own product, that where the language of others is set forth, quotation marks so indicate, and that appropriate credit is given where I have used the language, ideas, expressions or writings of another. I declare that the report describes original work that
has not previously been presented for the award of any other degree of any institution.
Karla Kort
optic radiation caused by glaucoma
Karla Kort
Graduation report
Submitted to Hanze University of Applied Sciences Groningen in partial fulfillment of the requirements for the master’s degree Sensor System
Engineering.
The research described in this thesis was supported by the laboratory of experimental ophthalmology at the University Medical Center
Groningen. June 2019
SUMMARY
This thesis investigates and proves a new method that helps distinguish between the optic radiations of a healthy brain and those of a brain affected by glaucoma. This new method uses fixel based analysis.
Glaucoma is the leading cause of irreversible blindness. This disease does not only affect the eyes, but also the brain. To be able to research these effects, a method to clearly identify the effects on different parts of the brain needs to be developed. The optic radiations are a part of the visual pathway and they are affected by glaucoma. In this part it is hard to see the difference between a healthy brain and one affected by glaucoma because of many crossing fibers. Therefore a new method needs to be developed to do this. This thesis does that, using the following research question and sub questions.
RQ: What methods can be used to better distinguish between the optic radiations of healthy controls and glaucoma patients, using the available dMRI data?
• SQ1: Would including only the fixels with the highest streamline density per voxel be a good method to distinguish between healthy controls and glaucoma patients?
• SQ2: What other methods could be used to distinguish between healthy controls and glaucoma patients, using the available dMRI data?
• SQ3: How can machine learning help with the classification of healthy controls and glaucoma patients?
The hypothesis is that, as suggested in SQ1, the fixels with the highest streamline density are more affected by glaucoma because they are a more important part of the optic radiations. It was found that looking at only these selected fixels indeed shows a significantly better difference between healthy subjects and glaucoma patients than when using all fixels that are part of the optic radiations. The second, third and fourth densest fixels were also analyzed separately. They showed no significant difference between the two groups. This would mean that when looking at all fixels, all lower order fixels were practically noise, making the difference less significant. The data used for this research included 12 glaucoma patients and 15 healthy controls. This is a rather small amount of subjects and this fact should be taken into account when looking at the results.
This thesis investigates and proves a new method that helps distinguish between the optic radiations of a healthy brain and those of a brain affected by glaucoma. This new method uses fixel based analysis.
The hypothesis this thesis proves is that using only the fixels that have the highest streamline density per voxel in the optic radiation will show a more significant difference than using all fixels in the optic radiation (as was done previously) because the fixels with the highest streamline density are the most likely to really be part of the optic radiation, therefore it was expected that these fixels would be more affected by glaucoma than
the other fixels. To prove this, a mask was built that can filter out the unwanted fixels for the right or the left optic radiation. Using this filter on the fiber density files of each subject gave significantly better results when comparing the two groups than before with all fixels in the optic radiations. The second, third and fourth densest fixels were also filtered out separately and analyzed. Most of these showed no significant difference between healthy subjects and glaucoma patients, which makes sense, because when using all fixels the difference is less, so the fixels that do not have the highest streamline density per fixel could be seen as noise.
CONTENTS
List of figures 3
1. Introduction 7
1.1. Glaucoma 7
1.2. The visual pathway 9
1.3. The future of glaucoma 11
2. Situational and theoretical analysis 12
2.1. MRI 12
2.2. Diffusion-weighted MRI 13
2.3. Diffusion tensor imaging 13
2.4. Crossing fibers problem 17
2.5. Fiber Orientation Distribution 18
2.6. Fixel-based morphology 19
2.7. Tractography 20
2.8. White matter deterioration 22
2.9. Project data 23
2.10. Hypothesis 23
2.11. Conceptual model 23
2.12. Research design 25
3. Implementation 26
3.1. The preprocessing pipeline 26
3.2. Programming language 27
3.3. MRtrix fixel file structure 28
optic radiation 37 4.3. The second densest fixels in the right optic
radiation 37
4.4. Location of significantly different fixels 37
4.5. Machine learning 42
5. Conclusions and recommendations 43
5.1. Conclusions 43
5.2. Recommendations 44
5.3. Ethics 45
6. Definitions and abbreviations 47
7. References 49
Appendices 53
A: File analysis 53
B: Creating the fixel masks 57
C: Machine learning 59
D: Machine learning with histograms 67
E: Comparing features 76
F: Mask images 78
G: Simplifying the script 85
H: Pseudocode 93
I: MRtrix community involvement 97
LIST OF FIGURES
Figure 1: Growing world population, split in age groups. Data source: United Nations (2015). World population prospects: The 2015 revision.
