Modeling the Evolution of Dynamic Brain Processes During an Associative Learning Experiment

We develop a new time series model to investigate the dynamic interactions between the nucleus accumbens and the hippocampus during an associative learning experiment. Preliminary analyses indicated that the spectral properties of the local field potentials at these two regions changed over the trials of the experiment. While many models already take into account nonstationarity within a single trial, the evolution of the dynamics across trials is often ignored. Our proposed model, the slowly evolving locally stationary process (SEv-LSP), is designed to capture nonstationarity both within a trial and across trials. We rigorously define the evolving evolutionary spectral density matrix, which we estimate using a two-stage procedure. In the first stage, we compute the within-trial time-localized periodogram matrix. In the second stage, we develop a data-driven approach that combines information from trial-specific local periodogram matrices. Through simulation studies, we show the utility of our proposed method for analyzing time series data with different evolutionary structures. Finally, we use the SEv-LSP model to demonstrate the evolving dynamics between the hippocampus and the nucleus accumbens during an associative learning experiment. Supplementary materials for this article are available online.

本研究构建了一种新型时间序列模型，用于探究联想学习实验过程中伏隔核（nucleus accumbens）与海马体（hippocampus）之间的动态交互作用。初步分析显示，上述两个脑区的局部场电位（local field potentials）的频谱特性会随实验试次发生变化。尽管已有诸多模型可捕捉单次试次内的非平稳性，但跨试次的动态演化过程往往被忽视。本研究提出的慢演化局部平稳过程（slowly evolving locally stationary process, SEv-LSP）模型，旨在同时捕捉单次试次内与跨试次的非平稳性。我们严格定义了演化谱密度矩阵，并采用两阶段流程对其进行估计：第一阶段计算试次内的时间局部化周期图矩阵；第二阶段提出一种数据驱动方法，整合各试次特异性局部周期图矩阵的信息。通过仿真研究，我们验证了所提方法在分析具有不同演化结构的时间序列数据时的实用性。最后，我们利用SEv-LSP模型，展示了联想学习实验中海马体与伏隔核之间的动态演化过程。本文的补充材料可在线获取。