Beer

The simulation paradigm, performed using the MATLAB^™ computing environment, proceeded as follows: First, all raw optical intensity measurements for each of the 20 datasets were converted into changes in optical density (OD). A timing vector, which provides 25 trial onset positions spaced randomly throughout the 10 min dataset but with a minimum separation of 20 s was then constructed. This vector mimics the experimental design of a typical functional NIRS experiment, with each onset position corresponding to the beginning of a functional task. A simulated HRF was then designed that consisted of a gamma function with a time-to-peak of 7 s, a duration of 20 s and an amplitude defined so as to produce a 15 μM increase in HbO concentration and a 5 μM decrease in HbR concentration [these figures include a partial volume correction factor of 50 (Strangman et al., 2003 (link))]. Such amplitudes are consistent with those observed in real NIRS studies and have also been used in previous functional NIRS simulations (Gagnon et al., 2011 (link), 2012 (link)). These amplitudes are approximately equivalent to an intensity change of 0.9% from baseline for the 690 nm channels and 2% from baseline for the 830 nm channels.
Three of the eight NIRS channels from each of the 20 NIRS datasets were randomly selected and the simulated HRF was added to the OD time-course of these channels at the 25 onset positions defined by the timing vector. Lastly, the automatic motion detection algorithm hmrMotionArtifact was applied to each NIRS dataset to define periods of motion after the simulated HRFs had been added to the data.
Once the simulated functional dataset had been completed, it was then passed through six different processing streams. The first was the recovery of the HRF without motion correction or the rejection of trials. The data was band-pass filtered (a third order Butterworth filter between 0.01 and 0.5 Hz) to remove low-frequency drift and cardiac oscillations before being converted into HbO and HbR using the modified Beer–Lambert law (Obrig et al., 2000 (link)). The periods of data around each of the 25 stimulus trials were then block-averaged to produce the mean HRF. The second processing stream was a standard trial rejection NIRS processing approach. After band-pass filtering the output of hmrMotionArtifact (calculated previously) was applied such that if a stimulus trial coincided with a defined period of motion, then that stimulus was rejected. The remaining stimuli periods were then block-averaged in order to recover the mean HRF.
The first step of the remaining four processing streams consisted of the implementation of each of the four motion correction techniques: PCA, spline, wavelet, and Kalman respectively. The resulting corrected data was then subjected to the same band-pass filter as the standard processing approaches, followed by conversion to HbO and HbR. All stimulation trials, irrelevant of how effective the motion correction process may have been, were then included in the block-average calculation of the mean HRF.
This entire process was repeated five times for each dataset using a different random selection of channels and a different stimulus timing vector in order to improve the robustness of the results.

In addition to scoring putative motif site matches with p-values as described above, we have also incorporated a number of other scoring schemes into the STORM and MODSTORM software. The additional scoring methods include standard PWM threshold scoring, the percentage of maximum score, and the functional depth.
A common and intuitive approach for cutoff selection takes the maximum possible score derived from a given matrix, and sets the threshold for occurrence at some percentage of the maximum score. This idea was shown to have merit by Tronche et al., [53 (link)] who showed that HNF1 sites with a score greater than 83% of the maximum score of the scoring matrix showed experimental evidence of binding. Although this score of 83% of the maximum score works well for HNF1, it is expected that different factors will have different percentages of maximum scores allowed for binding.
The term "functional depth" was first introduced by Beer and Tavazoie [54 (link)] as a term to represent the threshold above which functional binding will occur for a particular factor represented by a PWM. We define the functional depth for a PWM score S as,
functional depth=S−SminSmax−Smin MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGMbGzcqqG1bqDcqqGUbGBcqqGJbWycqqG0baDcqqGPbqAcqqGVbWBcqqGUbGBcqqGHbqycqqGSbaBcqqGGaaicqqGKbazcqqGLbqzcqqGWbaCcqqG0baDcqqGObaAcqGH9aqpdaWcaaqaaiabdofatjabgkHiTiabdofatnaaBaaaleaaieGacqWFTbqBcqWFPbqAcqWFUbGBaeqaaaGcbaGaem4uam1aaSbaaSqaaiab=1gaTjab=fgaHjab=Hha4bqabaGccqGHsislcqWGtbWudaWgaaWcbaGae8xBa0Mae8xAaKMae8NBa4gabeaaaaaaaa@5684@
where S_min and S_max are the minimum and maximum scores possible for the PWM.

For studies 1 to 21 (Table 1), NIRS data was preprocessed in the same way as in the original publications (or sources, e.g., unpublished PhD dissertations), which was similar across most studies. Briefly, light intensities were converted to optical densities and to hemoglobin concentration changes using the modified Beer–Lambert Law with the absorption coefficients ${\mu }_a$ , ${\mathrm{mm}}^{-1}\times {\mathrm{mM}}^{-1}$ : ${\mu }_a(\mathrm{HbO},695\mathrm{nm})=0.0955$ , ${\mu }_a(\mathrm{HbO},760\mathrm{nm})=0.1496$ , ${\mu }_a(\mathrm{HbO},830\mathrm{nm})=0.2320$ , ${\mu }_a(\mathrm{HbO},850\mathrm{nm})=0.2526$ ; ${\mu }_a(\mathrm{HbR},695\mathrm{nm})=0.4513$ , ${\mu }_a(\mathrm{HbR},760\mathrm{nm})=0.3865$ , ${\mu }_a(\mathrm{HbR},830\mathrm{nm})=0.1792$ ; and ${\mu }_a(\mathrm{HbR},850\mathrm{nm})=0.1798$ . The product of the optical pathlength and the differential pathlength factor was set to 1, resulting in concentration changes being expressed in $\mathrm{mM}\times \mathrm{mm}$ . A bandpass filter between 0.01 and 0.7 Hz was applied to concentration changes using an $fft$ digital filter. Then, as illustrated in Ref. 10 (link), blocks of single-trial data were rejected if they contained motion artifacts or if the light intensity reached the saturation value, with motion artifacts defined as signal changes larger than $0.1\mathrm{mM}\times \mathrm{mm}$ over 0.2 s. The artifact detection and trial rejection procedures were performed independently for each channel, and channels with less than at least two valid blocks were discarded from the analysis. The trial inclusion rate for each study ranged between 52% and 100% (M: 65.1%, SD: 12.8%). Finally, for the nonrejected blocks, a baseline was linearly fit between the mean of the 5 s preceding the onset of the block and the mean of the 5 s preceding the onset of the next one. Blocks were then averaged within each infant to obtain channel-wise block averages for each condition as well as across infants to obtain grand averages. This preprocessing routine has been shown to yield an accurate recovery of the infant hemodynamic response.¹⁰ (link) Study-level grand averages were employed to compute study-level effect sizes, whereas individual trial averages were employed to compute infant-level effect sizes (Sec. 2.2.2).
For studies 22 and 23 (Table 1), we obtained each subject’s channel-wise average activation to each experimental condition, i.e., we obtained preprocessed data from the authors and had no access to the raw data. For these studies, we could, therefore, only compute the study-level effect size but not the individual infant-level effect size. Data processing for these datasets is described in the original publication.²⁷ (link)