2.1.

Scattering Coefficient Depends on White Matter Tract Orientation

Spinal cord gray matter consists mainly of neuron and glial cell bodies along with nonuniform combinations of myelinated and nonmyelinated nerve fibers. On the other hand, spinal cord white matter is built up almost entirely of highly organized myelinated nerve fibers. While the anisotropic nature of neural tissue is often ignored, it is generally accepted that overall, the myelinated axons in white matter lead to increased scattering in comparison with gray matter.^25–29 We show here that this is not always true and that the direction of light propagation with respect to white matter fiber tracts plays a profound role in the observed scattering and attenuation.

Specifically interesting, the white matter in the spinal cord has lower scattering in the longitudinal direction (along axons) and higher scattering in the radial direction (perpendicular to axons) compared with the gray matter present on the same slices. The results of these integrating sphere measurements are tabulated in Table 1. The difference in scattering power between the longitudinal and radial white matter was profound, with a 50% decrease measured in the longitudinal direction in all the tissues considered. The measurements in gray matter, however, produced similar results in both directions, suggesting that this effect arises due to the organized myelinated structures in white matter. While we measured ${\mu }_{\mathrm{s}}^{\prime }$ in each Cartesian direction ($x$, $y$, and $z$), we reduce the terms to radial and longitudinal due to the symmetry of the organized myelin structures resulting in equal ${\mu }_{s_x}^{\prime }$ and ${\mu }_{s_z}^{\prime }$. Moreover, our results in radial white matter are very much in agreement with previous measurements of ${\mu }_{\mathrm{s}}^{\prime }$ using a fiber optic probe.³⁰ In all of our integrating sphere measurements, the measured absorption coefficient in all tissue regions and sections were below $0.1{\mathrm{mm}}^{-1}$. These measurements are purposefully taken at 633 nm to minimize absorption contributions, to better isolate and analyze directional scattering. While the main result here is the observed ratio of the scattering power between the two directions, the absolute values may also be useful due to limited reports in spinal cord tissue.

Table 1

Measured values of μs′ in the longitudinal and radial directions at 633 nm.

We further validated the directional dependence of attenuation by imaging two 1-mm fixed macaque tissue samples in both the radial and longitudinal directions using a transmission microscope [Figs. 1(a) and 1(b)]. Indeed, we see the white matter regions have a directional dependence with respect to transmission, which is in good agreement with the inverse of the scattering relationship (white matter transmits more than gray matter in the longitudinal direction and less than gray matter in the radial direction). We also include images we have taken using coherent anti-Stokes Raman scattering (CARS) in primate spinal cord, in the various directions, showing the organization of the spinal cord segments at subcellular scale for reference [Figs. 1(c) and 1(d)].

Fig. 1

Transmission images of 1-mm spinal cord sections. (a) Transmission microscope image of 1-mm slice of macaque spinal cord in the longitudinal direction. There is higher transmission in white matter when imaging in this direction. (b) Transmission microscope image of 1 mm slice of macaque spinal cord in the radial direction. There is higher transmission in gray matter when imaging in this direction. (c) Backward-detected CARS images of white and gray matters in the longitudinal direction showing subcellular myelin composition. (d) Backward-detected CARS images of white and gray matters in the radial direction showing subcellular myelin composition. WL, white matter in longitudinal direction; GL, gray matter in longitudinal direction; WR, white matter in radial direction; GR, gray matter in radial direction.

As an additional and final validation that the reduced scattering coefficient is anisotropic in the white matter of the spinal cord, we performed the punch-through²³ method. We experimentally estimate the relative values of ${\mu }_{\mathrm{eff}}$ in perfused mouse and macaque spinal cord white and gray matter sections, also in the longitudinal and radial directions. Due to the limited thickness of mouse spinal cord, it is not possible to obtain tissue samples for which the diffusion approximation is valid and ${\mu }_{\mathrm{eff}}=\sqrt{{\mu }_a({\mu }_a+{\mu }_s(1-g)}$.³¹ Nevertheless, the initial exponential decrease is related to ${\mu }_{\mathrm{eff}}$. As seen in Table 2, we found the light traveling along the white matter tract axis is also roughly 50% less attenuated than light traveling perpendicular to the white matter tract. We again observed the lack of a directional preference in the gray matter structures, due once again to the lack of organized myelin. What is important to take away from these observations is the ratio of the coefficients between the two directions.

