martedi 8 novembre 2005

UNIONE EUROPEA

Grid-based cancer growth simulations

Davide Alemani, Francesco Pappalardo, Marzio Pennisi, Emilio

Mastriani, Santo Motta

martedi 8 novembre 2005

UNIONE EUROPEA

Plan of the talk

●  The hallmarks of cancer.

●  Modeling tumor growth and immune system competition.

●  Hybrid systems: computational and mathematical approaches.

●  Results.

●  Concluding remarks.

martedi 8 novembre 2005

UNIONE EUROPEA

The hallmarks of cancer ●  Recent research activities in cancer seems to reveal that there

is a set of six rules that govern the transformation of normal human cells into malignant cancers:

●  self-sufficiency in growth signals;

●  insensitivity to growth-inhibitory (antigrowth) signals;

●  evasion of programmed cell death (apoptosis);

●  limitless replicative potential;

●  sustained angiogenesis;

●  tissue invasion and metastasis.

martedi 8 novembre 2005

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Reproducing hallmarks of cancer

●  Models and simulation(s) of cancer must take care of these important points.

●  Immune system plays a relevant role in defending host from tumors.

●  A complete model of cancer growth should, therefore, take into account both cancer hallmarks and immune system response.

martedi 8 novembre 2005

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Proposed model ●  We introduce a new numerical method to simulate tumor growth

and immune system, by applying a hybrid Cellular Automata - Lattice Boltzmann (CA-LB) approach.

●  Cellular Automata method is used to keep track of the immune system and the tumor shape.

●  Lattice Boltzmann diffusion formulation is used to follow the variation of nutrient concentrations in the micro-environment of the tumor.

●  The main aim is to use the CA-LB model to describe the interactions between a growing tumor next to a nutrient source and the immune system of the host organism.

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The starting point ●  Ferreira et al., 2002 developed a reaction-diffusion

model for tumor growth in presence of nutrients. It was improved by Mallet and De Pillis, 2006 and by De Pillis et al., 2007 with the addition of a probabilistic CA model able to keep track of the immune system response to tumor growths and cell to cell adhesion.

●  However, the immune system is described only with natural killer (NK) cells and cytotoxic T lymphocytes (CTL).

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The starting point (continued) ●  Pappalardo et al., 2005, developed a model based on

a detailed description of the immune system at the cellular level with an agent-based method. The model is successfully used for cancer immunoprevention vaccine applications in mice [Motta et al., 2005].

●  However, tumor growth is not modeled in detail and diffusive nutrient effects are missing.

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The model

●  The reaction-diffusion equations (1) and (2) describe the interaction between the nutrients and the cells and the diffusion of the nutrients. The interaction nutrients-cells is described with linear first order reactions.

●  The reaction-diffusion equations (1) and (2) are turned into discrete Boltzmann equations on the lattice. We will not show the equations.

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The model (continued)

●  These probabilistic rules mimic the tumor growth.

●  They mimic the fact that: i) cell migration increases near the border of the tumor; ii) in region of low proliferative nutrient concentration and with a high population of cancer cells, cell division is inhibited and the probability of cell’s death increases; iii) in region of high survival nutrient concentration and with a high population of cancer cells, cell migration is enhanced and the probability of cell’s propagation increases.

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The model (continued)

●  θdiv tunes the division action; θmov tunes the propagation action and θdel tunes the death action. Tuning accurately these parameters allows us to reproduce different types of tumor patterns.

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The model (continued)

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Why we need the GRID

●  The model is able to mimic biological diversity.

●  We need to explore parameters space in order to statistically quantify cancer growth behavior.

●  Microenvironment and possible drug and vaccination strategies can interfere with the hallmarks of cancer.

●  The above mentioned factors lead to thousands of jobs per trial.

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Results

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Results (continued)

●  Simulation results of breast cancer in treated mice and untreated mice.

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Results (continued)

●  Tumor masses exhibit in general a necrotic core, made of necrotic cells, a quiescent layer made of necrotic and cancer cella and a proliferative layer made of cancer cells.

●  We have reproduced these three characteristics, as shown in the next two figures.

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Results (continued)

●  Cancer cells distribution. The cancer cells tend to accumulate near to the border of the tumor, giving rise to a proliferative layer of cancer cells.

martedi 8 novembre 2005

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Results (continued)

●  Necrotic cells distribution. The necrotic cells tend to accumulate to the center of the tumor mass, giving rise to a necrotic core.

martedi 8 novembre 2005

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Results (continued)

●  Cancer growth model is available as a module of ImmunoGrid simulator. Simulations run through Sicilian Grid.

martedi 8 novembre 2005

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Results (continued)

martedi 8 novembre 2005

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Conclusions ●  The model is able to reproduce early stage avascular tumors. In particular, it

is able to correctly predict the formation of three main stages: i) the necrotic cores made with necrotic cells, ii) the quiescent layer made essentially with cancer and necrotic cells and iii) the proliferating layer made with cancer cells.

●  Our model is able to qualitatively reproduce tumor shapes with border irregularity, by decreasing the consumption rate of nutrient by the cells. It is interesting to see that more than one necrotic core appear, that is an indication of malignancy in melanomas.

●  The model is, to our best knowledge, the first hybrid model which merges an accurate immune system response with a LB equations to model both tumor growth and elicited immune system response by vaccines.

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Reproducing hallmarks of cancer ●  θdiv could represent the capability of tumor cells to

generate many of their own growth signals and to be insensitive to growth-inhibitory signals.

●  θdel could represent the capability of cancer cells to evade from their natural programmed cell death.

●  θmov could represent the capability of tumor cells to invade the tissue and give metastasis.

●  Immune system response is included by agent based model (SimTriplex).

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References ●  S.C. Ferreira Jr, M.L. Martins, and M.J. Vilela. Reaction-diffusion model for

the growth of avascular tumor. Physical Review E, 65:021907, 2002.

●  L.G. De Pillis, D.G. Mallet, and A.E. Radunskaya. Spatial tumor-immune modeling. Computational and Mathematical Methods in Medecine, 7(2):159-176, 2007.

●  S. Motta, F. Castiglione, P. Lollini, and F. Pappalardo. Modelling vaccination schedules for a cancer immunoprevention vaccine. Immunome Research, 1:5, 2005.

●  F. Pappalardo, P.-L. Lollini, Castiglione F., and S. Motta. Modeling and simulation of cancer immunoprevention vaccine. Bioinformatics, 21(12):2891–2897, 2005.

martedi 8 novembre 2005

UNIONE EUROPEA

Thank you very much for your kind attention!