Mathematical modeling suggests that periodontitis behaves as a non-linear chaotic dynamical process

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

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Background: This study aims to expand on a previously presented cellular automata model and further explore the non-linear dynamics of periodontitis. Additionally the authors investigated whether their mathematical model could predict the two known types of periodontitis, aggressive (AgP) and chronic periodontitis (CP). Methods: The time evolution of periodontitis was modeled by an iterative function, based on the hypothesis that the host immune response level determines the rate of periodontitis progression. The chaotic properties of this function were investigated by direct iteration, and the model was validated by immunologic and clinical parameters derived from two clinical study populations. Results: Periodontitis can be described as chaos with the level of the host immune response determining its progression rate; the dynamics of the proposed model suggest that by increasing the host immune response level, periodontitis progression rate decreases. Renormalization transformations show the presence of two overlapping zones of disease activity corresponding to AgP and CP. By k-means cluster analysis, immunologic parameters corroborated the findings of the renormalization transformations. Periodontitis progression rates are modeled to scale with a power law of 1.3, and the mean exponential speed of the system is found to be 1.85 (metric entropy); clinical datasets confirmed the mathematical estimates. Conclusions: This study introduces a mathematical model that identifies periodontitis as a non-linear chaotic process. It offers a quantitative assessment of the disease progression rate and identifies two zones of disease activity that correspond to the existing classification of periodontitis in the AgP and CP types.

Original languageEnglish
JournalJournal of Periodontology
Volume84
Issue number10
DOIs
Publication statusPublished - Oct 2013
Externally publishedYes

Fingerprint

Periodontitis
Chronic Periodontitis
Theoretical Models
Aggressive Periodontitis
Nonlinear Dynamics
Entropy
Cluster Analysis
Disease Progression
Population

Keywords

  • Aggressive periodontitis
  • Chronic periodontitis
  • Fractals
  • Immunity
  • Models
  • Non-linear dynamics
  • Theoretical

ASJC Scopus subject areas

  • Periodontics

Cite this

Mathematical modeling suggests that periodontitis behaves as a non-linear chaotic dynamical process. / Papantonopoulos, G.; Takahashi, K.; Bountis, T.; Loos, B. G.

In: Journal of Periodontology, Vol. 84, No. 10, 10.2013.

Research output: Contribution to journalArticle

Papantonopoulos, G. ; Takahashi, K. ; Bountis, T. ; Loos, B. G. / Mathematical modeling suggests that periodontitis behaves as a non-linear chaotic dynamical process. In: Journal of Periodontology. 2013 ; Vol. 84, No. 10.
@article{9cff6b7228604057b98f13f00400ed21,
title = "Mathematical modeling suggests that periodontitis behaves as a non-linear chaotic dynamical process",
abstract = "Background: This study aims to expand on a previously presented cellular automata model and further explore the non-linear dynamics of periodontitis. Additionally the authors investigated whether their mathematical model could predict the two known types of periodontitis, aggressive (AgP) and chronic periodontitis (CP). Methods: The time evolution of periodontitis was modeled by an iterative function, based on the hypothesis that the host immune response level determines the rate of periodontitis progression. The chaotic properties of this function were investigated by direct iteration, and the model was validated by immunologic and clinical parameters derived from two clinical study populations. Results: Periodontitis can be described as chaos with the level of the host immune response determining its progression rate; the dynamics of the proposed model suggest that by increasing the host immune response level, periodontitis progression rate decreases. Renormalization transformations show the presence of two overlapping zones of disease activity corresponding to AgP and CP. By k-means cluster analysis, immunologic parameters corroborated the findings of the renormalization transformations. Periodontitis progression rates are modeled to scale with a power law of 1.3, and the mean exponential speed of the system is found to be 1.85 (metric entropy); clinical datasets confirmed the mathematical estimates. Conclusions: This study introduces a mathematical model that identifies periodontitis as a non-linear chaotic process. It offers a quantitative assessment of the disease progression rate and identifies two zones of disease activity that correspond to the existing classification of periodontitis in the AgP and CP types.",
keywords = "Aggressive periodontitis, Chronic periodontitis, Fractals, Immunity, Models, Non-linear dynamics, Theoretical",
author = "G. Papantonopoulos and K. Takahashi and T. Bountis and Loos, {B. G.}",
year = "2013",
month = "10",
doi = "10.1902/jop.2013.120637",
language = "English",
volume = "84",
journal = "Journal of Periodontology",
issn = "0022-3492",
publisher = "American Academy of Periodontology",
number = "10",

