Cellular Model for Avascular Tumor Growth

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Cellular Model for Avascular Tumor Growth

• Jelena Pješivac
• Ramapo College of New Jersey
• Yi Jiang
• T7, Los Alamos National Lab

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Outline

• Tumor
• Existing/Relevant Models
• Model for Avascular Tumor Growth
• Results
• Summary
• Future development

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Tumor

• Tumor (neoplasm) is a relentlessly growing mass
  of abnormal cells, whose growth rate exceeds the
  growth rate of surrounding normal cells.
• Avascular tumor is a benign tumor that grows in a
  spherical, layered structure consisting of
  necrotic, quiescent and proliferating cells.

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Tumor, cont.
Malignant brain tumor (glioma)

• Outer layer - viable rim
• Intermediate layer - quiescent cells
• The innermost layer - necrotic core

Interdisciplinary Development of Computational
Tumor Model Torquato S., Deisboeck T.S.
http//www.elsevier.com/locate/biosystems/
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Existing/Relevant models

• Continuum Models
• Rate Equations of Population Growth
• Coupled Reaction-Diffusion Equations
• Discrete Models
• Cellular Automata
• Q Potts model
• Original
• Extensions

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Original Q Potts model

• Cells are positioned on a lattice
• Each cell is assigned unique ID
• Driving force is minimization of surface energy

• Evolution
• a random site is chosen and assigned to one of
  its neighbors
• ?H is calculated
• probability of accepting this change is

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Extended Q Potts model

• Includes various extensions to Original Q Potts
  model
• Coupling between spins (e.g. surface tension)
• Coupling to external fields (e.g. potential
  energy)
• Constrains (e.g. surface or area constrain)
• Applications
• Grain growth in polycrystalline solids
• Foam drainage and rheology
• Cell sorting and growth
• etc.

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Model for Avascular Tumor Growth

• Processes to be considered in simulating
• tumor growth
• cell-environment chemotaxis interactions
• intercellular adhesion
• mitosis and cell growth
• mutations
• nutrient absorption and diffusion
• waste production and diffusion
• geometry and structure of cells

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Multicellular Tumor Spheroid

• MTS is an in vitro tumor model
• Used to assay tumor growth, reaction to the
  treatments, cell signaling, etc.
• Distinct phases in the growth of MTS
• initial phase (exponential growth)
• layering phase
• plateau phase

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Multicellular Tumor Spheroid, cont.
Mean diameter and standard deviation of 70
isolated MTS
V-79 Chinese hamster lung cancer cross section
Folkman and Hochberg 1973
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Our Model

• Extended large-Q Potts model in 3D
• Lattice Monte Carlo model coupled with continuous
  reaction-diffusion chemical dynamics
• Includes all important processes in a tumor cell
  growth

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Total energy

• Total energy of the cell aggregate

S - cell identification number ?(S) - cell type
(proliferating, quiescent, or necrotic) J?(S)?(S)
- coupling energy between cell types ?(S) and
?(S) ? v - elasticity vs - cell Volume Vs -
target Volume
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ChemicalReaction-diffusion dynamics
DO2, Dn, Dw diffusion constants for oxygen,
nutrients, and waste, respectively a, b, c
consumption/production rate of oxygen, nutrients
and waste, respectively, of cell occupying site
(x,y,z) c F(a, b)
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Results Early Spheroid growth Number of Cells
vs. Time
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Results Chemical distribution
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Results Beginning of Layering phase
Tumor aggregate after 440 Monte Carlo steps Cell
quiescence occurred
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Results Number of cells vs. time
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Summary

• At early stage of MTS development, exponential
  growth of the aggregate was obtained. This is
  consistent with experiments.
• Nutrient deficit/waste production could cause
  quiescence
• Plateau phase, that starts with onset of necrosis
  will occur in near future

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For future development

• Detailed comparison to the existing spheroid
  experimental data
• Extending model to describe vascular tumors by
  introducing angiogenesis
• Chemotaxis
• Development of continuous cellular model?
• combining continuous and discrete model in a
  unique integrated cellular model

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Angiogenesis

• Process in which new blood vessels are formed
• Occurs in
• healthy body
• healing wounds
• restoring blood flow to tissues
• after injury
• tumors/cancers
• Controlled by
• Stimulating growth factors
• Inhibitors

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Chemotaxis

• Movement of cell along a chemical concentration
  gradient either toward or away from the chemical
  stimulus
• Total energy term would have to be modified to
  include

? - effective chemical potential towards the
chemical C(x,y,z,t) - local concentration of the
chemical at the time t

• Dictyostelium Mound Formation

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Reference

• Suthreland R.M., Cell and Environment
  Interactions in Tumor Microregions The Multicell
  Spheroid Model
• Freyer J.P., Sutherland R.M., Proliferative and
  Clonogenic Heterogeneity of cells from EMT/Ro
  Multicellular Tumor Spheroids induced by the
  glucose and oxygen supply
• Freyer J.P., Role of Necrosis in Regulating the
  Growth Saturation of Multicellular Tumor
  Spheroids
• E.L. Stott, N.F. Britton, J.A. Glazier, M. Zajac,
  Stochastic Simulation of Benign Avascular Tumor
  Growth Using the Potts Model
• Y. Jiang, H. Levine, J.A. Glazier, Possible
  collaboration of Differential Adhesion and
  Chemotaxis Cooperate in Mound Formation of
  Dictyostelium