2.1.

Reflectance Fiber Probe System

Figure 1 shows a schematic diagram of the single-reflectance fiber-probe system with the two source-collection geometries used in the present study. The system consists of a light source, bifurcated fiber, a reflectance fiber probe, and two spectrometers under the control of a personal computer. The bifurcated fiber has two fibers of the same diameter of $400\mu \mathrm{m}$ side-by-side in the common end. The reflectance fiber probe has one $600\text{-}\mu \mathrm{m}\text{-}\text{diameter}$ fiber in the center surrounded by six $600\text{-}\mu \mathrm{m}\text{-}\text{diameter}$ fibers. The common end of the bifurcated fiber is connected to one end of the center fiber of the reflectance probe by a fiber connector. A halogen lamp light (HL-2000, Ocean Optics Inc., Dunedin, Florida, USA), which covers the visible-to-NIR wavelength range, is used to illuminate the sample via one lead of bifurcated fiber and the central fiber of the reflectance probe. Diffusely reflected light from the sample is collected by the central fiber and the six surrounding fibers. The center-to-center distances between the central fiber and the surrounding fibers are $700\mu \mathrm{m}$. The light collected by the central fiber is delivered to a multichannel spectrometer (USB4000, Ocean Optics Inc.) via another lead of the bifurcated fiber, whereas that collected by the six surrounding fibers is delivered to a different multichannel spectrometer (USB4000, Ocean Optics Inc.). A solution of Intralipid 10%³⁵ was prepared as a reference solution. Diffuse reflectance spectra $R_{\mathrm{c}}(\lambda )$ and $R_{\mathrm{s}}(\lambda )$ were calculated from the spectral intensities of light collected by the central fiber and the six surrounding fibers, respectively, based on the reflected intensity spectra from the reference solution.

Fig. 1

A single fiber probe system for measuring the diffuse reflectance spectra with two source-collection geometries.

2.2.

Monte Carlo Simulation of Light Transport in Tissue

In order to estimate the absorption coefficient ${\mu }_{\mathrm{a}}$ and the reduced scattering coefficient ${\mu }_{\mathrm{s}}^{\prime }$ based on the measured diffuse reflectance, we performed Monte Carlo simulations for light transport using the source-collection geometries of the reflectance fiber probe shown in Fig. 1. Figures 2(a) and 2(b) show the simulation models for $R_{\mathrm{c}}$ and $R_{\mathrm{s}}$, respectively. Each simulation model consists of a fiber and a sample. We used the Monte Carlo simulation code developed by Wang et al.,¹⁹ in which the Henyey-Greenstein phase function is applied to a sampling of the scattering angle of photons. The source code was modified for the two source-collection fiber configurations. The source and collection areas were located on the boundary between the fiber and the scattering medium. The source and collection areas were identical in the simulation model for $R_{\mathrm{c}}$ [Fig. 2(a)]. The distance between the source and collection fiber areas was $700\mu \mathrm{m}$ in the simulation model for $R_{\mathrm{s}}$ [Fig. 2(b)]. In a single simulation, 1,000,000 photons were randomly launched uniformly within the radius of the source fiber. Photons were launched with equal probability over the entire face of the source fiber and were propagated into the medium under scattering and absorption. Then, a portion of the scattered light returns from the medium and is finally emitted from the surface of the medium. For all of the simulations, the refractive index of the fiber, $n_{\mathrm{f}}$, and that of the medium, $n_{\mathrm{m}}$, were fixed at 1.458 and 1.4, respectively. Only photons that had an angle less than or equal to the maximum acceptance angle and passed back through the face of collection fiber were counted into the collected light intensity. In order to estimate $R_{\mathrm{s}}$ collected by all of the surrounding fibers, the diffuse reflectance simulated by the multiple-fiber geometry shown in Fig. 2(b) is multiplied by 6. In the Monte Carlo simulations, $R_{\mathrm{c}}$ and $R_{\mathrm{s}}$ were calculated for the ranges of ${\mu }_{\mathrm{a}}=0.1$ to $50.0{\mathrm{cm}}^{-1}$ and ${\mu }_{\mathrm{s}}^{\prime }=5.0$ to $70.0{\mathrm{cm}}^{-1}$. Figures 3(a) and 3(b) show the results obtained from the Monte Carlo simulation for $R_{\mathrm{c}}$ and $R_{\mathrm{s}}$, respectively. The value of $R_{\mathrm{c}}$ increases monotonically as ${\mu }_{\mathrm{s}}^{\prime }$ increases, whereas $R_{\mathrm{s}}$ reaches a plateau for larger values of ${\mu }_{\mathrm{s}}^{\prime }$. Both $R_{\mathrm{c}}$ and $R_{\mathrm{s}}$ decrease exponentially as ${\mu }_{\mathrm{a}}$ increases, but the effect is more pronounced for $R_{\mathrm{s}}$.

