Polarimetric visualization of healthy brain fiber tracts under adverse conditions: ex vivo studies

: We suggest using the wide-field imaging Mueller polarimetry to contrast optically anisotropic fiber tracts of healthy brain white matter for the detection of brain tumor borders during neurosurgery. Our prior studies demonstrate that this polarimetric imaging modality detects correctly the in-plane orientation of brain white matter fiber tracts of a flat formalin-fixed thick brain specimen in reflection geometry [IEEE Trans. Med. Imaging 39 , 4376 (2020)]. Here we present the results of ex vivo polarimetric studies of large cross-sections of fresh calf brain in reflection geometry with a special focus on the impact of the adverse measurement conditions (e.g. complex surface topography, presence of blood, etc.) on the quality of polarimetric images and the detection performance of white matter fiber tracts and their in-plane orientation.

The ability to identify fiber tracts non-invasively and in real time in the tissue-at-sight would be a breakthrough for brain tumor surgery. With the well-known location and course of the brain's main fiber tracts in mind the surgeon would be able to identify the fiber tracts in his/her field of view thanks to their in-plane spatial orientation. This ability would be a significant addition to existing techniques. For instance, if baseline testing is too poor or if compliance of a patient becomes too low during speech mapping, fiber identification would allow the surgeon to identify and preserve the arcuate fascicle. Other tracts, which surgeons cannot reliably identify during surgery at present, such as the visual pathway, could be identified and spared.
Optical imaging has already become a reliable technique for medical diagnostics. The classical intensity images taken with either an endoscope or a binocular microscope provide visual information about the biological tissue, such as its color, vascularization, surface texture, presence of lesions, etc. For example, these imaging modalities are routinely used for the characterization of superficial tissue layers in gynecology, dermatology, stomatology, ophthalmology and gastroenterology [13][14][15][16][17]. Confocal microscopy and optical coherence tomography (OCT) techniques make use of ballistic (non-scattered) photons to produce the microscopic depthresolved images. For both modalities the acquired images provide very detailed information on a micrometer scale about the structure of explored tissue. However, their field of view is typically less than a few square millimeters, and their penetration depth does not exceed a few hundred microns [18,19]. One can also analyze spectrally and/or angularly light scattered by a sample in order to extract information about the size and density of scatterers, as well as the absorption or fluorescence properties of a sample [20]. For these techniques the penetration depth of light may be significantly greater compared to OCT or confocal imaging, but they do not provide the image of a sample.
However, optics may offer the complementary dataset by exploring the polarization of light, which represents its fundamental property [21] and is known to be extremely sensitive to the microstructure of the illuminated object. The non-exhaustive list of optical techniques that measure changes of the polarization state of incident light induced by its interaction with the sample includes, for example, polarized light microscopy, orthogonal state contrast measurements, ellipsometry, Stokes polarimetry, and complete Mueller polarimetry [22][23][24][25][26][27][28][29][30].
Quite often biological tissues exhibit significant depolarization. Sometimes the depolarization is combined with other changes in polarimetric properties such as birefringence (anisotropy of the refractive index) and diattenuation (anisotropy of the absorption). Hence, the most complete polarimetric technique, (i.e. Mueller polarimetry) is required for the characterization of tissue's optical properties for biomedical diagnosis [31]. White matter of healthy brain has highly ordered architecture due to the presence of densely packed nerve fiber bundles (or fiber tracts) that are destroyed by brain tumor. The ability to identify fibers as a surrogate marker for healthy brain tissue enables the surgeon to identify brain tumors, simply by the former's lack of aligned fibers.
We suggest using the multi-spectral wide-field imaging Mueller polarimetry (IMP) for the visualization of healthy brain fiber tracts by measuring the depolarization and birefringence of brain tissue without scanning [32]. In our study we investigated the capability of the IMP to detect the fiber tracts of a fresh calf brain under the adverse measurement conditions that mimic the constrains of in vivo polarimetric measurements during neurosurgery (complex surface topography, presence of blood, etc).

Stokes-Mueller formalism
In the framework of linear optics one may use the Jones formalism that describes the transformation of the complex amplitudes of electric field vector of polarized light by its interaction with a sample. However, more general Stokes-Mueller formalism makes use of the second moments of the distributions of electric field amplitudes (i. e. intensities of light) and may be used for the description of polarized, partially polarized as well as unpolarized light [21]. We define the Stokes vector of a light beam as where I 0 • and I 90 • are the intensities of horizontal and vertical linear polarization, respectively. I +45 • and I −45 • represent the intensity of linear polarization at the angles +45 • and −45 • , I R and I L are the intensities of right-and left-handed circularly polarized light.
Upon interaction with a sample the transformation of Stokes vector of incident light S in is described by a 4 × 4 real-valued matrix M [21], called the Mueller matrix (MM) of a sample.
Mueller matrix M contains all information on polarimetric properties of a sample, whereas the physical interpretation of each Mueller matrix element is not always straightforward. By measuring all 16 elements of a MM and applying an appropriated decomposition method a complete set of relevant polarization and depolarization parameters (e. g. dichroism, polarizance, retardance, depolarization, etc.) can be obtained [33].

