2.1.

Infant Head Structure and AAL Atlas

The anatomical head structure of the infants and the corresponding brain atlas used in this study were obtained from publicly available data.⁴⁰ In the present study, we used age-appropriate average structural images acquired with a 3T magnetic resonance imaging (MRI) scanner. A set of longitudinal images of 95 healthy infants [56 males and 39 females, gestational age at birth: $37.9\pm 1.8$ (mean ± standard deviation) weeks] were scanned three times when their postmenstrual age was $41.5\pm 1.7$, $94.2\pm 3.4$, and $146.2\pm 4.9$ weeks, respectively. Based on the difference in subtracting gestational age from postmenstrual age, the population used in this study could be divided into three age groups concentrating around 0, 1, and 2 years of age. All participants in our dataset had normal fetal ultrasound during pregnancy and were free of congenital anomalies, metabolic disease, and focal lesions after birth. T2-weighted images were obtained with a voxel size of $1.25\times 1.25\times 1.95{\mathrm{mm}}^3$ for 0-yo and T1-weighted images were obtained with a voxel size of $1\times 1\times 1{\mathrm{mm}}^3$ for 1- and 2-yo. The tissue probability maps of GM, WM, and cerebrospinal fluid (CSF) that exhibited similar geometry to the structural images were also used for head tissue segmentation (see Sec. 2.2.1).

To obtain the optics-based SCC between the fiducial points and brain regions, we chose the automated anatomical labeling (AAL) atlas⁴¹ to parcellate the infant’s brain. The AAL atlas is widely used in cognitive neuroscience. In addition, remarkably, it parcellates a human brain into multiple non-overlapping regions according to the identification of main sulci, which are already clearly visible from birth and preserved throughout normal brain development.²² We used the AAL atlas with 90 brain regions (Table S2 in the Supplementary Material) in the infant space, which maintains the consistency of the AAL map propagation from the adult Colin 27 brain to the infant images using indirect fusion approach and a feature-based groupwise registration algorithm (see Ref. 40). Infant atlases from 0-, 1-, and 2-yo were built using infant MRI segmentation and groupwise registration methods. The atlases are publicly available on the NITRC website.⁴²

2.2.

Light Propagation Analysis

2.2.1.

Construction of age-appropriate structural head models

We can use an age-appropriate template of the head to substitute the subject-specific head anatomy to localize the macroanatomical structure when individual infant MRIs are not available.^24,25 Hence, we constructed three age-appropriate head models by segmenting the tissues of average MRI images from 0-, 1-, and 2-yo infants for further light propagation analysis. Specifically, a semiautomatic approach was used to segment the MRI images into air and five types of head tissues with different optical properties. First, the head masks, i.e., the air/scalp boundaries, were extracted from the average T2-weighted images for 0-yo, and T1-weighted images for 1- and 2-yo using a simple thresholding method. Second, the tissue probability maps of the CSF, GM, and WM were converted to binary intracranial regions in each image. It was difficult to identify the scalp/skull and skull/CSF boundaries in the average MRI images because of the thin structures of the scalp and skull and blurring caused by the averaging of slightly misaligned multi-subject images. Thus, we applied morphological operations to extract the scalp/skull and skull/CSF boundaries based on the representative thickness of the scalp (3.5, 4, and 4 mm for 0-, 1-, and 2-yo, respectively) and skull (2.2, 3, and 3.8 mm for 0-, 1-, and 2-yo, respectively), as described in the literature.^43,44 Finally, five-layered head models of 0-, 1-, and 2-yo infants were created by integrating the above intracranial regions and boundaries of superficial tissues. Contradictions in the integration process were manually and/or automatically corrected. The age-appropriate five-layered models for the three age groups are shown in Fig. 1.

Fig. 1

Age-appropriate five-layered head models for (a) 0-yo; (b) 1-yo; and (c) 2-yo infants, which comprise the scalp, skull, CSF, GM, and WM. The first, second, and third columns show the sagittal, axial, and coronal views of the head models, respectively.

2.2.3.