Fig. 2

Schematic diagram of the Monte Carlo simulation models that represents the fiber configurations of the reflectance probe used in the present study. (a) Single-fiber configuration in which a central fiber of the reflection probe is used both as the source and for collection of light. (b) Multiple-fiber configuration in which the central fiber is used as the source and the surrounding fibers are used for collection of light.

Fig. 3

Results obtained from the Monte Carlo simulations for (a) $R_{\mathrm{c}}$ collected by the center fiber and (b) $R_{\mathrm{s}}$ collected by the surrounding six fibers.

2.3.

Determination of Empirical Formulas for Estimating ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$

In order to estimate ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$ from the measurements of $R_{\mathrm{c}}$ and $R_{\mathrm{s}}$, we consider the following empirical equation based on the results of the Monte Carlo simulation:

Fig. 4

Estimated and given values obtained from the numerical investigations for (a) the reduced scattering coefficient ${\mu }_{\mathrm{s}}^{\prime }$ and (b) the absorption coefficient ${\mu }_{\mathrm{a}}$.

2.4.

Calculation of Tissue Oxygen Saturation from ${\mu }_{\mathrm{a}}(\lambda )$

The absorption coefficient spectrum is given by the sum of absorption due to oxygenated and deoxygenated hemoglobin as follows:

Using the absorption coefficient spectrum ${\mu }_{\mathrm{a}}(\lambda )$ as a response variable and the extinction coefficient spectra of ${\epsilon }_{\mathrm{HbO}}(\lambda )$ and ${\epsilon }_{\mathrm{Hb}}(\lambda )$²⁶ as predictor variables, the multiple regression model can be applied to Eq. (3) as follows:

3.1.

Validation of the Proposed Method Using Optical Phantoms

Before the in vivo experiments, preliminary experiments were carried out using optical phantoms. The phantoms were prepared using Intralipid stock solution (Fresenius Kabi AB, Sweden) as scattering materials and hemoglobin solution extracted from red blood cells of horse blood as the absorber. We prepared the scattering solutions by diluting Intralipid stock solution with saline. The absorption coefficients of hemoglobin were experimentally determined based on the transmittance measurements of hemoglobin solutions within a cuvette using a spectrometer. The reduced scattering coefficients of Intralipid solutions were evaluated based on the published values.³⁵ We first produced 12 phantoms with ranges of ${\mu }_{\mathrm{a}}=0.2$ to $7.9{\mathrm{cm}}^{-1}$ and ${\mu }_{\mathrm{s}}^{\prime }=10.3$ to $45.1{\mathrm{cm}}^{-1}$ in the wavelength range from 500 to 900 nm to compare the estimated and given optical properties. We also performed the phantom experiments based on the standard protocols developed within the European Thematic Network MEDPHOT (optical methods for medical diagnosis and monitoring of diseases).³⁶ The MEDPHOT protocol is composed of five criteria: accuracy, linearity, noise, stability, and reproducibility. The accuracy of the measurement is defined as the capacity of the instrument for obtaining a value for the measurable value $x_{\mathrm{meas}}$ as close as possible to the conventionally true value $x_{\mathrm{conv}}$. In the accuracy assay, the crosstalk in the estimation of ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$ can also be investigated by the results of experiments in which ${\mu }_{\mathrm{s}}^{\prime }$ is estimated when only ${\mu }_{\mathrm{a}}$ changes and vice versa in order to evaluate how much a change in an optical property interferes with the estimation of the other property. A linearity assay was performed by measurement of a set of phantoms combining five values for the hemoglobin concentration, with three values for the concentration of Intralipid solution to check whether the system can follow changes in given values of ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$ without distortions. The noise assay was performed by repeating a series of measurements on the same phantom. We investigated the coefficient of variation CV of a certain number of repeated measurements against the injected energy $E_{\text{in}}$ as follows:

