Poiseuille Flow of a Non-Local Non-Newtonian Fluid with Wall Slip: A First Step in Modeling Cerebral Microaneurysms

Drapaca, Corina S.

doi:10.3390/fractalfract2010009

Cited by 9 publications

(6 citation statements)

References 47 publications

(76 reference statements)

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“…In [5], a Mathematical model has been proposed based on the Caputo fractional derivative, to analyze cerebral microaneurysms. In this paper, the author proposes a model to describe the formation of microaneurysms that involves the chemo-mechanical coupling of blood and endothelial and neuroglial cells.…”

Section: Fractional Methods In Bio-medical Areasmentioning

confidence: 99%

Fractional Dynamics

Cattani

Spigler

2018

Fractal Fract

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Modelling, simulation, and applications of Fractional Calculus have recently become increasingly popular subjects, with impressive growth concerning applications. The founding and limited ideas on fractional derivatives have achieved an incredibly valuable status. The variety of applications in mathematics, physics, engineering, economics, biology, and medicine, have opened new, challenging fields of research. For instance, in soil mechanics, a suitable definition of the fractional operator has shed some light on viscoelasticity, explaining memory effects on materials. Needless to say, these applications require the development of practical mathematical tools in order to extract quantitative information from models, newly reformulated in terms of fractional differential equations. Even confining ourselves to the field of ordinary differential equations, the well-known Bagley-Torvik model showed that fractional derivatives may actually arise naturally within certain physical models, and are not merely fanciful mathematical generalizations. This Special Issue focuses on the most recent advances in fractional calculus, applied to dynamic problems, linear and nonlinear fractional ordinary and partial differential equations, integral fractional differential equations, and stochastic integral problems arising in all fields of science, engineering, and other applied fields. In this issue, we have collected several significant papers devoted to applications of fractional methods with a focus on dynamical aspects. The applications range from theoretical mathematical-numerical aspects [1,2] to bio-medical subjects [3-7]. Applications to complex materials are investigated in [8], aiming at proposing a generalized definition of fractional operators. Special diffusion models are studied in [9-11].

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Section: Fractional Methods In Bio-medical Areasmentioning

confidence: 99%

Fractional Dynamics

Cattani

Spigler

2018

Fractal Fract

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“…An inevitable complication of foam flow in a pipe is the wall slip phenomenon. Given the shear‐thinning nature of blood (Nanda et al, 2017), wall slip is not only a likely phenomenon in physiological vessels, but also it has been attributed to vascular malformations such as microaneurysms (Drapaca, 2018). A consequence of wall slip is inconsistent shear rate calculations for a constant pressure drop over different pipe diameters (Herzhaft, 1999).…”

Section: Physical Characterization Of Sclerosing Foamsmentioning

confidence: 99%

Foam‐in‐vein: A review of rheological properties and characterization methods for optimization of sclerosing foams

et al. 2020

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Varicose veins are chronic venous defects that affect >20% of the population in developed countries. Among potential treatments, sclerotherapy is one of the most commonly used. It involves endovenous injection of a surfactant solution (or foam) in varicose veins, inducing damage to the endothelial layer and subsequent vessel sclerosis. Treatments have proven to be effective in the short-term, however recurrence is reported at rates of up to 64% 5-year post-treatment. Thus, once diagnosed with varicosities there is a high probability of a permanently reduced quality of life. Recently, foam sclerotherapy has become increasingly popular over its liquid counterpart, since foams can treat larger and longer varicosities more effectively, they can be imaged using ultrasound, and require lower amounts of sclerosing agent. In order to minimize recurrence rates however, an investigation of current treatment methods should lead to more effective and long-lasting effects. The literature is populated with studies aimed at characterizing the fundamental physics of aqueous foams; nevertheless, there is a significant need for appropriate product development platforms. Despite successfully capturing the microstructural evolution of aqueous foams, the complexity of current models renders them inadequate for pharmaceutical development. This review article will focus on the physics of foams and the attempts at optimizing them for sclerotherapy. This takes the form of a discussion of the most recent numerical and experimental models, as well as an overview of clinically relevant parameters. This holistic approach could contribute to better foam characterization methods that patients may eventually derive long term benefit from.

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“…Indeed, fractional order derivatives and integrals are by definition non-local operators and appear suitable in modeling non-local phenomena [41,42]. This strategy has been proposed both for integral models [43][44][45][46] and for gradient models [47,48], not only in non-local elasticity but also in non-local fluid mechanics [49][50][51]. Recently, it has been shown that a proper definition of a fractional non-local model is capable of modeling both stiffening and softening non-local effects [52], typical of integral and gradient models, respectively.…”

Section: Introductionmentioning

confidence: 99%

An unified formulation of strong non-local elasticity with fractional order calculus

2021

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The research of a formulation to model non-local interactions in the mechanical behavior of matter is currently an open problem. In this context, a strong non-local formulation based on fractional calculus is provided in this paper. This formulation is derived from an analogy with long-memory viscoelastic models. Specifically, the same kind of power-law time-dependent kernel used in Boltzmann integral of viscoelastic stress-strain relation is used as kernel in the Fredholm non-local relation. This non-local formulation leads to stress-strain relation based on the space Riesz integral and derivative of fractional order. For unbounded domain, proposed model can be defined in stress- and in strain-driven formulation and in both cases the stress–strain relation represent a strong non-local model. Also, the proposed strain driven and stress driven formulations defined in terms of Riesz operators are proved to be fully consistent each another. Moreover, the proposed model posses a mechanical meaning and for unbounded non-local rod is described and discussed in detail.

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Poiseuille Flow of a Non-Local Non-Newtonian Fluid with Wall Slip: A First Step in Modeling Cerebral Microaneurysms

Cited by 9 publications

References 47 publications

Fractional Dynamics

Fractional Dynamics

Foam‐in‐vein: A review of rheological properties and characterization methods for optimization of sclerosing foams

An unified formulation of strong non-local elasticity with fractional order calculus

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