Analysis of lattice-gas cellular automaton models for tumor growth by means of fractal scaling

Sebastiano De Franciscis, Haralambos Hatzikirou, Andreas Deutsch

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Mathematical modeling of tumor development has become a real hype within the last decade. The abundance of mathematical models has created a great need for the validation of their biological relevance. Recently, in order to characterize the tumor growth dynamics, Brú et al. have determined some statistical properties of both in vitro and in vivo solid tumor-surfaces by using fractal scaling analysis. Surprisingly, for all tumor surfaces, the statistical observables converged to a unique set of critical exponents which indicates some common features of tumor growth dynamics (linear growth rate, growth activity limited to the outer rim of the tumor mass and diffusion of newborn tumor cells on the surface from lower to higher curvature regions, typical of Molecular Beam Epitaxy (MBE) Universality). Here, we develop and analyze a lattice-gas cellular automaton (LGCA) model of solid tumor growth. Random walk dynamics are assumed for tumor cell migration and a density-dependent birth process describes the cell mitotic dynamics. Fractal scaling analysis shows that for any parameter variation the model interface dynamic follows Edward - Wilkinson (EW) Universality, which differs from experimental findings. However, the model recovers some features, i.e. linear growth rate for tumor size and proliferative activity restricted to the outer layer, observed in experiments.

Original languageEnglish
Pages (from-to)167-182
Number of pages16
JournalActa Physica Polonica B, Proceedings Supplement
Volume4
Issue number2
DOIs
Publication statusPublished - 2011

Fingerprint

cellular automata
fractals
tumors
scaling
gases
rims
random walk
mathematical models
molecular beam epitaxy
curvature
exponents

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Analysis of lattice-gas cellular automaton models for tumor growth by means of fractal scaling. / De Franciscis, Sebastiano; Hatzikirou, Haralambos; Deutsch, Andreas.

In: Acta Physica Polonica B, Proceedings Supplement, Vol. 4, No. 2, 2011, p. 167-182.

Research output: Contribution to journalArticle

De Franciscis, Sebastiano ; Hatzikirou, Haralambos ; Deutsch, Andreas. / Analysis of lattice-gas cellular automaton models for tumor growth by means of fractal scaling. In: Acta Physica Polonica B, Proceedings Supplement. 2011 ; Vol. 4, No. 2. pp. 167-182.
@article{cba82060ed3b40d99ec068d2b41f1743,
title = "Analysis of lattice-gas cellular automaton models for tumor growth by means of fractal scaling",
abstract = "Mathematical modeling of tumor development has become a real hype within the last decade. The abundance of mathematical models has created a great need for the validation of their biological relevance. Recently, in order to characterize the tumor growth dynamics, Br{\'u} et al. have determined some statistical properties of both in vitro and in vivo solid tumor-surfaces by using fractal scaling analysis. Surprisingly, for all tumor surfaces, the statistical observables converged to a unique set of critical exponents which indicates some common features of tumor growth dynamics (linear growth rate, growth activity limited to the outer rim of the tumor mass and diffusion of newborn tumor cells on the surface from lower to higher curvature regions, typical of Molecular Beam Epitaxy (MBE) Universality). Here, we develop and analyze a lattice-gas cellular automaton (LGCA) model of solid tumor growth. Random walk dynamics are assumed for tumor cell migration and a density-dependent birth process describes the cell mitotic dynamics. Fractal scaling analysis shows that for any parameter variation the model interface dynamic follows Edward - Wilkinson (EW) Universality, which differs from experimental findings. However, the model recovers some features, i.e. linear growth rate for tumor size and proliferative activity restricted to the outer layer, observed in experiments.",
author = "{De Franciscis}, Sebastiano and Haralambos Hatzikirou and Andreas Deutsch",
year = "2011",
doi = "10.5506/APhysPolBSupp.4.167",
language = "English",
volume = "4",
pages = "167--182",
journal = "Acta Physica Polonica B, Proceedings Supplement",
issn = "1899-2358",
publisher = "Jagellonian University",
number = "2",

}

TY - JOUR

T1 - Analysis of lattice-gas cellular automaton models for tumor growth by means of fractal scaling

AU - De Franciscis, Sebastiano

AU - Hatzikirou, Haralambos

AU - Deutsch, Andreas

PY - 2011

Y1 - 2011

N2 - Mathematical modeling of tumor development has become a real hype within the last decade. The abundance of mathematical models has created a great need for the validation of their biological relevance. Recently, in order to characterize the tumor growth dynamics, Brú et al. have determined some statistical properties of both in vitro and in vivo solid tumor-surfaces by using fractal scaling analysis. Surprisingly, for all tumor surfaces, the statistical observables converged to a unique set of critical exponents which indicates some common features of tumor growth dynamics (linear growth rate, growth activity limited to the outer rim of the tumor mass and diffusion of newborn tumor cells on the surface from lower to higher curvature regions, typical of Molecular Beam Epitaxy (MBE) Universality). Here, we develop and analyze a lattice-gas cellular automaton (LGCA) model of solid tumor growth. Random walk dynamics are assumed for tumor cell migration and a density-dependent birth process describes the cell mitotic dynamics. Fractal scaling analysis shows that for any parameter variation the model interface dynamic follows Edward - Wilkinson (EW) Universality, which differs from experimental findings. However, the model recovers some features, i.e. linear growth rate for tumor size and proliferative activity restricted to the outer layer, observed in experiments.

AB - Mathematical modeling of tumor development has become a real hype within the last decade. The abundance of mathematical models has created a great need for the validation of their biological relevance. Recently, in order to characterize the tumor growth dynamics, Brú et al. have determined some statistical properties of both in vitro and in vivo solid tumor-surfaces by using fractal scaling analysis. Surprisingly, for all tumor surfaces, the statistical observables converged to a unique set of critical exponents which indicates some common features of tumor growth dynamics (linear growth rate, growth activity limited to the outer rim of the tumor mass and diffusion of newborn tumor cells on the surface from lower to higher curvature regions, typical of Molecular Beam Epitaxy (MBE) Universality). Here, we develop and analyze a lattice-gas cellular automaton (LGCA) model of solid tumor growth. Random walk dynamics are assumed for tumor cell migration and a density-dependent birth process describes the cell mitotic dynamics. Fractal scaling analysis shows that for any parameter variation the model interface dynamic follows Edward - Wilkinson (EW) Universality, which differs from experimental findings. However, the model recovers some features, i.e. linear growth rate for tumor size and proliferative activity restricted to the outer layer, observed in experiments.

UR - http://www.scopus.com/inward/record.url?scp=79960799876&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79960799876&partnerID=8YFLogxK

U2 - 10.5506/APhysPolBSupp.4.167

DO - 10.5506/APhysPolBSupp.4.167

M3 - Article

VL - 4

SP - 167

EP - 182

JO - Acta Physica Polonica B, Proceedings Supplement

JF - Acta Physica Polonica B, Proceedings Supplement

SN - 1899-2358

IS - 2

ER -