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Abstract: In the last decades the Lattice Boltzmann method (LB) has been successfully used to simulate a variety of processes. The LB model describes the microscopic processes occurring at the cellular level and the macroscopic processes occurring at the continuum level with a unique function, the probability distribution function. Recently, it has been tried to couple deterministic approaches with probabilistic cellular automata (probabilistic CA) methods with the aim to model temporal evolution of tumor growths and three dimensional spatial evolution, obtaining hybrid methodologies. Despite the good results attained by CA-PDE methods, there is one important issue which has not been completely solved: the intrinsic stochastic nature of the interactions at the interface between cellular (microscopic) and continuum (macroscopic) level. CA methods are able to cope with the stochastic phenomena because of their probabilistic nature, while PDE methods are fully deterministic. Even if the coupling is mathematically correct, there could be important statistical effects that could be missed by the PDE approach. For such a reason, to be able to develop and manage a model that takes into account all these three level of complexity (cellular, molecular and continuum), we believe that PDE should be replaced with a statistic and stochastic model based on the numerical discretization of the Boltzmann equation: The Lattice Boltzmann (LB) method. In this work we introduce a new hybrid method to simulate tumor growth and immune system, by applying Cellular Automata Lattice Boltzmann (CA-LB) approach. [Copyright &y& Elsevier]

Multiple sclerosis is a disease of the central nervous system that involves the destruction of the insulating sheath of axons, causing severe disabilities. Since the etiology of the disease is not yet fully understood, the use of novel techniques that may help to understand the disease, to suggest potential therapies and to test the effects of candidate treatments is highly advisable. To this end we developed an agent based model that demonstrated its ability to reproduce the typical oscillatory behavior observed in the most common form of multiple sclerosis, relapsing–remitting multiple sclerosis. The model has then been used to test the potential beneficial effects of vitamin D over the disease. Many scientific studies underlined the importance of the blood–brain barrier and of the mechanisms that influence its permeability on the development of the disease. In the present paper we further extend our previously developed model with a mechanism that mimics the blood–brain barrier behavior. The goal of our work is to suggest the best strategies to follow for developing new potential treatments that intervene in the blood–brain barrier. Results suggest that the best treatments should potentially prevent the opening of the blood–brain barrier, as treatments that help in recovering the blood–brain barrier functionality could be less effective. [ABSTRACT FROM AUTHOR]