Studies$$$^{1,2,3}$$$ have shown that a significant amount of BOLD signal variance is explained by the heart rate. This is further underpinned by the fact that cardiac regressors share variance with the global signal.$$$^2$$$However, it is still unclear how the heart rate exactly impacts BOLD fluctuations. For the first time, we provide evidence that the heart rate is inherent in BOLD-fMRI images.

The cardiac cycle causes pulsatile arterial blood flow. This pulsation is translated into brain tissue and fluids bounded by the cranial cavity. We exploit this pulsality effect to obtain the heart rate hidden in the slice-wise global signal. To recover the heart rate, we rearrange all acquired BOLD slices depending on their acquisition time. We then average across all voxels that lie within the brain mask of a slice to obtain a signal sampled every slice rather than every volume. A short-window Fourier transform is applied to this slice-wise global signal to obtain the time-frequency spectrogram. We obtain the heart rate from this spectrogram by walking along frequency trajectories. A frequency trajectory is defined as a trajectory through the spectrogram that comprises exactly one frequency for each time point. The frequency trajectory that maximises the energy while traveling from time $$$t_1$$$ to $$$t_n$$$ is the wanted heart rate as depicted in Figure 1. To reduce the noise in the spectrogram, we apply a 1d-Gaussian filter ($$$\sigma^2=0.1$$$) and fit a Gaussian frequency mixture model to the power spectrum at each time point $$$t_i$$$. Examples of the resulting spectrograms are depicted in Figure 3, 4 and 5.

We tested our proposed heart rate extraction from the slice-wise global signal by comparing the obtained heart rate with pulse oximetry recordings in three resting-state fMRI cohorts. Cohort 1 comprises 108 subjects comparing term vs preterm individuals, average age 19 years, scanned on a Philips 3T Achieva (TR 3000ms, TE 30ms, flip angle 80$$$^{\circ}$$$, voxel size 2.5x2.5x3 mm, field of view (FoV) 240 mm$$$^2$$$, 50 oblique transverse slices, slice-order descending). Cohort 2 is a previously published open source data set$$$^4$$$ of 22 subjects, 4 scans per subject, average age 23 years, acquired on a Siemens MAGNETOM 7T (TR 3000ms, TE 17 ms, flip angle 70$$$^{\circ}$$$, voxel size 1.5mm isotropic, field of view (FoV) 192mm$$$^2$$$, 70 oblique transverse slices, slice-order interleaved). We excluded 5 scans because of a corrupted physiological recording or acquisition error.$$$^4$$$ Cohort 3 consists of 21 subjects that are part of a study looking at lifelong health and ageing, average age 69, acquired on a Siemens MAGNETOM 3T (TR 2020ms, TE 30ms, flip angle 75$$$^{\circ}$$$, voxel size 3x3x4 mm, field of view (FoV) 192 mm$$$^2$$$, 36 oblique transverse slices, slice-order interleaved). We projected motion realignment parameters, linear and quadratic trends out of all fMRI scans before obtaining the slice-wise global signal. We then bandpass-filtered (0.6-2Hz) the slice-wise global signal. First, we manually compared the spectrogram of the pulse oximetry recording with the spectrogram of the slice-wise global signal. We found traces of the heart rate in the slice-wise global signal in 98.15% (106/108) of cohort 1, in 100% (83/83) of cohort 2 and in 95.24% (20/21) of cohort 3. Our heuristic heart rate extraction algorithm achieved a median error (difference between extracted heart rate and heart rate from physiological recording) below 0.05Hz in 82.86% of cohort 1, 71.08% of cohort 2 and 47.63% of cohort 3 depicted in Figure 2. The identification of the heart rate in the slice-wise global signal by our algorithm was mainly compromised by artefacts due to large or periodic motion.There is an ongoing debate about wether to use a global signal in resting-state fMRI preprocessing.$$$^{5,6}$$$ Projecting a global signal out of BOLD time series aims to remove non-neural effects that affect large numbers of voxels. However, since the global signal is an unknown mixture of neural and non-neural fluctuations, its removal will ultimately change inter-regional correlations and hamper their interpretation.$$$^2$$$

We have proven for the first time that the heart rate is inherent in the slice-wise global signal. We identified heart rate traces in BOLD-fMRI images across different scanners, sequences and population cohorts, and provide thus a way to circumvent the undesirable use of the global signal as noise regressor when physiological recordings are not available. Our finding proves that the heart rate affects many voxels, showing the importance of physiological monitoring in BOLD-fMRI. In future studies, we will investigate new physiological noise models that incorporate joint information from physiological recordings and the slice-wise global signal.