Backscattering Mueller matrix polarimetry estimates microscale anisotropy and orientation in complex brain tissue structure

Abstract.

Purpose

Diffusion magnetic resonance imaging (dMRI) quantitatively estimates brain microstructure, diffusion tractography being one clinically utilized framework. To advance such dMRI approaches, direct quantitative comparisons between microscale anisotropy and orientation are imperative. Complete backscattering Mueller matrix polarized light imaging (PLI) enables the imaging of thin and thick tissue specimens to acquire numerous optical metrics not possible through conventional transmission PLI methods. By comparing complete PLI to dMRI within the ferret optic chiasm (OC), we may investigate the potential of this PLI technique as a dMRI validation tool and gain insight into the microstructural and orientational sensitivity of this imaging method in different tissue thicknesses.

Approach

Post-mortem ferret brain tissue samples (whole brain, $n=1$ and OC, $n=3$) were imaged with both dMRI and complete backscattering Mueller matrix PLI. The specimens were sectioned and then reimaged with PLI. Region of interest and correlation analyses were performed on scalar metrics and orientation vectors of both dMRI and PLI in the coherent optic nerve and crossing chiasm.

Results

Optical retardance and dMRI fractional anisotropy showed similar trends between metric values and were strongly correlated, indicating a bias to macroscale architecture in retardance. Thick tissue displays comparable orientation between the diattenuation angle and dMRI fiber orientation distribution glyphs that are not evident in the retardance angle.

Conclusions

We demonstrate that backscattering Mueller matrix PLI shows potential as a tool for microstructural dMRI validation in thick tissue specimens. Performing complete polarimetry can provide directional characterization and potentially microscale anisotropy information not available by conventional PLI alone.

1. Introduction

Tractography, a technique enabled by diffusion magnetic resonance imaging (dMRI), offers the unique ability to non-invasively visualize white matter pathways within the brain. Used clinically for preoperative planning in neurosurgery, tractography provides an indirect way to view structural connections and white matter microstructure. dMRI and its associated frameworks estimate microscale metrics of tissues and map fiber tract pathways within the brain by measuring the displacement of water. dMRI measures tissue microstructure, referring to the small-scale arrangement of neurons within brain tissue; however, dMRI may be affected by macrostructure, referring to the larger-scale gross tissue architecture. Although the most common dMRI technique, diffusion tensor imaging (DTI), captures the anisotropic motion of water molecules within brain tissue,^1,2 it can be biased by macrostructural architecture.^3,4 Consequently, DTI metrics derived from diffusion tensor eigenvectors such as fractional anisotropy (FA) lack biological specificity and are unable to capture complex geometry such as crossing fibers. Recently, more sophisticated techniques have been developed to represent crossing fibers. Most notably, detailed representations of microstructural geometry have given rise to improved representations of orientation capable of tracking fiber pathways such as constrained spherical deconvolution (CSD) fiber orientation methods which produce CSD tractography and fiber orientation distribution (FOD) glyphs. In parallel, novel dMRI frameworks with greater complexity may be able to capture features of microscale anisotropy unbiased by macroscale architecture. For example, the mean apparent propagator MRI metric, propagator anisotropy (PA), reports high values of anisotropy in crossing fiber regions.⁵ In addition, double diffusion encoding microscale-anisotropy has been combined with tractography to improve the accuracy of tract mapping.⁶ The advancement of such dMRI approaches relies on validation by direct quantitative comparisons between estimates of microscale anisotropy and orientation within brain tissue structures.⁷

Polarized light imaging (PLI) is among the leading microscopy techniques implemented for the validation of dMRI tractography and microstructure in brain tissue.^8–10 This microscopy method encompasses a range of imaging techniques that use polarization-sensitive detectors and illuminators to measure how polarized light interacts with a material. In the brain tissue, PLI derives signal from the birefringence of the myelin that surrounds axons within white matter regions.^11,12 PLI is unique for its stain-free contrast and the ability to capture quantitative measurements of angular features. Developments in the field, namely of 3D-PLI, have allowed for high-resolution quantitative microstructural imaging of fiber tracts within the brain that can be used to validate orientational features captured in dMRI.^13–18 However, conventional PLI methods used for dMRI validation have notable drawbacks. These methods are typically limited to transmission imaging of sectioned tissue specimens, typically capturing only transmittance, retardance, and fiber orientation maps while ignoring other potentially relevant polarization metrics. Through the use of a complete Mueller matrix PLI, more robust polarization metrics may be evaluated in brain tissue samples.¹⁹ If polarization methods can be extended to thick tissue mapping—for example, by reflectance microscopy—they will have a greater impact on the validation of inherently three-dimensional diffusion MRI metrics.

