4.1. Data generation

Synthetic data was generated according to the montage and stimulus design employed in Gervain et al. (2012). In that study, NIRS was acquired in 22 newborns using a montage with 24 channels (Fig. 8). We thus generated a synthetic dataset with 22 “participants”, each with 24 time series corresponding to the 24 channels. Like in the original study, the time series comprised 14 trials, each lasting approximately 18 s, and spaced at time intervals of varying duration between 25 and 35 s.

The design of the experiment (figure adapted from Gervain et al., 2012).

Synthetic data was generated using tools available in the Brain AnalyzIR Toolbox for Matlab (Santosa et al., 2018). For each participant, baseline noise was produced by first generating white noise, then imposing temporal correlation on it by employing an autoregressive model of order 30. Different channels were not spatially correlated. Then, to simulate the contribution of heart rate, respiration and Mayer waves to the NIRS signal, the signal amplitude was increased by a factor ranging between 0.01 and 0.03 mM x mm (amounting to about 3–10 % of the total signal change, (Boas et al., 2004)) at frequencies typical of the newborn HRF, namely in the ranges around 1.5 ± 0.2 Hz, 0.25 ± 0.05 Hz and 0.1 ± 0.02 Hz, respectively.

To this “resting state” dataset, we then added HRFs and motion artifacts, simulating functional responses. Twenty different such functional datasets were created by systematically varying the parameters of the HRFs and the artifacts. Motion artifacts were added, in the form of spikes and baseline shifts. Spikes were modelled as a sudden change of voltage ranging between 0.1 and 2 V across the 20 datasets, while baseline shift artifacts were modelled as a random positive or negative change of voltage, also ranging between 0.1 and 2 V. In turn, HRFs had an amplitude value ranging between 0.1 and 0.35 mM x mm for HbO, between -0.05 and -0.175 mM x mm for HbR and an onset-to-peak time of 6 s. HRFs were added to 12 channels, i.e. 50 % of all channels. These will be referred to as “active channels”.

Using this procedure, for each participant, channels within the same datasets differed in terms of baseline and physiological noise but shared the same HRF and artifact amplitudes, while the same channel across different datasets shared the same baseline noise, but differed in terms of HRFs and motion artifacts.

The scheme in Fig. 3 describes the simulation steps and shows an example of simulated data. This approach for producing synthetic fNIRS data is similar to the one used in other studies investigating analysis methods (Barker et al., 2013; Gemignani et al., 2018; Huppert, 2016).

The scheme describes the workflow that was employed to produce the synthetic dataset. First, temporally correlated noise was generated. Then, the amplitude of the signal was increased at specific frequencies to resemble the contribution of physiological noise. After that, hemodynamic responses were added according to a stimulus design and lastly, motion artifacts were included in form of spikes and shifts. The last panel at the bottom shows an example of a simulated dataset (left: light intensities, right: corresponding concentration changes).