Fiducial points and arrangement of SD pairs

The international 10-10 system positions were virtually set on the age-appropriate head models of 0-, 1-, and 2-yo using custom analysis scripts written in MATLAB (MathWorks, Natick, Massachusetts). First, we manually identified the four anatomical landmarks, including the inion, nasion, and left and right periauricular points on the scalp surface of the infant head models. Then, 61 fiducial points of the 10-10 system^16,52 were automatically assigned to the scalp of the head model of every age, as depicted in Fig. 2.

Fig. 2

Superimposed anatomical landmarks (in dark green), 10-20 fiducial points (in yellow), and 10-10 fiducial points (in white) on the head models of (a) 0-yo; (b) 1-yo; and (c) 2-yo. For each row panel, five views of the head models are displayed.

Because the SD distance significantly affects the sampling regions, the distances between sources and detectors were set as 10, 15, 20, 25, and 30 mm, where the midpoints of the SD pairs were set at the 10-10 fiducial points. Two SD pairs were placed according to the circumferential and vertical orientations at each fiducial point to examine whether the probe orientation influences the SCC for 0-, 1-, and 2-yo. The SD pair arrangements on the head models for five different SD distances for each age are shown in Fig. 3.

Fig. 3

SD pair arrangements on head models for five different SD distances for (a) 0-yo; (b) 1-yo; and (c) 2-yo. The sources and detectors are indicated in red and blue dots, respectively. Two orientational SD pairs at the 10-20 fiducial points (yellow dots) are displayed only on the right hemisphere. Notably, SD pairs were also attached to the 10-10 fiducial points (white dots); however, the sources and detectors at these locations are not shown to avoid complications. The circumferential and vertical SD pairs at each fiducial point are indicated by two dashed black connections, respectively.

2.3.

Characterization of SCC

3.1.

Optics-Based SCC for a Representative Fiducial Point

To illustrate the changes in SSP due to SD distance and age, the PMDF of the circumferential SD pair at the fiducial point T4 is shown in Fig. 4. The spatial distribution of the PMDF broadened as the SD distance increased, regardless of age. The values of $L_{norm,M}$ higher than 0.01, at the fiducial point T4 are shown in Table 3. According to the definition of the $N_{CBR}$ (i.e., the number of brain regions whose $L_{norm,M}$ was $>0.05$), $N_{CBR}$ was 2 at the fiducial point T4, which depicts the right middle and inferior temporal gyrus (MTG-R and ITG-R, respectively). These two brain regions had dominant $L_{norm,M}$ at the fiducial point T4 for any age and SD distance (indicated in boldface in Table 3), where the MLCBR was MTG_R. In addition to MTG_R and ITG_R, other brain regions, the superior temporal gyrus (STG-R) and right temporal pole of the superior and middle temporal gyrus (TPOsup-R and TPOmid-R, respectively), were also associated with T4, and their $L_{norm,M}$ increased as the SD distance increased. Considering the STG_R of 0-yo as an example, T4 had a $L_{norm,STG\_R}$ of 0.009 for a 10-mm SD distance, whereas the $L_{norm,STG\_R}$ reached 0.022 when the SD distance was 30 mm (see Table 3). For the same SD distance, the $L_{norm,MTG\_R}$ of 1- or 2-yo was greater than that of 0-yo. For instance, the $L_{norm,MTG\_R}$ values for a 20-mm SD distance were 0.593, 0.786, and 0.861 for 0-, 1-, and 2-yo, respectively. The PMDF of the vertical SD pair set at fiducial point T4 is shown in Fig. S1 in the Supplementary Material. Likewise, we found that the vertical SD pair at T4 was mainly correlated with the two brain regions, that is, MTG_R and ITG_R. The maximum $L_{norm,STG\_R}$ of the vertical SD pair was only 0.060, 0.070, and 0.094 for 0-, 1-, and 2-yo, respectively (SD $\text{distance}=30\mathrm{mm}$). As shown in Table 3, the fiducial point T4 had the same MLCBR, that is, MTG_R, for any age and SD distance; therefore, the MLCBR was completely consistent among the three ages. The sensitivity of MLCBR ($L_{abs,MLCBR}$) is also shown in Table 3. We also observed an increase in the $L_{abs,MLCBR}$ at each age with increasing SD distance. The $L_{abs,MLCBR}$ of 0-yo was smaller than that of 1- and 2-yo, while $L_{abs,MLCBR}$ of 1-yo was almost similar or slightly larger than that of 2-yo.