The Mueller matrix describes how the polarization state of light is altered after interacting with a material, in this case, tissue. This $4\times 4$ matrix can be decomposed to obtain individual optical metrics that characterize the biophysical properties of the tissue. Although Muller matrix PLI probes numerous optical effects including circular polarization metrics, this study focuses on a subset of polarization metrics: depolarization, retardance, and diattenuation. Optical depolarization measures the amount of polarization loss experienced by backscattered light. Retardance measures the difference in phase delay between orthogonal polarization states. This metric is proportional to birefringence and has been directly related to structural or compositional anisotropy in various tissue types.^20–23 Diattenuation measures the differences in intensity due to differential absorption and scattering between orthogonal polarization states. Compared with retardance, diattenuation is much less studied in biomedical applications of PLI, though notable studies have found biological and orientational relevance for this metric.^24–26 Retardance and diattenuation are measures of the anisotropy of material interaction with light, both generating angular components, retardance and diattenuation angles, that indicate fiber orientation in the context of brain imaging.

Backscattering Mueller matrix PLI allows for the evaluation of both thin-sectioned tissues used for conventional transmission-based PLI methods and bulk tissue samples. Thin tissue samples are often preferred due to the limited impact of scattering effects on the PLI signal. Signal acquired from thick tissue is influenced by wavelength-dependent depth penetration and is highly influenced by multiple scattering events within the tissue; however, thick tissue specimens are significantly easier to prepare for imaging. Furthermore, thick tissues more closely reflect the natural structural environment of the tissue and are unaffected by sectioning artifacts, which suggests that studies using these tissues are more accurate measures. Determining whether thick tissue specimens show similar trends to recapitulate results found in thin-sectioned tissue may allow for a more accessible and accurate means of validation for anisotropic and orientational information within brain tissue regions of varying complexity.

The ability to capture complex fiber structures with high fidelity is necessary in brain imaging due to the fine microstructural geometry of brain tissue. The optic chiasm (OC), a well-characterized brain tissue structure where the decussation of visual signals occurs, is one example of a complex brain tissue structure. The OC contains two optic nerves both composed of coherent bundles of nerve fibers that cross at the chiasm and then separate into two optic tracts, forming the shape of an “X.” The coherent regions contain both macrostructural architecture and microstructural geometry, whereas the crossing region contains rich microstructure due to the intermixing of two distinct fiber orientations.^16,27,28 By examining scalar and angular PLI metrics in this brain tissue structure, we may determine the degree of microstructural sensitivity or macrostructural bias as well as orientational sensitivity within each metric.

In this study, we compare anisotropy and orientation estimates across backscattering Mueller matrix PLI and dMRI frameworks within the coherent fibers of the optic nerve and crossing fibers of the OC. To accomplish this, the scalar PLI metrics of retardance, diattenuation, and depolarization are directly compared with dMRI metrics of FA and PA to evaluate the relative sensitivity of each PLI metric to microscale anisotropy and the influence of tissue architecture on each. Angular PLI metrics are compared with dMRI orientational metrics to assess the ability to capture fiber orientation within the coherent and crossing regions. In addition, we evaluate the effect of tissue thickness on PLI signal to isolate the effects of light scattering and determine the capability of reflectance polarimetry to report microstructural features of thick tissue specimens for dMRI validation. Ultimately, advancing these PLI techniques will enable a more robust and widely applicable validation of dMRI frameworks.

2. Methods

2.1. Specimen Preparation

An overview of the methods is presented in Fig. 1. Ferret brain specimens (whole brain, $n=1$ and OC, $n=3$) were imaged during this study. Adult male ferrets underwent transcardial perfusion and brain specimens were fixed with 4% paraformaldehyde solution for 8 to 10 days, then stored in a solution containing 0.1% sodium azide in phosphate-buffered saline.²⁹ Optic tracts were dissected from three ferret brains to isolate the OC structure, which was imaged with MRI and PLI.

