response in the magnitude of infection and in its ascension.

Simulating urban growth in a developing nation's region using a cellular automata-based model

Urbanization is one of the most evident global changes. Research in the field of urban growth modelling has generated models that explore for drivers and components of the urban growth dynamics. Cellular automata (CA) modeling is one of the recent advances, and a number of CA-based models of urban growth have produced satisfactory simulations of spatial urban expansion over time. Most application and test of CA-based models of urban growth which provide likely and reliable simulations has been developed in urban regions of developed nations; urban regions in the United States, in particular. This is because most of the models were developed in universities and research centers of developed nations, and these regions have the required data, which is extensive. Most of the population growth in the world, however, occurs in the developing world. While some European countries show signs of stabilization of their population, in less developed countries, such as India, population still grows exponentially. And this growth is normally uncoordinated, which results in serious environmental and social problems in urban areas. Therefore, the use of existing dynamic–spatial models of urban growth in regions of developing nations could be a means to assist planners and decision makers of these regions to understand and simulate the process of urban growth and test the results of different development strategies. The pattern of growth of urban regions of developing nations, however, seems to be different of the pattern of developed countries. The former use to be more dense and centralized, normally expanding outwards from consolidated urban areas; while the second is normally more fragmented and sparse. The present paper aims to investigate to how extent existing CA-based urban growth models tested in developed nations can also be applied to a developing country urban area. The urban growth model was applied to Porto Alegre City, Brazil. An expected contiguous expansion from existing urban areas has been obtained as following the historical trends of growth of the region. Moreover, the model was sensitive and able to portray different pattern of growth in the study area by changing the value of its parameters.

An approximate Bayesian computation approach for estimating parameters of complex environmental processes in a cellular automata

Modelling an environmental process involves creating a model structure and parameterising the model with appropriate values to accurately represent the process. Determining accurate parameter values for environmental systems can be challenging. Existing methods for parameter estimation typically make assumptions regarding the form of the Likelihood, and will often ignore any uncertainty around estimated values. This can be problematic, however, particularly in complex problems where Likelihoods may be intractable. In this paper we demonstrate an Approximate Bayesian Computational method for the estimation of parameters of a stochastic CA. We use as an example a CA constructed to simulate a range expansion such as might occur after a biological invasion, making parameter estimates using only count data such as could be gathered from field observations. We demonstrate ABC is a highly useful method for parameter estimation, with accurate estimates of parameters that are important for the management of invasive species such as the intrinsic rate of increase and the point in a landscape where a species has invaded. We also show that the method is capable of estimating the probability of long distance dispersal, a characteristic of biological invasions that is very influential in determining spread rates but has until now proved difficult to estimate accurately.

Ergodicity and Mixing Rate of One-Dimensional Cellular Automata

One-and two-dimensional cellular automata which are known to be fault-tolerant are very complex. On the other hand, only very simple cellular automata have actually been proven to lack fault-tolerance, i.e., to be mixing. The latter either have large noise probability ε or belong to the small family of two-state nearest-neighbor monotonic rules which includes local majority voting. For a certain simple automaton L called the soldiers rule, this problem has intrigued researchers for the last two decades since L is clearly more robust than local voting: in the absence of noise, L eliminates any finite island of perturbation from an initial configuration of all 0's or all 1's. The same holds for a 4-state monotonic variant of L, K, called two-line voting. We will prove that the probabilistic cellular automata Kε and Lε asymptotically lose all information about their initial state when subject to small, strongly biased noise. The mixing property trivially implies that the systems are ergodic. The finite-time information-retaining quality of a mixing system can be represented by its relaxation time Relax(⋅), which measures the time before the onset of significant information loss. This is known to grow as (1/ε)^c for noisy local voting. The impressive error-correction ability of L has prompted some researchers to conjecture that Relax(Lε) = 2^(c/ε). We prove the tight bound 2^(c1log^21/ε) ＜ Relax(Lε) ＜ 2^(c2log^21/ε) for a biased error model. The same holds for Kε. Moreover, the lower bound is independent of the bias assumption. The strong bias assumption makes it possible to apply sparsity/renormalization techniques, the main tools of our investigation, used earlier in the opposite context of proving fault-tolerance.

Cellular automaton model for molecular traffic jams

We consider the time evolution of an exactly solvable cellular automaton with random initial conditions both in the large-scale hydrodynamic limit and on the microscopic level. This model is a version of the totally asymmetric simple exclusion process with sublattice parallel update and thus may serve as a model for studying traffic jams in systems of self-driven particles. We study the emergence of shocks from the microscopic dynamics of the model. In particular, we introduce shock measures whose time evolution we can compute explicitly, both in the thermodynamic limit and for open boundaries where a boundary-induced phase transition driven by the motion of a shock occurs. The motion of the shock, which results from the collective dynamics of the exclusion particles, is a random walk with an internal degree of freedom that determines the jump direction. This type of hopping dynamics is reminiscent of some transport phenomena in biological systems.

