Study design
In the present study, images from a healthy male subject (age: 32) and a male subject with penetrating right eyeball injury (age: 46) were used. Both subjects underwent a full ophthalmological examination, which included visual acuity, color vision, applanation measurement of intraocular pressure, evaluation of the anterior chamber and the fundus of the eye using a slit lamp and the Volk lens, optical coherence tomography examination of the macula and optic nerve disc (OCT), neurological field vision, and visual evoked potential (VEP) testing. In the tests conducted, no deviations from the normal condition were found in the subjects, while the trauma patient had endotamponade of the vitreous chamber of the right eye with silicone oil, lack of sense of light, secondary glaucoma, and atrophy of the right eye optic nerve, and correct ophthalmological examination of the left eye. In his medical history, the patient reported that prior to the penetrating injury (metal shard from a masonry hammer driven into the eyeball), the patient did not experience any deterioration in vision compared to the left eye. During active scanning, the patients tried not to blink and did not move their heads, while gazing at the red-locking LED outside the camera reflected in the mirror of the coil.
Diffusion tensor imaging
MRI data were acquired using a Biograph mMR 3-Tesla scanner (Siemens, Erlangen, Germany) with a 16-channel head-neck coil. Acquisition parameters were set up based on the article [61] and technician experience. The total duration of the EPI DTI examination was 10:34 min (8:05 and 2:29 for A>>P and P>>A phase encoding directions respectively). MRI acquisitions were obtained using a scanner with a maximum gradient amplitude of 45 mT/m and a maximum slew rate of 200 T/m/s. Parameters for used for echo planar (EPI) acquisition method were: TR 7000 ms, TE 113 ms, echo spacing 0.97 ms, bandwidth 1184 Hz/Px, EPI factor 128, voxel size 1.3×1.3×2.0 mm, 25 slices (transverse orientation), distance factor 0% for transverse plane and 50% for other planes, base resolution 128 and prescan normalization filtering. Sixty-four non-collinear diffusion directions for a \(b\) value of 1000 s/mm2 with one average were acquired for the A>>P encoding direction and six averages without diffusion-weighted acquisition for \(b\) value of 0 s/mm2 were acquired for both the A>>P and the P>>A encoding directions. Parallel imaging with an acceleration factor of 2 was enabled using the GRAPPA algorithm. Additionally, an anatomical T1-weighted (MP RAGE), scan time 5:21 min, voxel size 1.0×1.0×1.2 mm, was performed.
In addition to coronal magnetization-prepared rapid acquisition gradient-echo reconstruction, oblique transverse sections through both optic nerves were done. The exact positions and angulation of slices were further graphically specified and adjusted in the central sections of the left and right sagittal optic nerves. This procedure allowed for an exact adjustment of the EPI and T1 slices through both optic nerves. In general, positioning was focused on the part of the optic nerve closest to the eye to allow for optimal comparability in the case of a curved or kinked optic nerve.
Image post-processing
Diffusion images were converted from the DICOM format to the NIfTI format using the open source dcm2niix software [62], and the data were post-processed using the FSL software library (http://www.fmrib.ox.ac.uk/fsl) [63]. The ITK-SNAP software (http://www.itksnap.org) was used to create a binary mask of the brain, eyeballs, and optic nerves. FSL's tools were used for susceptibility -induced and eddy current -induced distortion correction, and movement artifacts correction [64–66]. The correction procedure assumes that the eddy current-induced field can be modelled as a combination of linear and quadratic terms. Calculations were parallelized with CUDA v9.1 on Nvidia Tesla K80 GPU. Computations were carried out at the Computer Center of University of Bialystok, Poland. Eddy current and motion-corrected diffusion-weighted images were used for voxel-by-voxel-based tensor calculations. Consequently, eigenvectors (\({V}_{1}\), \({V}_{2}\) and \({V}_{3}\)) and eigenvalues (\({L}_{1}\ge {L}_{2}\ge {L}_{3}\)) were obtained. Throughout the text, the largest eigenvalue \({L}_{1}\) will be called axial diffusivity. For all other calculations, the Wolfram Mathematica software was used and NIfTI images were imported using the QMRITools toolbox developed for the Wolfram language [67]. Fractional anisotropy (\(FA\)), mean diffusivity (\(MD\)) and radial diffusivity (\(RD\)) were defined as [7, 43, 61]:
\(FA=\frac{{\left({L}_{1}-{L}_{2}\right)}^{2}+{\left({L}_{2}-{L}_{3}\right)}^{2}+{\left({L}_{1}-{L}_{3}\right)}^{2}}{2\left({L}_{1}^{1}+{L}_{2}^{2}+{L}_{3}^{2}\right)},\) (1)
\(MD=\left({L}_{1}+{L}_{2}+{L}_{3}\right)/3,\) (2)
\(RD=\left({L}_{2}+{L}_{3}\right)/2\). (3)
Algorithm
The physical property of the diffusion tensor is that all eigenvalues are non-negative. However, correction algorithms and low-resolution data can lead to negative eigenvalues that are clearly non-physical. Therefore, in our procedure all negative, nonphysical eigenvalues were set to zero [68]. The data visualization algorithm consisted of six steps each having a significant impact on the displayed image. The visual effect accomplished by each step is presented in Fig. 2a-f and described below.
