Homogenization results for the calcium dynamics in living cells

Timofte, Claudia

doi:10.1016/j.matcom.2015.06.011

Cited by 11 publications

(5 citation statements)

References 20 publications

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“…The bidomain model can be obtained as the homogenized version of an electrical conduction problem posed at the scale of single cells (see, among others, [6,7,10,16,20,28,34,37,41]). However, the problem for the single cell can be, in turn, obtained as the upscaling of the ionic model (see, in the context of calcium dynamics, [25,27,29,40]).…”

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confidence: 99%

Homogenization of a modified bidomain model involving imperfect transmission

Amar¹,

Andreucci²,

Timofte³

2021

CPAA

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We study, by means of the periodic unfolding technique, the homogenization of a modified bidomain model, which describes the propagation of the action potential in the cardiac electrophysiology. Such a model, allowing the presence of pathological zones in the heart, involves various geometries and non-standard transmission conditions on the interface between the healthy and the damaged part of the cardiac muscle.

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confidence: 99%

Homogenization of a modified bidomain model involving imperfect transmission

Amar¹,

Andreucci²,

Timofte³

2021

CPAA

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“…Non-constant homogenized matrices in which a nonlinear function depending on the solution of the macroscopic problem appears can be found, in different contexts from ours and for particular types of nonlinearities, in the recent papers [3], [36], and [11]. For the case in which the homogenized matrix depends on the solution of the limit problem, we also refer the reader to [4], [5], [6], [51], and [20].…”

Section: Introductionmentioning

confidence: 84%

“…Related homogenization problems for reaction-diffusion problems in porous media were addressed, for instance, in [33], [34], [35], [46], [44], [45], [24], [25], [26], [27], [30], [42], [40], [49], [50], and [51]. Problems involving fast surface reaction terms can be encountered, for instance, in [7], [3], [4], and [36].…”

Section: Introductionmentioning

confidence: 99%

Homogenization results for a coupled system of reaction–diffusion equations

2019

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The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying several metabolic processes taking place in living cells, in which biochemical species can diffuse in the cytosol and react both in the cytosol and also on the organellar membranes. The coupling of the concentrations of the biochemical species is realized via various properly scaled nonlinear reaction terms. These nonlinearities, which model, at the microscopic scale, various volume or surface reaction processes, give rise in the macroscopic model to different effects, such as the appearance of additional source or sink terms or of a non-standard diffusion matrix.

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“…As a consequence of the investigation in [11], only two scalings result to be critical, in the sense that they preserve memory of the amplitude factor in the macroscopic model, obtained after passing to the limit ε → 0. It is worthwhile to notice that hierarchies of scalings are often considered in homogenization problems (see, for instance, [5,13,16,25,29,36] and the references therein). Therefore, in the present paper, we focus our analysis on the two critical scalings mentioned above, prescribing the first one in the contact condition of the first family of inclusions and the second one in the contact condition of the other family of inclusions.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic analysis for non-local problems in composites with different imperfect contact conditions

Amar

Andreucci

Timofte

2022

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We consider a composite material made up of a hosting medium containing an ε-periodic array of perfect thermal conductors. Comparing with the previous contributions in the literature, in the present paper, the inclusions are completely disconnected and form two families with dissimilar physical behaviour. More specifically, the imperfect contact between the hosting medium and the inclusions obeys two different laws, according to the two different types of inclusions. The contact conditions involve the small parameter ε and two positive constants D 1 , D 2 . We investigate the homogenization limit ε → 0 and the limits for D 1 , D 2 going to 0 or +∞, taken in any order, with the aim to find out the cases in which the two limits commute.

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Homogenization results for the calcium dynamics in living cells

Cited by 11 publications

References 20 publications

Homogenization of a modified bidomain model involving imperfect transmission

Homogenization of a modified bidomain model involving imperfect transmission

Homogenization results for a coupled system of reaction–diffusion equations

Asymptotic analysis for non-local problems in composites with different imperfect contact conditions

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