Fig. 1.

Overview of data acquisition methods. One whole brain and three OC structures were scanned ex vivo to acquire relevant dMRI data. The OC specimens were imaged with PLI to acquire depolarization, diattenuation, and retardance to compare dMRI and PLI metrics. Backscattering PLI setup and imaging locations in the OC are shown.

Following imaging, thin slices were prepared by the University of Arizona Comparative Pathology Core Laboratory. Briefly, the specimens were processed, embedded in paraffin, and then sectioned using a microtome to cut slices with $6\mu \mathrm{m}$ thickness, which were collected on charged slides without staining or coverslipping. These thin-slice specimens were then imaged using PLI and for comparison with the thick tissue images. One slide was stained with DiI and imaged with fluorescence microscopy using 4× and 10× objectives.

2.2. Diffusion MRI Acquisition

All ferret specimens were imaged using a Bruker 7T Biospec 70/20 pre-clinical MRI scanner to acquire 3D echo planar imaging volumes using a high angular resolution diffusion imaging encoding scheme. One whole ferret brain and three OC structures were imaged for this study. The details of both scans are shown in Table 1.

Table 1.

MRI acquisition specifications.

Specifications	Whole brain ($n=1$)	OC specimens ($n=3$)
Software	ParaVision 6.0.1	ParaVision 360 3.2
Transmitting coil	35-mm quadrature birdcage	86-mm quadrature birdcage
Receiving coil	35-mm quadrature birdcage	10-mm single loop
$B$-values ($\mathrm{s}/{\mathrm{mm}}^2$)	0, 1500, 3000, 4500, 6000, and 9000	0, 1500, 3000, 4500, and 6000
Echo time (ms)	52.25	40
Repetition time (ms)	1000	800
Segments	8	4
Acquisition matrix (voxels)	128 × 240 × 92	107 × 133 × 100
Resolution (mm)	0.25 × 0.25 × 0.25	0.15 × 0.15 × 0.15
Total scan time	14 h and 55 min	36 h and 16 min

The whole ferret brain specimen was immersed in fluorinert and imaged using a 35-mm quadrature birdcage radio frequency (RF) coil for transmission and reception. To perform diffusion encoding, $b$-values of 6000 and $9000\mathrm{s}/{\mathrm{mm}}^2$ were acquired having 48 and 72 non-colinear directions, respectively. Three unweighted images were also acquired. A second repetition of these diffusion-weighted images (DWIs) was collected with reverse phase encoding for geometric distortion correction.

Three optic nerve specimens were embedded together in agarose and imaged simultaneously using a single loop 10-mm receive-only RF surface coil and an 86-mm quadrature RF coil for transmission. To perform diffusion encoding, $b$-values of 1500 and $3000\mathrm{s}/{\mathrm{mm}}^2$ were acquired in 32 non-colinear directions; $b$-values of 4500 and $6000\mathrm{s}/{\mathrm{mm}}^2$ were acquired in 56 directions. Four unweighted images were also acquired. A second repetition of these DWIs was collected with reverse phase encoding for geometric distortion correction.

2.3. Diffusion MRI Processing

The TORTOISE processing pipeline was used to perform apparent motion and geometric distortion correction,^30,31 estimate the diffusion tensor and mean apparent propagator, and calculate metric maps for FA and PA. MRtrix3 software^32,33 was used to perform CSD (order = 6) using the corrected DWIs, and whole specimen tractography was performed using the tckgen command. FODs, tractograms, and eigenvectors were visualized using the mrview software. These MRI metrics are visualized in the whole ferret brain with emphasis on the OC in Fig. 2. From the diffusion tensor obtained in TORTOISE, the relative diffusion tensor angle was calculated by taking the absolute value of the angle between each diffusion tensor within the region of interest (ROI) and the average eigenvector for the whole ROI.

Fig. 2.

dMRI metrics overview in the whole ferret brain. The location of the OC structure is shown enlarged in the boxes (bottom row).

