Arterial viscoelasticity: a fractional derivative model

Craiem,; Armentano,

doi:10.1109/iembs.2006.4397597

Cited by 7 publications

(8 citation statements)

References 13 publications

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“…Because of its interesting properties of non-locality and memory, the interest on FD has grown in many fields of engineering and science. Examples of reallife applications include but not restricted to: viscoelastic, diffusive, biomedical and biological systems [20], [21], [22], [23]. The continuous fractional integro-differential operator D α t , where α and t are the limits of the operation, is defined as follows…”

Section: Methodsmentioning

confidence: 99%

Parameter Sensitivity and Experimental Validation for Fractional-Order Dynamical Modeling of Neurovascular Coupling

Belkhatir

Alhazmi

Bahloul

et al. 2021

Preprint

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Goal: Neurovascular coupling is a fundamental mechanism linking neural activity to cerebral blood flow (CBF) response. Modeling this coupling is very important to understand brain functions, yet challenging due to the complexity of the involved phenomena. One key feature that different studies have reported is the time delay that is inherently present between the neural activity and cerebral blood flow, which has been described by adding a delay parameter in standard models. An alternative approach was recently proposed where the framework of fractional-order modeling is employed to characterize the complex phenomena underlying the neurovascular. Thanks to its nonlocal property, a fractional derivative is suitable for modeling delayed and power-law phenomena. Methods: In this study, we analyzed and validated an effective fractional-order for the effective modeling and characterization of the neurovascular coupling mechanism. To show the added value of the fractional order parameters of the proposed model, we perform a parameter sensitivity analysis of the fractional model compared to its integer counterpart. Moreover, the model was validated using neural activity-CBF data related to both event and block design experiments that were acquired using electrophysiology and laser Doppler flowmetry recordings, respectively. Results: The validation results show the aptitude and flexibility of the fractional-order paradigm in fitting a more comprehensive range of well-shaped CBF response behaviors while maintaining a low model complexity. Comparison with the standard integer-order models shows the added value of the fractional-order parameters in capturing various key determinants of the cerebral hemodynamic response, e.g., post-stimulus undershoot. Conclusions: This investigation authenticates the ability and adaptability of the fractional-order framework to characterize a wider range of wellshaped cerebral blood flow responses while preserving low model complexity through a series of unconstrained and constrained optimizations.

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Section: Methodsmentioning

confidence: 99%

Parameter Sensitivity and Experimental Validation for Fractional-Order Dynamical Modeling of Neurovascular Coupling

Belkhatir

Alhazmi

Bahloul

et al. 2021

Preprint

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“…Many materials, like rubbers, polymers, bones, bitumen and so on, show a viscoelastic mechanical behavior; moreover also biological tissues have viscoelastic properties [23][24][25][26][27][28]. Viscoelasticity is the property of such materials that exhibit at the same time elastic and viscous behavior.…”

Section: Mechanical Models Of Fractional Viscoelasticitymentioning

confidence: 99%

Electrical analogous in viscoelasticity

Ala

Paola

Francomano

et al. 2014

Communications in Nonlinear Science and Numerical Simulation

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a b s t r a c tIn this paper, electrical analogous models of fractional hereditary materials are introduced. Based on recent works by the authors, mechanical models of materials viscoelasticity behavior are firstly approached by using fractional mathematical operators. Viscoelastic models have elastic and viscous components which are obtained by combining springs and dashpots. Various arrangements of these elements can be used, and all of these viscoelastic models can be equivalently modeled as electrical circuits, where the spring and dashpot are analogous to the capacitance and resistance, respectively. The proposed models are validated by using modal analysis. Moreover, a comparison with numerical experiments based on finite difference time domain method shows that, for long time simulations, the correct time behavior can be obtained only with modal analysis. The use of electrical analogous in viscoelasticity can better reveal the real behavior of fractional hereditary materials.

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“…Viscoelastic properties of human tissues were demonstrated in many examples: the brain and the central nervous system in general [10,44,49], the breast [12], the liver [41,81], the spleen [61], the prostate [36,95], the arteries [13,14], the muscles [31] (see also references for some other human and animal organs tissues [16,50,55,60,69]). Viscoelastic materials obey the following stress-strain relationship:…”

Section: Systems With Memorymentioning

confidence: 99%

Fractional Maps as Maps with Power-Law Memory

Edelman

2013

Nonlinear Systems and Complexity

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The study of systems with memory requires methods which are different from the methods used in regular dynamics. Systems with power-law memory in many cases can be described by fractional differential equations, which are integrodifferential equations. To study the general properties of nonlinear fractional dynamical systems we use fractional maps, which are discrete nonlinear systems with power-law memory derived from fractional differential equations. To study fractional maps we use the notion of α-families of maps depending on a single parameter α > 0 which is the order of the fractional derivative in a nonlinear fractional differential equation describing a system experiencing periodic kicks. α-families of maps represent a very general form of multi-dimensional nonlinear maps with power-law memory, in which the weight of the previous state at time t i in defining the present state at time t is proportional to (t − t i ) α−1 . They may be applicable to studying some systems with memory such as viscoelastic materials, electromagnetic fields in dielectric media, Hamiltonian systems, adaptation in biological systems, human memory, etc. Using the fractional logistic and standard α-families of maps as examples we demonstrate that the phase space of nonlinear fractional dynamical systems may contain periodic sinks, attracting slow diverging trajectories, attracting accelerator mode trajectories, chaotic attractors, and cascade of bifurcations type trajectories whose properties are different from properties of attractors in regular dynamical systems.

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Arterial viscoelasticity: a fractional derivative model

Cited by 7 publications

References 13 publications

Parameter Sensitivity and Experimental Validation for Fractional-Order Dynamical Modeling of Neurovascular Coupling

Parameter Sensitivity and Experimental Validation for Fractional-Order Dynamical Modeling of Neurovascular Coupling

Electrical analogous in viscoelasticity

Fractional Maps as Maps with Power-Law Memory

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