Disturbance and repair of solitary waves in blood vessels with aneurysm

Noubissié, Samuel; Kraenkel, Roberto André; Woafo, P.

doi:10.1016/j.cnsns.2007.08.008

Cited by 13 publications

(10 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, solitary waves may play an important role in interrogating the health state of arteries (e.g. presence of an aneurysm) through signal processing [16,17]. Solitary waves in a fluid-filled membrane tube were initially studied using a multiple-scale approach [18,19], but later Epstein and Johnston [20] demonstrated that this approach is not necessary because the reduced governing equations admit two integrals; the evolution equation can be derived by an elementary method.…”

Section: Introductionmentioning

confidence: 99%

Localized standing waves in a hyperelastic membrane tube and their stabilization by a mean flow

Ильичев

2014

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

We first give a complete analysis of the dispersion relation for traveling waves propagating in a pre-stressed hyperelastic membrane tube containing a uniform flow. We present an exact formula for the so-called pulse wave velocity, and demonstrate that as any pre-stress parameter is increased gradually, localized bulging would always occur before a superimposed small-amplitude traveling wave starts to grow exponentially. We then study the stability of weakly and fully nonlinear localized bulging solutions that may exist in such a fluid-filled hyperelastic membrane tube. Previous studies have shown that such localized standing waves are unstable under pressure control in the absence of a mean-flow, whether the fluid inertia is taken into account or not. Stability of such localized aneurysm-type solutions is desired when aneurysm formation in human arteries is modelled as a bifurcation phenomenon. It is shown that in the near-critical regime axisymmetric perturbations are governed by the Korteweg-de Vries equation, and so the associated (weakly nonlinear) aneurysm solutions are (orbitally) stable with respect to axisymmetric perturbations. Stability of the fully nonlinear aneurysm solutions are studied numerically using the Evans function method. It is found that for each wall-fluid density ratio there exists a critical mean-flow speed above which no axisymmetric unstable modes can be found, which implies that a fully nonlinear aneurysm solution may be completely stabilized by a mean flow.

show abstract

Section: Introductionmentioning

confidence: 99%

Localized standing waves in a hyperelastic membrane tube and their stabilization by a mean flow

Ильичев

2014

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

show abstract

“…There are various areas where the study of solitons appears in mathematical biology [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The dynamics of solitons in α-helix proteins has been extensively studied by various authors [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

“…The dynamics of solitons in α-helix proteins has been extensively studied by various authors [3][4][5]. The issue of aneurysm has also been connected with solitons [13]. Solitons also appear in microbiological sciences as well.…”

Section: Introductionmentioning

confidence: 99%

Solitons and Conservation Laws in Neurosciences

et al. 2013

View full text Add to dashboard Cite

This paper obtains the 1-soliton solution by the ansatz method for the proposed model that governs the propagation of solitons through the neurons. This model is an improved one that describes the solitons in neurosciences more accurately. The ansatz method is applied to obtain the 1-soliton solution to the model. The Lie symmetry analysis is subsequently applied to obtain the conservation laws for the model.

show abstract

“…The dynamics of shallow water waves along ocean and sea shores are modeled by several forms of nonlinear evolution equations (NLEEs) [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]. A few of the well-known models are Korteweg-de Vries (KdV) equation, Peregrine equation, Benjamin-Bona-Mahoney equation.…”

Section: Introductionmentioning

confidence: 99%

Solitons, Shock Waves, Conservation Laws and Bifurcation Analysis of Boussinesq Equation with Power Law Nonlinearity and Dual Dispersion

Biswas¹,

Song²,

Triki³

et al. 2014

Appl. Math. Inf. Sci.

View full text Add to dashboard Cite

This paper obtains the soliton solutions to the Boussinesq equation with the effect of surface tension being taken into account. The power law nonlinearity is considered. Three integration tools are adopted in order to extract the soliton solutions. They are the traveling wave hypothesis, ansatz method and the semi-inverse variational principle. Finally, the Lie symmetry approach is adopted to extract the conservation laws of this equation.

show abstract

Disturbance and repair of solitary waves in blood vessels with aneurysm

Cited by 13 publications

References 21 publications

Localized standing waves in a hyperelastic membrane tube and their stabilization by a mean flow

Localized standing waves in a hyperelastic membrane tube and their stabilization by a mean flow

Solitons and Conservation Laws in Neurosciences

Solitons, Shock Waves, Conservation Laws and Bifurcation Analysis of Boussinesq Equation with Power Law Nonlinearity and Dual Dispersion

Contact Info

Product

Resources

About