## 4 Results
### NIRS on Forehead: Experimental Results  
A broadband white-light tungsten-halogen light source is used along with a spectrometer to demonstrate the applicability of the described method using real NIRS data measured on a healthy subject at rest. A single subject was recruited from the University of Birmingham community, and written informed consent was obtained. A Tungsten-Halogen light source (Ocean optics HL-2000-FHSA, with approximately 5 minutes of stabilization time) is connected to an optical fiber and used as the source placed on the forehead of the subject. Another fiber as connected to a spectrometer (Ocean optics Flame-S) is used as the detector placed on the forehead of the subject at a distance 10, 20, 30, 40 mm away from the source. The 50 mm measurement was not used due to its low SNR. The two fibers (Ocean Optics: QP1000-2-VIS-BX) utilized in this experiment have a 1000 \(\upmu\)  
Figure 10: Estimated values of extra-cerebral tissue thickness with head-based recovery model for 10 subject head models, along with the ground-truth probability density function of extra-cerebral tissue thickness in the region of interest. core diameter, with the efficient wavelength range from 300-1100 nm. The spectrometer consists of an entrance slit of 200 \(\upmu\)m, and a grating with groove density of 600 grooves per mm. The signal is collected over different acquisition times of 30 ms, 1.5 s, 15 s, and 30 s, for the source-detector distances of 10, 20, 30 and 40 mm respectively, to obtain a good SNR. The collected signal is time-averaged by normalizing each measurement by its corresponding acquisition time. The spectrometer measures the intensities from 340 nm to 1015 nm at a spectral resolution of 0.3 nm, which is later down-sampled to a resolution of 10 nm by averaging every 33 (10/0.3) spectral data points, and is then cropped to the wavelength range 650 nm to 850 nm to match with measurement model considered in simulations. The intensity measurements at different source-detector distances were measured sequentially (starting from 10 mm to 40 mm) due to instrumental limitations. The subject is at rest during the measurements for all experiments. Each experiment was performed once a day with no stimuli and the subject position and data acquisition protocol was kept constant for all measurements, and therefore it was assumed that the hemodynamic changes over the entire duration of measurements (approx. 3 to 5 mins) were insignificant as often seen during the base-line measurements [23] while the subject is at rest. The proposed head-based recovery method as described in Section 4.2 was implemented using the boundary information of the forehead obtained from the MRI of the subject, and later the layer-1 thickness and tissue parameters of two layers were obtained. It should be noted that, while the MRI of the subject was obtained in a supine position, and the subject was measured while sitting on a chair at rest during the experiment and the position was kept constant for all measurements. As the anatomical boundary information of the subject comes from the thin skin/scalp tissue situated on the rigid structure of skull which is unaffected by the subject posture, the boundary information remains the same between the measurements and the acquired MRI. The NIRS experiment is repeated on three different days and the recovery of the parameters are as shown in Table 4. Although the physiological parameters of the tissue may have changed over different days, consistent values of tissue thickness over three days were recovered to ascertain the repeatability of the proposed method.