1.

Introduction

Diffuse optical imaging (DOI) is an appropriate tool for noninvasive exploration of hemoglobin concentration changes arising in biological tissues. ^{1, 2, 3, 4, 5} In the case of adult human brains, ^{6, 7, 8, 9} reflectance DOI (rDOI) has been popularly applied because of the poor transparency of human brain tissues to near-infrared light. In rDOI, near-infrared light irradiates the brain tissues through optical fibers, and is received by detectors placed on the same surface as the sources. To date, the most widely used instruments for performing rDOI have been continuous-wave (CW) ones.^{10, 11, 12} In CW instruments, the signal detected by one measurement may be influenced by absorption changes occurring in a large area, which was defined as the field of view (FOV) of the measurement. Hence the spatial resolution of rDOI has been limited. In addition, challenges occur in reconstructing high-quality images.

Numerous methods ^{13, 14, 15, 16, 17} have been developed to improve the image quality of DOI, of which enhancement of the overlapping measurement constituted an important group. Most researchers think that overlapping measurements are helpful for localizing the activations. In practice, such overlapping measurements were mainly obtained by the geometric arrangement of optical fibers. Several efforts have been made to improve the image quality through better arrangements of the optical fibers. ^{18, 19, 20, 21} However, several challenges for the further improvement of the imaging performance of rDOI still exist for the following reasons.

This work presents a multicentered mode for the arrangement of optical fibers. In this mode, several sources were located in the central area, and around these more detectors were placed. Significant improvements in overlapping measurements and image quality were shown by the results from simulations using a semi-infinite model. Experiments on a single human subject indicated that multicentered geometries are appropriate for probing human brains.

2.

Arrangements

Single-centered and multicentered hexagonal geometries were evaluated in this study (Fig. 1 ). The sides of the equilateral hexagons were all $4\mathrm{cm}$ . The dots and open circles indicate the sources and detectors, respectively.

Fig. 1

(a) Single-centered single-density (SS) geometry, (b) single-centered double-density (SD) geometry, (c) multicentered single-density (MS) geometry, and (d) multicentered double-density (MD) geometry. The sources and detectors are indicated by dots and open circles, respectively.

Figure 1b shows that the single-centered double-density (SD) geometry had 12 more detectors than the single-centered single-density (SS) geometry, which is shown in Fig. 1a. Detector 13 in the SD geometry was located $5.8\mathrm{mm}$ below the top edge and was equidistant from detectors 1 and 2. The other 11 detectors were similarly located.

The multicentered geometries included multicentered single-density (MS) and multicentered double-density geometries (MD). They were formed by adding six more sources to the SS and SD geometries, respectively. As shown in Figs. 1c and 1d, sources 2 were located on the lines defined by sources 1 and detectors 1, and were $1.15\mathrm{cm}$ away from the centers of the hexagons. The other five sources were placed in the same way.

In the MD geometry, the required dynamic ranges for every detector shown in Table 1 were all within the 60-dB dynamic range of our CW5 instrument (TechEn, Milford, MA). In the proposed geometries, each detector could receive signals from all of the sources, so the measurements achieved in the four geometries were SS - 12, SD - 24, MS - 84, and MD - 168. The imaging regions of the four geometries were the regions covered by the hexagons, and the pixel sizes were $1\times 1\mathrm{mm}$ .

Table 1

The maximal to minimal separation ratios, and the required dynamic ranges to maintain an SNR of 100 for every detector in the proposed MD geometry.

3.

Theories

4.

Methods for Image Quality Evaluation

5.

Simulation Results

In this section, we first compare the imaging performance of the multicentered geometries with the single-centered ones. Then, we show that our proposed multicentered geometries can achieve good image quality both in depths of 1.5 and $2.0\mathrm{cm}$ . Finally, we reveal the advancement in imaging performance by our multicentered geometries compared with previous geometries.

5.1.

Comparison of Multicentered Geometries to Single-Centered Ones

5.1.1.

Improvement in overlapping measurements

We monochromized the sensitivity matrix of the measurements at a depth of $1.5\mathrm{cm}$ with corresponding half-maxima. The number of overlapped FOVs at each pixel was counted afterward, and the achieved overlapping maps for the four geometries are shown in Fig. 2 . The maximum overlapping measurements for the single-centered geometries were 3 and 6, while the multicentered ones were 19 and 42. The overlapping measurements in the center areas of the geometries were higher than those of the peripherals, as shown in Fig. 2. To fully evaluate the image quality of the geometries, we chose two positions: position 1 in the centers and position 2 in the peripheries. As seen in Fig. 2, the distances between all the positions 2 and the positions 1 were $25\mathrm{mm}$ .

