Cao Xuefei, Sandstede Björn, Luo Xi
Division of Applied Mathematics, Brown University, Providence, RI, United States.
Department of Biostatistics and Data Science, School of Public Health, The University of Texas Health Science Center at Houston, Houston, TX, United States.
Front Neurosci. 2019 Feb 27;13:127. doi: 10.3389/fnins.2019.00127. eCollection 2019.
Functional MRI (fMRI) is a popular approach to investigate brain connections and activations when human subjects perform tasks. Because fMRI measures the indirect and convoluted signals of brain activities at a lower temporal resolution, complex differential equation modeling methods (e.g., Dynamic Causal Modeling) are usually employed to infer the neuronal processes and to fit the resulting fMRI signals. However, this modeling strategy is computationally expensive and remains to be mostly a confirmatory or hypothesis-driven approach. One major statistical challenge here is to infer, in a data-driven fashion, the underlying differential equation models from fMRI data. In this paper, we propose a causal dynamic network (CDN) method to estimate brain activations and connections simultaneously. Our method links the observed fMRI data with the latent neuronal states modeled by an ordinary differential equation (ODE) model. Using the basis function expansion approach in functional data analysis, we develop an optimization-based criterion that combines data-fitting errors and ODE fitting errors. We also develop and implement a block coordinate-descent algorithm to compute the ODE parameters efficiently. We illustrate the numerical advantages of our approach using data from realistic simulations and two task-related fMRI experiments. Compared with various effective connectivity methods, our method achieves higher estimation accuracy while improving the computational speed by from tens to thousands of times. Though our method is developed for task-related fMRI, we also demonstrate the potential applicability of our method (with a simple modification) to resting-state fMRI, by analyzing both simulated and real data from medium-sized networks.
功能磁共振成像（fMRI）是一种在人类受试者执行任务时研究大脑连接和激活的常用方法。由于fMRI以较低的时间分辨率测量大脑活动的间接和复杂信号，通常采用复杂的微分方程建模方法（例如动态因果建模）来推断神经元过程并拟合得到的fMRI信号。然而，这种建模策略计算成本高昂，并且在很大程度上仍然是一种验证性或假设驱动的方法。这里的一个主要统计挑战是以数据驱动的方式从fMRI数据中推断潜在的微分方程模型。在本文中，我们提出了一种因果动态网络（CDN）方法来同时估计大脑激活和连接。我们的方法将观察到的fMRI数据与由常微分方程（ODE）模型建模的潜在神经元状态联系起来。使用功能数据分析中的基函数展开方法，我们开发了一种基于优化的准则，该准则结合了数据拟合误差和ODE拟合误差。我们还开发并实现了一种块坐标下降算法，以有效地计算ODE参数。我们使用来自实际模拟和两个与任务相关的fMRI实验的数据说明了我们方法的数值优势。与各种有效连接方法相比，我们的方法在将计算速度提高数十到数千倍的同时，实现了更高的估计精度。虽然我们的方法是为与任务相关的fMRI开发的，但我们也通过分析来自中等规模网络的模拟和真实数据，展示了我们的方法（经过简单修改）对静息态fMRI的潜在适用性。
