Discretization-dependent model for weakly connected excitable media

Physical Review. E
Pedro André ArroyoRodrigo Weber Dos Santos

Abstract

Pattern formation has been widely observed in extended chemical and biological processes. Although the biochemical systems are highly heterogeneous, homogenized continuum approaches formed by partial differential equations have been employed frequently. Such approaches are usually justified by the difference of scales between the heterogeneities and the characteristic spatial size of the patterns. Under different conditions, for example, under weak coupling, discrete models are more adequate. However, discrete models may be less manageable, for instance, in terms of numerical implementation and mesh generation, than the associated continuum models. Here we study a model to approach discreteness which permits the computer implementation on general unstructured meshes. The model is cast as a partial differential equation but with a parameter that depends not only on heterogeneities sizes, as in the case of quasicontinuum models, but also on the discretization mesh. Therefore, we refer to it as a discretization-dependent model. We validate the approach in a generic excitable media that simulates three different phenomena: the propagation of action membrane potential in cardiac tissue, in myelinated axons of neurons, and concentrat...Continue Reading

References

Aug 1, 1994·IEEE Transactions on Bio-medical Engineering·J M Rogers, A D McCulloch
Oct 20, 1998·Circulation Research·J P KuceraS Rohr
May 15, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P G KevrekidisE S Titi
Feb 5, 2004·Journal of Theoretical Biology·Erik M Rauch, Mark M Millonas
Jan 7, 2006·Chaos·Irving R Epstein, Vladimir K Vanag
Jan 17, 2007·Europace : European Pacing, Arrhythmias, and Cardiac Electrophysiology : Journal of the Working Groups on Cardiac Pacing, Arrhythmias, and Cardiac Cellular Electrophysiology of the European Society of Cardiology·E G NewallP D Larsen
May 22, 2007·Nature Reviews. Neuroscience·Bruce P Bean
Feb 11, 1972·Science·A T Winfree
Dec 12, 2012·Computational and Mathematical Methods in Medicine·Bruno Gouvêa de BarrosRodrigo Weber dos Santos
Jan 2, 2013·Current Opinion in Genetics & Development·Luciano Marcon, James Sharpe
Aug 31, 2013·The European Physical Journal. E, Soft Matter·Shashi Thutupalli, Stephan Herminghaus
Mar 19, 2014·Nature Reviews. Neurology·Manuel A FrieseLars Fugger
Jun 13, 2014·Journal of the Royal Society, Interface·Alfonso Bueno-OrovioKevin Burrage
Aug 17, 2014·Journal of Molecular and Cellular Cardiology·Yann Prudat, Jan P Kucera
Apr 12, 2013·Physical Review Letters·Sergio Alonso, Markus Bär
Oct 8, 2014·Annual Review of Cell and Developmental Biology·Klaus-Armin Nave, Hauke B Werner
Feb 11, 2016·Scientific Reports·Ivan V KazbanovAlexander V Panfilov
May 11, 2016·IEEE Transactions on Medical Imaging·Alfonso Bueno-OrovioVicente Grau
Aug 16, 2016·Reports on Progress in Physics·Sergio AlonsoBlas Echebarria
Sep 7, 2017·Journal of Physics. Condensed Matter : an Institute of Physics Journal·C ChongC Daraio

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Related Papers

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
G B Makkes van der Deijl, Alexander V Panfilov
Journal of Mathematical Biology
Je-Chiang Tsai, James Sneyd
© 2022 Meta ULC. All rights reserved