2.4. Backscattering Mueller Matrix PLI Acquisition

The OC specimens were imaged using a Nikon BX41 Mueller Matrix Polarimeter.³⁴ The instrument operates in reflectance mode and illuminates the sample sequentially with five wavelengths on the visible spectrum (405, 445, 473, 543, and 632 nm) using a fiber-coupled multi-LED light source. Images were collected using a 5× microscope objective with a resolution of $10\mu \mathrm{m}$ and a 3-mm field of view. The polarization state of the illumination arm is automatically cycled during acquisition to capture the full polarization interaction of the sample. On the detection end, the light is collected in a dark-field configuration, which is passed through a pair of Savart plates to encode the Stokes vector components in the spatial frequency domain. The system operation is discussed in extensive detail in past publications.^34–36 The acquired data is a spatial mapping of the sixteen Mueller matrix parameters for the sample. The Mueller matrix for each pixel was decomposed using the Lu-Chipman decomposition technique to isolate the effects of depolarization, retardance, and diattenuation using the pySCATMECH package in Python 3. Depolarization is a unitless metric, retardance is expressed in radians, and diattenuation is ratiometric and unitless. The angular component retardance angle and diattenuation angle are expressed in radians. The mathematical basis for this Mueller matrix decomposition technique is derived and discussed by Lu and Chipman.³⁷

Both sectioned and bulk OC specimens were imaged using backscattering Mueller matrix PLI. Bulk OC specimens were imaged by placing each sample on a glass slide and rehydrating the sample for at least 10 min between images to prevent tissue dehydration. One image of the crossing region of the OC and one image of the coherent region of the optic nerve were acquired for each sectioned and bulk tissue sample. For analysis of PLI data, thick tissue was observed at 632 nm, whereas thin tissue was observed at 405 nm due to the relative penetration depths of each wavelength as well as the relative scattering experienced by each wavelength. It is known that as wavelength increases, scattering decreases, for both Rayleigh and Mie scattering regimes. A longer wavelength was chosen for thick tissue due to its increased penetration depth to gather information regarding depth-related multiple scattering effects while using a wavelength less prone to the effects of scattering. A shorter wavelength was chosen for thin tissue specimens due to its decreased penetration depth, using a wavelength more sensitive to scattering. Although there are no explicit studies to our knowledge that measure the estimated penetration depth across wavelengths in fixed ferret brain tissue, the penetration depth in fresh frozen human white matter is 0.5 to 0.22 mm for blue light and up to 0.79 mm for red light;³⁸ however, these measurements may differ somewhat from fixed ferret white matter.

Phase unwrapping corrections were applied to the diattenuation angle such that $\pi$ was subtracted from values greater than zero. To mirror the relative diffusion tensor angle, the relative retardance angle and relative diattenuation angle were calculated by subtracting each value within the ROI from the average value for the whole ROI.

2.5. Landmark Registration and Correlation Analysis

To enable pixel-wise comparisons between MRI and PLI maps, the MRI scans for each OC were registered to PLI of the same specimen as follows. First, MRI images of the OC were repositioned and resliced using medical image processing, analysis, and visualization software for coarse alignment with the optical images. A single MRI slice in the middle of the OC showing similar features to the thin tissue OC specimen was extracted. For the bulk tissue specimens, this MRI slice was registered to PLI images obtained with the 632-nm light source using landmark registration in MATLAB. To evaluate the distribution and variance of PLI and MRI values within regions of coherent or crossing fiber geometry, ROI masks were created in ImageJ³⁹ and used to generate metric value histograms. To determine the pixel-wise correlation between MRI and PLI values, a whole specimen ROI mask was used, and Pearson’s correlation analysis was performed in Python 3. The process was repeated for thin tissue specimens using PLI images acquired with the 405-nm light source.

3. Results and Discussion

3.1. Scalar Metrics Across Modalities

To evaluate the effect of anisotropy across imaging modalities within coherent and crossing structures, dMRI metrics FA and PA were compared with scalar PLI metrics: depolarization, retardance, and diattenuation. Figure 3 provides a visual comparison across anisotropic dMRI and scalar PLI metrics in one thin tissue and one thick tissue OC specimen. The locations of the coherent and crossing ROIs are indicated.

Fig. 3.

Visualization of anisotropic dMRI and scalar PLI images. (a) FA and PA across the three OC specimens, where the coherent optic nerve ROI is labeled with the number one in yellow, and the crossing OC ROI is labeled with the number two in blue. (b) Thin tissue scalar PLI metrics depolarization, retardance in radians, and diattenuation. (c) Thick tissue PLI metrics.