Fig. 4

PMDF for a given fiducial point T4 at five SD distances for 0-yo, 1-yo, and 2-yo when the SD pair was attached in a circumferential orientation. Dashed lines in different colors indicate the AAL brain region boundaries. The PMDF superimposed on age-appropriate brain structures of (a) 0-yo; (b) 1-yo; and (c) 2-yo.

Table 3

Normalized PPL of corresponding brain regions (Lnorm,M) and the sensitivity of MLCBR (Labs,MLCBR) for the circumferential SD pair set at the fiducial point T4 at five SD distances for 0-yo, 1-yo, and 2-yo.

The brain regions correlated with the two orientational SD pairs at all 10-10 fiducial points and their normalized PPL from 0-, 1-, and 2-yo infants are provided in Tables S3-7 in the Supplementary Material for SD distances of 10, 15, 20, 25, and 30 mm, respectively.

3.2.

Evaluation of SCC at All Fiducial Points

The SCC metrics $N_{CBR}$, selectivity, and sensitivity at all 10-10 fiducial points are shown in Figs. 5Fig. 6–7, respectively. The summary statistics of the SCC metrics across all fiducial points are shown in Fig. 8.

Fig. 5

$N_{CBR}$ for all 10-10 fiducial points at five different SD distances for (a) 0-yo; (b) 1-yo; and (c) 2-yo. Darker red regions indicate larger $N_{CBR}$.

Fig. 6

Selectivity of MLCBR for all 10-10 fiducial points at five different SD distances for (a) 0-yo; (b) 1-yo; and (c) 2-yo. Areas in magenta and blue indicate higher and lower selectivity, respectively.

Fig. 7

Sensitivity of MLCBR for all 10-10 fiducial points at five different SD distances for (a) 0-yo; (b) 1-yo; and (c) 2-yo. Area in magenta and blue indicate higher and lower sensitivity, respectively.

Fig. 8

Box plots summarizing the SCC metrics, (a) $N_{CBR}$; (b) selectivity; and (c) sensitivity, at all scalp fiducial points of the 10-10 system for each age and SD distance. The individual colored dots indicate the SCC metrics of each fiducial point. Boxes indicate the interquartile range. The black horizontal line within the boxes indicates the median. Whiskers extend 1.5 times above and below the interquartile range limits. Statistical significance of post-hoc test for (d) $N_{CBR}$; (e) selectivity; and (f) sensitivity are indicated with matrices. * $p<0.05$, ** $p<0.01$, *** $p<0.001$, white and gray blanks are not significant and not applicable, respectively.

We calculated the $N_{CBR}$ value for all 10-10 fiducial points over five SD distances at three ages. As shown in Fig. 5 for circumferential SD pairs, fiducial points neighboring the longitudinal fissure, for example, Fpz, FCz, Cz, CPz, and POz, were correlated with more brain regions for every SD distance and age. Additionally, the larger the SD distance, the larger the $N_{CBR}$ of the fiducial points for every age group. The $N_{CBR}$ of 0-yo was larger than that of 1- and 2-yo, while the $N_{CBR}$ of 1- and 2-yo was similar for each SD distance. According to a nonparametric statistical analysis, we found significant main effects of SD distance [$\mathrm{WTS}(4)=195.88$, $p<0.001$] and age [$\mathrm{WTS}(2)=10.37$, $p<0.01$], but no interaction [$\mathrm{WTS}(8)=9.01$, $p=0.34$]. For the age factor [Figs. 8(a) and 8(d) upper panel], multiple comparisons with the Bonferroni adjustment showed that the $N_{CBR}$ of 0-yo was larger than that of 1- and 2-yo ($p<0.001$, corrected); however, no significant differences were found between 1- and 2-yo ($p=0.92$, corrected). For the SD distance factor [Figs. 8(a) and 8(d) lower panel], multiple comparisons between $N_{CBR}$ of any two SD distances produced significantly different values, and the $N_{CBR}$ values of larger SD distances were greater than those of smaller SD distances ($p<0.001$, corrected). Similar results for the $N_{CBR}$ of the vertical SD pairs are shown in Fig. S2 in the Supplementary Material.

