Wavefront invasion for a chemotaxis model of Multiple Sclerosis

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2 Citazioni (Scopus)

Abstract

In this work we study wavefront propagation for a chemotaxis reaction-diffusion system describing the demyelination in Multiple Sclerosis. Through a weakly non linear analysis, we obtain the Ginzburg–Landau equation governing the evolution of the amplitude of the pattern. We validate the analytical findings through numerical simulations. We show the existence of traveling wavefronts connecting two different steady solutions of the equations. The proposed model reproduces the progression of the disease as a wave: for values of the chemotactic parameter below threshold, the wave leaves behind a homogeneous plaque of apoptotic oligodendrocytes. For values of the chemotactic coefficient above threshold, the model reproduces the formation of propagating concentric rings of demyelinated zones, typical of Baló’s sclerosis.
Lingua originaleEnglish
pagine (da-a)423-434
Numero di pagine12
RivistaRicerche di Matematica
Volume65
Stato di pubblicazionePublished - 2016

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Multiple Sclerosis
Chemotaxis
Invasion
Wavefronts
Wave Front
Traveling Wavefronts
Threshold Parameter
Ginzburg-Landau Equation
Nonlinear analysis
Concentric
Reaction-diffusion System
Nonlinear Analysis
Progression
Propagation
Ring
Numerical Simulation
Computer simulation
Coefficient
Model

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cita questo

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title = "Wavefront invasion for a chemotaxis model of Multiple Sclerosis",
abstract = "In this work we study wavefront propagation for a chemotaxis reaction-diffusion system describing the demyelination in Multiple Sclerosis. Through a weakly non linear analysis, we obtain the Ginzburg–Landau equation governing the evolution of the amplitude of the pattern. We validate the analytical findings through numerical simulations. We show the existence of traveling wavefronts connecting two different steady solutions of the equations. The proposed model reproduces the progression of the disease as a wave: for values of the chemotactic parameter below threshold, the wave leaves behind a homogeneous plaque of apoptotic oligodendrocytes. For values of the chemotactic coefficient above threshold, the model reproduces the formation of propagating concentric rings of demyelinated zones, typical of Bal{\'o}’s sclerosis.",
author = "Sammartino, {Marco Maria Luigi} and Rachele Barresi and Francesco Gargano and Lombardo, {Maria Carmela} and Bilotta and Pantano",
year = "2016",
language = "English",
volume = "65",
pages = "423--434",
journal = "Ricerche di Matematica",
issn = "0035-5038",
publisher = "Springer-Verlag Italia",

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T1 - Wavefront invasion for a chemotaxis model of Multiple Sclerosis

AU - Sammartino, Marco Maria Luigi

AU - Barresi, Rachele

AU - Gargano, Francesco

AU - Lombardo, Maria Carmela

AU - Bilotta, null

AU - Pantano, null

PY - 2016

Y1 - 2016

N2 - In this work we study wavefront propagation for a chemotaxis reaction-diffusion system describing the demyelination in Multiple Sclerosis. Through a weakly non linear analysis, we obtain the Ginzburg–Landau equation governing the evolution of the amplitude of the pattern. We validate the analytical findings through numerical simulations. We show the existence of traveling wavefronts connecting two different steady solutions of the equations. The proposed model reproduces the progression of the disease as a wave: for values of the chemotactic parameter below threshold, the wave leaves behind a homogeneous plaque of apoptotic oligodendrocytes. For values of the chemotactic coefficient above threshold, the model reproduces the formation of propagating concentric rings of demyelinated zones, typical of Baló’s sclerosis.

AB - In this work we study wavefront propagation for a chemotaxis reaction-diffusion system describing the demyelination in Multiple Sclerosis. Through a weakly non linear analysis, we obtain the Ginzburg–Landau equation governing the evolution of the amplitude of the pattern. We validate the analytical findings through numerical simulations. We show the existence of traveling wavefronts connecting two different steady solutions of the equations. The proposed model reproduces the progression of the disease as a wave: for values of the chemotactic parameter below threshold, the wave leaves behind a homogeneous plaque of apoptotic oligodendrocytes. For values of the chemotactic coefficient above threshold, the model reproduces the formation of propagating concentric rings of demyelinated zones, typical of Baló’s sclerosis.

UR - http://hdl.handle.net/10447/201098

UR - http://link.springer.com/journal/11587

M3 - Article

VL - 65

SP - 423

EP - 434

JO - Ricerche di Matematica

JF - Ricerche di Matematica

SN - 0035-5038

ER -