2.1.

In Vivo Experiments

Nine Sprague–Dawley rats (275 to 450 g) were used in this part. All experimental procedures were approved by the Animal Care Committee at Rutgers University, New Jersey. Under a single injection of urethane anesthesia ($1.25\mathrm{g}/\mathrm{kg}$, IP), a $4\times 6\mathrm{mm}$ cranial opening was made immediately rostral to the bregma on the right side of the central fissure [Fig. 1(a)]. Dexamethasone ($3\mathrm{mg}/\mathrm{kg}$, IM) was injected prior to surgery to reduce edema of the brain. Some protrusion of the brain pressing against the edge of the skull through the cranial opening was allowed to stabilize the tissue and minimize the motion artifact due to respiration and cardiac pulsation. A slight traction on the tail further reduced the brain motion in some cases. Connective tissue and any blood clot over the surface were cleaned without removing the dura mater. Surgical wax was applied to seal between the dura and the skull around the edges of the opening, and a shallow pool of normal saline ($<1$-mm high) was made to prevent dehydration. The rectal temperature was continuously monitored and maintained at 36°C using a temperature regulated heating pad underneath the animal. The end-tidal ${\mathrm{CO}}_2$ was observed to stay within the normal range throughout the experiment, which usually lasted about 6 to 7 h including the surgery.

Fig. 1

(a) Sketch of the cranial opening made rostral to the bregma on the right side of the central fissure. (b) The preparation used to measure light intensities in the rat brain.

After positioning the head perfectly horizontally in the stereotaxic frame, a 26-g needle was slowly inserted from below at a point a few millimeters right of the trachea, until the tip of the needle passed through a hole at the base of the skull and reached a few millimeters below the cortical surface in the center of the skull opening [Fig. 1(b)]. Care was taken to stay away from major blood vessels of the cortex. An optical fiber ($\varnothing 100\mu \text{m}$, graded index, Newport Inc., CA) was desheathed from its plastic insulation and cladding for about 5 cm of its tip. The fiber tip was polished flat by three different grain size sand papers in a decreasing order (3, 1, and 0.5 μm), attached to a micromanipulator facing up, and inserted through the lower end of the needle until its tip was leveled with the pial surface under the dura. The fiber tip was visible through the dura under $40\times$ microscopic vision. A free-air, NIR laser beam (74 mW, 830 nm, DLS-500-830FS-100, StockerYale, Canada) with a circular footprint of 0.4 mm in diameter was aimed at the fiber tip from 13.5 cm above the cortex. The light power entering the polished end of the optical fiber was measured with a photodiode and a current amplifier is connected to the other end of the fiber. The laser activation pattern and data acquisition were controlled through matlab™.

A train of NIR pulses (10 ms pulse width, 25 pulses at 0.5-s intervals) was sent to the cortex while the light intensities were measured at depths from 0 to 2500 μm in steps of 50 or 100 μm from the dura. Pulsed laser was preferred over continuous exposure to avoid overheating the tissue. For each depth of the fiber tip position, the laser source was horizontally moved in a rostral or caudal direction in steps of 50 or 100 μm up to 1000 μm away from the fiber axis while repeating the light measurements. Thus, an intensity map was developed in a parasagittal plane for an area of $1000\times 2500\mu \text{m}$. Due to the vertical placement of the optical fiber, photons traveling from top to bottom were collected more efficiently than those traveling in other directions. Thus, it should be noted that the light intensity measurements were directionally biased in this study.

The laser intensity profile at a distance of 13.5 cm was verified using a commercial photodiode (G9842, Hamamatsu, GaAs PIN photodiode, $\varnothing 0.08\mathrm{mm}$) as shown in Fig. 4(a) on top. The profile was Gaussian with a circular cross section. The radius was taken as the $\surd 2\sigma$ value of the Gaussian intensity curve, which is the horizontal distance where the intensity profile drops down to $1/e$ of its peak in the center. This diameter was equal to that of a flat profile beam with the same peak power intensity and the same total power as the Gaussian profile laser that was used. The light power that was collected by the optical fiber just underneath the dura mater was measured as the calibration value. All measurements inside the brain were normalized by this maximum light intensity level. If the fiber optic tip was broken or damaged during an experiment, it was prepared again by sand papering; then the calibration measurement was repeated and used as normalization value for further experiments. Measurements of the light power obtained by placing the fiber in air were compared with the subdural values to estimate the contribution of the dura matter to NIR light attenuation.

2.2.

Data Processing

The average of 25 pulses in the laser train was taken as the representative light intensity measurement at the corresponding point in the brain. This averaging step substantially reduced the periodic variations due to cardiac and respiration artifacts. The trial was repeated when the animal had a sigh, which caused a small but significant mechanical displacement of the brain.

The exact peak position of the light intensity profile in the horizontal direction usually occurred between two adjacent measurement points, although we decreased the step size to 50 μm near the center. Cubic spline interpretation was used to find the exact horizontal position of the maximum as well as all the other rostrocaudal points at 50 μm steps from the new horizontal zero point.

2.3.