The selectivity of the MLCBR shown in Fig. 6 shows the ratio of the PPL in the MLCBR to its sum in the 90 AAL brain region. In a sense, the selectivity represents the probability that the fNIRS signal originates from the MLCBR. For most fiducial points, higher selectivity was observed for shorter SD distances, regardless of age. Moreover, the selectivity of 1- and 2-yo was larger than that of 0-yo. These observable findings were supported by statistically significant main effects of age [$\mathrm{F}(\mathrm{2,180})=4.89$, $p<0.05$, ${{\eta }_{\mathrm{G}}}^2=0.049$] and SD distance [$\mathrm{F}(\mathrm{1.41,253.25})=266.11$, $p<0.001$, ${{\eta }_{\mathrm{G}}}^2=0.067$] on selectivity; however, no statistically significant two-way interactions were found between age and SD distance on the selectivity, $\mathrm{F}(\mathrm{2.81,253.25})=0.93$, $p=0.42$, ${{\eta }_{\mathrm{G}}}^2=0.001$ [Fig. 8(b)]. The results of the post-hoc multiple comparisons are shown in Fig. 8(e). For the age factor [Fig. 8(e), upper panel], multiple pairwise independent sample t-tests showed that the selectivity of 0-yo was lower than that of 1- and 2-yo for all fiducial points on average ($p<0.001$, Bonferroni-corrected). In contrast, multiple pairwise paired $t$-tests for the SD distance [Fig. 8(e), lower panel] showed that comparisons from any two SD distances were significantly different ($p<0.001$, corrected) and that the selectivity decreased with increasing SD distance. Similar results for the selectivity of vertical SD pairs are shown in Fig. S3 in the Supplementary Material.

With regard to the sensitivity of the MLCBR over all 10-10 fiducial points, we found an obvious increase in $L_{abs,MLCBR}$ with increasing SD distance for each age (Fig. 7). However, no differences in age were observed during the visual inspection. The 3 (age) × 5 (SD distance) mixed ANOVA revealed significant main effects of age [$\mathrm{F}(\mathrm{2,180})=4.87$, $p<0.01$, ${{\eta }_{\mathrm{G}}}^2=0.047$] and SD distance [$\mathrm{F}(\mathrm{1.37,247.25})=837.02$, $p<0.001$, ${{\eta }_{\mathrm{G}}}^2=0.306$]. However, these main effects were further qualified by the presence of a significant interaction between age and SD distance, $\mathrm{F}(\mathrm{2.75,247.25})=8.67$, $p<0.001$, ${{\eta }_{\mathrm{G}}}^2=0.009$ [Fig. 8(c)]. The simple main effect of age was significant for all SD distances, that is, 10, 15, 20, 25, and 30 mm (all $p<0.05$). The results of the post-hoc multiple comparisons are shown in Fig. 8(f). At a 10-mm SD distance, the mean sensitivity of 1-yo was significantly higher than that of 2-yo ($p<0.05$, Bonferroni-corrected). The mean sensitivity of 1-yo was significantly higher than that of 0-yo at SD distances of 15 mm ($p<0.05$, corrected), 20 mm ($p<0.01$, corrected), 25 mm ($p<0.01$, corrected), and 30 mm ($p<0.01$, corrected). The simple main effect of the SD distance was also significant for any of the 0-, 1-, and 2-yo infants (all $p<0.001$). At all years of age, the sensitivity of larger SD distances was significantly greater than that of smaller SD distances [Figs. 8(c) and 8(f), $p<0.001$, corrected]. Similar results for the sensitivity of the vertical SD pairs are presented in Fig. S4 in the Supplementary Material.

