Information Technology Reference
In-Depth Information
1.3
Uniform and Non-uniform CA
Cellular automata (CA) provide us with a means to model complex dynamical
phenomena by reformulating the macroscopic behaviour into microscopic and
mesoscopic rules that are discrete in space and time. The states of the discrete
elements (cells) organised in a regular grid, are updated synchronously according
to a uniform local interaction rule [8]. Uniform CAs have three notable features:
massive parallelism, locality of cellular interactions and simplicity of cells (finite
state machines). Non-uniform CAs have first been investigated by Vichniac [11]
who discussed a one-dimension CAin which a cell probabilistically selects one of
tworules,ateachtimestep.Inthisstudy,weusenon-uniformCAstoexplorethe
huge space of this complex system. The three essential CAfeatures are preserved
in this non-uniform model.
1.4
Computational Task and Related Work
Modelling the population dynamics of cells in immune response relevant to HIV
has recently attracted a considerable interest [2,3,5,6,7,12]. Currently, the only
two ways to model this dynamics of the immune response with respect to the
pathology and therapy of HIV infection are analytic PDE and ODE models and
cellular automata models. Analytical approaches are successful to describe dif-
ferentaspectsofHIVinfectiondynamics[4,3,6].Buttheyhavestronglimitations
to describe the two time scales observed in the time course of infection in term
of weeks and years and have serious di
A
culties in exploiting spatial information.
Cellular automata are recently regarded as a good strategy to model this spatial-
temporal dynamics with emphasis on local interactions. Mielke et al., developed
a fuzzy interaction model for mutating HIV with a fuzzy set of 10 interactions
for macrophages, helper cells, cytotoxic cells and virion [5]. Hershberg et al.,
(2001) indicated, using a microscopic simulation, that the time course of AIDS
is determined by the interactions of the virus and the immune cells in the shape
space of antigens, and that it is the virus's ability to move more rapidly in this
space (its high mutability) which cause the time course and eventual “victory”
of the disease [2]. This model clearly showed the three stages of the disease.
Asimple set of CArules was used to model the evolution of HIV infection by
Zorenon dos Santos et al. (2001). The three phase patterns were also presented
and the results indicated that the infected cells organise themselves into spatial
structures, which are responsible for the decrease in the concentration of un-
infected cells, leading to AIDS [13]. This CA model inspires the drug therapy
simulation presented here. In this model we can investigate the HIV infection
dynamics with therapy using microscopic simulations. The main ingredients in
our model are destruction of previously emerged spatial patterns (wave-like and
solid-like structures) and reconstruction of new spatial patterns (wave-like struc-
tures) due to incorporation of the drug therapy concept. In the sequel we will
refer to the Zorenon dos Santos's model as the HIV Infection Model (HI model)
and our model as the Drug Therapy of HIV Infection Model (DTHI model).