In Vitro Experiments

The description of in vitro experiments can be found elsewhere¹⁹ and they are summarized, here, for clarity of this paper. Seven Sprague–Dawley rats were used for in vitro measurements. The brain was explanted quickly after sacrificing the animal and placed in sucrose cutting media (0.75 mmol KCl, 0.625 mmol ${\mathrm{NaH}}_2{\mathrm{PO}}_4$, 6.5 mmol $\mathrm{NaHC}{\mathrm{O}}_3$, 2.5 mmol glucose, 0.25 mmol ${\mathrm{MgCl}}_2$, 50.39 mmol sucrose, 0.5 mmol $\mathrm{CaC}{\mathrm{l}}_2$, $\sim 0°\mathrm{C}$). Horizontal brain slices were cut using a Vibratome at various thicknesses from 300 to 1500 μm. The sliced samples were kept in the sucrose cutting media for less than 3 h until in vitro measurements were completed.

A commercial photodiode (G9842) was used to measure the transmitted light intensity through the brain slices. The photodiode was first secured at the bottom of a $9\times 9\mathrm{mm}$ plastic chamber such that the photodiode active area was even with the bottom surface. The same free-air laser source of the in vivo experiments was aimed at the surface of the tissue slab from above and aligned with the center of the photodiode.

The incident light power was measured first with no neural tissue present. The brain slices were then laid out on the bottom of the chamber in direct contact with the photodiode. The samples were kept moist with normal saline during measurements, which took maximally a few minutes. The horizontal extent of the tissue sample orthogonal to the incident light beam was assumed to be sufficiently large to neglect the boundary effects. The transmittance values were obtained for various thicknesses of the gray matter samples in the center of the laser beam.

2.4.

Monte Carlo Simulations

A public domain software was utilized for the Monte Carlo simulations.²⁰ An infinitely narrow photon beam was vertically aimed at an infinitely wide tissue (Fig. 2). Each layer was characterized by the refractive index ($n$), the absorption coefficient (${\mu }_a$), the scattering coefficient (${\mu }_s$), the anisotropy factor ($g$), and the thickness of the layer ($d$). The simulation software keeps a score of the photon densities on a three-dimensional grid inside the tissue (fluence) and across the surfaces of the medium boundaries, i.e., reflectance at the entry surface and transmittance on the opposite side.

Fig. 2

The three-dimensional model geometry for Monte Carlo simulations. Tissue slice extends infinitely in the two-dimensional (2-D) horizontal plane.

Neural tissue has an inhomogeneous structure with multiple regions of different scattering coefficients.¹⁸ From our measurement of light intensity in the cortex, it was also evident that multiple layers with varying slopes of the photon density curve existed in deep locations ($>1500\mu \text{m}$).

The scattering coefficient was estimated from the averaged NIR light intensity curve. The scattering coefficient was adjusted iteratively in the simulations to curve fit the light intensity values measured during the in vivo and in vitro experiments ($T_{\text{exp}}$) as a function of depth in the beam center. The transmittance for an infinitely narrow beam size (Monte Carlo modeling of light transport in multi-layered tissues component of software package) was computed first and then the results were convolved (convolution program component) with the Gaussian beam profile to simulate the experimental case. Finally, the scattering coefficient was incrementally adjusted while repeating the simulations until a minimum was found for the average percent error for all depths (or slice thicknesses for the in vitro data) between the simulated ($T_{\text{sim}}$) and experimental curves ($T_{\text{exp}}$).

Other parameters of simulation included the following: number of photons 1,000,000, refractory index for saline $n_s=1.33$ and gray matter $n_g=1.38$^10,18; absorption coefficient for biological tissue ${\mu }_a{=0.1\mathrm{cm}}^{-1}$ (Ref. 18); and anisotropy factor $g=0.9$.^10,18 All simulations were conducted on a computer with Intel 2.3 GHz processor and each run took less than 3 min.

3.1.

In Vivo Experiments

Photon density decreased exponentially with depth from the dura at the center of the laser beam (Fig. 3). Photon densities were $79\pm 4.5\%$ at 100 μm and $0.04\pm 0.003\%$ ($\text{mean}\pm \mathrm{SE}$) at 3000 μm into the cerebrum. In order to exclude the effect of the dura, the light intensities were plotted in percentages as a fraction of the subdural light intensity in the beam center. This was necessary to factor out the large variations we noticed in the dura thickness and the subdural light intensities between the animals. Light attenuation by the dura was calculated separately and found to be $58\pm 4\%$ by comparing the subdural and in-air measurements. Results obtained from postmortem animals (red curve in Fig. 3) were significantly different ($p\le 0.01$) from that of the alive photon densities between 100 and 1500 μm.

Fig. 3

The average NIR light intensity inside the brain as a function of depth at the center of the laser beam. (×) Average data from 16 penetrations in nine live animals and (▪) data shortly after termination in six animals. (Δ) Average in vitro transmittance as a function of slice thickness ($N=8$). The in vivo light intensities from 1500 to 3000 μm are reported in the inset on a larger vertical scale.