We found that almost half of 10-10 fiducial points correlated with the completely consistent MLCBR across the three ages for each SD distance (Fig. 9). The average number of fiducial points correlated with the completely consistent MLCBR for all SD distances was $41.6\pm 1.5$ and $39.6\pm 0.9$ for circumferential and vertical SD pairs, respectively, as shown in green circles in Fig. 9. However, fiducial points correlated with inconsistent MLCBR across the three ages (yellow and red circles) were found around the longitudinal fissure for both SD pair orientations. To help fNIRS researchers examine longitudinal functional development from 0- to 2-yo, we have also provided fiducial points whose MLCBR was completely consistent at certain SD distances for the circumferential and vertical SD pairs across 0-, 1-, and 2-yo infants (Table 4).

Fig. 9

Consistency of MLCBR at five SD distances for (a) circumferential and (b) vertical SD pairs. The consistency of the MLCBR among 0-yo, 1-yo, and 2-yo for every fiducial point is indicated by circles with different colors.

Table 4

Summary of fiducial points whose MLCBR was completely consistent at some SD distances for the circumferential and vertical SD pairs across 0-yo, 1-yo, and 2-yo infants.

3.3.

Suitable SD Distances for infant fNIRS Based on SCC Metrics

Based on the results in Sec. 3.2, we found that the sensitivity and selectivity of the MLCBR increased and decreased, respectively, as the SD distance increased. In other words, there is a trade-off between the sensitivity and selectivity of the MLCBR in determining a suitable SD distance for targeting the brain regions of interest in infant fNIRS. Therefore, a suitable SD distance that achieves a good balance between the sensitivity and selectivity of the MLCBR in infant fNIRS was explored.

First, we drew a scatter plot of the selectivity and sensitivity for all 10-10 fiducial points at five SD distances at each infant age [Figs. 10(a)–10(c)]. Then, we empirically chose thresholds 3 and 0.4 for the sensitivity and the selectivity, respectively, to categorize every point in the scatter plot into three zones. Because sensitivity takes precedence over selectivity in fNIRS, we defined the red zone as an area with a sensitivity $<3$. The remaining region was divided into two zones based on the selectivity threshold. Fiducial points with a sensitivity lower and $>0.4$, were classified into yellow and green zones, respectively. Therefore, the SD distance with a larger number of fiducial points categorized into the green zone indicates that both higher sensitivity and selectivity can be achieved.

Fig. 10

Relation between sensitivity and selectivity for each SD distance in (a) 0-yo; (b) 1-yo; and (c) 2-yo. Black circles in figures (a)–(c) indicate data from each 10-10 fiducial point. (d) Ratios of the number of fiducial points in the green, yellow, and red zones to the number of all 10-10 fiducial points.

As shown in Fig. 10, the distribution of points in the scatter plot varies with the SD distance for infants at all ages [Figs. 10(a)–10(c) for 0-, 1-, and 2-yo infants, respectively]. For shorter and longer SD distances, more fiducial points were observed in the red and yellow zones, respectively. The ratios of the number of fiducial points in each zone to all fiducial points are shown in Fig. 10(d). For the green zone, inverted U-shaped curves were observed for all three age groups. On the other hand, the ratio of fiducial points in the yellow and red zones showed a monotonic increase and decrease as the SD distance increased. These findings suggest that excessive short and long SD distances are unsuitable for infant fNIRS. Therefore, the SD distance between 15 mm and 25 mm could be suitable for 0-, 1-, and 2-yo infants. A 25 mm SD distance was more suitable if the sensitivity was emphasized, whereas a 15-mm SD distance was more appropriate if the selectivity was considered as a priority. A relatively balanced trade-off can be obtained when the SD distance is 20 mm. To validate the robustness of this finding, we examined the same problem with different thresholds 4 and 0.5 for sensitivity and selectivity, respectively. Although the thresholds changed modestly, the shapes of the graph, as shown in Fig. 10(d), were maintained (Fig. S5 in the Supplementary Material).

4.1.

Optics-Based SCC Derived from Age-Appropriate Sophisticated Head Models

Several studies have taken an important step toward the establishment of infant SCC;^22–25 however, they only considered the head size of infants based on the simplified fNIRS principle that the signal comes from the cortical projection point below the midpoint of the SD pair. In fact, an fNIRS channel measures absorption changes in a broad cortical area, rather than at a single point. Thus, to establish a precise optics-based SCC that reflects light diffusion in the brains of 0-, 1-, and 2-yo infants, the key step is to construct sophisticated realistic head models that comprise multiple biological tissues with distinct optical properties such as scalp, skull, CSF, and brain tissues.

