Spatial Aspects of HIV Infection
Human immunodeficiency virus type 1 (HIV-1) is one of the most and intensely studied viral pathogens in the history of science. However, despite the huge scientific effort, many aspects of HIV infection dynamics and disease pathogenesis within a host are
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1 Introduction Human immunodeficiency virus type 1 (HIV-1) is one of the most and intensely studied viral pathogens in the history of science. However, despite the huge scientific effort, many aspects of HIV infection dynamics and disease pathogenesis within a host are still not understood. Mathematical modeling has helped to improve our understanding of the infection as well as the dynamics of the immune response. Fitting models to clinical data has provided estimates for the turnover rate of target cells [82, 83, 111], the lifetime of infected cells and viral particles [104, 109], as well as for the rate of viral production by infected cells [21, 44]. Most mathematical models applied to experimental data on viral infections have been formulated as systems of ordinary differential equations (ODE) [91, 101, 104]. While helpful and appropriate in many situations, ODE models simplify the actual biological processes and have some limitations. One limitation is the assumption that the interacting viral and cell populations are well mixed and homogeneously distributed. This assumption, which may be realistic for populations in blood, is not realistic for populations interacting in tissues [36]. Within a tissue virus may not be distributed homogeneously and an infected cell will interact preferentially with neighboring cells. As HIV mainly infects CD4+ T cells [42] which are most abundant and densely packed in secondary lymphoid organs, such as lymph nodes and the spleen, the spatial arrangement of cells might influence the infection dynamics. Furthermore, during the establishment of infection, stochastic effects influenced by spatial conditions, such as the local availability of approF. Graw • A.S. Perelson () Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM 87545, USA e-mail: [email protected]; [email protected]
U. Ledzewicz et al., Mathematical Methods and Models in Biomedicine, Lecture Notes on Mathematical Modelling in the Life Sciences, DOI 10.1007/978-1-4614-4178-6 1, © Springer Science+Business Media New York 2013
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priate target cells, may strongly affect the outcome [43, 47, 100]. Basic ODE models are not able to capture the spatial or stochastic aspects of infection. Thus for some purposes spatial models may be preferred to ODE models. The utilization of specific types of mathematical models requires appropriate biological data for their justification. Previous experimental techniques allow the quantification of cell or virion populations in the blood or specific organs, making the analysis of those data mainly suitable for ODE models. Recent advances in imaging techniques allow the observation of infection processes in vivo on a cellular and viral level [71, 72]. Spatial models that incorporate these observations might increase our understanding of the infection process. Cellular automaton simulations and agent-based models, which treat cells or virions as individual agents, are modeling frameworks that are able to incorporate this level of detail.
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