A total of 15 phantoms were constructed by combining three concentrations of Intralipid solution with five concentrations of hemoglobin. These phantoms were labeled with a letter and a number, in which the letter stands for the scattering ($X$, $Y$, and $Z$ corresponding to ${\mu }_{\mathrm{s}}^{\prime }=32.1$, 40.2, and $48.2{\mathrm{cm}}^{-1}$, respectively) and the number indicates the absorption (1, 2, 3, 4, and 5 corresponding to ${\mu }_{\mathrm{a}}=1.0$, 1.25, 1.5, 1.75, and $2.0{\mathrm{cm}}^{-1}$, respectively). In addition, one more phantom was constructed for the reproducibility assay by the combination of a polystyrene latex beads solution and hemoglobin and with identical values of ${\mu }_{\mathrm{s}}^{\prime }=73.6{\mathrm{cm}}^{-1}$ and ${\mu }_{\mathrm{a}}=2.0{\mathrm{cm}}^{-1}$ at 500 nm. The reflectance fiber probe was inserted vertically within the phantoms to a depth of $\sim 1.0\mathrm{cm}$ from the surface. The face of the reflectance fiber probe was pointing toward the bottom of the container.

3.2.

Animal Experiments

The animal care and experimental procedures of this study were approved by the Animal Research Committee of Tokyo University of Agriculture and Technology. Intraperitoneal anesthesia was implemented using a mixture of $\alpha$-chloralose ($50\mathrm{mg}/\mathrm{kg}$) and urethane ($600\mathrm{mg}/\mathrm{kg}$) in nine male Wister rats (80 to 286 g). Anesthesia was maintained at a depth such that the rat had no response to toe pinch. The rat head was placed in a stereotaxic frame. Figure 5(a) shows a schematic diagram of the measurement area and the stimulation sites on the rat head. A longitudinal incision $\sim 20\mathrm{mm}$ long was made along the head midline. The skull bone overlying the parietal cortex was removed using a high-speed drill to form an ellipsoidal cranial window (major axis: 8.0 mm, minor axis: 6.0 mm). The cranial window was bathed with normal saline. The end of the reflectance fiber probe was placed on the exposed cortex with care taken to avoid large blood vessels. A burr hole (diameter: 2 mm) was drilled in the ipsilateral frontal bone as a site for contacting the cortex with a 3 M KCl solution. The center-to-center distance between the burr hole and the reflectance fiber probe was 9.3 mm. CSD was induced by applying a droplet of the KCl solution to the burr hole. The extracellular local field potential (LFP) was recorded using a single Ag/AgCl electrode with a ball-shaped tip (tip diameter: 1 mm). The recording electrode was placed on the cortex anterior to the edge of the reflectance fiber probe with care taken to avoid large blood vessels. The center-to-center distance between the burr hole and the recording electrode was 6.9 mm on average. An Ag/AgCl reference electrode (RC5, World Precision Instruments Inc., Sarasota, Florida, USA) was placed in the neck muscle. Figure 5(b) shows a schematic diagram of the experimental setup. Measurements of $R_{\mathrm{c}}(\lambda )$ and $R_{\mathrm{s}}(\lambda )$ were obtained simultaneously in the wavelength range of 500 to 900 nm at 10 s intervals for 50 min. The KCl solution was applied to the cortical surface through the burr hole 1 min after the onset of measurement and was washed out 16 min after the onset of measurement. The LFP signal was amplified at 1 to 100 Hz using a differential amplifier (DAM50, World Precision Instruments Inc.) and was digitized at 5 Hz using an oscilloscope (TDS1000C-EDU, Tektronix) connected to a personal computer running Open Choice software.

Fig. 5

Schematic diagram of (a) measurement and stimulation sites on the rat head and (b) experimental setup for in vivo rat brain during cortical spreading depression.

Since the proposed method requires the fiber probe to be in contact with the surface of the exposed brain, it is difficult to measure the LFP signal at the same position as the reflectance fiber probe. Therefore, we estimate the time of the negative peak of the LFP at a position under the reflectance fiber probe as the arrival time of CSD. First, the propagation speed of CSD, $p$ (mm/min), is calculated as follows:

4.1.