In this study, we constructed a five-layered head model for each age, distinguishable from a four-layered model where the skull and scalp constitute a single extracerebral layer.^36,46,59 Separating the scalp and skull in infantile light propagation analysis could guarantee more accurate SCC compared with using the four-layered model, as these two types of infant tissues have their own optical properties^35,51 and physical development.^43,44

In addition, we employed template-based head models for light propagation analyses, because the acquisition of subject-specific MRI is generally challenging owing to the difficulty in controlling the motion of infants and undermines the intrinsic advantage of the fNIRS technique for facilitating functional brain measurements during early development. Notably, previous adult or infant studies have shown that the use of a template-based head model is useful for identifying the activation focus, although there are anatomical differences between subject-specific and template-based head models.^{24,25,60–62} Furthermore, the template-based model used in this study was derived from anatomical images of 95 healthy infants and reflects the general anatomical structure of infants. Therefore, the optics-based SCC obtained by analyzing light propagation in template-based infant head models of 0-, 1-, and 2-yo could provide a reliable database to guide fNIRS users in designing probe geometry, and to explain fNIRS data.

Light propagation analysis depends on the optical properties of head tissues. In this study, the same optical properties of the neonate were assigned to all three age models because no established optical properties of head tissues were available for each age group in this study. On the other hand, optical properties in these ages may change due to alterations in tissue composition, such as myelination and bone mineral density during the first 2 years of life. As the level of bone mineral density was almost constant during the first year⁶³ and slightly increased in the second year,⁶⁴ the optical properties of the skull may not change during those years. In contrast, a substantial amount of myelination occurs in a wide range of brains.⁶⁵ Thus, the alteration of the optical properties of WM and GM will definitely be at a non-negligible level. Light propagation is affected by differences in optical properties between adults and infants.³⁵ To address the effect of changes in optical properties on the SCC, we attempted to use the optical properties of the GM and WM of adults to calculate the SCC for the oldest 2-yo head model. Compared to the results with infants’ optical properties, additional simulation results revealed that the optical properties of adults applied to 2-yo had little effect on the SCC. Although a slightly broadened SSP was observed owing to the stronger scattering (Fig. S6 in the Supplementary Material for comparison between the optical properties of the neonate and adult), the consistency of the MLCBR among 0-, 1-, and 2-yo was unaffected by the difference in the optical properties (see Fig. S7 and Table S8 in the Supplementary Material for the optical properties of the adults). The actual changes in optical properties due to development from 0- to 2-yo would be smaller than those assumed here for neonates to adults. Therefore, we claim that our findings using the same optical properties for all three age groups could be used as a reference for developmental cognitive neuroscience. Meanwhile, the accuracy of optics-based SCC will be improved with the advance of in vivo measurement techniques for characterizing the optical properties of tissues.⁶⁶ However, the measurement of accurate optical properties in vivo is still a challenging issue, as shown by the wide range of values reported by measurement techniques.³⁶

4.2.

Effect of SD Distance and Physical Development on the SCC

For a given fiducial point, the SSP was found to be a function of the SD distance, that is, the spatial range of the SSP broadened as the SD distance increased. This finding was consistent with previous studies, regardless of slab models^30,67 or realistic head models⁶⁸ being utilized. Intriguingly, the spatial distribution of the SSP values was also affected by age for a consistent SD distance (Fig. 4). Age-related alterations in SSP may be caused by changes in the local anatomical structures across the three age groups.

The optics-based SCC results (Table 4 and Table. S3-7 in the Supplementary Material) demonstrate that fNIRS signals interrogated by an SD pair always originate from multiple brain regions, even if the SD distance is 10 mm. The one-to-many relationship between an SD pair and cortical regions is due to strong light scattering in the head tissue. In addition, we found several aspects related to $N_{CBR}$. As for the spatial characteristics, fiducial points around the longitudinal fissure were correlated with more brain regions than other points (Fig. 5), which may be because the cortices around the longitudinal fissure were parcellated into a relatively large number of regions in the AAL atlas. From the perspective of age-related change, we found that although the $N_{CBR}$ of 0-yo was larger than that of 1- and 2-yo, there were no significant differences between the $N_{CBR}$ values of 1-o and 2-yo [Fig. 8(d)], which suggests that the similar spatial range of SSP for the same SD distance will occupy fewer brain regions when the head becomes larger owing to the physical development of the infant. In terms of the dependency on the SD distance, the finding that a larger SD distance had more corresponding brain regions [Figs. 5, 8(a), and 8(d)] could be clearly explained by the wider SSP at larger SD distances, as shown in Fig. 4.

