Anomalous diffusion and transport in heterogeneous systems separated by a membrane

Lenzi, E. K.; Ribeiro, Haroldo V.; Tateishi, A. A.; Evangelista, L. R.

doi:10.1098/rspa.2016.0502

Cited by 18 publications

(10 citation statements)

References 42 publications

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“…Note that by no means the above described models exhaustively cover the range of models that are known to exhibit anomalous diffusion (see e.g., [30][31][32]). However, the CTRW, fBM, and random walks in a fractal models have been extensively studied; more importantly, they have the potential to map parameters of the model to relevant biological and biophysical features.…”

Section: Brownian Vs Anomalous Diffusionmentioning

confidence: 99%

Anomalous Subdiffusion in Living Cells: Bridging the Gap Between Experiments and Realistic Models Through Collaborative Challenges

et al. 2020

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The life of a cell is governed by highly dynamical microscopic processes. Two notable examples are the diffusion of membrane receptors and the kinetics of transcription factors governing the rates of gene expression. Different fluorescence imaging techniques have emerged to study molecular dynamics. Among them, fluorescence correlation spectroscopy (FCS) and singleparticle tracking (SPT) have proven to be instrumental to our understanding of cell dynamics and function. The analysis of SPT and FCS is an ongoing effort, and despite decades of work, much progress remains to be done. In this paper, we give a quick overview of the existing techniques used to analyze anomalous diffusion in cells and propose a collaborative challenge to foster the development of state-of-the-art analysis algorithms. We propose to provide labelled (training) and unlabelled (evaluation) simulated data to competitors all over the world in an open and fair challenge. The goal is to offer unified data benchmarks based on biologically-relevant metrics in order to compare the diffusion analysis software available for the community. Diffusion in cells | continuous-time random walks | fractional Brownian Motion | fluorescence correlation spectroscopy | single-particle tracking.

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Section: Brownian Vs Anomalous Diffusionmentioning

confidence: 99%

Anomalous Subdiffusion in Living Cells: Bridging the Gap Between Experiments and Realistic Models Through Collaborative Challenges

et al. 2020

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“…The model that we are proposing requires the solution of a type of non-locality that changes with the dynamics of the tumour through its motion and growth. To the best of our knowledge, this is a generalisation of a setting adopted in several papers (see, e.g., [60, 67–69]), where the non-locality is accounted for in advection–diffusion equations without considering the deformation or structural change of the media in which such equations are defined.…”

Section: Introductionmentioning

confidence: 99%

Influence of non-local diffusion in avascular tumour growth

Ramírez-Torres

Stefano

Grillo

2021

Mathematics and Mechanics of Solids

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The availability and evolution of chemical agents play an important role in the growth of a tumour and, therefore, the mathematical description of their consumption is of special interest. Usually, Fick’s law of diffusion is adopted for describing the local character of the evolution of chemicals. However, in a highly complex, heterogeneous medium, as is a tumour, the progression of chemical species could be influenced by non-local interactions. In this respect, our goal is to investigate the influence of such types of diffusion on the growth of a tumour in the avascular stage. For our purposes, we consider a diffusion equation for the evolution of the chemical agents that accounts for the existence of non-local interactions in a non-Fickean manner, and that involves notions of fractional calculus. In particular, the introduction of derivatives or integrals of fractional type of order [Formula: see text] has proven to be an effective mathematical tool in the description of various non-local phenomena. To achieve our goals, we adopt part of the modelling assumptions outlined in previous works, in which the growth of a tumour is described in terms of mass transfer among the tumour’s constituents and structural changes that occur in the tumour itself in response to growth. The latter ones are characterised by means of the Bilby–Kröner–Lee decomposition of the deformation gradient tensor. We perform numerical simulations, whose results indicate the relevance of embracing a fractional framework in modelling tumour growth. Specifically, the real parameter [Formula: see text]‘dominates’ the way in which the tumour grows, since it permits the modelling of a variety of growth patterns ranging from the standard growth to no growth at all.

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“…Many processes in biology and engineering can be described by systems separated by a membrane . Lenzi et al studied anomalous diffusion of particles in a heterogeneous system separated by a semipermeable membrane, where the particle dynamics was governed by fractional diffusion equations in the bulk and by kinetic equations on the membrane, which characterizes an interface between two different media. For 0 < β < 1, the mathematical model that was offered in Lenzi et al is

{scriptD}_{0 +, t}^{β} u false(t, x false) - k \frac{\partial^{2}}{\partial x^{2}} u false(t, x false) = 0,

where k is a generalized diffusion coefficient.…”

Section: Introductionmentioning

confidence: 99%

“…1,2 Lenzi et al 3 studied anomalous diffusion of particles in a heterogeneous system separated by a semipermeable membrane, where the particle dynamics was governed by fractional diffusion equations in the bulk and by kinetic equations on the membrane, which characterizes an interface between two different media. For 0 < < 1, the mathematical model that was offered in Lenzi et al 3 is…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Anomalous diffusion phenomena with conservation law for the fractional kinetic process

Tokmagambetov

Torebek

2018

Math Methods in App Sciences

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Anomalous diffusion and transport in heterogeneous systems separated by a membrane

Cited by 18 publications

References 42 publications

Anomalous Subdiffusion in Living Cells: Bridging the Gap Between Experiments and Realistic Models Through Collaborative Challenges

Anomalous Subdiffusion in Living Cells: Bridging the Gap Between Experiments and Realistic Models Through Collaborative Challenges

Influence of non-local diffusion in avascular tumour growth

Anomalous diffusion phenomena with conservation law for the fractional kinetic process

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