Validation of the Proposed Method Using Optical Phantoms

Figure 6 shows the estimated and given values for the reduced scattering coefficient ${\mu }_{\mathrm{s}}^{\prime }$ [Fig. 6(a)] and the absorption coefficient ${\mu }_{\mathrm{a}}$ [Fig. 6(b)]. Reasonable results were obtained for both ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$. Correlation coefficients between the estimated and given values are $R=0.95$ ($p<0.0001$) and $R=0.96$ ($p<0.0001$) for ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$, respectively. The average root mean square error for ${\mu }_{\mathrm{s}}^{\prime }$ is $8.7\pm 7.2\%$ and that for ${\mu }_{\mathrm{a}}$ is $40.6\pm 28.0\%$. The proposed method yields, in principle, good results for both ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$, as shown in Figs. 4(a) and 4(b). In Fig. 6(b), however, the estimated error for ${\mu }_{\mathrm{a}}$ increases as the given value increases, which could be attributed to the fact that the current simulation model does not accurately represent the actual experimental conditions, e.g., the distance between the central and surrounding fibers is not taken into consideration. As described in Sec. 2.2, the value of $R_{\mathrm{s}}$ detected by the surrounding fiber is sensitive to the change in ${\mu }_{\mathrm{a}}$. Therefore, the distance between the central fiber and the surrounding fiber has an impact on the estimation of ${\mu }_{\mathrm{a}}$. The cause of the error in ${\mu }_{\mathrm{a}}$ should be investigated in the future.

Fig. 6

Estimated and given values obtained from the phantom experiments for (a) the reduced scattering coefficient ${\mu }_{\mathrm{s}}^{\prime }$ and (b) the absorption coefficient ${\mu }_{\mathrm{a}}$.

Figure 7 shows the accuracy plots of ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$ for the 15 phantoms at 500 nm. The corresponding given values (conventional true values) are also plotted as grid lines. The value of ${\mu }_{\mathrm{a}}$ has a tendency to be underestimated with the increase of ${\mu }_{\mathrm{s}}^{\prime }$, whereas the estimated values of ${\mu }_{\mathrm{s}}^{\prime }$ are almost independent of the values of ${\mu }_{\mathrm{a}}$. Figure 8 shows the linearity plots of ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$ for the 15 phantoms at 500 nm. In Fig. 8(a), the estimated value of ${\mu }_{\mathrm{a}}$ is increased linearly as the given value increases. A maximum error in the estimated value of ${\mu }_{\mathrm{a}}$ was 39.9% for the given values of ${\mu }_{\mathrm{a}}=1.0{\mathrm{cm}}^{-1}$ and ${\mu }_{\mathrm{s}}^{\prime }=48.2{\mathrm{cm}}^{-1}$. In Fig. 8(b), it can be clearly observed that the tendency of the estimated value of ${\mu }_{\mathrm{a}}$ is to decrease with increasing the given value of ${\mu }_{\mathrm{s}}^{\prime }$, which indicates a scattering-to-absorption coupling. In contrast, the plots of the estimated values of ${\mu }_{\mathrm{s}}^{\prime }$ versus the given values of ${\mu }_{\mathrm{a}}$ in Fig. 8(c) show that there is no significant coupling of ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$. Figure 8(d) shows the plots of the estimated values of ${\mu }_{\mathrm{s}}^{\prime }$ versus the given values of ${\mu }_{\mathrm{s}}^{\prime }$. Although the estimated value of ${\mu }_{\mathrm{s}}^{\prime }$ for each condition shows a reasonable result, the system is linear up to ${\mu }_{\mathrm{s}}^{\prime }\le 40.2{\mathrm{cm}}^{-1}$, and then it begins to deviate from linearity.

Fig. 7

Accuracy plots at 500 nm obtained from the phantom experiments. Each square identifies the estimated ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$ obtained for each of the 15 phantoms. The grid lines correspond to the given values.

Fig. 8

Linearity plots at 500 nm obtained from the phantom experiments. Four different views of the data are presented, corresponding to the changes of the estimated ${\mu }_{\mathrm{a}}$ against (a) the given ${\mu }_{\mathrm{a}}$ and (b) the given ${\mu }_{\mathrm{s}}^{\prime }$, as well as to the changes of the estimated ${\mu }_{\mathrm{s}}^{\prime }$ against (c) the given ${\mu }_{\mathrm{a}}$ and (b) the given ${\mu }_{\mathrm{s}}^{\prime }$. The letters and the numbers in the figure legends identify the scattering and absorption labels of the phantoms.