Table 2

Measured values for μeff in the longitudinal and radial directions at 594 nm.

3.1.

Simulating 3-D Optogenetic Activation Volumes Using Multidirectional Scattering Coefficients

Using the different experimental evidences, we have shown that the scattering coefficient along the myelin fibers is approximately half the value obtained across the myelin fibers. Here, we investigate the impact on the light distribution in tissue by performing simplified light propagation simulations in spinal cord tissue volumes, showing the repercussions of directional light scattering on the optogenetic activation volume using an adjacent optical fiber illumination source. To do this, we have edited an existing open-source 3-D Monte Carlo package (mcxyz)²⁴ to use multidirectional scattering coefficients (see Sec. 5 for more information). It is understood that it would require a complete treatment modeling the cylindrical structures of the white matter to obtain accurate simulations for these anisotropic structures. However, the focus is to obtain an estimate of the volume of tissue illuminated and the impact of an anisotropic scattering coefficient on that volume’s eccentricity. The results of these simulations with 10-mW laser power at 473 nm (channel rhodopsin excitation wavelength), in the various species’ spinal cords can be seen in Fig. 2. Described further in Sec. 5, one of the reasons for using the mcxyz program as a base for our modification is the package’s ability to generate generic tissue volumes with user-defined chromophore absorption (i.e., hemoglobin), at any given wavelength, as well as its ability to automatically calculate the relative scattering coefficient at any wavelength (herein 473 nm) in reference to a measured one (herein 633 nm).

Fig. 2

Monte Carlo simulation of fluence rate in different mammalian spinal cords using modified mcxyz. (a) Light deposition in mouse spinal cord. Also included here is the color-coded tissue type for each of the simulations and the legend for the optogenetic activation volume. (b) Light deposition in macaque spinal cord. (c) Light deposition in human spinal cord. (I) Tissue-type defined volume with photon trajectory in longitudinal plane. (II) Tissue-type defined volume with photon trajectory in radial plane. (III) Results of simulation in longitudinal plane with activation circles for optogenetic planning. (IV) Results of simulation in radial plane with activation circles for optogenetic planning. Input power is 10 mW in all simulations. Scale bars in (III) are 1 mm.

The spinal cords are to scale in this simulation and we can see here the obvious difficulties and importance of accurate planning in translating optogenetics to larger animals. For the case of the mouse simulation, ${\mu }_{\mathrm{s}}^{\prime }$ values from the macaque spinal cord were used, as small size made it too difficult to separately measure ${\mu }_{\mathrm{s}}^{\prime }$ in the white and gray matter regions. We believe this to be a satisfactory assumption based on the similarity in measured ${\mu }_{\mathrm{eff}}$ in the macaque and mouse spinal cord. To elaborate on the implications of illumination volume in the mouse spinal cord, 10 mW is enough optical power to activate channel rhodopsin (activation intensity: $1{\mathrm{mW}/\mathrm{mm}}^2$)^32,33 in every laminae down to the upper edges of the laminae 7. This corresponds to about 1.2 mm of tissue being activated in the dorsal to ventral direction, when the fiber output is perpendicular to the myelin sheaths. In the longitudinal direction, with the same fiber orientation, channel rhodopsin can be activated up to 1.6 mm away from the fiber tip’s midline, in both directions. A cervical vertebrae length in mice is about $800\mu \mathrm{m}$, meaning that effective simulations that take into account anisotropic scattering are important for optogenetic planning, especially if only specific vertebrae are to be optogenetically investigated.³⁴ In the macaque and human, this illumination scheme does not penetrate deep enough to activate even the first laminae. While increasing input power is an option, more elaborate fiber optic placement will become a critical factor in planning the optogenetic experiments in larger animals, and the observations provided herein will be useful for this.

3.2.

Myelinated Axons May Act as Naturally Occurring Optical Waveguides

Perhaps the most interesting theory for the observed anisotropy was proposed by Kumar et al., who put forth the idea of myelin sheaths acting as natural optical waveguides.³⁵ While their hypothesis was only investigated theoretically, we believe this to be a plausible answer. As an initial test, we imaged a $500\text{-}\mu m$ and 1-mm-thick longitudinal spinal cord section in a transmission arrangement to see if the myelin sheaths were indeed visible and more bright than the axon core. At this thickness, without any waveguiding effects the sheaths should not be visible due to multiple scattering events. However, we did indeed observe myelin rings appearing brighter than the axon cores in the transmission orientation (see Appendix 1 for more information). These results, while not conclusive, suggest a clear need for further investigation of the waveguide hypothesis. Similarly, if a waveguiding effect is confirmed, it would indicate that the scattering coefficients we measured are not true reduced scattering coefficients since guiding effects are not assumed to be present for their derivations.