We found that the selectivity of MLCBR decreased with increasing SD distance [Figs. 6 and 8(b)]. As mentioned before, the larger the SD distance, the wider the spatial range of the SSP in the brain. Hence, the increase in the normalized PPL of brain regions other than the MLCBR resulted in a relative decrease in the normalized PPL of the MLCBR. In addition, the selectivity of 1- and 2-yo was higher than that of 0-yo on average for all fiducial points (Fig. 6). The difference in the physical development of the head in each year would have determined the degree of age-dependent change in the normalized PPL of the MLCBR. The 0-yo head size is obviously smaller than that of 1- and 2-yo, while 1- and 2-yo have an almost similar head size (see Fig. 1 for example). In other words, the constant area of the brain surface is occupied by a small number of brain regions in the large brains of 1- and 2-yo, but by a large number in the small brains of 0-yo. Furthermore, the spatial range of the SSP was almost constant for the same SD distance, regardless of age. Thus, the constant spatial range of SSP across age was mainly occupied by the MLCBR in the larger brains of 1- and 2-yo, but distributed across several brain regions in the smaller brain of the 0-yo. Therefore, the normalized PPL in the MLCBR of the 0-yo infants was significantly smaller than that of the 1- and 2-yo infants.

We found that the sensitivity of the MLCBR significantly increased as the SD distance increased from 10 to 30 mm at 5-mm intervals for each age [Fig. 8(f)]. This finding is in accordance with evidence obtained from the change in GM sensitivity as a function of SD distance in the neonatal and adult head models.³⁵ The sensitivity of 1-yo was significantly higher than that of 0-yo at 15-, 20-, 25-, and 30-mm SD distances; however, the sensitivity of 2-yo was significantly lower than that of 1-yo at a 10 mm SD distance [Fig. 8(f)]. One possible explanation for the increase or decrease in the sensitivity depending on the time of growth is that physical development differs between brain tissue and superficial layers such as the scalp and skull; the increase in the sensitivity from 0- to 1-yo may be caused by the considerable expansion of the cortical surface during this period. Conversely, from 1- to 2-yo, the decrease in sensitivity may be due to relatively smaller expansion of the cortical surface, although the thickness of the superficial layers continues to increase.

We also found that the MLCBR was completely consistent at almost half of 10-10 fiducial points of 0-, 1-, and 2-yo for each SD distance. In other words, almost half of the fiducial points were correlated with one specific brain region with the largest normalized PPL (Fig. 9 and Table 4). This finding indicates that we can measure identical MLCBRs in longitudinal studies from 0- to 2-yo with fNIRS without the subject’s own structural MRI when a probe of the same SD distance is attached at the scalp fiducial points. Thus, this finding is extremely uplifting for fNIRS users who are interested in the functional development of such MLCBRs. On the other hand, the MLCBR corresponding to fiducial points just above the longitudinal fissure was mostly inconsistent across the three ages (Fig. 9). The $N_{CBR}$ and $L_{norm,MLCBR}$ of the fiducial points were relatively larger and smaller than those of the other points, respectively (Figs. 5 and 6), which suggests that the MLCBR at a certain age may easily be replaced by another brain region at another age because of the slight change in the light path. One possibility for age-related changes in the light path is that the thickness of the skull in the frontal, parietal, and occipital regions along with the longitudinal fissure changes more drastically than in other locations from 0- to 2-yo.⁴⁴ Another possibility is that the cortical surface expands relatively more in regions of the superior parietal, prefrontal, occipital cortices, and postcentral gyrus than in other regions during the first two years.²

The consistency of the MLCBR revealed in the present study could provide strong support for the reliability of findings from longitudinal developmental studies using fNIRS in which the probe was attached based on scalp fiducial points. In recent years, by executing the longitudinal cohort study projects [e.g., Brain Imaging for Global Health (BRIGHT) project], several laboratories worldwide have devoted themselves to investigating functional brain development during the first two postnatal years, including studies of visual working memory,⁶⁹ social cognition,^70,71 and resting-state functional networks.⁷² The present study will be especially useful for a large cohort of longitudinal or cross-sectional studies of early brain development, as structural MRI scanning, which is a demanding task for young populations, is not necessarily required.