As shown in Fig. 2, FA values were qualitatively reduced in the crossing region of the OC when compared with PA. This is consistent with previous studies showing the greater bias of FA by complex fiber geometry and the inability of DTI to resolve crossing fibers. Also as expected, PA values appeared to be less influenced by this effect in OC maps. Backscattering Mueller matrix PLI metrics did not appear to decrease in the region of crossing, although PLI values appeared somewhat heterogeneous across the ROIs. There exists a faint annular imaging artifact in thin tissue diattenuation and speckling in thick tissue diattenuation, potentially due to surface-related scattering effects.

Histograms were generated from the MRI and PLI metric values within the crossing and coherent ROIs (Fig. 4). FA within the coherent region had a narrower histogram than the crossing region, indicative of bias by macroscale architecture, whereas PA demonstrated consistent, narrow distribution across coherent and crossing fiber regions, indicating sensitivity to microscale geometry without bias from crossing fiber architecture. This behavior is consistent with existing literature regarding coherent and complex fiber regions within FA and PA.^3,5 The histogram distributions of FA and PA reflect their well-characterized dependencies on microstructure and bias by macrostructure and serve as the reference for the evaluation of similar dependencies for scalar PLI metrics in this study.

Fig. 4.

Intensity distributions across anisotropic dMRI and scalar PLI metrics in coherent and crossing ROIs. (a) FA and PA intensity distributions across the three OC samples within the coherent ROI, denoted by the yellow dashed box, and crossing ROI, denoted by the blue dashed box. (b) Thin tissue scalar PLI metrics across the three samples. (c) Thin tissue scalar PLI metrics averaged across the three samples displaying average coherence in yellow and average crossing in blue. (d) Thick tissue scalar PLI metrics across samples. (e) Thick tissue scalar PLI metrics averaged across samples.

All three OC specimens show similar trends across PLI scalar metric histograms when comparing results from thin and thick tissue specimens. Within each plot, the distribution shapes and maxima occur at similar metric values across the three specimens with the exception of thin tissue sample 1. When comparing the variance of thick and thin tissue groups across depolarization, diattenuation, and retardance, thick tissue showed a consistently increased variance compared with thin tissue (Fig. 5), which is reflected in the broadness of the histogram distributions. Because the reflected signal from thin tissue specimens was less influenced by depth-related multiple scattering effects, the distributions for all thin tissue PLI metrics were much narrower than thick tissue where detected light has undergone many scattering events, potentially manifesting as a wider distribution and higher variance in PLI values.

Fig. 5.

Variance of scalar PLI metrics across tissue samples, coherent and crossing fiber populations, and thick and thin specimens.

Comparisons of average histograms for depolarization, retardance, and diattenuation in crossing and coherent regions showed different patterns across PLI metrics [Figs. 4(c) and 4(e)]. Depolarization did not strongly differentiate between the crossing and coherent fiber populations. Because there was only a small difference in depolarization between crossing and coherent ROIs, this indicates that this metric is less biased by macrostructure. This is not surprising, as the majority of depolarization will likely occur due to scattering, which is primarily influenced by cellular-level features.¹⁹ Despite imaging fresh tissue, Gros et al. and Felger et al. find similar depolarization profiles when imaging regions of white matter within the brain, observing values near 1.^40,41 However, we observed increased depolarization in thin specimens compared to thick specimens. In this measurement system, the detected signal is inherently backscattered due to the dark field configuration. Therefore, it is possible that the multiple scattering in thick specimens does not necessarily contribute more depolarization than the inherent backscatter required to collect the light in general; rather, it could produce an averaging of effects over multiple depths, giving rise to the distribution broadening we see. Other potential explanations for this behavior include the increased scattering associated with shorter wavelengths, as well as the possible increased scattering due to the presence of paraffin in the thin tissue specimens. In addition, differences in the collected signal and exposure time may result in different normalization during calibration, making it challenging to draw robust conclusions about not only depolarization, but also diattenuation and retardance in an absolute sense across the thin tissue and thick tissue datasets. Diattenuation also shows fairly similar distributions across coherent and crossing regions, indicating that this metric is also less biased by the macrostructure. Here, diattenuation values appear relatively small; however, this result is consistent with previous studies that show biologically relevant signals where values are reported as $<0.03$.^24–26 However, these measurements were conducted using transmission polarimetry, whereas we use reflectance polarimetry, which may give rise to some disparities. The differences in thin and thick tissue result in diattenuation may occur due to the surface reflection effect where different amounts of $s$- and $p$-polarizations are reflected. However, the polarimeter used in this study operates in a darkfield configuration,³⁴ which likely mitigates this issue to some extent.

