Biomedical Engineering Reference
In-Depth Information
must be overcome is the intrinsic multiple scale nature of tumor growth. We
present recent research that have been carried with the aim of formulating
multiscales model of tumor growth.
In 2004, Alarcon et al. 3 established a modeling framework for develop-
ing a realistic multiple scale model of tumor growth. They used the hybrid
cellular automaton as a basic theoretical framework to combine models that
couple scales ranging from the tissue scale (e.g. vascular structural adap-
tation) through to the intracellular scale (e.g. cell cycle). This has enabled
them to tackle questions such as the eect on tumor growth of blood ow
heterogeneity (Alarcon et al., 2 ) and the eciency of current chemotherapy
protocols for the treatment of non-Hodgkins lymphomas. In their modeling
framework, intercellular processes are represented by ordinary dierential
equations, extracellular processes by partial dierential equations and cell
processes by rules in a cellular automaton. Their models are still largely
phenomenological and simple, with many processes not included. As more
detail is incorporated the computational implementation and analysis be-
come more dicult. The challenge is developing appropriate numerical and
analytical techniques in order to eciently implement, understand, and
exploit these models.
In 2005, Jiang et al. 38 presented a mathematical model for avascular
tumor growth and development that spans three distinct scales. At the cel-
lular level, a lattice Monte Carlo model describes cellular dynamics (pro-
liferation, adhesion, and viability). At the subcellular level, a Boolean net-
work regulates the expression of proteins that control the cell cycle. At the
extracellular level, reaction-diusion equations describe the chemical dy-
namics (nutrient, waste, growth promoter, and inhibitor concentrations).
Data from experiments with multicellular spheroids were used to deter-
mine the parameters of the simulations. Starting with a single tumor cell,
this model produces an avascular tumor that quantitatively mimics experi-
mental measurements in multicellular spheroids. Based on the simulations,
they predicted:
(1) the microenvironmental conditions required for tumor cell survival, and
(2) growth promoters and inhibitors have diusion coecients in the range
between 106 and 107 cm 2 =h, corresponding to molecules of size 8090
kDa. Using the same parameters, their model also accurately predicted
spheroid growth curves under dierent external nutrient supply condi-
tions.
In 2006, Ayati et al. 6 presented multiscale models of cancer tumor inva-
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