Osborne Hugh, de Kamps Marc
School of Computing, University of Leeds, Leeds, United Kingdom.
Leeds Institute for Data Analytics, University of Leeds, Leeds, United Kingdom.
Front Neuroinform. 2022 Jul 22;16:883796. doi: 10.3389/fninf.2022.883796. eCollection 2022.
Population density techniques can be used to simulate the behavior of a population of neurons which adhere to a common underlying neuron model. They have previously been used for analyzing models of orientation tuning and decision making tasks. They produce a fully deterministic solution to neural simulations which often involve a non-deterministic or noise component. Until now, numerical population density techniques have been limited to only one- and two-dimensional models. For the first time, we demonstrate a method to take an N-dimensional underlying neuron model and simulate the behavior of a population. The technique enables so-called graceful degradation of the dynamics allowing a balance between accuracy and simulation speed while maintaining important behavioral features such as rate curves and bifurcations. It is an extension of the numerical population density technique implemented in the MIIND software framework that simulates networks of populations of neurons. Here, we describe the extension to N dimensions and simulate populations of leaky integrate-and-fire neurons with excitatory and inhibitory synaptic conductances then demonstrate the effect of degrading the accuracy on the solution. We also simulate two separate populations in an E-I configuration to demonstrate the technique's ability to capture complex behaviors of interacting populations. Finally, we simulate a population of four-dimensional Hodgkin-Huxley neurons under the influence of noise. Though the MIIND software has been used only for neural modeling up to this point, the technique can be used to simulate the behavior of a population of agents adhering to any system of ordinary differential equations under the influence of shot noise. MIIND has been modified to render a visualization of any three of an N-dimensional state space of a population which encourages fast model prototyping and debugging and could prove a useful educational tool for understanding dynamical systems.
种群密度技术可用于模拟遵循共同基础神经元模型的神经元群体的行为。它们此前已被用于分析方向调谐和决策任务的模型。它们为通常涉及非确定性或噪声成分的神经模拟产生完全确定性的解决方案。到目前为止，数值种群密度技术仅限于一维和二维模型。我们首次展示了一种方法，可采用N维基础神经元模型并模拟群体行为。该技术能够实现动力学的所谓优雅降级，在保持速率曲线和分岔等重要行为特征的同时，在精度和模拟速度之间实现平衡。它是MIIND软件框架中实现的数值种群密度技术的扩展，该框架用于模拟神经元群体网络。在此，我们描述了向N维的扩展，并模拟了具有兴奋性和抑制性突触电导的漏电积分发放神经元群体，然后展示了精度降级对解决方案的影响。我们还在E-I配置中模拟了两个单独的群体，以展示该技术捕捉相互作用群体复杂行为的能力。最后，我们模拟了受噪声影响的四维霍奇金-赫胥黎神经元群体。尽管到目前为止MIIND软件仅用于神经建模，但该技术可用于模拟在散粒噪声影响下遵循任何常微分方程组的智能体群体的行为。MIIND已被修改，以呈现群体N维状态空间中任意三个维度的可视化，这有助于快速进行模型原型设计和调试，并且可能成为理解动态系统的有用教育工具。