Wide-field imaging Mueller polarimetric system
A custom-built multi-spectral wide-field imaging Mueller polarimetric system used in these studies is described in details elsewhere [34][35][36][37]. For the sake of completeness we recall the main specifications of the instrument here. It makes use of ferroelectric liquid crystals (FLCs) for the fast polarization modulation and can record 16 raw intensity images of a sample in 5 seconds. The system operates in a visible wavelength range (450 nm -700 nm). The construction and optimization of such a system is described in [38]. The photo and schematic of the instrument are presented in Fig. 1.
The polarization state generator (PSG) represents a sequential assembly of a linear polarizer and two voltage-driven FLCs (Citizen Finetech Miyota, Japan) with a quarter-wave plate inserted between them. The polarization state analyser (PSA) is made of the same optical elements, but assembled in a reverse order. A xenon lamp is used as the source of incoherent white light. Each FLC operates as a wave plate with constant retardation and switchable orientation of the optical axis at either 0 • or 45 • . The angle of incidence is about 15 • , the beam is slightly divergent. Maximal dimension of the elliptical spot in the imaging plane is about 10 cm. The light scattered by a sample passes through the PSA and one of the 40 nm bandpass interference filters (with a central wavelength varying from 450 to 700 nm in steps of 50 nm) that are placed in a rotating wheel for performing spectral measurements. We use a CCD camera (Stingray F080B, Allied Vision, Germany, resolution 512 × 386 pixels) for recording the intensity images. Camera's optical axis is placed normal to the sample imaging plane. The use of the wide bandpass dichroic filters helps to increase the signal to noise ratio and to erase the speckle pattern. The reference calibration samples (two polarizers with the eigenaxes oriented at 0 • and 90 • , respectively, and a wave plate with the fast axis oriented at 30 • in the laboratory reference frame) are placed in a rotating wheel before the PSA. The optimal PSG and PSA polarization states are defined by the eigenvalue calibration method [39]. The acquisition of 16 intensity images for four different input and four different output polarization states is performed sequentially at each measurement wavelength. The MM of a sample is calculated pixel-wise from the raw intensity images [39] taken at each measurement wavelength.

Lu-Chipman decomposition of Mueller matrix
Lu-Chipman polar decomposition of MM represents the algorithm of a non-linear compression of polarimetric data. It was demonstrated that any physically realizable MM can be represented as the product of MMs of three basic optical elements, namely, diattenuator (M D ), retarder (M R ) and polarizing depolarizer (M ∆ ) [33]: and T u denotes the transmittance (or reflectance) for unpolarized light, D -3 × 1 vector of diattenuation, P -3 × 1 vector of polarizance, m D , m R and m ∆ -real-valued 3 × 3 matrices. The matrix product does not commute, so the sequential order of the appearance of polarimetric effects is fixed for this decomposition algorithm. The total depolarization is calculated as The combined effect of linear and circular birefringence is defined as M R can be expressed as a combination of a Mueller matrix of linear retarder with the linear retardance R and the azimuth of the optical axis φ and a Mueller matrix of a circular retarder with optical rotation angle ψ [40]. These parameters are calculated as )︃ We have focused our studies on the images of the total depolarization coefficient ∆, and the azimuth φ of the optical axis of linear birefringent medium, because both images demonstrate useful contrast for the visualization of brain white matter fiber tracts.

Brain samples
Fresh calf brain samples (aka cervelle de veau) were bought from a local French butcher the day of the experiment. The brain samples were not rinsed with water in order to perform the polarimetric measurements on fresh brain tissues that contain blood residual.