Figure 2: Section of the human eye and cells of the retina. Source: Rensselaer Polytechnic Institute (2017)
Figure 3: A: The visual pathway from the retina to the visual cortex. B: The optic radiation white matter fiber bundles. Source: Hofer S, Karaus A and Frahm J (2010)
Figure 4: Visual field loss in glaucoma. Different stages are shown, from normal vision on the left to an advanced stage of glaucoma on the right. The top shows visual field maps as can be made with the results of a visual field test. The bottom images show a simulation of the field of vision in each stage. The location of the scotoma’s (blind spots) can be different for each patient and lost vision can never be restored. The central vision is usually the last to go. (Kim et al. 2015). Source: Chika Ohara Eye Clinic
Figure 5: T1 and T2 weighted MRI scans of the human brain. Source: Preston, DC (2006), http://casemed.case.edu/ clerkships/neurology/web%20neurorad/mri%20basics. htm
Figure 6: Illustration of restricted diffusion as can be found in white matter. (Hecke et al. 2016)
7 8 9 10 12 13
Figure 8: Illustration of free diffusion. A: Paths of molecules in free diffusion. B, C, D: Location of molecules over time, caused by free diffusion. This happens in cerebrospinal fluid. (van Hecke et al. 2016)
Figure 9: A: Isotropic. B: Low Anisotropy. C: High anisotropy Figure 10: Mathematical tensor representation with eigenvalues
and eigenvectors in DTI. This tensor is pretty anisotropic and could therefore be part of white matter. Source: www.dsi-labsolver.org
Figure 11: Different ways fibers can cross in a voxel. From left to right: Kissing fibers, crossing fibers, fanning fibers. Source: Vilanova et al. 2004
Figure 12: Visualisation of the crossing fibers problem, reality vs. tensor representation. Source: Dismore, 2015
Figure 13: CSD FOD Image of the brain (van Hecke et al. 2016) Figure 14: Showing the difference in accuracy between DTI and
CSF. On the left are two images of the dMRI data, in the middle the tensor representation and on the right CSD. Source: bioRxiv
Figure 15: dMRI image showing fiber orientations per voxel, called fixels. Source: Project data
14 15 16 17 17 18 18 19
Figure 16: A schematic representation of a fiber bundle cross section. The grey circles represent axons and the grid represents voxels. Source: Raffelt et al. 2017
Figure 17: Comparison of tractography streamlines. On the left deterministic DTI streamlines, in the middle CSD deterministic streamlines and on the right CSD probabilistic streamlines. The streamlines in the CSD probabilistic way are closest to reality. Source: Tournier et al. 2012
Figure 18: Schematic of diffusion MRI data, from MRI scan to fixel based analysis.
Figure 19: Schematic of a neuron. Source: Queensland Brain Institute, Australia
Figure 20: Looking at the template image with fixels in mrview. (screenshot)
Figure 21: The amount of fixels that are included in each mask. Figure 22: P-values and effect sizes with different fixel masks. Figure 23: Box-and-whisker plots representing the FD data
from the left optic radiation of glaucoma subjects and healthy controls for the original fixel mask, the first order mask, 2nd order mask and 3rd order mask.
Figure 24: Box-and-whisker plots representing the FD data from the right optic radiation of glaucoma subjects and healthy controls for the original fixel mask, the first order mask, 2nd order mask and 3rd order mask.
19 20 21 22 27 32 32 33 34
Figure 26: ROC curves for the FD data with all four masks from the right optic radiation and values for the AUC. The first order mask shows a slight improvement.
Figure 27: One transverse slice that shows fixels that are part of the first order fixel mask. The black fixels are fixels that show a significant difference between the two groups. The white fixels are other fixels that are included in the mask, but do not show a significant difference between the two groups.
Figure 28: Fixels in the first order mask that show a significant difference between the two groups, all collapsed into one plane, so fixels from all slices. Many fixels overlap, so there are more than it might look.
Figure 29: One transverse slice that shows fixels that are part of the second order fixel mask. The black fixels are fixels that show a significant difference between the two groups. The white fixels are other fixels that are included in the mask, but do not show a significant difference between the two groups.
Figure 30: Fixels in the second order mask that show a significant difference between the two groups, all collapsed into one plane, so fixels from all slices. The left OR does not have any fixels that show a significant difference.
Figure 31: Human brain art by J. Sayuri.
36 38 39 40 41 46
INTRODUCTION
1.1 Glaucoma
Glaucoma is the leading cause of irreversible blindness. It is an age related, progressive, chronic disease with a prevalence of about 3.5% in people aged 40 - 80. This means that worldwide, this disease affects about 70 million people in this age group. Because
of the growing and aging population, this number is expected to grow to 111.8 million in 2040 (Tham et al. 2014).
Glaucoma is characterized by changes in the optic nerve head and the retinal nerve fiber layer. Visual field loss and the progressive
Figure 1: Growing world population, split in age groups. Data source: United Nations (2015). World population prospects: The 2015 revision.
death of retinal ganglion cells are associated with these changes (Anon 2014). A way to restore lost parts of the visual field has not been found yet. Visual field loss is usually not noticed in the beginning stages of the disease because of compensation by the brain and the other eye. When glaucoma is left untreated or detected too late, the chance of dying blind is 50%, while this is less than 5% when detected on time and treated well (van Gestel et al. 2010).
The exact pathological changes that are part of Glaucoma are not yet fully understood
(Agarwal et al. 2009). Damages to the optic nerve and retinal ganglion cells (RGCs) are often associated with high intraocular pressure (IOP), but can also occur in eyes with an IOP that is considered normal, leading to normal-tension glaucoma (NTG). Therefore, a high IOP is not a required symptom to diagnose glaucoma. It is however one of the main risk factors. Other risk factors include a family history of glaucoma, old age and myopia. Current clinically proven treatments focus on lowering the IOP through medication and surgery.