Fig. 2

Overlapping maps for the (a) SS, (b) SD, (c) MS, and (d) MD geometries.

The first four columns of Table 2 show the mean overlapping measurements within $7.5\mathrm{mm}$ in the radius around each position 1 and position 2 for the four geometries. From columns five and six in Table 2, we can see the improvement in overlapping measurements provided by double-density geometries. Columns seven and eight show that multicentered geometries can increase the overlapping measurements even more significantly both in the center and periphery. Considering that the multicentered geometries had just six additional sources, it can be concluded that the multicentered mode is likely to effectively increase the overlapping measurements.

Table 2

The first four columns show the mean overlapping measurements within 7.5mm in radius around position 1 and position 2 for the four geometries. Columns five and six were obtained by dividing columns two and four by columns one and three, respectively. Columns seven and eight were the quotients obtained by dividing columns three and four by columns one and two, respectively.

	SS	SD	MS	MD	SD/SS	MD/MS	MS/SS	MD/SD
P1	1.29	3.07	17.20	35.51	2.38	2.06	13.33	11.57
P2	1.01	1.47	7.74	11.71	1.46	1.51	7.66	7.97

5.1.2.

Enhancement in image quality: a contrast-to-noise ratio analysis

At each position proposed before, we changed the radii of the objects from 0.05 to $1.5\mathrm{cm}$ , and the contrast levels from 1.05 to 3.0. The intervals for the sizes and the contrast levels were $0.05\mathrm{cm}$ and 0.05, respectively. For each size and contrast level of the objects, imaging simulation was performed and the CNR value of the reconstructed image was calculated. The CNR maps of the four geometries for position 1 are shown in Fig. 3 , followed by the CNR maps for position 2 in Fig. 4 . The brighter areas indicating CNR values above 4.0 in the maps marked the objects that could be clearly recognized from reconstructed images. The threshold of 4.0 was chosen subjectively using the method suggested by Song ²⁹

Fig. 3

CNR maps for the (a) SS, (b) SD, (c) MS, and (d) MD geometries in position 1.

Fig. 4

CNR maps for the (a) SS, (b) SD, (c) MS, and (d) MD geometries in position 2.

For these specified sizes and contrast levels of objects, larger CNR values were found in double-density geometries than in single-density ones, as shown in Figs. 3 and 4. Also, additional improvements could be observed in multicentered geometries than in single-centered ones, as seen in Figs. 3 and 4. This supports the conclusion that it was the multicentered mode, rather than the additional detectors, which was most effective in improving the image quality of rDOI.

Figures 3c and 3d show that the spatial resolutions were $1\mathrm{mm}$ and the contrast resolution limits were less than 1.05 for the multicentered geometries in position 1. Figures 4c and 4d reveal that the limits were $2\mathrm{mm}$ and 1.1 in position 2. As illustrated in Figs. 3a and 3b and Figs. 4a and 4b, the single-centered geometries had higher spatial and contrast resolution limits in both positions.

5.1.3.

Enhancement in image quality: illustrational analysis

We located objects with radii of $0.75\mathrm{cm}$ and contrast levels of 3.0 at a depth of $1.5\mathrm{cm}$ for the two positions. The real images are shown in Figs. 5a and 6a . The radii of the inscribed circles and the circumcircles of the objects in Figs. 5a and 6a were 0.70 and $0.75\mathrm{cm}$ , respectively. The reconstructed images with the four geometries in position 1 are shown in Figs. 5b, 5c, 5d, 5e, followed by the reconstructed images in position 2 in Figs. 6b, 6c, 6d, 6e. The corresponding CNR and CR values of the reconstructed images are shown in Table 3 .

Fig. 5

The (a) true image and the reconstructed images using (b) SS, (c) SD, (d) MS, and (e) MD geometries in position 1. The objects were located $1.5\mathrm{cm}$ deep in a semi-infinite model. The black lines indicate the objects detected using the half-maximum method. The CNR and CR values are shown in Table 3.

Fig. 6

The (a) true image and the reconstructed images with the (b) SS, (c) SD, (d) MS, and (e) MD geometries in position 2. The objects were located $1.5\mathrm{cm}$ deep in a semi-infinite model. The black lines indicate the objects detected using the half-maximum method. The CNR and CR values were shown in Table 3.

