title: A fully parallel in time and space algorithm for simulating the electrical activity of a neural tissue.
abstract: BACKGROUND
  The resolution of a model describing the electrical activity of neural tissue and its propagation within this tissue is highly consuming in term of computing time and requires strong computing power to achieve good results.
  
  
  METHODS
  In this study, we present a method to solve a model describing the electrical propagation in neuronal tissue, using parareal algorithm, coupling with parallelization space using CUDA in graphical processing unit (GPU).
  
  
  RESULTS
  We applied the method of resolution to different dimensions of the geometry of our model (1-D, 2-D and 3-D). The GPU results are compared with simulations from a multi-core processor cluster, using message-passing interface (MPI), where the spatial scale was parallelized in order to reach a comparable calculation time than that of the presented method using GPU. A gain of a factor 100 in term of computational time between sequential results and those obtained using the GPU has been obtained, in the case of 3-D geometry. Given the structure of the GPU, this factor increases according to the fineness of the geometry used in the computation.
  
  
  CONCLUSIONS
  To the best of our knowledge, it is the first time such a method is used, even in the case of neuroscience.
  
  
  CONCLUSIONS
  Parallelization time coupled with GPU parallelization space allows for drastically reducing computational time with a fine resolution of the model describing the propagation of the electrical signal in a neuronal tissue.
authors.affiliation: Rhenovia Pharma SA, Mulhouse, France; Laboratoire LMIA, EA3993, Université de Haute Alsace, Mulhouse, France; Laboratoire MIPS, EA2332, Université de Haute Alsace, Mulhouse, France. Electronic address: bedez.mathieu@gmail.com.
authors.forename: Mathieu
authors.initials: M
authors.lastname: Bedez
authors.affiliation: Laboratoire LMIA, EA3993, Université de Haute Alsace, Mulhouse, France.
authors.forename: Zakaria
authors.initials: Z
authors.lastname: Belhachmi
authors.affiliation: Laboratoire MIPS, EA2332, Université de Haute Alsace, Mulhouse, France.
authors.forename: Olivier
authors.initials: O
authors.lastname: Haeberlé
authors.affiliation: Rhenovia Pharma SA, Mulhouse, France.
authors.forename: Renaud
authors.initials: R
authors.lastname: Greget
authors.affiliation: Firalis SAS, Huningue, France.
authors.forename: Saliha
authors.initials: S
authors.lastname: Moussaoui
authors.affiliation: Rhenovia Pharma SA, Mulhouse, France; Department of Biomedical Engineering, University of Southern California, Los Angeles, CA, USA.
authors.forename: Jean-Marie
authors.initials: JM
authors.lastname: Bouteiller
authors.affiliation: Rhenovia Pharma SA, Mulhouse, France.
authors.forename: Serge
authors.initials: S
authors.lastname: Bischoff
mesh_terms: D000465:Algorithms; D002462:Cell Membrane / Q000502:physiology; D003196:Computer Graphics; D003198:Computer Simulation; D004560:Electricity; D005110:Extracellular Space / Q000502:physiology; D008564:Membrane Potentials / Q000502:physiology; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D013995:Time
keywords: GPU; MPI; Neural activity; Parareal algorithm; Partial differential equations