4.3.

Consideration of Suitable SD Distances for Infant fNIRS

The suitable SD distance for infants remains a matter of debate, as its choice is dependent on several factors. By considering a trade-off between the selectivity and sensitivity of the MLCBR, this study provided recommendations on suitable SD distances for 0-, 1-, and 2-yo. The most desirable SD distance is the one that has both the maximum number of fiducial points with high selectivity and sensitivity, and a minimum number of fiducial points with low selectivity and sensitivity. Based on this perspective, we determined that the suitable SD distances in fNIRS for infants during the first 2 years ranged from 15 to 25 mm. This finding supports the results of a previous study in which the highest sensitivity was obtained at an SD distance of 20 mm in 3-month-old infants.³⁹ In practical applications, we suggest that fNIRS users choose the SD distance according to the criteria (sensitivity or selectivity) more important to them. If the users focus on selectivity, an SD distance of 15 mm could be a better choice, whereas 25 mm is suitable for sensitivity as the priority. In addition, if fNIRS users pursue a relatively balanced trade-off between selectivity and sensitivity, we recommend an SD distance of 20 mm. Our findings also revealed that the optimal SD distance for infants is different from that for adults. Previous adult studies have demonstrated that fNIRS probes should ideally be designed with 30- to 35-mm SD distances,^68,73 as most light passes through the extra-cerebral superficial tissues at SD distances $<20\mathrm{mm}$.⁶⁷ Compared with that for adults, and the most suitable SD distances for infants are smaller than 30 mm, which indicates that thin superficial layers allow much more photons to pass through the brain tissue.

4.4.

Future Directions and Limitations

In the current study, we found that the orientation of SD pairs over 10-10 positions had no significant effect on our results, which was consistent with findings from photon propagation in the adult brain.^34,38 Notably, only the AAL atlas was adopted to obtain the SCC in this study. The orientation of SD pairs may influence the SCC when other infant brain atlases with finer anatomical parcellation are available with advances in MRI techniques.

For the application of this work, the precise optics-based SCC for SD pairs at all 10-10 system scalp locations (Table S3-7 in the Supplementary Material) can be used as a reference table to guide fNIRS users in designing the probe arrangement for targeting specific brain regions, as well as to help them explain fNIRS data obtained according to the 10-10 system. Importantly, the summary of scalp positions whose MLCBR was completely consistent across 0-, 1-, and 2-yo infants (Table 4) is beneficial for the investigation of functional development for one specific brain region. However, the spatial density of the 10-10 fiducial points for analyzing the optics-based SCC would be relatively sparse because a few brain regions had only a small chance of being corresponded. Our future work will calculate the optics-based SCC by using a denser placement system,⁷⁴ which can guarantee all brain regions with a high probability of being corresponded and estimate underlying brain regions for any arrangement of SD pairs. In addition, the established age-appropriate infant head models and the proposed method for calculating the optics-based SCC can be used to estimate brain regions at any scalp position by virtually placing the SD pairs on the scalp of 0-, 1-, and 2-yo infants, even without infant head structures.

The head tissues within the first postnatal year undergo dramatic growth, such as the total volume of the brain expanding up to double its size.^44,75,76 Furthermore, several studies have reported the discovery of longitudinal functional brain development during this period.^71,77,78 However, the 0-yo infant head model used in this study was constructed with a template-based MRI of an approximately 1-month-old infant. Establishing optics-based SCC at a fine temporal scale (every 3 months from birth to 12 months), which is in line with physical development during the first year after birth, it is expected to provide useful information for investigating the longitudinal development of brain functions using the fNIRS technique.