Table 3

The CNR and CR values of reconstructed images from the SS, SD, MS, MD, and rectangular geometries with objects located at 1.5cm depth in a semi-infinite model.

	P1					P2
Geometry	SS	SD	MS	MD	Rectangular	SS	SD	MS	MD	Rectangular
CNR	2.52	2.89	10.22	10.37	4.94	4.99	6.60	8.43	9.17	4.38
$R_{ins}$ (cm)	1.70	1.60	0.70	0.70	0.85	0.65	0.55	0.75	0.75	1.20
$R_{cir}$ (cm)	2.45	2.20	0.75	0.75	1.20	1.25	1.05	0.85	0.80	1.50
CR	0.44	0.38	0.07	0.07	0.41	0.92	0.91	0.13	0.07	0.25

In the case of objects located in position 1, only a few measurements could see the objects in single-centered geometries, [seen in Figs. 2a and 2b and Table 2], so the reconstructed images were very blurred [shown in Figs. 5b and 5c]. However, the multicentered geometries had many more overlapping measurements in position 1 [seen in Figs. 2c and 2d and Table 2], which helped to accurately ascertain the absorbers [shown in Figs. 5d and 5e]. And as a result, large CNR values were achieved.

In position 2, the objects detected by the single-centered geometries were localized compared to the blurred objects in position 1, as shown in Figs. 6b and 6c. However, the reconstructed objects were clearly oval shaped rather than circular and large CR values were obtained, as can be seen in Table 3. However, in the multicentered geometries, with increased densities of measurements [seen in Figs. 2c and 2d and Table 2], the shapes of the detected objects were clearly more nearly accurate [as in Figs. 6d and 6e and Table 3].

5.2.

Image Quality at Different Depths

The absorbers were located $2.0\mathrm{cm}$ deep in the semi-infinite model. The reconstructed images for the four geometries are shown in Fig. 7 . The corresponding CNR and CR values are shown in Table 4 . A decrease in CNR values can be observed by comparing Table 3 with Table 4. The reconstructed images with the multicentered geometries were a little more blurred in Fig. 7 than those in Figs. 5 and 6. However, much better image quality could be obtained when comparing the reconstructed images with multicentered geometries to those with single-centered ones, as can be seen in Table 4 and Fig. 7. This indicated that the proposed multicentered geometries could achieve better image quality than single-centered ones both in depths of 1.5 and $2.0\mathrm{cm}$ .

Fig. 7

Reconstructed images using the (a) SS, (b) SD, (c) MS, and (d) MD geometries in position 1. Also the reconstructed images using (e) SS, (f) SD, (g) MS, and (h) MD in position 2. The absorbers were located $2.0\mathrm{cm}$ deep in the semi-infinite model. The black lines indicate the objects detected using the half-maximum method. The CNR and CR values are shown in Table 4.

Table 4

The CNR and CR values of reconstructed images using the SS, SD, MS, MD, and rectangular geometries with objects located at 2.0cm depth in a semi-infinite model.

	P1					P2
Geometry	SS	SD	MS	MD	Rectangular	SS	SD	MS	MD	Rectangular
CNR	0.87	2.29	6.62	7.13	4.14	3.73	3.92	5.31	5.89	3.92
$R_{ins}$ (cm)	—	1.15	0.90	0.90	1.20	0.75	0.80	0.90	0.80	1.30
$R_{cir}$ (cm)	—	1.85	1.00	0.95	1.50	1.15	1.15	1.00	0.90	1.60
CR	—	0.61	0.11	0.06	0.25	0.53	0.44	0.11	0.13	0.23

5.3.

Comparing Multicentered Geometries to Previous Geometries

To compare the image quality of the proposed multicentered geometries to previous ones done by other researchers, we compared ours with rectangular geometry, which has been demonstrated to have the best overlapping measurements and image quality of all the previously reported geometries used in rDOI.²¹

As seen in Fig. 8b , rectangular geometry could achieve a maximum of nine overlapping measurements, and the mean overlapping measurements in positions 1 and 2 were 5.64 and 4.45, respectively. This indicates that the number of overlapping measurements in the rectangular geometry were much fewer than the number in our multicentered geometries. The reconstructed images from the rectangular geometry in Figs. 8d and 8f had smaller CNR values and larger CR values compared with those of multicentered geometries, as seen in Table 3. This also indicates that our multicentered geometries could achieve better image quality than rectangular geometry.

