ArticleJournal of mathematical biology2009
Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions.
Article in Journal of mathematical biology, 2009. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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Who cites it
10 citing papers in PubMed.
- A new implicit high-order iterative scheme for the numerical simulation of the two-dimensional time fractional Cable equation.Scientific reports · 2023Article
- Fractional-Order Traveling Wave Approximations for a Fractional-Order Neural Field Model.Frontiers in computational neuroscience · 2022Article
- Increased Signal Delays and Unaltered Synaptic Input Pattern Recognition in Layer III Neocortical Pyramidal Neurons of the rTg4510 Mouse Model of Tauopathy: A Computer Simulation Study With Passive Membrane.Frontiers in neuroscience · 2021Article
- Electrodiffusion phenomena in neuroscience: a neglected companion.Nature reviews. Neuroscience · 2017Review
- Induced mitochondrial membrane potential for modeling solitonic conduction of electrotonic signals.PloS one · 2017Article
- Numerical simulation of fractional Cable equation of spiny neuronal dendrites.Journal of advanced research · 2014Article
- Neuronal spike timing adaptation described with a fractional leaky integrate-and-fire model.PLoS computational biology · 2014Article
- Electrodiffusive model for astrocytic and neuronal ion concentration dynamics.PLoS computational biology · 2013Article
- Moving boundary problems governed by anomalous diffusion.Proceedings. Mathematical, physical, and engineering sciences · 2012Article
- Dendritic vulnerability in neurodegenerative disease: insights from analyses of cortical pyramidal neurons in transgenic mouse models.Brain structure & function · 2010Review
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Authors and funding
3 authors.
Funding
Abstract
We introduce fractional Nernst-Planck equations and derive fractional cable equations as macroscopic models for electrodiffusion of ions in nerve cells when molecular diffusion is anomalous subdiffusion due to binding, crowding or trapping. The anomalous subdiffusion is modelled by replacing diffusion constants with time dependent operators parameterized by fractional order exponents. Solutions are obtained as functions of the scaling parameters for infinite cables and semi-infinite cables with instantaneous current injections. Voltage attenuation along dendrites in response to alpha function synaptic inputs is computed. Action potential firing rates are also derived based on simple integrate and fire versions of the models. Our results show that electrotonic properties and firing rates of nerve cells are altered by anomalous subdiffusion in these models. We have suggested electrophysiological experiments to calibrate and validate the models.
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19221755What OpenQuestion holds
Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.