Dynamic causal models (DCMs) of electrophysiological data allow, in principle, for inference on hidden, bulk synaptic function in neural circuits. The directed influences between the neuronal elements of modeled circuits are subject to delays due to the finite transmission speed of axonal connections. Ordinary differential equations are therefore not adequate to capture the ensuing circuit dynamics, and delay differential equations (DDEs) are required instead. Previous work has illustrated that the integration of DDEs in DCMs benefits from sophisticated integration schemes in order to ensure rigorous parameter estimation and correct model identification. However, integration schemes that have been proposed for DCMs either emphasize speed (at the possible expense of accuracy) or robustness (but with computational costs that are problematic in practice).

In this technical note, we propose an alternative integration scheme that overcomes these shortcomings and offers high computational efficiency while correctly preserving the nature of delayed effects. This integration scheme is available as open-source code in the Translational Algorithms for Psychiatry-Advancing Science (TAPAS) toolbox and can be easily integrated into existing software (SPM) for the analysis of DCMs for electrophysiological data. While this paper focuses on its application to the convolution-based formalism of DCMs, the new integration scheme can be equally applied to more advanced formulations of DCMs (e.g. conductance based models). Our method provides a new option for electrophysiological DCMs that offers the speed required for scientific projects, but also the accuracy required for rigorous translational applications, e.g. in computational psychiatry.

电生理数据的动态因果模型 (DCM) 原则上允许推断神经回路中隐藏的大量突触功能。由于轴突连接的有限传输速度，建模电路的神经元元件之间的直接影响会受到延迟。因此，普通微分方程不足以捕捉随后的电路动态，而是需要延迟微分方程 (DDE)。先前的工作表明，DCM 中的 DDE 集成受益于复杂的集成方案，以确保严格的参数估计和正确的模型识别。然而，

在本技术说明中，我们提出了一种替代集成方案，该方案克服了这些缺点并提供了高计算效率，同时正确地保留了延迟效应的性质。该集成方案在精神病学推进科学 (TAPAS) 工具箱中作为开源代码提供，并且可以轻松集成到现有软件 (SPM) 中，用于分析 DCM 的电生理数据。虽然本文侧重于其在基于卷积的 DCM 形式中的应用，但新的集成方案同样可以应用于更高级的 DCM 公式（例如基于电导的模型）。我们的方法为电生理 DCM 提供了一种新的选择，它提供了科学项目所需的速度，同时也提供了严格的转化应用所需的准确性，例如