Multiple studies have shown that the damage to the RGCs extends to the axons that form the visual pathway. Changes can be seen in the white matter along the entire length of the optic pathway and even in the grey matter (Boucard et al. 2009; Garaci et al. 2009; Hernowo et al. 2011; Li et al. 2012; Zikou et al. 2012; Liu et al. 2012; Z. Chen et al. 2013; W. W. Chen et al. 2013; Yu et al. 2013; Wang et al. 2013; Dai et al. 2013; Murai et al. 2013; Li et al. 2014). Recently, researchers have even started arguing that glaucoma might not necessarily start in the retinal ganglion cells, but in the brain and because of it’s effects on the brain should not be seen as purely an eye disease, but also as a brain disease (Hanekamp, S. 2017).
1.2 The visual pathway
The path from light in the eye to an image in the brain starts with the retina. Figure 2 shows a visualization of the retinal cells. The photoreceptors, rods and cones, translate light into electrical signals. Those are then sent through the bipolar cells that in their turn connect to the RGCs. The axons of the RGCs will form the optic nerve and go into the brain.
The optic nerves partly cross in the optic chiasm, so the information from the left visual field from both eyes goes to the right
Figure 3: A: The visual pathway from the retina to the visual cortex. B: The optic radiation white matter fiber bundles. Source: Hofer S, Karaus A and Frahm J (2010)
and vice versa. After the optic chiasm the path is called the optic tract. This ends and synapses at the lateral geniculate nucleus (LGN) of the thalamus. The last part of the
visual pathway is the optic radiation (OR), which goes from the LGN to the visual cortex. As mentioned before, glaucoma can affect this entire pathway.
Figure 4: Visual field loss in glaucoma. Different stages are shown, from normal vision on the left to an advanced stage of glaucoma on the right. The top shows visual field maps as can be made with the results of a visual field test. The bottom images show a simulation of the field of vision in each stage. The location of the scotoma’s (blind spots) can be different for each patient and lost vision can never be restored. The central vision is usually the last to go. (Kim et al. 2015). Source: Chika Ohara Eye Clinic
1.3 The future of glaucoma
There have been studies about reversing glaucoma (Iomdina et al. 2015; Chamling et al. 2016; Cwerman-Thibault et al. 2017) and many studies about curing blindness, some of which could also work for blindness caused by glaucoma. (Fernández et al. 2015; Ghezzi 2015) To test these new methods, it is important to be able to identify the effectiveness of the treatment not only in the RGCs, but also in the rest of the visual pathway, which is why this thesis focuses on finding a method to identify changes in the optic radiations.
SITUATIONAL AND
THEORETICAL ANALYSIS
2.1 MRI
Magnetic resonance imaging (MRI) is a non-invasive way to visualize tissues and structures that are inside the body, such as the brain. The human body is mostly made out of water molecules, which have two hydrogen atoms with each have one proton in their nucleus. A proton has a positive electrical charge that is spinning around it, which makes each proton a tiny magnet. MRI is based on influencing these protons with an external, stronger magnet.
When a strong magnetic field is applied, most protons in the body will align parallel to this field and some anti-parallel. When a radiofrequency (RF) pulse is emitted by the MRI-scanner, some of the protons that were aligned in a parallel way will go into an anti-parallel alignment. When the RF pulse stops, the protons go back to their original alignment, which produces a signal that is measured by the MRI-scanner. Different types of tissue produce different types of signals because they have different concentrations of water. The brain consists of two main types of tissue and a liquid that is all around the brain, called the cerebrospinal fluid (CSF). The gray mater (GM) is mainly in
the peripheral part of the brain, it is where the brain cells are doing their processing. The white matter (WM) connects all the brain cells and is mainly in the center of the brain. The described method produces so-called T1 weighted images, which have great contrast between white matter, grey matter and cerebrospinal fluid.
When the RF pulse is applied, the protons will also start precessing in phase. Once the pulse stops, the protons get out of phase again. How long this takes can also be measured, this gives a T2 weighted image. (Schild 1994)
Figure 5: T1 (left) and T2 (right) weighted MRI scans of the human brain. Source: Preston, DC (2006), http://casemed.case.edu/clerkships/neurology/ web%20neurorad/mri%20basics.htm
2.2 Diffusion-weighted MRI
The type of MRI data that was used for this project is diffusion-weighted MRI (dMRI). This measures the directions of movement of protons in the body. This movement is called diffusion. There are three types of diffusion. Free diffusion (figure 8) is completely isotropic, which means that it is equal in all directions. The protons can move around freely, like in CSF or water. Hindered diffusion (figure 7) is also isotropic, but the protons move less far on average, because objects in their path restrict their movements occasionally, this is what happens in grey matter. Restricted diffusion (figure 6) is anisotropic, meaning that it has a specific direction and is not equal in all directions. This happens in white matter, where the protons diffuse along the direction of the white matter fiber tracts, which they cannot get out of because of the myelin sheath. (van Hecke et al. 2016)
2.3 Diffusion tensor imaging
To acquire diffusion data from an MRI scan, different gradient directions are used. These are the directions in which the diffusion is measured. The more directions are used, the more precise the result is. The data for this project was measured in 64 directions, which is considered HARDI (High Angular Resolution Diffusion Imaging) data.
