TY - JOUR T1 - An efficient population density method for modeling neural networks with synaptic dynamics manifesting finite relaxation time and short-term plasticity JF - eneuro JO - eNeuro DO - 10.1523/ENEURO.0002-18.2018 SP - ENEURO.0002-18.2018 AU - Chih-Hsu Huang AU - Chou-Ching K. Lin Y1 - 2018/12/06 UR - http://www.eneuro.org/content/early/2018/12/06/ENEURO.0002-18.2018.abstract N2 - When incorporating more realistic synaptic dynamics, the computational efficiency of population density methods (PDMs) declines sharply due to the increase in the dimension of master equations. To avoid such a decline, we develop an efficient PDM, termed colored-synapse PDM (csPDM), in which the dimension of the master equations does not depend on the number of synapse-associated state variables in the underlying network model. Our goal is to allow the PDM to incorporate realistic synaptic dynamics that possesses not only finite relaxation time but also short-term plasticity. The model equations of csPDM are derived based on the diffusion approximation on synaptic dynamics and probability density function methods for Langevin equations with colored noise. Numerical examples, given by simulations of the population dynamics of uncoupled exponential integrate-and-fire neurons, show good agreement between the results of csPDM and Monte-Carlo simulations. Compared to the original full-dimensional PDM, the csPDM reveals more excellent computational efficiency because of the lower dimension of the master equations. In addition, it permits network dynamics to possess the short-term plastic characteristics inherited from plastic synapses. The novel csPDM has potential applicability to any spiking neuron models because of no assumptions on neuronal dynamics, and, more importantly, this is the first report of PDM to successfully encompass short-term facilitation/depression properties.Significance Statement Our study successfully solve an outstanding problem—how to reduce the dimension of population density equations when realistic synaptic dynamics is incorporated. With the newly proposed Fokker-Planck formalism, PDM is conferred STP properties and therefore becomes more widely applicable. As such, our method offers an opportunity to use the PDM to gain new insights into neural mechanisms of brain functions that are strongly dependent on STP synapses. This is the first step toward macroscopic description of large-scale neural network activities, reflected in some commonly used neurophysiological measurements, e.g., EEG, MEG, fMRI and voltage-sensitive dye imaging data. ER -