Depolarization mask for filtering polarimetric images of brain
The images of 3 cm × 3 cm section of cerebellum [41] of a fresh calf brain are shown in Fig. 2. The polarimetric images of brain tissue namely, depolarization and the azimuth of the optical axis were obtained by applying pixel-wise the Lu-Chipman polar decomposition (Eqs. (3)-7). The cell-dense cortex consistently shows less depolarization compared to the brain white matter. In order to improve visibility of in-plane fiber tract orientation within the white matter zone we suggest using a mask based on the depolarization threshold (∆ < 0.85) to remove less depolarizing areas of cortex and zones of specular reflection in the images of the azimuth of the optical axis and to highlight the directions of white matter fiber tracts.
Both total intensity and depolarization images demonstrate the contrast between cortex and white matter (Fig. 2(a) and Fig. 2(b)). We observe the orientation of brain white matter fiber tracts in the image of the azimuth of the optical axis (Fig. 2(c)). The zones of cortex demonstrate random orientation of the azimuth at the spatial resolution scale of the IMP system and visually "contaminate" the image, thus, making it difficult to trace brain fibers. The application of the binary mask that contains the pixels with only high values of depolarization allows to filter out the cortex zones and the zones of specular reflection that saturate the CCD camera in the image of the azimuth of the optical axis. An example of binary depolarization mask with a threshold value of ∆ = 0.85 is shown in Fig. 2(d). Assuming that all pixels of the azimuth image that demonstrate the depolarization value ∆<0.85 correspond to cortex zone of brain tissue, we render these pixels in black in the filtered image of the azimuth (Fig. 2(e)). It is worth to note that the zones of the image of the azimuth labelled by (1) and rendered in blue (horizontal orientation), labelled by (2) and rendered in yellow (135 • orientation), labelled by (3) and rendered in red (vertical orientation), and labelled by (4) and rendered in green (45 • orientation) suggest the presence of in-plane U-fibers connecting the cortical areas (A) and (B) as was shown in [32].
In order to demonstrate the capability of IMP to visualize white matter fiber tracts of a non-fixed brain we prepared a cadaveric calf hemisphere, removing the temporal lobe and large parts of the frontal lobe including the frontal operculum and the insula (see Fig. 3(a)). The intensity image show almost no contrast within the white matter zone apart from the tiny bright regions of specular reflection that is due to uneven surface of the specimen. We applied the depolarization mask with a threshold of ∆ = 0.85 for filtering out the cortex zones in the image of the azimuth of the optical axis. Azimuth map reveals a variety of cerebro-spinal (or spino-cerebral) as well as longitudinal tracts -parts of the superior longitudinal fascicle (see Fig. 3(c)). Fig. 3. Cerebral tracts of a cadaveric calf brain: a) photo of a prepared cavity with brain deep white matter tracts. The imaged zone of the size of 3 cm × 3 cm is marked by a blue box; b) intensity image; c) azimuth of the optical axis: the parieto-spinal (label 1, green color), centro-spinal (label 2, red color) and fronto-spinal (label 3, yellow color) tracts; longitudinal tracts (labels 4 and 5, blue color) measured at 550 nm.

Polarimetric imaging of ex vivo brain sample under adverse conditions
In our prior feasibility tests we took the images of a flat surface of 1 cm thick section of either formalin-fixed human brain or fresh calf brain in the laboratory settings [32]. However, the IMP system is meant for intra-operative use. Uneven surfaces, irrigation fluids and blood might obscure the tissue and negatively impact the capability of our IMP system to identify fiber tracts. We, therefore, tested our system under adverse conditions and applied a depolarization-based mask to the azimuth images in order to filter out the zones of gray matter and specular reflection.

Tilt and rotation of a brain sample
First we imaged the intra-hemispheric corpus callosum (a wide, thick nerve tract, consisting of a flat bundle of fibers, connecting the left and right cerebral hemispheres [42]) of an entire brain that was put in a Petri dish (Fig. 4(a)), and then we tilted a Petri dish by 30 • with respect to the imaging plane and imaged a brain sample again (Fig. 4(d)). The intensity images and maps of the azimuth of the optical axis of a corpus callosum are shown in Figs. 4(b), 4(c) and Figs. 4(e), 4(f). The depolarization mask 0.85<∆ was applied to the azimuth maps to filter out the zones of cortex and specular reflection. As expected, the central horizontal part of a corpus callosum demonstrates vertical orientation of fiber tracts. One should note the presence of the residual fibers of the cingular gyri [42] that are not oriented vertically and obscure the top and bottom zones of a corpus callosum azimuth map. The tilt of a sample is visible in the intensity images as the bright zones of specular reflection seen in the left part of a corpus callosum in the intensity image (Fig. 4(b)) disappear in the corresponding image shown in Fig. 4(e) because of brain sample surface inclination. However, the azimuth of the optical axis of a central part of a corpus callosum is not influenced by sample tilt (Fig. 4(c) and Fig. 4(f)).  Fig. 5. The central part of a corpus callosum is rendered in yellow in the azimuth maps recorded for both non-tilted and tilted brain sample at the rotation angle of 45 • (Fig. 5(b) and Fig. 5(e)). It corresponds to 45 • orientation of the fiber tracts that is consistent with the images in Fig. 5(a) and Fig. 5(d), where the orientation of the corresponding fibers is 90 • (i.e. vertical). Accordingly, the central part of a corpus callosum demonstrates horizontal orientation of the fiber tracts for both tilted and non-tilted sample for the rotation angle of 90 • . Thus, surface tilt and rotation do not represent a major problem for polarimetric imaging of brain fiber tracts.

