6533b83afe1ef96bd12a7a11

RESEARCH PRODUCT

Wavefront invasion for a chemotaxis model of Multiple Sclerosis

Marco SammartinoMaria Carmela LombardoPietro PantanoR. BarresiFrancesco GarganoEleonora Bilotta

subject

General Mathematics01 natural sciencesConcentric ringQuantitative Biology::Cell Behavior010305 fluids & plasmasOpticsChemotaxis; Ginzburg–Landau equation; Multiple Sclerosis; Mathematics (all); Applied Mathematics0103 physical sciencesMultiple SclerosimedicineMathematics (all)0101 mathematicsSettore MAT/07 - Fisica MatematicaMathematicsGinzburg–Landau equationWavefrontbusiness.industryMultiple sclerosisNumerical analysisApplied Mathematics010102 general mathematicsMathematical analysisChemotaxisChemotaximedicine.diseaseNonlinear systemAmplitudeHomogeneousbusiness

description

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 Balo’s sclerosis.

yearjournalcountryeditionlanguage
2016-03-31
10.1007/s11587-016-0265-0http://hdl.handle.net/10447/201098