Figure 7: Illustration of hindered diffusion as can be found in grey matter. (Hecke et al. 2016)
Figure 6: Illustration of restricted diffusion as can be found in in white matter. (Hecke et al. 2016)
Figure 8: Illustration of free diffusion. A: Paths of molecules in free diffusion. B, C, D: Location of molecules over time, caused by free diffusion. This happens in cerebrospinal fluid. (van Hecke et al. 2016)
To visualize the diffusion in each voxel (3D pixel), diffusion tensor imaging (DTI) can be used. This is not a method that was used for this project, but it will help to understand diffusion MRI and the other methods that were used, which are based on DTI and are discussed in the following chapters.
For DTI, the data from all directions that were measured in the diffusion MRI is used to find the eigenvectors and eigenvalues, so all directions are essentially reduced to three directions (see figure 10). The eigenvalues are the magnitude of the directions. The eigenvectors are orthogonal vectors that represent the directions of diffusion. These eigenvectors and eigenvalues can be
visualized as spheres or ellipsoids, called tensors. These are visualised in figure 9. From this tensor model, four values can be derived which can be used for analysis. Fractional anisotropy (FA) is a measure of how anisotropic a tensor is. A value of 0 means that it is isotropic, 1 means maximum anisotropy, so all diffusion would be exactly in the same direction. It uses the standard deviation of the eigenvalues. Mean diffusivity (MD) is the mean of the eigenvalues. Radial diffusivity (RD) is the mean of the second and third eigenvalues and axial diffusivity (AD) is the first eigenvector. The eigenvectors are sorted from highest value (λ1) to lowest value (λ3). (van Hecke et al. 2016)
Figure 9: A: Isotropic. B: Low Anisotropy. C: High anisotropy
Figure 10: Mathematical tensor representation with eigenvalues and eigenvectors in DTI. This tensor is pretty anisotropic and could therefore be part of white matter. Source: www.dsi-labsolver.org
2.4 Crossing fibers problem
A big problem with the tensor model is the crossing fibers problem. The size of the voxels in the data that was used in this project is 1.3x1.3x1.3 mm, but most white matter fibers are smaller than 2 micrometers. (Liewald et. al 2014) So it is no surprise that 60% - 90% of voxels in a diffusion MRI image contain crossing fibers. (van Hecke et al. 2016)
This results in a tensor shaped like a disc or even a sphere, which is highly inaccurate and makes it hard to find the actual directions of diffusion. Figure 11 shows different ways of fiber crossing. The crossing is not always actual crossing, fibers can also be ‘’kissing’’ or fanning. Figure 12 shows the tensor representation of crossing fibers.
Figure 11: Different ways fibers can cross in a voxel. From left to right: Kissing fibers, crossing fibers, fanning fibers. Source: Vilanova et al. 2004
Figure 12: Visualisation of the crossing fibers problem, reality vs. tensor representation. Source: Dismore, 2015
2.5 Fiber orientation distribution
There are a few higher order models to visualize and analyze diffusion data, which were developed more recently. Because the data that was worked with was acquired using 64 different gradient directions, turning this into a tensor, which would mean only three eigenvectors and three eigenvalues, would mean a great loss of data and many problems with crossing fibers. So the fiber orientation
distribution (FOD) model was used instead. This uses constrained spherical deconvolution (CSD) to get its characteristic balloon shapes. CSD is a complicated mathematical method that will not be discussed in detail here but it can be found in van Hecke et al. 2015. A great advantage is that FOD represents multiple directions as can be seen in figure 13, which, although still not perfect, is a good way of solving the crossing fibers problem.
Figure 13: CSD FOD Image of the brain (van Hecke et
al. 2016) Figure 14: Showing the difference in accuracy between DTI and CSF. On the left are two images of the dMRI data, in the middle the tensor representation and on the right CSD. Source: bioRxiv
2.6 Fixel-based morphometry
Fixels play a very important role in this project. A fixel is defined as a specific fiber population within a voxel. The orientation and location of each fixel can be computed via segmentation of each FOD lobe. Some diffusion MRI models compute fixels directly and don’t need the extra FOD segmentation step. (Raffelt et al. 2015)
These fixels can be used for different methods of fixel-based analysis (FBA). The one that was used in this project is fixel-based morphometry (FBM). This combines information from within voxel microscopic
fiber density and macroscopic morphology (cross-section). This combined measure is called the fiber density and cross-section (FDC), but these two measures can also be looked at separately. Both fiber density (FD) and fiber-bundle cross-section (FC) are derived from the Jacobian matrix that is used for normalization and template registration by non-linear warping. The combined measure is simply found by multiplying FD with FC. More details on this can be found in Raffelt et al. 2017. In this project these three measures were used to compare glaucoma patients to healthy control subjects.