Figure 9 shows the plot of the noise level as a function of the input energy for both measurements of ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$ at 500 nm. In this case, measurements of ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$ require energies of 1.1 and $3.0\mu \mathrm{J}$, respectively, to reach a noise level of 6%. Figure 10 shows the results of the stability assay at 500 nm for ${\mu }_{\mathrm{s}}^{\prime }$ [Fig. 10(a)] and ${\mu }_{\mathrm{a}}$ [Fig. 10(b)]. The time courses are taken immediately after the instrument has been switched on, for a total of 1 h. The horizontal dashed lines represent a range of $\pm 0.5$ and $\pm 1.0\%$ with respect to the average value calculated in the last 15 min of the measurement period. A reasonable warm-up time seems to be 40 min, after which the instrument is stable in the assessment of both ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$ within $\pm 0.5\%$. Figure 11 shows the results of the reproducibility assay for both ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$ at 500 nm over five different days. All experimental conditions were kept as constant as possible (e.g., maintaining room temperature, allowing adequate warm-up time, etc.). The average dispersions of ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$ were 1.6 and 4.6%, with the maximum displacements of 3.7 and 8%, respectively.

Fig. 9

Plots of the noise levels for the estimations of ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$ at 500 nm expressed by the coefficient of variation CV calculated for different values of the energy injected into the phantoms.

Fig. 10

Stability plots obtained from the phantom experiments for (a) ${\mu }_{\mathrm{s}}^{\prime }$ and (b) ${\mu }_{\mathrm{a}}$ at 500 nm. The dashed lines in each figure correspond to $\pm 0.5$ and $\pm 1.0\%$ changes with respect to the average of estimated value over the last 15 min of measurements.

Fig. 11

Reproducibility plots obtained from the phantom experiments for ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$ at 500 nm. The plots represent the relative displacements of the estimated ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$ at each measurement day with respect to the average values calculated over five days.

4.2.

Animal Experiments

Figure 12 shows the typical time courses of the reduced scattering coefficient spectrum ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$ [Fig. 12(a)] and the absorption coefficient spectrum ${\mu }_{\mathrm{a}}(\lambda )$ [Fig. 12(b)] during KCl-induced CSD, obtained using the proposed method. In Fig. 12(a), the reduced scattering coefficient spectrum ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$ has a broad scattering spectrum, exhibiting a larger magnitude at shorter wavelengths. The estimated scattering spectrum also has two peaks in the wavelength range of 500 to 600 nm, which are probably due to scattering by red blood cells (RBCs).³⁷ In Fig. 12(b), the wavelength-dependence of ${\mu }_{\mathrm{a}}(\lambda )$ is dominated by the spectral characteristics of hemoglobin.³⁷ CSD is associated with a brief and small initial hypoperfusion followed by a profound hyperemia.^9,10 This pattern of hemodynamic response to CSD can be clearly observed in temporal changes in ${\mu }_{\mathrm{a}}(\lambda )$ after KCl stimulation, as shown in Fig. 12(b). Note that the elevations of both ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ in the wavelength range of 500 to 600 nm occurred repeatedly after the topical application of KCl.

Fig. 12

Typical time courses of (a) the reduced scattering coefficient spectrum ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$ and (b) the absorption coefficient spectrum ${\mu }_{\mathrm{a}}(\lambda )$ during KCl-induced cortical spreading depression (CSD) obtained using the proposed method.