Simulation of dynamic recrystallization using random grid cellular automata

Computer simulation is a powerful tool to predict microstructure and its evolution in dynamic and post-dynamic recrystallization. CAFE proposed as an appropriate approach by combining finite element (FE) method and cellular automata (CA) for recrystallization simulation. In the current study, a random grid cellular automaton (CA), as micro-scale model, based on finite element (FE), as macro-scale method, has been used to study initial and evolving microstructural features; including nuclei densities, dislocation densities, grain size and grain boundary movement during dynamic recrystallization in a C-Mn steel. An optimized relation has been established between mechanical variables and evolving microstructure features during recrystallization and grain growth. In this model, the microstructure is defined as cells located within grains and grain boundaries while dislocations are randomly dispersed throughout microstructure. Changes of dislocation density during deformation are described considering hardening, recovery and recrystallization. Recrystallization is assumed to initiate near grain boundaries and nucleation rate was considered constant (site-saturated condition). The model produced a mathematical formulation which captured the initial and evolving microstructural entities and linked their effects to measurable macroscopic variables (e.g. stress).

Microstructural modeling of dynamic recrystallization using irregular cellular automata

Cellular automaton (CA) was used to simulate dynamic recrystallization (DRX) during thermomechanical deformation. Initial grain size, initial grain orientation and dislocation density were used as input data to the CA model. Flow curve, dislocation density, final grain size and orientation, and DRX volume fraction were the output data which were compared with experimental data to validate the model. The model proposed in this work considered the thermomechanical parameters (e.g., temperature and strain rate) and their role on the nucleation and growth kinetics during DRX. It was shown that the CA model can predict the final microstructure and flow curve to a high degree of accuracy and was able to successfully simulate the volume fraction of DRX as a function of strain for a wide range of deformation conditions.

Evolutionary modeling of larval dispersal in blowflies using non-uniform cellular automata

When the food supply flnishes, or when the larvae of blowflies complete their development and migrate prior to the total removal of the larval substrate, they disperse to find adequate places for pupation, a process known as post-feeding larval dispersal. Based on experimental data of the Initial and final configuration of the dispersion, the reproduction of such spatio-temporal behavior is achieved here by means of the evolutionary search for cellular automata with a distinct transition rule associated with each cell, also known as a nonuniform cellular automata, and with two states per cell in the lattice. Two-dimensional regular lattices and multivalued states will be considered and a practical question is the necessity of discovering a proper set of transition rules. Given that the number of rules is related to the number of cells in the lattice, the search space is very large and an evolution strategy is then considered to optimize the parameters of the transition rules, with two transition rules per cell. As the parameters to be optimized admit a physical interpretation, the obtained computational model can be analyzed to raise some hypothetical explanation of the observed spatiotemporal behavior. © 2006 IEEE.

Modelling fungus dispersal scenarios using cellular automata

This study focused on representing spatio-temporal patterns of fungal dispersal using cellular automata. Square lattices were used, with each site representing a host for a hypothetical fungus population. Four possible host states were allowed: resistant, permissive, latent or infectious. In this model, the probability of infection for each of the healthy states (permissive or resistant) in a time step was determined as a function of the host's susceptibility, seasonality, and the number of infectious sites and the distance between them. It was also assumed that infected sites become infectious after a pre-specified latency period, and that recovery is not possible. Several scenarios were simulated to understand the contribution of the model's parameters and the spatial structure on the dynamic behaviour of the modelling system. The model showed good capability for representing the spatio-temporal pattern of fungus dispersal over planar surfaces. With a specific problem in mind, the model can be easily modified and used to describe field behaviour, which can contribute to the conservation and development of management strategies for both natural and agricultural systems. © 2012 Elsevier B.V.

LATTICE BOLTZMANN METHOD AND CELLULAR AUTOMATA SIMULATION OF PARTICLE MOTION AND DEPOSITION IN 2-D CASE

This technical report discusses the application of the Lattice Boltzmann Method (LBM) and Cellular Automata (CA) simulation in fluid flow and particle deposition. The current work focuses on incompressible flow simulation passing cylinders, in which we incorporate the LBM D2Q9 and CA techniques to simulate the fluid flow and particle loading respectively. For the LBM part, the theories of boundary conditions are studied and verified using the Poiseuille flow test. For the CA part, several models regarding simulation of particles are explained. And a new Digital Differential Analyzer (DDA) algorithm is introduced to simulate particle motion in the Boolean model. The numerical results are compared with a previous probability velocity model by Masselot [Masselot 2000], which shows a satisfactory result.