Figure 15: dMRI image showing the fiber populations in each voxel, called fixels. The color of the fixels can be based on different measures such as FD, FDC or FC. Source: Project data
Figure 16: A schematic representation of a fiber bundle cross section. The grey circles represent axons and the grid represents voxels. Source: Raffelt et al. 2017
2.7 Tractography
Using tensors, FOD, fixels or other higher order diffusion MRI models, a map of the fiber tracts can be made, using tractography. There are two different ways to track fibers, deterministic and probabilistic. Deterministic follows only the most likely route. Probabilistic takes all possible routes. Deterministic tractography looks a lot smaller than probabilistic tractography because of this. The amount of tracts and the maximum angle are variable parameters that determine that path of the tracts in probabilistic tractography. The more limited these are, the
closer the probabilistic tractography will look to deterministic tractography. Probabilistic Tractography is closer to reality in most cases. Only data from the OR was used in this project. To know which voxels are parts of the OR, tractography was used. Tractography of the OR is quite challenging (Benjamin et al. 2014). One of the main problems is that the anterior part of the OR, called the Meyers Loop, has relatively sharp corners, which makes it hard to get the right parameters that include the complete Meyers loop, but do not include non-OR voxels somewhere else. There are also many crossing fibers in Figure 17: Comparison of tractography streamlines. On the left deterministic
DTI streamlines, in the middle CSD deterministic streamlines and on the right CSD probabilistic streamlines. The streamlines in the CSD probabilistic way are closest to reality. Source: Tournier et al. 2012
the OR. Luckily this problem was already tackled before this project was started, so there was a good voxel mask available that could be used to separate the OR voxels. A measure that can be derived from tractography using fixels is the streamline
density. This measure is an important part of this project because the new method discussed in this thesis was based on this. The streamline density is directly related to the number of streamlines that run through a fixel, so the fixel that has the most streamlines running through it will have the highest streamline density.
Figure 18: Schematic of diffusion MRI data, from MRI scan to fixel based analysis.
Figure 19: Schematic of a neuron. Source: Queensland Brain Institute, Australia
2.8 White matter deterioration
White matter deterioration can be described as the progressive loss of function and structure in neurons and cell death. To understand white matter deterioration it is important to understand what neurons are. A neuron (brain cell) has a cell body (soma), an axon and multiple dendrites. The brain contains about 86 billion of these cells, which are connected by about 850.000 kilometers of axons and dendrites. Most of these connections, about 80%, are short range; they are about 680 microns in length on average. The other 20% of connections are long range. These are the global connections with an average length of a few centimeters. These
are myelinated and form the white matter of the brain. It is called white matter because the myelin makes the axons look white. (McCaslin 2018) The purpose of myelination is insulation. Unmyelinated axons are much slower. Neurons connect via their axons and dendrites. The axon of one neuron connects to the dendrites of other neurons. The point where they connect is called the synapse. When two neurons connect, the one sending information, whose axon is part of the connection, is called the presynaptic neuron. The neuron receiving the information with its dendrites is called the postsynaptic neuron. In the visual pathway, the RGC, whose axons form the optic nerve, synapse at the LGN. Here they connect to other cells that form the optic radiation.
Neurodegeneration can be passed on by neurons via synapses, so that could be the reason glaucoma also affects the rest of the visual pathway. But as mentioned earlier, it was recently discovered that it is very likely that glaucoma is not only caused by the deterioration of RGCs, but that there is also a factor in the brain itself contributing to the changes in the visual pathway and visual cortex. The deterioration of the OR and visual cortex is way more extensive than what could be caused by the deterioration of the RGCs and glaucoma has been found to have similarities with cortical atrophy, a subtype of dementia, also called the visual variety of Alzheimer’s disease. They both affect the vision-related parts of the brain. (Hanekamp, 2017)
2.9 Project data
The data that was used to study the optic radiation had already been acquired prior to the start of this project and consisted of dMRI data from 12 glaucoma patients and 15 healthy controls. This data had already been preprocessed (denoising, template registration, etc.). The FOD and fixels were already computed and the data was ready for fixel based analysis.
2.10 Hypothesis
The hypothesis that this thesis proves is that only looking at the fixel with the highest streamline density per voxel that is part of the optic radiation, will give a more significant difference between glaucoma patients and healthy control subjects when looking at the FD.
2.11 Conceptual model
This project was a small step towards curing the leading cause of irreversible blindness in the world, glaucoma. It did so by helping to diagnose the damage in the optic radiation, caused by glaucoma. By being able to tell the state of the optic radiation, it is easier to find the right way to cure the disease.
Glaucoma causes white matter deterioration in the optic radiation. At the moment, the best way to study in vivo white matter integrity is diffusion MRI. The way to use this data used to be DTI. The main problem in DTI is that it takes an average over the whole voxel and it is impossible to study individual fiber populations that share the space of a single voxel. Since most voxels contain these crossing fibers, including the voxels that are part of the OR, the FOD model was used. This is a higher order model that can distinguish between different fiber populations.