Figure 13 shows the typical time courses of the reduced scattering coefficient ${\mu }_{\mathrm{s}}^{\prime }$ and the absorption coefficient ${\mu }_{\mathrm{a}}$ at specific wavelengths, ${\mathrm{StO}}_2$, and LFP during CSD. The negative peak of LFP was observed at 158 s after the application of KCl. The propagation speed of the first CSD was $p=2.62\mathrm{mm}/\min$. The estimated time of the negative peak of LFP at the position under the reflectance fiber probe was expected to be $t_c=272\mathrm{s}$ [dashed lines in Figs. 13(a) and 13(b)]. The temporal increases in ${\mu }_{\mathrm{a}}$ in Figs. 13(a), 13(b), and 13(c) are indicative of the hemodynamic response to CSD. The response of ${\mathrm{StO}}_2$ to the application of KCl may indicate the temporal change of arterial blood flow due to CSD. In contrast, the value of ${\mu }_{\mathrm{a}}$ at 800 nm decreases during CSD, as shown in Fig. 13(d), and is not correlated with ${\mu }_{\mathrm{a}}$ at 500, 570, and 585 nm, which is indicative of the change, independent of the hemodynamic response during CSD. The value of ${\mu }_{\mathrm{s}}^{\prime }$ at 570 nm during CSD is well correlated with that of ${\mu }_{\mathrm{a}}$ [Fig. 13(b)]. In the wavelength range of 530 to 570 nm, light is strongly absorbed by hemoglobin and is scattered by RBCs. Therefore, the changes in ${\mu }_{\mathrm{s}}^{\prime }$ at 570 nm may reflect the scattering by RBCs due to hemodynamics in the cerebral cortex. In contrast, ${\mu }_{\mathrm{s}}^{\prime }$ at 500 nm [Fig. 13(a)] and 585 nm [Fig. 13(c)] peaked at $t=276\mathrm{s}$ before the profound increase in ${\mu }_{\mathrm{a}}$, which corresponds to the estimated time of the negative peak of LFP at the position under the reflectance fiber probe. The second peaks of ${\mu }_{\mathrm{s}}^{\prime }$ observed at 500 and 585 nm, corresponding to the profound increase in ${\mu }_{\mathrm{a}}$, are probably due to the hemodynamic-related scattering change. On the other hand, ${\mu }_{\mathrm{s}}^{\prime }$ at 800 nm [Fig. 13(d)] decreases before and after the estimated time of the negative peak of LFP at the position under the reflectance fiber probe. This difference in the time course of ${\mu }_{\mathrm{s}}^{\prime }$ between the shorter-wavelength region (500 and 585 nm) and the longer-wavelength region (800 nm) indicates the change in the wavelength dependence of the scattering spectrum by CSD.

Fig. 13

Typical time courses of absorption coefficient ${\mu }_{\mathrm{a}}$ and reduced scattering coefficient ${\mu }_{\mathrm{s}}^{\prime }$ during KCl-induced CSD for (a) 500 nm, (b) 570 nm, (c) 585 nm, and (d) 800 nm. Tissue oxygen saturation (${\mathrm{StO}}_2$) and local field potential (LFP) are compared with ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ for each wavelength. The dashed lines indicate the estimated time of the negative peak of LFP at the position under the reflectance fiber probe.

Figure 14 shows the time courses of LFP measured by electrode 1, electrode 2, ${\mu }_{\mathrm{s}}^{\prime }$ (500), ${\mu }_{\mathrm{a}}$ (500), and ${\mathrm{StO}}_2$ during CSD. The estimated time of the negative peak of LFP at the position under the reflectance fiber probe calculated by the electrical signal of electrode 1 was 357 s, whereas that calculated by the signal of electrode 2 was 355 s. Therefore, the calculation of the estimated time for the negative peak of the LFP at the position under the reflectance fiber probe is independent of the electrode position. The first peak of ${\mu }_{\mathrm{s}}^{\prime }$ (500) was observed at 369 s, which corresponds to the estimated times of the negative peak of LFP obtained by electrodes 1 and 2.

Fig. 14

Time courses of LFP1 and LFP2 during KCl-induced CSD for 500 nm. Reduced scattering coefficient (${\mu }_{\mathrm{s}}^{\prime }$) at 500 nm, absorption coefficient (${\mu }_{\mathrm{a}}$) at 500 nm, and tissue oxygen saturation (${\mathrm{StO}}_2$) are compared with the signals of LFP1 and LFP2. The dashed lines indicate the estimated time of the negative peaks of LFP1 and LFP2 at the position under the reflectance fiber probe.

Figure 15 shows the estimated time of the negative peak of LFP at the position under the reflectance fiber probe and the first peak time of scattering ${\mu }_{\mathrm{s}}^{\prime }$ at 500 nm obtained from all nine samples. The estimated arrival time agrees well with the first peak time of scattering ${\mu }_{\mathrm{s}}^{\prime }$ at 500 nm. The correlation coefficient between the estimated time of negative peak of LFP at the position under the reflectance fiber probe and the first peak time of scattering ${\mu }_{\mathrm{s}}^{\prime }$ at 500 nm is $R=0.99$ ($p<0.0001$). This result indicates that the scattering change at this wavelength synchronizes with the dc shift of LFP. The negative dc shift of LFP has been said to be coincident with a rise in extracellular potassium and can evoke cell deformation generated by water movement between intracellular and extracellular compartments, and, hence, light scattering by tissue.^38,39 Therefore, the increase in ${\mu }_{\mathrm{s}}^{\prime }$ before the profound increase in ${\mu }_{\mathrm{a}}$ observed at both 500 and 585 nm is indicative of changes in light scattering by tissue.