3.3.

Tissue Fixation Caused Negligible Effects in Data Analysis

In our work, we used perfused, paraformaldehyde (PFA)-fixed tissue to explicitly remove any hemoglobin absorption that could be present in the measurements. This allowed us to directly compare the attenuation and scattering power of the tissue in the different directions without compounding factors. While tissue fixation has been reported to change the optical properties of the sample, at 633 nm, the effects of formalin fixation have been shown to be minimal both in terms of birefringence profiles and measured scattering power.^36,37 We strengthen this claim by comparing our fresh and fixed human tissue measurements using the integrating sphere setup (see Table 1 for results), showing that fixation does not significantly alter the absolute values or directional ratio of the measured reduced scattering coefficients at this wavelength.

3.4.

Spinal Cord Measurements Along with DTI Tractography of the Brain Could Make Present Myelin Information Translatable

Due to the symmetry of the myelin sheath and the spinal cord organization, we use the terminology radial and longitudinal rather than Cartesian units for ${\mu }_{\mathrm{s}}^{\prime }$ in $x$, $y$, $z$. We believe that this representation is more translational for expanding the technique to the brain along with diffuse tensor imaging (DTI) of white matter tractography.³⁸

Some work has been done in measuring the optical properties of brain tissue in all 3-D in rat using discrete raster-scanned slices with a similar integrating sphere arrangement used here.³⁹ This could offer an interesting opportunity to compare a full 3-D Monte Carlo simulation using these measured values for ${\mu }_{\mathrm{s}}^{\prime }$ in $x$, $y$, $z$ with a two-dimensional (2-D) symmetry-inspired ${\mu }_{\mathrm{s}}^{\prime }$ simulation in just the radial and longitudinal directions using noninvasive DTI, in the future goal of patient-specific simulations. This ability could improve both optogenetic experiments and clinical technologies, such as tissue oximeters.

5.1.

Scattering and Absorption Coefficient Calculation

The scattering and absorption coefficients were acquired using double-integrating-sphere setups, which measure the total diffuse reflection and transmission of a laser beam traveling through the tissue sample located between the two spheres. These measurements were performed on fixed macaque and human spinal cord tissue as well as fresh human tissue. This technique is routine and is explained in detail elsewhere.⁴⁰ All tissue samples were cut in 1-mm intervals in both the longitudinal direction (along length of the spinal cord) and in the radial direction (along width of spinal cord) and measured along the two directions using the integrating sphere arrangement. With the measures of the integrating spheres, the inverse adding doubling (IAD) algorithm was performed to estimate the optical properties of the tissue under investigation. Also a routine technique, the procedure and theory of the calculation can be read elsewhere.⁴¹ Attention was given to assure the tissue sections were indeed homogeneous in the areas of measurements, as is a requirement for IAD. The laser wavelength used for these measurements was 633 nm and the beam spot was about 1 mm. The laser wavelength was specifically chosen to diminish absorption effects caused by hemoglobin as to target the directional dependence of scattering.

5.2.

Attenuation Coefficient Estimation

Light transmission measurements were conducted with mouse and macaque spinal cord slices using a fiber punch-through method.²³ 594-nm (MBL-FN, Changchun New Industries Optoelectronics Technology, China) laser light was delivered to a $105\text{-}\mu \mathrm{m}$-diameter optical fiber (FG105UCA, Thorlabs). The fiber tip was then lowered into the tissue in $5\mu \mathrm{m}$ steps, and the light intensity was collected on the underside of the slice by a low numerical aperture (N.A.) objective ($10\times$, 0.25NA) and recorded by a CMOS camera (DMK23UP031, Imaging Source), seen in Fig. 3(a). Optical transmittance, the amount of light transmitted through a slice, decays exponentially with the tissue thickness and thereby its evolution can be parameterized by fitting the observed intensity profiles with a single exponential function, as seen in Fig. 3(b).

Fig. 3

Punch-through method. (a) Spinal cord slices were illuminated by 594-nm laser beam coupled to a multimode optical fiber. The fiber was lowered into the tissue and the light transmitted through a slide was collected on the underside by a low numerical aperture objective and detected using a CMOS camera. (b) Optical transmittance as a function of tissue thickness. Experimental measurements (black) and exponential fit (red line).