Something that would help to make the images better would be to use a higher resolution for the dMRI scan. But because this would require either a better machine that most hospitals don’t have, or an unrealistically long scan-time, this was not a real option to consider. A new method is most valuable if it can be used by most hospitals. To study each fiber population per voxel separately, fixels were used. By comparing all fixels in all voxels that are part of the optic radiation, it was already possible to distinguish between healthy subjects and glaucoma patients. But it was not yet possible for individual subjects. This is why there needed to be a new, more accurate method to do this. An idea that the PhD student that was worked with, Shereif Haykal, came up with was to take only the fixel of each voxel with the highest streamline density in that voxel for all voxels in the OR and use those to compare the two groups. Because these have the most streamlines running through them, they are more likely to be an important part of the OR and therefore are probably more affected and most likely show the most significant changes. This theory was tested and documented in the following chapters. The template that all images are registered to can be seen as the average of all subjects, (but it is a little more complicated than that). This template was also used for tractography,
which was then used to produce a file that contained all streamline density values. To only have the densest fixel in each voxel, a mask that filters out all other fixels in the template was made during this project. This mask was then applied to all individual subject files. Making a mask like this is not a standard function in MrTrix (the software that was used), so this function had to be specially made by looking into the software code and the file structure.
One concern was that the template has streamline densities that are an average of all subjects, so healthy subjects as well as glaucoma patients. If the glaucoma patients get the average streamline density of a fixel down, another fixel might become the densest one in this voxel, even though in only healthy controls there is a denser one, which probably shows more significant results. To fix this problem it would have been possible to make a new template, using only the healthy control subjects. But doing this would have taken quite some extra time (multiple weeks) and according to Shereif Haykal, who has worked with this data for a long time, it would not actually have made much of a difference since the changes caused by glaucoma have such a small influence on the fixel density values that the densest fixel per voxel would probably stay the same for most voxels anyway.
2.12 Research design
A large part of the research contributing to this thesis was actually all the background information documented in the first two chapters. This research has worked towards the following research question and sub questions:
RQ: What methods can be used to better distinguish between the optic radiations of healthy controls and glaucoma patients, using the available dMRI data?
• SQ1: Would including only the fixels with the highest streamline density per voxel be a good method to distinguish between healthy controls and glaucoma patients? • SQ2: What other methods could be used to distinguish between healthy controls and glaucoma patients, using the available dMRI data?
• SQ3: How can machine learning help with the classification of healthy controls and glaucoma patients?
The second big part of research was for the implementation and can be found in the next chapter. Here many things had to
be researched to be able to make the new function that tests SQ1 and part of SQ2. This involved extensive research into existing MrTrix functions, the way this software works and processes data and the way the files store the information as well as some specific coding research. To make sure that it was actually possible to make the function and that there wasn’t already something like this, the problem was posted to the MRtrix community page. The received answer confirmed this. The post and answer can be found in appendix I: MRtrix community involvement.
After finding the best method from SQ1 and SQ2 using a statistical approach, the resulting data was also classified using machine learning in different ways, answering SQ3 in chapter 4: Results.
The last bit of research, mainly mentioned in the conclusion, involved making the script easier to use in the future, preferably being able to run it from the command line like all other MRtrix functions.
3.1 The preprocessing pipeline
The preprocessing pipeline starts with the data that the MRI machine spits out. After this, there is a whole list of things that need to be done before the data can be used for analysis. All of these things can be done using MRtrix, an open-source command-line based software that provides many tools for working with diffusion MRI. The exact steps and commands can be found under documentation on MRtrix.org. The preprocessing was already done before this project started, but it is important to know at least the basics of what happened to the data to be able to understand it and work with it.
The first steps of the pipeline include different types of corrections like denoising, unringing and motion and distortion correction. After these corrections, different normalization, registration and realignment processes are executed. The result is a template file that is produced using all (or a selected part of all) subjects. There is also a file for each subject now that is registered to the template. This includes FOD as well as fixel files. All voxels
are upsampled to have a size of 1.3x1.3x1.3 and they are spatially aligned. The fixels are also reoriented to be aligned. This means that all subject files and the template file have the same voxels and the same fixels that represent the same areas of the brain. They all have fixels that are in the same orientation. Because all images are now in the same space and orientation it is possible to perform different types of analysis. During the normalization and registration process, values for FD, FC and FDC are extracted. These measures are generated entirely from the warps that were generated during registration.
Next, (whole brain) tractography can be performed and streamline densities can be found. All results can be visualized in different ways with the viewing function of MRtrix, mrview. Regions of interest (ROI) can be selected, images can be color-coded and thresholds can be set. A good amount of time was spent for familiarizing with the different viewing options in MRtrix and the different analysis and statistics functions that are executed from the command line.
IMPLEMENTATION
3.2 Programming language
The main language that is used in MRtrix is C++. So programming in this language would make the most sense for the software and this was also suggested by an experienced
user on the MRtrix community platform. Learning and using this language was therefore considered, but after some more research into this language it was decided that it would take too much time to learn,
since it is very different from the known language, Python. This research and a short video tutorial did however help with being able to read and better understand the MRtrix code written in C++.
The next option that would make sense is MatLab. MRtrix has already provided MatLab functions for reading and writing MRtrix files, making it easy to work with. Some more research into this language found that it is quite similar to Python and would not be that hard to learn. But because of the lack of experience in this language it was first researched if it would be possible to use Python instead and save some time.
