Vakorin Vasily A, Krakovska Olga O, Borowsky Ron, Sarty Gordon E
Rotman Research Institute of Baycrest, Canada.
Neuroimage. 2007 Nov 1;38(2):248-60. doi: 10.1016/j.neuroimage.2007.06.033. Epub 2007 Jul 19.
The blood oxygen level-dependent (BOLD) fMRI signal does not measure neuronal activity directly. This fact is a key concern for interpreting functional imaging data based on BOLD. Mathematical models describing the path from neural activity to the BOLD response allow us to numerically solve the inverse problem of estimating the timing and amplitude of the neuronal activity underlying the BOLD signal. In fact, these models can be viewed as an advanced substitute for the impulse response function. In this work, the issue of estimating the dynamics of neuronal activity from the observed BOLD signal is considered within the framework of optimization problems. The model is based on the extended "balloon" model and describes the conversion of neuronal signals into the BOLD response through the transitional dynamics of the blood flow-inducing signal, cerebral blood flow, cerebral blood volume and deoxyhemoglobin concentration. Global optimization techniques are applied to find a control input (the neuronal activity and/or the biophysical parameters in the model) that causes the system to follow an admissible solution to minimize discrepancy between model and experimental data. As an alternative to a local linearization (LL) filtering scheme, the optimization method escapes the linearization of the transition system and provides a possibility to search for the global optimum, avoiding spurious local minima. We have found that the dynamics of the neural signals and the physiological variables as well as the biophysical parameters can be robustly reconstructed from the BOLD responses. Furthermore, it is shown that spiking off/on dynamics of the neural activity is the natural mathematical solution of the model. Incorporating, in addition, the expansion of the neural input by smooth basis functions, representing a low-pass filtering, allows us to model local field potential (LFP) solutions instead of spiking solutions.
血氧水平依赖（BOLD）功能磁共振成像信号并不直接测量神经元活动。这一事实是解释基于BOLD的功能成像数据时的一个关键问题。描述从神经活动到BOLD响应路径的数学模型使我们能够通过数值方法解决估计BOLD信号背后神经元活动的时间和幅度的逆问题。事实上，这些模型可被视为脉冲响应函数的一种高级替代。在这项工作中，在优化问题的框架内考虑了从观测到的BOLD信号估计神经元活动动态的问题。该模型基于扩展的“球囊”模型，通过血流诱导信号、脑血流量、脑血容量和脱氧血红蛋白浓度的过渡动态描述神经元信号向BOLD响应的转换。应用全局优化技术来寻找一个控制输入（模型中的神经元活动和/或生物物理参数），使系统遵循一个可接受的解，以最小化模型与实验数据之间的差异。作为局部线性化（LL）滤波方案的替代方法，该优化方法避免了过渡系统的线性化，并提供了寻找全局最优解的可能性，避免了虚假的局部最小值。我们发现，可以从BOLD响应中稳健地重建神经信号、生理变量以及生物物理参数的动态。此外，研究表明神经活动的脉冲发放开/关动态是该模型的自然数学解。此外，通过用表示低通滤波的平滑基函数扩展神经输入，我们能够对局部场电位（LFP）解而不是脉冲发放解进行建模。