Retardance distributions show distinct differences between coherent and crossing regions. When observing the average distributions, retardance is increased in coherent regions and reduced in crossing regions. In coherent tissue structures, the relative difference in phase delay for two orthogonal polarization states is expected to occur along one axis, dictated by the direction of the coherent fibers. This may result in a greater difference between the phases of the orthogonal polarization states and thus increased retardance in coherent tissue structures. The crossing fiber structure, on the contrary, contains two near-perpendicular fiber orientations, resulting in some proportion of the axons aligning with two near-orthogonal polarization states. This may result in a smaller difference in phase delay between orthogonal polarization states and overall reduced retardance. The work of Ivanov et al. supports this finding, where they observed a similar decrease in retardance in crossing fibers compared with coherent fibers in formalin-fixed paraffin-embedded histological sections of the brain tissue.⁴² When comparing retardance across thin and thick tissue specimens, we find that retardance decreases with higher wavelengths, consistent with previous work using this polarimeter.³⁵ However, these results are contradictory to the findings of Mieites et al. who observed that as wavelength increases, retardance increases in fresh brain tissue.⁴³ Although differences in study design may account for this, there is some chance that our results are influenced by phase wrapping of the retardance. In addition, inconsistent absolute intensity values between the two different tissue thicknesses may arise from different normalizations during calibration.

The behavior of retardance is remarkably similar to that of FA where intensity is reduced due to complex tissue orientation, a trend that is most pronounced in thin tissue. When comparing distributions between FA and thin tissue retardance, both plots show a high and narrow distribution in the coherent ROI and a lower and wider distribution in the crossing ROI. This similarity between FA and retardance indicates that retardance is biased by macrostructural architecture in the region of crossing.

Although we have used histogram distributions to gain insight into the presence of macrostructural bias, we can also use correlations to evaluate relationships between modalities more directly. By registering dMRI to PLI images, pixel-wise correlation analysis between the two modalities was performed across all tissue geometric in the sample. Figure 6 displays Pearson correlation coefficients between dMRI anisotropy metrics and PLI scalar metrics. When correlating thin tissue dMRI and PLI metrics, we found a strong positive relationship between thin tissue retardance and FA, consistent across the three OC samples. This direct comparison further indicates that retardance, such as FA, is biased by macrostructure, supporting the relationship between FA and retardance intensity distribution observed in Fig. 5. Diattenuation did not show consistent metric relationships across samples; therefore, no microstructural sensitivity or macrostructural bias may be inferred. Thick tissue specimen values were found to have lower correlation coefficients, but similar trends to correlations in thin tissue were observed.

Fig. 6.

Pixelwise Pearson correlation between anisotropic dMRI and scalar MRI metrics. (a) The full correlation matrix averaged across the three thin specimens is displayed. The values in the yellow box on the average correlation matrix are shown across each sample below. (b) Correlation matrix for thick tissue specimens.

3.2. Orientational Metrics Across Modalities

To evaluate the effect of orientation across imaging modalities within coherent and crossing structures, CSD tractography and fluorescence microscopy images were compared with angular PLI metrics retardance angle and diattenuation angle. Figure 7 provides a visual comparison between CSD tractography, fluorescence microscopy, and angular PLI metrics in thick and thin tissue specimens. The fast axis of the retardance angle is shown. Here, the results show that the fast axis is aligned parallel to the physiological fiber axis, as myelinated fibers are known to exhibit negative uniaxial birefringence. Thin tissue diattenuation maps were found to have a pronounced annular imaging artifact. Due to the lack of sufficient return signal in thin tissue diattenuation, an artifact intrinsic to this measurement system was magnified. Future work aims to understand and potentially minimize this artifact; however, in this study, we exclude the diattenuation angle from subsequent quantitative reporting.

Fig. 7.

Visualization of orientational metrics. (a) CSD tractography overlayed on FA across samples. The coherent and crossing areas are indicated in yellow and blue, respectively. A magnified view of the crossing region is shown below. (b) Fluorescence microscopy of the OC where magnified regions of crossing and coherent fibers are shown below. (c) Thin tissue retardance angle and diattenuation angle in crossing and coherent regions. (d) Thick tissue retardance angle and diattenuation angle in crossing and coherent regions.

