Approximation of Transient 1D Conduction in a Finite Domain Using Parametric Fractional Derivatives

Pineda, Sergio M.; Dı́az, Gerardo; Coimbra, Carlos F.M.

doi:10.1115/1.4003544

Cited by 7 publications

(5 citation statements)

References 33 publications

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“…For a finite domain, this approximation is valid as long as the penetration Fourier number for the domain length remains small15. The value of is determined by fitting Equation (5) to the results of the axisymmetric simulations at t = 10 s. Using other time points that still fulfill the above Fourier criterion results in the same value of (maximum deviation of 1%).…”

Section: Methodsmentioning

confidence: 99%

Glymphatic solute transport does not require bulk flow

Asgari

Zélicourt

Kurtcuoglu

2016

Sci Rep

244

304

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Observations of fast transport of fluorescent tracers in mouse brains have led to the hypothesis of bulk water flow directed from arterial to venous paravascular spaces (PVS) through the cortical interstitium. At the same time, there is evidence for interstitial solute transport by diffusion rather than by directed bulk fluid motion. It has been shown that the two views may be consolidated by intracellular water flow through astrocyte networks combined with mainly diffusive extracellular transport of solutes. This requires the presence of a driving force that has not been determined to date, but for which arterial pulsation has been suggested as the origin. Here we show that arterial pulsation caused by pulse wave propagation is an unlikely origin of this hypothetical driving force. However, we further show that such pulsation may still lead to fast para-arterial solute transport through dispersion, that is, through the combined effect of local mixing and diffusion in the para-arterial space.

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Section: Methodsmentioning

confidence: 99%

Glymphatic solute transport does not require bulk flow

Asgari

Zélicourt

Kurtcuoglu

2016

Sci Rep

244

304

View full text Add to dashboard Cite

show abstract

“…This is reflected by the increased number of publications (i.e., books [9,[15][16][17], review monograms [10], and scientific articles) devoted to the topic in a variety of fields, like anomalous diffusion [18], semi-infinite tree networks of mechanical, electrical, and hydrodynamic equipment [19,20], and viscoelastic systems [21], among others. In the context of modeling and control of thermal devices and phenomena, studies, such as those Complexity 3 of Aoki et al [22], Pineda et al [23], Gabano and Poinot [24], and Caponetto et al [25], demonstrate that fractional derivatives provide good approximations for describing the dynamic behavior of heat transfer processes.…”

Section: Background On Fractional Calculusmentioning

confidence: 99%

Fractional‐Derivative Approximation of Relaxation in Complex Systems

Sen

Pacheco-Vega

2018

Complexity

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In this paper, we present a system identification (SI) procedure that enables building linear time-dependent fractional-order differential equation (FDE) models able to accurately describe time-dependent behavior of complex systems. The parameters in the models are the order of the equation, the coefficients in it, and, when necessary, the initial conditions. The Caputo definition of the fractional derivative, and the Mittag-Leffler function, is used to obtain the corresponding solutions. Since the set of parameters for the model and its initial conditions are nonunique, and there are small but significant differences in the predictions from the possible models thus obtained, the SI operation is carried out via global regression of an error-cost function by a simulated annealing optimization algorithm. The SI approach is assessed by considering previously published experimental data from a shell-and-tube heat exchanger and a recently constructed multiroom building test bed. The results show that the proposed model is reliable within the interpolation domain but cannot be used with confidence for predictions outside this region. However, the proposed system identification methodology is robust and can be used to derive accurate and compact models from experimental data. In addition, given a functional form of a fractional-order differential equation model, as new data become available, the SI technique can be used to expand the region of reliability of the resulting model.

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“…The dispersion coefficient may be derived from the above three-dimensional model by fitting the simulated axial concentration with the analytical solution of the dispersion equation in a semi-infinite domain [ 11 ]: where x is the spatial coordinate in axial direction, t is time, is the initial concentration, and is the dispersion coefficient in a segment of length L. For a finite domain, this approximation is valid as long as the penetration Fourier number for the domain length remains small [ 22 ]. The value of is determined by fitting Eq.…”

Section: Methodsmentioning

confidence: 99%

Barrier dysfunction or drainage reduction: differentiating causes of CSF protein increase

Asgari

Zélicourt

Kurtcuoglu

2017

Fluids Barriers CNS

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BackgroundCerebrospinal fluid (CSF) protein analysis is an important element in the diagnostic chain for various central nervous system (CNS) pathologies. Among multiple existing approaches to interpreting measured protein levels, the Reiber diagram is particularly robust with respect to physiologic inter-individual variability, as it uses multiple subject-specific anchoring values. Beyond reliable identification of abnormal protein levels, the Reiber diagram has the potential to elucidate their pathophysiologic origin. In particular, both reduction of CSF drainage from the cranio-spinal space as well as blood–CNS barrier dysfunction have been suggested ρas possible causes of increased concentration of blood-derived proteins. However, there is disagreement on which of the two is the true cause.MethodsWe designed two computational models to investigate the mechanisms governing protein distribution in the spinal CSF. With a one-dimensional model, we evaluated the distribution of albumin and immunoglobulin G (IgG), accounting for protein transport rates across blood–CNS barriers, CSF dynamics (including both dispersion induced by CSF pulsations and advection by mean CSF flow) and CSF drainage. Dispersion coefficients were determined a priori by computing the axisymmetric three-dimensional CSF dynamics and solute transport in a representative segment of the spinal canal.ResultsOur models reproduce the empirically determined hyperbolic relation between albumin and IgG quotients. They indicate that variation in CSF drainage would yield a linear rather than the expected hyperbolic profile. In contrast, modelled barrier dysfunction reproduces the experimentally observed relation.ConclusionsHigh levels of albumin identified in the Reiber diagram are more likely to originate from a barrier dysfunction than from a reduction in CSF drainage. Our in silico experiments further support the hypothesis of decreasing spinal CSF drainage in rostro-caudal direction and emphasize the physiological importance of pulsation-driven dispersion for the transport of large molecules in the CSF.

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Approximation of Transient 1D Conduction in a Finite Domain Using Parametric Fractional Derivatives

Cited by 7 publications

References 33 publications

Glymphatic solute transport does not require bulk flow

Glymphatic solute transport does not require bulk flow

Fractional‐Derivative Approximation of Relaxation in Complex Systems

Barrier dysfunction or drainage reduction: differentiating causes of CSF protein increase

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