Fig. 15

Estimated time of the negative peak of LFP at the position under the reflectance fiber probe and the first peak time of scattering ${\mu }_{\mathrm{s}}^{\prime }$ at 500 nm obtained from all nine samples.

The difference in the time course of ${\mu }_{\mathrm{s}}^{\prime }$ between the shorter-wavelength region (500 and 585 nm) and the longer-wavelength region (800 nm) is interpreted based on the change in the wavelength dependence of the scattering spectrum by CSD. Figure 16 shows the reduced scattering coefficient ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$ before, during, and after CSD obtained using the proposed method. The slope of scattering spectrum during CSD becomes steeper than that before or after CSD. This change in the slope of ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$ causes an increase in ${\mu }_{\mathrm{s}}^{\prime }$ at the shorter wavelength in the visible wavelength region (500 to 600 nm) and a decrease in ${\mu }_{\mathrm{s}}^{\prime }$ at the longer wavelength in the visible wavelength region (600 to 780 nm). The spectrum of the reduced scattering coefficient ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$ of biological tissues can be treated as a combination of ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$ for cellular and subcellular structures of different sizes.⁴⁰ Generally, the sizes of the cellular and subcellular structures in biological tissues are distributed as follows: membranes, $<0.01\mu \mathrm{m}$;⁴¹ ribosomes, $<0.01\mu \mathrm{m}$;⁴² vesicles, 0.1 to $0.5\mu \mathrm{m}$;⁴¹ lysosomes, 0.1 to $0.5\mu \mathrm{m}$;⁴³ mitochondria, 1 to $2\mu \mathrm{m}$;⁴⁰ nuclei, 5 to $10\mu \mathrm{m}$;⁴⁰ and cells, 5 to $75\mu \mathrm{m}$.⁴⁰ Figure 17 shows the spectra of the reduced scattering coefficient ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$ calculated by the Mie theory for spheres of various sizes. In the Mie-theory-based calculation, the refractive indices of a sphere and the surrounding medium were set to be 1.46 and 1.35 at a volume concentration of 2%. The slope of ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$ decreases as the diameter of the sphere $d$ increases. The entire spectrum of ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$ increases as the diameter of the sphere $d$ increases in the range of $d=0.01$ to $0.2\mu \mathrm{m}$, but decreases as the diameter of the sphere $d$ increases in the range of $d=0.6$ to $10.0\mu \mathrm{m}$. Therefore, the dependence of ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$ on the particle size in the visible wavelength region shown in Fig. 17 implies that the volume increases in structures $<0.2\mu \mathrm{m}$ (membranes, ribosomes, and small vesicles) contribute to the increase in ${\mu }_{\mathrm{s}}^{\prime }$ at the shorter wavelength in the visible wavelength region, whereas the volume increases in structures $>0.6\mu \mathrm{m}$ (mitochondria, nuclei, and cells) contribute to the decrease in ${\mu }_{\mathrm{s}}^{\prime }$ in the longer wavelength in the visible wavelength region. If the volume increases in all cellular and subcellular structures occur simultaneously, the net scattering spectrum will have a greater slope of ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$. On the other hand, it has been reported that the slope of the scattering spectrum obtained from the cultured cells during apoptosis, in which the cellular and subcellular shrinkages occur, becomes more gentle than that for nonapoptotic cells.⁴⁴ Therefore, the changes in the slope of ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$ in the visible wavelength region during CSD obtained by the proposed method indicate the swelling of cellular and subcellular structures generated by water movement between intracellular and extracellular compartments induced by depolarization due to the temporal depression of the neuronal bioelectrical activity. On the other hand, the slope of ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$ in the NIR region in Fig. 16 appears to be the same at baseline and during and after CSD. As shown in Fig. 17, the slope of ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$ in the NIR region (800 to 900 nm) is almost independent of the diameter of the sphere except for the case of $d=0.2\mu \mathrm{m}$. As we mentioned above, the spectrum of the reduced scattering coefficient can be expressed as a combination of ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$ for the cellular and subcellular structures of different sizes. Therefore, it is likely that the slope of ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$ in the NIR region is constant even if that in the visible wavelength region is changed due to the morphological changes in the cellular and subcellular structure during CSD. Kohl et al.⁴⁵ assumed that any change in ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$ of the tissue does not alter its wavelength dependence, which can be justified for ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$ in the NIR region calculated by Mie and Rayleigh scattering theory for the size and relative refractive indices of the scattering components in tissue.⁴⁶

Fig. 16

Change in the spectrum of the reduced scattering coefficient ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$ before, during, and after CSD obtained using the proposed method.