The remaining angular PLI metric maps displayed fiber orientation in concordance with both tractography and fluorescence microscopy images in the coherent fiber region. For both thin and thick specimens, the retardance angle appeared to report the average orientation of the crossing fiber geometry. For the thick tissue diattenuation angle, there was evidence for the resolution of single fiber orientation in the crossing region. The speckled appearance of the chiasm may indicate adjacent microdomains having different orientations; however, it is possible that this appearance is a result of an artifact. The lack of clearly defined microdomains within crossing fibers in angular PLI may be caused by a poorer resolution when compared with fluorescence microscopy or blurring effects from the spatial frequency encoding of polarization states during detection.

Angle histograms were generated from the diffusion tensor and angular PLI metrics within the crossing and coherent ROIs (Fig. 8). Average diffusion tensor angle has distinct intensity distributions for crossing and coherent regions that are consistent across samples, indicating that this metric is sensitive to changes in the complexity of fiber orientation.

Fig. 8.

Intensity distributions across relative orientational dMRI and relative angular PLI metrics in coherent and crossing ROIs. (a) Relative diffusion tensor distributions in radians across the three samples within the coherent ROI, denoted by the yellow dashed box, and crossing ROI, denoted by the blue dashed box. (b) Thin tissue retardance angle in radians across the three samples. (c) Thin tissue retardance angle in radians averaged across the three samples displaying average coherence in yellow and average crossing in blue. (d) Thick tissue angular PLI metrics in radians across samples. (e) Thick tissue angular PLI metrics in radians averaged across samples.

PLI angular distributions also show sensitivity to fiber orientation, especially for thick tissue values [Figs. 8(d) and 8(e)]. It should be noted that because we examined the relative retardance angle and relative diattenuation angle by subtracting the mean of the distribution, the optical axis for the linear retarder and orientation angle of the transmission axis for the diattenutator have both been artificially centered at zero. Thick tissue relative retardance angle and diattenuation angle distinguish crossing and coherent fiber populations. In the coherent region, thick tissue relative retardance angle and diattenuation angle contain one dominant peak at the origin, both indicative of the single fiber population present. In the crossing region, relative diattenuation angle histograms have two distinct peaks indicating the two fiber orientations present and one smaller peak at zero where no signal is acquired. Histograms of thick tissue relative retardance angle are more varied across specimens than diattenuation angle, with the average histograms showing two wide peaks, which suggest lower specificity to fiber orientation than diattenuation angle. This may also be influenced by the broadening effects of the thick tissue multiple scattering that we observed in the scalar metrics above. Interestingly, the diattenuation angle does not seem to be influenced as much and more specifically captures crossing orientation when compared to the retardance angle.

Thin tissue angular PLI struggles to resolve fiber orientation. Thin tissue relative retardance angle in the coherent ROI shows a narrow peak at the origin, consistent with thick tissue; however, it is unable to capture the multiple fiber orientations present in the crossing ROI, showing only a small peak at the origin. The thin tissue diattenuation angle was omitted due to the strong imaging artifact displayed in Fig. 7. When performing pixel-wise correlations between the relative diffusion tensor angle and the angular PLI metrics, no significant correlations were found.

From orientational MRI and PLI metrics, we may visualize the angle of the fibers present in the coherent and crossing regions of the OC structure. In Fig. 8, we determined that thick tissue angular PLI metrics show sensitivity to fiber orientation, whereas thin tissue is affected by imaging artifacts and weak signals. As a result, we have chosen to compare thick tissue angular PLI to a dMRI model of fiber orientation. Figure 9 shows a comparison of orientation between dMRI FOD glyphs and angular PLI metrics in thick tissue specimens.

Fig. 9.

Orientational comparison across metrics. (a) FOD glyphs across samples where the locations of coherent and crossing FODs are indicated. A magnified view of the crossing region is shown below. (b) Vector plots of thick tissue retardance angle and diattenuation angle. The color-coded arrows indicate the perceived fiber orientation. (c) Comparison of one FOD glyph and average angular PLI displayed in polar coordinates in degrees for the coherent (top) and crossing (bottom) ROIs.