}

TY - JOUR

T1 - Mathematical modeling suggests that periodontitis behaves as a non-linear chaotic dynamical process

AU - Papantonopoulos, G.

AU - Takahashi, K.

AU - Bountis, T.

AU - Loos, B. G.

PY - 2013/10

Y1 - 2013/10

N2 - Background: This study aims to expand on a previously presented cellular automata model and further explore the non-linear dynamics of periodontitis. Additionally the authors investigated whether their mathematical model could predict the two known types of periodontitis, aggressive (AgP) and chronic periodontitis (CP). Methods: The time evolution of periodontitis was modeled by an iterative function, based on the hypothesis that the host immune response level determines the rate of periodontitis progression. The chaotic properties of this function were investigated by direct iteration, and the model was validated by immunologic and clinical parameters derived from two clinical study populations. Results: Periodontitis can be described as chaos with the level of the host immune response determining its progression rate; the dynamics of the proposed model suggest that by increasing the host immune response level, periodontitis progression rate decreases. Renormalization transformations show the presence of two overlapping zones of disease activity corresponding to AgP and CP. By k-means cluster analysis, immunologic parameters corroborated the findings of the renormalization transformations. Periodontitis progression rates are modeled to scale with a power law of 1.3, and the mean exponential speed of the system is found to be 1.85 (metric entropy); clinical datasets confirmed the mathematical estimates. Conclusions: This study introduces a mathematical model that identifies periodontitis as a non-linear chaotic process. It offers a quantitative assessment of the disease progression rate and identifies two zones of disease activity that correspond to the existing classification of periodontitis in the AgP and CP types.

AB - Background: This study aims to expand on a previously presented cellular automata model and further explore the non-linear dynamics of periodontitis. Additionally the authors investigated whether their mathematical model could predict the two known types of periodontitis, aggressive (AgP) and chronic periodontitis (CP). Methods: The time evolution of periodontitis was modeled by an iterative function, based on the hypothesis that the host immune response level determines the rate of periodontitis progression. The chaotic properties of this function were investigated by direct iteration, and the model was validated by immunologic and clinical parameters derived from two clinical study populations. Results: Periodontitis can be described as chaos with the level of the host immune response determining its progression rate; the dynamics of the proposed model suggest that by increasing the host immune response level, periodontitis progression rate decreases. Renormalization transformations show the presence of two overlapping zones of disease activity corresponding to AgP and CP. By k-means cluster analysis, immunologic parameters corroborated the findings of the renormalization transformations. Periodontitis progression rates are modeled to scale with a power law of 1.3, and the mean exponential speed of the system is found to be 1.85 (metric entropy); clinical datasets confirmed the mathematical estimates. Conclusions: This study introduces a mathematical model that identifies periodontitis as a non-linear chaotic process. It offers a quantitative assessment of the disease progression rate and identifies two zones of disease activity that correspond to the existing classification of periodontitis in the AgP and CP types.

KW - Aggressive periodontitis

KW - Chronic periodontitis

KW - Fractals

KW - Immunity

KW - Models

KW - Non-linear dynamics

KW - Theoretical

UR - http://www.scopus.com/inward/record.url?scp=84884891522&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884891522&partnerID=8YFLogxK

U2 - 10.1902/jop.2013.120637

DO - 10.1902/jop.2013.120637

M3 - Article

VL - 84

JO - Journal of Periodontology

JF - Journal of Periodontology

SN - 0022-3492

IS - 10

ER -