title: Uniformization method for solving cardiac electrophysiology models based on the Markov-chain formulation.
abstract: This paper compares different numerical methods for the solution of myocyte models of cardiac electrophysiology. In particular, it presents how the technique called uniformization method substantially increases the stability of simple first-order methods such as Euler explicit method and Rush-Larsen (RL) method, for the solution of modern electrophysiology models that are based on continuous-time Markov chains (MCs) for the description of subcellular structures, such as ion channels. The MCs are often associated with stiff ordinary differential equations that severely limit the time step used by these traditional methods. By using the uniformization method, we could significantly increase the time steps for the solution of different cardiac electrophysiology models and improve the computational performance up to 150 times compared to the performance of Euler's and RL's methods.
authors.forename: Johnny Moreira
authors.initials: JM
authors.lastname: Gomes
authors.forename: Adriele
authors.initials: A
authors.lastname: Alvarenga
authors.forename: Ricardo Silva
authors.initials: RS
authors.lastname: Campos
authors.forename: Bernardo Martins
authors.initials: BM
authors.lastname: Rocha
authors.forename: Ana Paula Couto
authors.initials: AP
authors.lastname: da Silva
authors.forename: Rodrigo Weber
authors.initials: RW
authors.lastname: dos Santos
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D002478:Cells, Cultured; D003198:Computer Simulation; D006329:Heart Conduction System / Q000502:physiology*; D006801:Humans; D008390:Markov Chains; D008955:Models, Cardiovascular; D015233:Models, Statistical; D032383:Myocytes, Cardiac / Q000502:physiology*