Department of Neuroimaging, King's College London, UK.
Department of Mathematics, Imperial College London, UK.
Magn Reson Imaging. 2021 May;78:69-79. doi: 10.1016/j.mri.2021.02.009. Epub 2021 Feb 12.
The assumption that functional magnetic resonance imaging (fMRI) noise has constant volatility has recently been challenged by studies examining heteroscedasticity arising from head motion and physiological noise. The present study builds on this work using latest methods from the field of financial mathematics to model fMRI noise volatility.
Multi-echo phantom and human fMRI scans were used and realised volatility was estimated. The Hurst parameter H ∈ (0,1), which governs the roughness/irregularity of realised volatility time series, was estimated. Calibration of H was performed pathwise, using well-established neural network calibration tools.
In all experiments the volatility calibrated to values within the rough case, H < 0.5, and on average fMRI noise was very rough with 0.03 < H < 0.05. Some edge effects were also observed, whereby H was larger near the edges of the phantoms.
The findings suggest that fMRI volatility is not only non-constant, but also substantially more irregular than a standard Brownian motion. Thus, further research is needed to examine the impact such pronounced oscillations in the volatility of fMRI noise have on data analyses.
最近的研究挑战了功能磁共振成像（fMRI）噪声具有恒定波动性的假设，这些研究考察了源自头部运动和生理噪声的异方差性。本研究使用金融数学领域的最新方法来构建基于此的 fMRI 噪声波动性模型。
使用多回波体模和人类 fMRI 扫描进行了实验，并实现了波动率的估计。 Hurst 参数 H ∈（0,1），它控制了实现波动率时间序列的粗糙度/不规则性，被估计出来。使用成熟的神经网络校准工具，通过路径对 H 进行校准。
在所有实验中，将波动率校准到粗糙情况下的值，即 H < 0.5，并且平均而言，fMRI 噪声非常粗糙，0.03 < H < 0.05。还观察到一些边缘效应，即 H 在体模边缘附近更大。
研究结果表明，fMRI 波动性不仅是非恒定的，而且比标准布朗运动更不规则。因此，需要进一步研究来检查 fMRI 噪声波动性的这种显著波动对数据分析的影响。