MRtrix does have a few things written in Python, but looking at those didn’t help much since they were using very complicated code and were hard to understand. The next idea was to look for the possibility of using MatLab functions in Python so it would be possible to use the MatLab functions for reading and writing MRtrix files in Python. Luckily a quick search found that there are multiple options to achieve this. A few different options were tested, before deciding on using ‘’MatLab Engine’’. This is provided by MatLab and is considered the best and easiest way to use MatLab functions in Python.
It might not be the most logical choice to pick Python as the programming language for this project, but it was definitely the easiest one and no problems were experienced with using this language so there are no regrets to this choice.
3.3 MRtrix fixel file structure
MRtrix works with more common fileformats such as the Nifti format, but it also has it’s own file formats. For fixel files, the data is split into multiple files that have to stay together in the same folder to work. This always includes a index.mif or index.nii and a directions.mif or directions.nii file. Apart from these two files there has to be at least one file that contains the actual data.
The index file contains data in a 4-dimensional array. The first three dimensions form a 3D volume that shows the location of each voxel. The first 3D volume in the fourth dimension contains the number of fixels in each voxel. The second 3D volume contains the index of the first fixel in that voxel in the data file. If a voxel has more than one fixel, these are stored sequential to the first one.
The fixel data file and the directions file have three dimensions with size n x p x 1 where n is the total number of elements in the image and p is the number of parameters
per element. In the directions file, p is 3. The directions file only contains all orientations of the fixels. In the fixel data files that were used in this project, p is 1, so the data file could also be seen as a list. Combining the index values from the index file and the values from the data file, the value of any fixel in any voxel can be found. Examples of the type of data the values in the fixel data file represent are streamline density, FD, FDC and FC.
When opening any of these files, a dictionary is returned. The keys in this dictionary are ['dim', 'lognorm_scale', 'MRtrix_version', 'layout', 'datatype', 'data', 'transform', 'comments', 'prior_dw_scheme', 'command_ history', 'vox']. The most important one is obviously the ‘data’ key, as this contains all the actual data in the file. The ‘dim’ key shows the size and amount of dimensions of the data, which is also very useful. The ‘layout’ key can also be interesting, because where is location (0, 0, 0)? It could be any corner of the 3D image, or maybe even the center. The layout key has a way of showing how the data is arranged. More information on how this works and on what the other keys show can be found under documentation on MRtrix.org. To see how the files were explored during this project, see appendix A: File analysis.
3.4 Creating the script
To create the masks, the fixel files with streamline density values that only contain the fixels of the optic radiations were used. Those are separate for the left and right optic radiation. The index.mif file was also needed. The files with only the data from the optic radiations were used to reduce the amount of data that had to be put through the program, compared to using values from the whole brain. To be able to use this mask on any subject file, it is a binary mask, containing only values of 1 and 0. So input files were:
• L_OR_fixel_mask.mif • R_OR_fixel_mask.mif • Index.mif
The complete code can be found in appendix B: Creating the fixel masks. Pseudocode can also be found in the appendx, appendix H: Pseudocode. This chapter will explain what the code does and why.
After the files are imported, the data part of each of the three files is extracted. The data from the ORs is put in two lists to make it more easily accessible. There are also two new lists made, these will be edited later on to form the new files. When they are made they only contain zeros.
The next part is the most important. Here, the program loops through each voxel. For each voxel, the number of elements (or number of fixels) and the index of the first element (or fixel) is found. These come from the index.mif file. The code in the appendix creates a mask for the 5th densest fixel, but this code can be used for any order of density, also the densest, with very little changes. To simplify this explanation, we will assume we’re creating a mask for the densest fixel. In this case, any time the number of elements in a voxel is zero, we are not interested in this voxel because there are no fixels in it. If there is one fixel in a voxel, this is automatically the densest one. Using the index number, we know where we can find the value of this fixel in the data file. In the new list that was made before, containing only zeros, the zero with the corresponding index is now turned into a one. If a voxel has more than one fixel, the number of elements will be 2 or higher. If this is the case, the program goes into the data file and finds all values of the fixels in this voxel. Now, the one with the highest value (densest) can be found, and with it it’s index. So again, the zero in the new list with the corresponding index will be turned into a one. This goes on until the program has looped through all voxels. Then the new list is turned back into the right format and the new MRtrix file is written to a specified location. This happens for both the left and the right OR at the same time.
A problem that came up was that these new files still had values everywhere in the brain and it wasn't immediately clear why, so another binary mask including only the OR was compared to it creating a new mask that takes the minimum value for each fixel from the two input masks. This was done by using the MRtrix command ‘mrcalc L_OR_5th_densest_fixel_mask.mif L_OR_fixel_mask_thr_1.mif –min new_L_ OR_5th_densest_fixel_mask.mif' in the terminal. Luckily it has been figured out what caused this problem and it has been fixed. What happend was that the index file still included all fixels of the whole brain, even though the values corresponding to these non-OR fixels were zero because they were filtered out of the files. The index file said that there were more than zero fixels in a voxel, so the densest one, even if it had a value of zero, got the value one in the new mask. To fix this, a simple check to see if the densest fixel has the value zero was added and if that is the case, the voxel will be ignored and the value of all fixels in that voxel will stay zero. To be able to use the new masks, they need to be in a folder containing the index.mif and the directions.mif files that were in the folder of the input files. For fixel images of the different fixel masks, see appendix F: Mask images.