PLI vector plots of retardance angle and diattenuation angle show a similar orientation to that of the FOD glyphs. Thick tissue angular PLI metrics displayed on a polar plot show comparable orientation to that of individual FOD glyphs taken from the coherent and crossing regions. In the coherent region, the FOD glyph is consistent with the retardance angle and the diattenuation angle polar plot, all indicating one fiber direction. In the crossing region, the FOD glyph indicates that two perpendicular fiber directions are present. The thick tissue retardance angle shows a wide range of fiber orientations through the crossing region, while the diattenuation angle appears more specific to the two perpendicular fiber orientations present, producing more comparable results to the FOD than the retardance angle. The reduced specificity to crossing fiber orientations indicates that the retardance angle may be more biased by macrostructural architecture than the diattenuation angle.

4. Conclusion

In this study, we demonstrated the microscale, macroscale, and orientational sensitivity of backscattering muller matrix PLI, as well as the potential of this method as a tool for microstructural dMRI validation in thick tissue specimens. We observed that retardance and FA behave similarly in both thick and thin tissue specimens, suggesting that retardance is biased by macroscale architecture. When comparing angular metrics, thick tissue specimens display comparable fiber orientation to dMRI, showing notable similarities between diattenuation angle and FODs in the crossing region that is not evident for retardance angle. This implies that performing complete polarimetry using the Mueller matrix framework can provide distinct directional characterization and potentially microscale anisotropy information that is not currently available using conventional transmission PLI and retardance estimations alone. In addition, this study identifies the strength of thick tissue imaging for the mapping of angular metrics and limitations for scalar metric mapping.

In this study, we measure paraffinized thin tissue slices; however, potential confounds exist when measuring paraffinized tissue with polarimetry. Paraffinization may contaminate the polarimetric tissue signature due to the dehydration that occurs in its preparation as well as the birefringence of paraffin. This can result in intranuclear birefringent inclusions, an artifact that has been reported in formalin-fixed paraffin-embedded specimens which may contaminate polarization measurements.^44,45 This study uses thin fixed and paraffin-embedded tissue and thick fixed tissue that is not paraffin-embedded, which may result in inconsistencies when comparing thin and thick tissues.

While the PLI measurement system used in this study experiences some limitations caused by imaging artifacts and may potentially experience artifacts due to the paraffinization of thin tissue, advancing the techniques demonstrated here has the potential to enable a more robust and widely applicable validation of diffusion MRI data. This could be done through hardware optimization including testing different polarimeter architectures, optimizing field of view, depth of field, and resolution, in addition to improving image reconstruction techniques. Ongoing and future work in this area^35,36 aim to understand the influence of imaging artifacts inherent to the PLI measurement system, determine the PLI signal dependence on wavelength and tissue thickness, incorporate computational methods for data synthesis and advanced multimodal analysis, integrate polarization-sensitive optical coherence tomography to resolve depth-dependent effects, and translate this work to image superficial brain tissue structures in vivo.

Biographies

Rhea Carlson is a current PhD student in biomedical engineering at the University of Arizona, where she also previously received her BS degree in biomedical engineering. Her research interests include brain imaging both using MRI and optical methods.

Justina Bonaventura is a PhD student at the University of Arizona. She previously received degrees in Physics and Visual Arts from Alfred University. Her research primarily focuses on label-free optical imaging of tissues including polarimetry.

Noelle Daigle is a PhD student at the University of Arizona. She received her BS degree in physics and mathematics at the University of Nevada Reno. Her research interests include optical imaging of tissues including fluorescence, multiphoton and polarization imaging, as well as mathematical modeling.

Travis W. Sawyer, PhD, is an assistant professor of optical sciences at the University of Arizona. He previously received his BS, MS, and PhD degrees in optical sciences from the University of Arizona and his MPhil in physics from the University of Cambridge. He leads the Biomedical Optics and Optical Measurement Laboratory, where his laboratory’s research interests are primarily focused on label-free biomedical imaging and gastrointestinal cancers.

Biographies of the other authors are not available.

Disclosures

The authors have no relevant financial interests or potential conflicts to disclose.

Code and Data Availability

All code used in this study is available through GitHub at the following URL: https://github.com/UAmsbil/PLI-MRI_OpticChiasm. The data used in this study can be accessed at the following DOI: 10.25422/azu.data.27764895.