Figure 4(a) shows the two-dimensional (2-D) illumination profile in the parasagittal plane of the measurements. In the horizontal direction near the surface, the light intensity profile drops quickly, almost following a similar course to the laser intensity. In deeper locations, however, the light intensity profile becomes more spread horizontally [Fig. 4(b)]. The illumination contours extend a few times the laser diameter in the vertical direction and becomes wider at depths, resembling the shape of a bulb. A possible explanation for this shape is that the scattering increases in deeper regions of the brain.

Fig. 4

(a) Two-dimensional illumination inside the rat brain in a parasagittal plane. Results shown are the average data from four animals. Measurements were made in steps of 100 μm in the vertical and horizontal directions and then interpolated for intermediate points. The light intensities are normalized by the intensity measured subdurally in the beam center and expressed on a logarithmic scale. Measurements were made in half the plane since the data are vertically symmetrical. The bell shaped curve on the top shows the laser intensity profile at the dura surface. (b) Horizontal spread of the illumination profile at 2100 μm from dura.

3.2.

In Vitro Experiments

The transmittance measurement for each slice thickness was obtained by averaging measurements from seven animals (green curve in Fig. 3). Specifically, the transmittance values were $65.0\pm 0.02\%$, $44.9\pm 0.02\%$, $32.2\pm 0.02\%$, $22.7\pm 0.03\%$, $14.1\pm 0.01\%$, $7.78\pm 0.005\%$, $5.38\pm 0.005\%$, and $3.02\pm 0.004\%$ ($\mathrm{mean}\pm \mathrm{SD}$) at thicknesses of 300, 400, 500, 600, 800, 1000, 1200, and 1500 μm respectively. These in vitro values were much larger than the light intensities obtained from live and postmortem animals (paired $t$-test, $p\le 0.01$). Note that the in vitro experiments were normalized with the light intensity received by the photodiode without any tissue present, whereas in vivo measurements were normalized to the subdural light intensity. Using the Fresnel equation [$R={(n1-n2)}^2/{(n1+n2)}^2$, where $n1=1$ for air and $n2=1.38$ for neural], the reflection for a light beam entering the tissue perpendicularly was calculated as 2.55%, and neglected in the in vitro plot. This means the reflected light at the surface of entry was lumped into the attenuation by the tissue.

3.3.

Monte Carlo Simulations

The scattering coefficient for in vitro samples was estimated by fitting simulated transmittance curves to the measured values and found to be $108{\mathrm{cm}}^{-1}$.¹⁹ The average deviation from the experimental curve was 9.9% for the optimal fit. The mean error would approximately double if the scattering coefficient was set to 90 or ${125\mathrm{cm}}^{-1}$ on each side of the optimal value. Thus, the optimal value of ${\mu }_s$ (${108\mathrm{cm}}^{-1}$) clearly produced the minimum error within this range. Simulations were repeated using two extreme values of absorption coefficient to investigate the effect of ${\mu }_a$ on transmittance.¹⁸ The average deviation from the in vitro transmittance curve was 9.4% at ${\mu }_a=0.01$ and ${1.0\mathrm{cm}}^{-1}$, which was smaller than the mean error at optimal ${\mu }_s$. This indicated that ${\mu }_a$ had a minimal effect on the simulated transmittance. Therefore, we varied the scattering coefficient alone and fixed ${\mu }_a$ at a typical value of ${0.1\mathrm{cm}}^{-1}$ (Ref. 21) in further simulations.

The scattering coefficient was estimated also from in vivo data using the Monte Carlo method. This time, however, the curves appeared to have multiple regions with different exponentials. Figure 5 depicts the goodness of the fit using three different values of the scattering coefficient (${\mu }_s=125$, 175, or ${370\mathrm{cm}}^{-1}$). Two main regions with different optical properties existed as shown in the figure; first from the surface down to 1500 μm and the second from 1500 to 3000 μm. The photon intensity curve could be approximated with a single scattering coefficient (${125\mathrm{cm}}^{-1}$) in the first region with an average error of 7.42% only. If the measurements at 100 to 400 μm were excluded, the average error would reduce to 3.81%. In the second region, multiple layers with different coefficients were present. The average deviations from the experimental curve were 77.5%, 36.5%, and 31.2% for scattering coefficient values of 125, 175, ${370\mathrm{cm}}^{-1}$, respectively. Each scattering value was good only for a small section of the curve but not for the entire range. We concluded that the optimal scattering coefficient varied between 125 and ${370\mathrm{cm}}^{-1}$ at depths of 1500 to 3000 μm in the rat brain.

Fig. 5

Photon density simulations using different scattering coefficients. The simulated values are fitted to the experimental group averages by adjusting the scattering coefficient. Experimental data (•, blue), simulated data using ${\mu }_s{=125\mathrm{cm}}^{-1}$ (×), ${\mu }_s{=175\mathrm{cm}}^{-1}$ (Δ), and ${\mu }_s{=370\mathrm{cm}}^{-1}$ (▪). The data points from 1000 to 3000 μm are reported in the inset on a larger vertical scale.