Improved cerebrovascular reactivity mapping using coherence weighted general linear model in the frequency domain

Cerebrovascular reactivity (CVR) is a prognostic indicator of cerebrovascular health. Estimating CVR from endogenous end-tidal carbon dioxide (CO₂) fluctuation and MRI signal recorded under resting state can be difficult due to the poor signal-to-noise ratio (SNR) of signals. Thus, we aimed to improve the method of estimating CVR from end-tidal CO₂ and MRI signals. We proposed a coherence weighted general linear model (CW-GLM) to estimate CVR from the Fourier coefficients weighted by the signal coherence in frequency domain, which confers two advantages. First, it requires no signal alignment in time domain, which simplifies experimental methods. Second, it limits the GLM analysis within the frequency band where CO₂ and MRI signals are highly correlated, which automatically suppresses noise and nuisance signals. We compared the performance of our method with time-domain GLM (TD-GLM) and frequency-domain GLM (FD-GLM) in both synthetic and in-vivo data; wherein we calculated CVR from signals recorded under both resting state and sinusoidal stimulus. In synthetic data, CW-GLM has a remarkable performance on CVR estimation from narrow band signals with a mean-absolute error of 0.7 % (gray matter) and 1.2 % (white matter), which was lower than all the other methods. Meanwhile, CW-GLM maintains a comparable performance on CVR estimation from resting signals, with a mean-absolute error of 4.1 % (gray matter) and 8 % (white matter). The superior performance was maintained across the 36 in-vivo measurements, with CW-GLM exhibiting limits of agreement of -16.7 % - 9.5 % between CVR calculated from the resting and sinusoidal CO₂ paradigms which was 12 % - 209 % better than current time-domain methods. Evaluating of the cross-coherence spectrum revealed highest signal coherence within the frequency band from 0.01 Hz to 0.05 Hz, which overlaps with previously recommended frequency band (0.02 Hz to 0.04 Hz) for CVR analysis. Our data demonstrates that CW-GLM can work as a self-adaptive band-pass filter to improve CVR robustness, while also avoiding the need for signal temporal alignment.