5.3.

3-D Monte Carlo Simulations with Multidirectional Scattering Coefficients

We achieve the simulations using an altered 3-D Monte Carlo program (mcxyz) provided open-source by Jacques, used previously in the brain.^24,39 This program is a verified variation of the 2-D Monte Carlo program created for multilayered tissue (MCML), used routinely for biological applications.⁴² Using a simple segmentation program, we converted our spinal cord models from an image stack to a tissue-type-defined 3-D volume for the simulation.

An immense advantage of the mcxyz program is the inclusion of Jacques’s method for creating generic tissues, allowing a highly malleable simulation based on few input parameters.²⁵ First and foremost, it allows the ability to use a measured scattering coefficient acquired at any visible or NIR wavelength (in our case 633 nm) and to then perform a simulation at another wavelength by calculating a scattering coefficient relative to that point (i.e., 473 nm). Similarly, while the measurements are also made at a lower absorbing wavelength and often in bloodless tissue, mcxyz allows us to simply add an estimated blood concentration to each tissue type separately, for the inclusion of hemoglobin absorption at the simulation wavelength. This has previously been used for simulations in the brain.⁴³ Ultimately, this allows us to simulate the light propagation in living tissue at traditional optogenetic activation wavelengths. Lastly, the program allows to input the light source properties such as: angle of incidence, incident laser wavelength, beam divergence, and beam starting position. We display herein the case of a $105\text{-}\mu \mathrm{m}$ multimode optical fiber with a N.A. of 0.22 situated against and perpendicular to the white matter tracts in the center of the dorsal spinal cord (Fig. 2). The laser wavelength used in this simulation was 473 nm (to make the simulation relevant to those using channel rhodopsin) and a blood volume of 2.8% with an oxygen saturation: 62% was deployed, as was described for brain tissue in other work.^25,43

To accommodate our findings of a directional scattering dependence, we included a small alteration in the Monte Carlo action of the mcxyz program where rather than having a sole scattering coefficient for each pixel in the volume, there exists one for each 3-D direction. During the process of the photon step, where the scattering coefficient is considered, the three pixel-corresponding scattering coefficients are linearly combined using the unit vector of the photon’s current propagating direction, and from there the program resumes normally. The modified version has been validated to give identical results to the original mcxyz code when all 3-D scattering coefficients are equal.

5.4.

Sample Preparation

All animal tissues were obtained according to protocols that had been approved by the Institutional Animal Care and Use Committee (Comité de Protection des Animaux de l’Université Laval), and all procedures involving animals and their care were made in accordance with the Canadian Council on Animal Care’s Guide to the Care and Use of Experimental Animals. Human postmortem brain tissues were obtained from the human brain bank of the Centre de Recherche de l’Institut Universitaire en Santé Mentale de Québec (CERVO), which required informed consent before donation of tissues. CERVO’s Ethics Committee approved the brain collection, storage, and handling procedures, which were described in detail elsewhere.⁴⁴

6.1.

Myelin May Act as an Optical Waveguide

Recently, it has been theorized that myelin sheaths may act as natural optical waveguides.³⁵ To experimentally investigate this we imaged thick sections of longitudinal spinal cord where the myelin sheaths are highly organized at high magnification, in a transmission arrangement. While we have not exhausted the possibilities of other optical effects, it looks as though the myelin is indeed transmitting more light in the sheath, as opposed to the axon, which matches the theoretical investigation (see Fig. 4). We tried two different thicknesses and two different sources, and the pattern of brighter myelin sheaths remained in all cases.

Fig. 4

Possible transmission of light through myelin sheaths in thick longitudinal slices of spinal cord. (a) Optical arrangement for the imaging experiment. Light was collected on the underside of the slice by a $40\times$ objective and recorded by a CMOS cameras (DMK 23UP031, imaging source). (b) Magnified and contrasted image of bright myelin sheath and dark axon center from (c). (c) $500\text{-}\mu \mathrm{m}$ longitudinal slice illuminated using a 594-nm fiber laser source (MBL-FN, Changchun New Industries Optoelectronics Technology, China). Inset square shows location of zoomed image in (b). (d) 1-mm longitudinal slice illuminated with a fibered white lamp source (SLS201L, Thorlabs, New Jersey).