In the first step, the first eigenvector \({V}_{1}\) in each voxel is displayed as a line segment representing the main direction of diffusion in that voxel, and the line segments are given the same length (Fig. 2a). Because the morphological structure of the optic nerve favors the presence of one particularly distinguished direction of diffusion, we should focus especially on voxels in which diffusion is strongly directional i.e., \({L}_{1}{\gg L}_{2}\). Hence, in the second step, the length of the line segment in each voxel is adjusted to a value given by
\(\alpha {\left({L}_{1}-RD\right)}^{2},\) (4)
where \({\alpha }\) is a scaling parameter. This means that the more \({L}_{1}\) deviates from \(RD\), the longer the line segment for that voxel (Fig. 2b).
Another important piece of information is the strength of diffusion in each voxel. Thus, in the third step, the opacity of the line segment in each voxel is set proportional to the product of the mean and radial diffusivities,
\(\beta \left(MDFA\right)\), (5)
where \({\beta }\) is a scaling parameter. This means that the stronger the diffusion, the more opaque the segment for that voxel (Fig. 2c).
The 4th step in our algorithm is an RGB color assignment that improves image clarity based on \({L}_{1}\) values as follows
\(Red={\gamma L}_{1N}\),
\(Green=1-{L}_{1N}\),
\(Blue=0\), (6)
where \(\gamma\) is a scaling parameter for setting the intensity of red color, and \({L}_{1N}\) is a normalized value, \({L}_{1N}{=L}_{1}/{L}_{1max}\), where \({L}_{1max}\) is the maximal value among all voxels \({L}_{1}\) (Fig. 2d).
The goal of the standard tractography color coding rejecting is to assume that the \({L}_{1}\) values should be similar along the entire length of the optic pathway, and therefore, it should be presented in a similar color. Furthermore, standard tractography color coding appears to be ineffective for the optic pathway because this structure does not form a straight-line segment in three-dimensional projections and such coding would unnecessarily introduce different colors on different sections of the optic nerve and tract. For this reason, for optic pathway visualization, more than one layer must be used. Therefore, we propose a new approach. In step five, we projected the three-dimensional shape of the visual pathways onto the transverse plane (Fig. 2e). Consequently, although the information about shape in the direction of the projection is lost, we gain a much-improved visibility in the two other directions (i.e., the plane perpendicular to the projection direction). On the transverse plane, the visual pathway is best visualized, but to show the complete location of the nerve, we project manually the segmented optic pathway onto the sagittal and coronal planes (Fig. 3). After the projection of a few layers onto one plane, we obtain a superposition of line segments in each voxel, producing enhanced visibility. However, segment superposition can affect image clarity and for this reason we implement a 6th step in which short line segments are discarded based on the following cutoff condition
\({L}_{1}>RD+\sigma ,\) (7)
where \(\sigma\) is a threshold value (Fig. 5). The result is that line segments are displayed only if the axial diffusivity exceeds the radial diffusivity by more than a chosen value for σ (Fig. 2f).
The presented algorithm and projections in three directions are particularly suited for the imaging of fiber structures. The optic nerves are clearly visualized in Fig. 3 (arrows). The right-hand side nerve is visualized as a single fiber, while the left-hand side nerve is split on coronal and sagittal projections because it is located just between the two planes used in the imaging protocol. Because the imaging protocol includes pre-scan normalization filtering, the parameters \(\alpha\), \(\beta\), \(\gamma\) and \(\sigma\) were selected once to ensure the best visibility of the visual pathways. These parameters may require modifications if any changes in the protocol arise or when different scanner devices are used. An unexpected but useful result is that the parameter \(\sigma\) can serve as a quantitative measure in the diagnostics of nerve atrophy as shown later in the manuscript.
Image quality testing
Diffusion tensor estimation can produce indefinite diffusion tensors that arise in locations where the diffusion-weighted signal is disturbed by noise and the degree of anisotropy is high [69]. In biological tissue, all eigenvalues of the diffusion tensor are assumed to be positive but due to noise or signal drop, negative eigenvalues may be generated [68]. The fraction of voxels for which negative eigenvalues have been generated relative to the total number of all voxels, expressed as a percentage, can be used as a measure of image quality. For a healthy subject, those values were 0.61%, 6.5% and 9.0% for \({L}_{1}\), \({L}_{2}\) and \({L}_{3}\) maps, respectively. In the case of a subject with a damaged eyeball, these values reached the values of 0.99%, 2.3%, and 9.5%, respectively.