Fig. 8

The (a) rectangular geometry and its (b) overlapping map together with the real images in (c) position 1 and (e) position 2 and the reconstructed images in (d) position 1 and (f) position 2. The black lines in the reconstructed images indicate the objects detected using the half-maximum method. The CNR and CR values are shown in Table 3.

We reconstructed the images with the rectangular geometry and absorbers located $2.0\mathrm{cm}$ deep in the semi-infinite model. The corresponding CNR and CR values are shown in Table 4. Smaller CNR values and larger CR values can be found in Table 4 when comparing rectangular to multicentered geometries. This indicates that the proposed multicentered geometries are better than rectangular geometry both in depths of 1.5 and $2.0\mathrm{cm}$ .

6.

Preliminary Experimental Results

We confirmed our theoretical results by experiments using a CW5 instrument. Following a complete description of the experiments, written informed consent was obtained from a single human subject before the initiation of the experiments. These experiments were ethically approved by the Institutional Review Board at the Institute of Automation, Chinese Academy of Sciences. In the experiments, sources 1 in the multicentered and single-centered geometries were put on C3 in the EEG 10–20 system. The subject was asked to tap the right hand for $30\mathrm{s}$ , followed by $30\mathrm{s}$ of rest. Data collection lasted $420\mathrm{s}$ .

The data collected throughout the $420\mathrm{s}$ were averaged per minute to achieve averaged data for $60\mathrm{s}$ . The mean values of the first $30\mathrm{s}$ were viewed as $\Phi$ and those of the last $30\mathrm{s}$ were viewed as ${\Phi }_0$ . The images of $\mathrm{\Delta }{\mu }_a$ were then reconstructed using Eqs. 2, 3. As shown in Fig. 9 , the reconstructed images with multicentered geometries were much clearer than those with the single-centered ones. As can be seen in Fig. 9, the areas of the reconstructed activations were 470 and $237{\mathrm{mm}}^2$ from the MS and MD geometries.

Fig. 9

Reconstructed images using the (a) SS, (b) SD, (c) MS, and (d) MD geometries from the experiments on a human subject.

During the experiments, the sources in the proposed multicentered geometries could be turned on simultaneously. As seen in Figs. 1c and 1d, every detector would have no more than two measurements with separations shorter than $3.0\mathrm{cm}$ . Since the signals decreased rapidly for longer separations, the total power of the signals received by the detectors would be low. The lower signal power made it possible for the detectors to undergo amplification to maintain a good SNR.

Among the 168 measurements using the MD geometry, there were only three measurements that had an SNR of less than 100 during the experiments. When placed on a human head, the deformation of the multicentered geometries was small, and the optodes were able to contact tightly with the scalp, which also helped to achieve a good SNR.

7.

Discussion

In rDOI, the quality of the reconstructed objects is primarily determined by the different types and degree of overlap of the measurements that are sensed by the absorbers. In locations with few overlapping measurements, absorbers with different shapes would influence the same or similar numbers of measurements. Since the overlapping areas of these measurements would remain unchanged, the reconstructed objects would appear to have the same shapes. However, using dozens of measurements sensitive to the objects, the image quality could become satisfactory in most cases.

The multicentered geometries were quite variable in practice. The distances from the centers to the sources and to the detectors were both alterable, and even the shape of hexagons could be easily changed to other polygons. The multicentered geometries that we propose were designed to be connected with each other to cover larger regions. After being linked, the image quality in the peripheral regions could be further improved.

In the MD geometry proposed, there were eight separations between sources and detectors: 2.0, 2.3, 3.1, 3.5, 4.0, 4.2, 4.6, and $5.0\mathrm{cm}$ . The multiseparations in the multicentered geometries are thought to be helpful for improving depth resolution.¹⁵

8.

Conclusions

In this study, we propose a multicentered mode for the arrangement of optical fibers to improve the imaging performance of rDOI. The image quality and the practical performance of the multicentered geometries are evaluated. The results from the simulations show a significant enhancement in image quality compared with both single-centered and previous geometries. Preliminary experimental results on a human subject indicate that the proposed multicentered geometries are useful in practice for their good SNR and experimental convenience. In brief, the proposed multicentered geometries could advance the imaging performance of rDOI in both image quality and experimental performance.