Fig. 17

Reduced scattering coefficient ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$ calculated by the Mie theory for spheres of various sizes.

As shown in Fig. 12(a), both spectral features of scattering by tissue and RBCs appeared in the estimated spectrum of ${\mu }_{\mathrm{s}}^{\prime }(\lambda )$. If the estimated reduced scattering spectrum is separated into the spectrum of the tissue itself and that of RBCs, the size distribution of scatter in the tissue may be calculated by applying the least-squares fitting with the scattering spectra shown in Fig. 17 to the extracted spectrum of the tissue itself. This issue should be investigated in the future.

The proposed technique works properly when the optical fiber probe is directly in contact with the surface of the exposed brain. In addition, it was necessary to contact the ball-shaped LFP electrode to the surface of the exposed brain. Therefore, the LFP electrode and the reflectance fiber probe cannot be at the same position. When the six sets of the spectrometer and an optical fiber are used for the surrounding detection, the six reflectance spectra can be separately obtained. In such a case, more valuable information about the arrival time of CSD at the reflectance fiber probe may be obtained with a more dispersed geometry. However, in the proposed instrument, the six individual reflectance spectra collected by the six surrounding fibers are integrated and detected by spectrometer 2 as a single reflectance spectrum $R_{\mathrm{s}}$. Spreading the distances between the central fiber and the six surrounding fibers can increase the time lags among the six individual signals since the CSD wave propagates across the measuring area under the reflectance fiber probe. In such a case, therefore, the signals of $R_{\mathrm{s}}$ will experience temporal blurring due to those time lags. This temporal blurring has the effect of averaging the time courses of $R_{\mathrm{s}}$ together. Temporal blurring may also complicate estimations of ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$. Therefore, we did not consider spreading the probes around at various angles. On the other hand, spreading the distances between the central fiber and the six surrounding fibers may be useful for increasing the sampling depth. It will be possible to evaluate ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ at deeper regions of the cerebral cortex during CSD by regulating the optical fiber geometry. This issue should be investigated in the future.

Kohl et al.⁴⁵ used a spectroscopic analysis to show changes in optical properties in rats during CSD. They treated the attenuation change $\mathrm{\Delta }A(\lambda )$ measured at the specific light-source-detector distance based on the modified Lambert-Beer law. A diffusion theory model of spatially resolved, steady-state diffuse reflectance was used to specify the differential path-length factors for evaluating changes in the chromophore concentrations and the scattering change. Their technique works precisely when the source-collector separation is much larger than 5 mm as the condition for the diffusion equation is fulfilled. For this constraint, it may be difficult to specify a position where the intrinsic optical signals (IOSs) change during CSD. On the other hand, the proposed method estimates the absolute values of ${\mu }_{\mathrm{s}}^{\prime }$ and ${\mu }_{\mathrm{a}}$ at each wavelength by using the empirical equation established from the results of Monte Carlo simulations. In addition, the proposed method is enabled even if the source-collector separation is much smaller than 5 mm since the Monte Carlo simulation is used for modeling light transport. This is advantageous in specifying a position where the IOSs change during CSD.

One major disadvantage of the proposed method is the lack of a spatial map for absorption and scattering spectra since it is a nonimaging technique. On the other hand, a potentially significant advantage of the proposed method over the conventional multispectral imaging techniques is the capability to perform rapid measurements of the absorption and scattering spectra. Most conventional multispectral imaging requires much time for the wavelength scanning operation. The proposed method will be useful for evaluating the fast IOSs and an in vivo real-time monitoring of brain tissue viability. The results of the present study indicate the potential applicability of the proposed method for evaluating the depolarization of in vivo brains based on the scattering change due to the intrinsic optical signal without the electrophysiological method.