Using cellular automata experiments to model periodontitis

G. Papantonopoulos, K. Takahashi, T. Bountis, B. G. Loos

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Cellular automata (CA) are time and space discrete dynamical systems that can model biological systems. The aim of this study is to simulate by CA experiments how the disease of periodontitis propagates along the dental root surface. Using a Moore neighborhood on a grid copy of the pattern of periodontal ligament fibers (PDLF) supporting and anchoring the teeth to bone, we investigate the fractal structure of the associated pattern using all possible outer-totalistic CA rules. On the basis of the propagation patterns, CA rules are classified in three groups, according to whether the disease was spreading, remaining constant or receding. These are subsequently introduced in a finite state Markov model as probabilistic state-rules and the model is validated using datasets retrieved from previous studies. Based on the maximum entropy production principle, we identified the state-rule that most appropriately describes the PDLF pattern, showing a power law distribution of periodontitis propagation rates with exponent 1.3. Entropy rates and mutual information of Markov chains were estimated by extensive data simulation. The scale factor of the PDLF used to estimate the conditional entropy of Markov chains was seen to be nearly equal 1.85. This possibly reflects the fact that a dataset representing tooth percentage with bone loss equal to 50% or more of their root length, is found to have a fractal dimension (FD) of about 1.84. Similarly, datasets of serum neutrophil, basophil, eosinophil, monocyte counts and IgG, IgA, IgM levels taken from periodontitis patients, showed a FD ranging from 1.82 to 1.87. Our study presents the first mathematical model to our knowledge that suggests periodontitis is a nonlinear dynamical process. Moreover, the model we propose implies that the entropy rate of the immune-inflammatory host response dictates the rate of periodontitis progression. This is validated by clinical data and suggests that our model can serve as a basis for detecting periodontitis susceptible individuals and shaping prognosis for treated periodontitis patients.

Original languageEnglish
Article number1350056
JournalInternational Journal of Bifurcation and Chaos
Volume23
Issue number3
DOIs
Publication statusPublished - Mar 2013
Externally publishedYes

Fingerprint

Cellular automata
Cellular Automata
Ligaments
Entropy
Fiber
Bone
Fractal Dimension
Experiment
Fractal dimension
Markov chain
Experiments
Markov processes
Roots
Propagation
Monocytes
Fibers
Neutrophils
Conditional Entropy
Fractal Structure
Discrete Dynamical Systems

Keywords

  • cellular automata
  • entropy
  • inflammation
  • Markov chains
  • nonlinear dynamics
  • Periodontitis

ASJC Scopus subject areas

  • Applied Mathematics
  • General
  • Engineering(all)
  • Modelling and Simulation

Cite this

Using cellular automata experiments to model periodontitis. / Papantonopoulos, G.; Takahashi, K.; Bountis, T.; Loos, B. G.

In: International Journal of Bifurcation and Chaos, Vol. 23, No. 3, 1350056, 03.2013.

Research output: Contribution to journalArticle

Papantonopoulos, G. ; Takahashi, K. ; Bountis, T. ; Loos, B. G. / Using cellular automata experiments to model periodontitis. In: International Journal of Bifurcation and Chaos. 2013 ; Vol. 23, No. 3.
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