Irrigation of a brain sample with saline / blood solution
During open brain neurosurgery the presence of blood within the surgical cavity is a factor that needs to be taken into account when testing the capability of IMP to visualize the brain white matter fiber tracts. We applied blood / saline solutions with different concentrations of blood onto the exposed corpus callosum of a calf brain (Fig. 6). The brain was minimally tilted (5 • -10 • with respect to the imaging plane) to allow excess blood /saline solution to drain. The residual fibers of the cingular gyri were removed, the saline/blood solutions with the concentration of blood of 10% (which we estimate to most accurately represent intra-operative conditions), 50% (the results are not presented here), and 100% were subsequently applied. The intensity images are slightly affected by the presence of 10% blood solution (Fig. 6(e)), the impact of blood becomes more pronounced for 100% blood solution (Fig. 6(h)). At the same time the presence of blood solution does not influence the maps of the azimuth of the optical axis measured at 550 nm and filtered using depolarization mask for removing the cortex and specular reflection zones (Fig. 6(c) and Fig. 6(f)), and the vertical orientation of a corpus callosum fiber tracts remains visible even after irrigation with 100% blood, as shown in Fig. 6(i).
Next, we created a 2 mm deep pool of undiluted blood by using another piece of brain tissue as a barrier on top of the imaged corpus callosum and preventing blood from draining (Figs. 7(a), 7(d)). The zone of blood is rendered in black in the gray scale image of intensity measured at 550 nm ( Fig. 7(b)), but looks more bright in the corresponding image taken at 650 nm ( Fig. 7(e)). This is explained by the strong peak of blood hemoglobin absorption at around 550 nm that drops sharply at the wavelength of 650 nm [43]. The previous spatially homogeneous map of the azimuth within the corpus callosum zone was lost for the image recorded at 550 nm (Fig. 7(c)), but the impact of blood on the map of azimuth was mitigated once we switched to 650 nm wavelength of probing light (Fig. 7(f)). Thus, small amounts of spilt blood will not be a major obstacle for intra-operative use of IMP, because surgical cavity is rinsed with a saline solution regularly during neurosurgery.

Impact of complex surface topography
The surgical resection of brain tumor creates a resection cavity, and the area of interest for fiber tract detection with the wide-field IMP might be located within the surgical cavity, and not be   7. Images of the corpus callosum in a cadaveric calf brain with a 2 mm deep pool of 100% blood: a) color photo; b) intensity image; c) azimuth of the optical axis measured at 550 nm; d) corpus callosum (1) with a ∼ 2 mm thick tissue specimen (2) creating a 2 mm deep pool of whole blood (3); e) intensity image and f) azimuth of the optical axis measured at 650 nm. on a flat surface. Thus, in order to mimic in vivo conditions we performed IMP measurements in a 2 cm deep resection cavity in a calf brain sample (see Fig. 8). The depolarization mask 0.85<∆ was applied to the azimuth map to filter out the zones of cortex and specular reflection. The dimension of the imaged zone is 3 cm × 3 cm, the wavelength of measurements is 550 nm. The image of the azimuth of the optical axis demonstrates clearly in-plane orientation of the thick fiber tracts that is consistent with the anatomy of this brain section. Hence, the quality of visualization of fiber tracts and their orientation with the wide-field IMP measurements within a cavity did not seem inferior to the measurements on a flat surface.

Conclusions
The proposed approach for the visualization of fiber tracts of healthy brain white matter using the multi-spectral wide-field IMP offers a non-invasive, staining-free, fast and reproducible method for identifying tumor margins by detecting in-plane fiber orientation during brain surgery. The correlation of the direction of brain fiber tracts with the orientation of the optical axis of linear birefringent medium measured with IMP modality was proven with the gold standard histology analysis of silver-stained thin sections of brain tissue [32]. Thus, we believe that the wide-field IMP technique has the potential to detect the precise border between optically anisotropic healthy brain white matter and isotropic brain tumor tissue, to increase the extent of resection in surgery on all intrinsic brain tumors, especially on low-grade glioma of young people, for which the current technologies have significant limitations and drawbacks, and to further decrease surgical morbidity.
Further studies are envisaged for the polarimetric imaging of freshly excised brain tumor specimens, especially the ones that may contain both tumor and healthy tissue to prove the validity of our hypothesis and relevance of IMP approach in near in vivo clinical settings.