4.1 Statistics
The data was visualized using box-and-whisker plots and it was tested for the significance of the difference between the two groups using a univariate general linear model and correcting for age. The p-values and effect size from this can be found in figure 22. The second statistical analysis was an ROC curve for each OR, shown in figure 25 and 26. These analyses were done for different values, but each time included only one value per subject per (left or right) OR. This value was the mean of all (FD, FC or FDC) values included in the particular mask. FD, FC and FDC are stored in fixel files in the same way the streamline density is. To get the mean the MRtrix command ‘mrstats’ was used. After all these values were extracted, they were put into SPSS to perform the different analyses. The plots and numbers shown in this chapter only show results using the FD, because this was the only measure that gave interesting results. In FC and FDC no significant difference can be found between the two groups, no matter which mask is used. This shows that the FC in the optic radiations is not significantly affected by glaucoma.
Looking at the first analysis, a clear improvement can be seen using the first order mask. The p-values are lower than with the old mask that included all fixels and the effect sizes are higher. Fourth and fifth order masks are not shown here but they were also made, those gave very bad results due to the fact that the fourth order masks contained less than 10 fixels for each OR, the fifth order masks did not contain any fixels in both the left and the right OR. See figure 21 for the amount of fixels in each mask. It makes sense that the second and third order masks show less difference between glaucoma patients and healthy subjects because the first order mask showed such an improvement. This means that values that usually cause the difference to be less significant have been filtered out. These filtered out values have to be the other fixels, which are now put in the second, third and fourth order masks.
The improvement with the 1st order mask in the right OR is especially interesting because this brings the p-value from not significant (>0.05) to significant (<0.05). So here the new mask is not only proving that it is better to look at just the densest fixels, it also proves
RESULTS
that glaucoma has a significant effect on the fiber density in the right OR.
The ROC curve and the AUC are another way to see how different two sets of values are and to see if it is possible to find a good cut-off value. It shows how well a certain cut-off value would work to classify the data. The value that is closest to the top left corner is the one that classifies the most data in the right way. A bad curve that represents random classification would be a diagonal line from the bottom left corner to the top
right corner. This analysis shows a slight improvement with the first order masks, but none of the masks makes it possible to classify well by just choosing a cut-off value.
4.2 The difference between the left
and right optic radiation
A pretty large difference between the left and right OR can be observed in the results. A difference between the two has been found by more researchers, however this is not always on the same side. (Li et al.
Figure 22: P-values and effect sizes with different fixel masks
Figure 21: The amount of fixels that are included in each mask.
Figure 23: Box-and-whisker plots representing the FD data from the left optic radiation of glaucoma subjects and healthy controls for the original fixel mask, the first order mask, 2nd order mask and 3rd order mask.
Figure 24: Box-and-whisker plots representing the FD data from the right optic radiation of glaucoma subjects and healthy controls for the original fixel mask, the first order mask, 2nd order mask and 3rd order mask.
Figure 25: ROC curves for the FD data with all four masks from the left optic radiation and values for the AUC. The first order mask shows a slight improvement.
Figure 26: ROC curves for the FD data with all four masks from the right optic radiation and values for the AUC. The first order mask shows a slight improvement.
2014) In glaucoma one eye is usually more affected than the other eye. In appendix J: Glaucoma subject eye tests, a table of eye tests of the glaucoma subjects is included but this cannot explain the difference. As shown in chapter 1, figure 3, each OR does not represent one eye, but rather one side of the visual field of both eyes. Visual field tests were also analyzed but no significant difference between the left and right visual field was found. It is most likely that the difference found here is a coincidence that has occurred because of the small group of subjects where, on average, glaucoma must affect the left OR more than the right OR which does not necessarily mean that the right optic field is more affected, this could just be the brain factor of glaucoma showing.
4.3 The second densest fixels in the
right optic radiation
The second densest fixels in the right optic radiation show something unexpected. They show a significant difference between the two groups that is even more significant than the difference in the densest fixels. But the difference in the second densest fixels is the other way around, meaning that the fixels from the glaucoma group have a higher FD than the healthy controls. Because this is a highly unexpected result, the correctness was checked with other tests but those gave the same results. No good explanation
for this could be found, so this result was presented to the other researchers at the lab. Possible causes that were brought up were that it might be because of the feature selection and the correlation between FD and streamline density or that it is another tract going to a different part of the brain in that location, since all significantly different fixels included in this mask are clustered in the same region. It could also be a coincidence caused by the small amount of subjects. It was suggested to look at the correlation between FD and streamline density, look at the FA in the region with the significantly different fixels and to do the same analysis on different tracts in the brain to see if it happens in other regions too or if it is specific to this tract.
4.4 Location of significantly different
fixels
The fixels that have the greatest effect on the difference between the two groups are the fixels that show a significant difference between the two groups. These are visualised in figure 27, 28, 29 and 30. Here you can see that for the densest mask, the significantly different fixels run in the direction of the OR, but most are at the middle/straight part. The reason for this is probably that these areas include less crossing fibers and are therefore easier to identify.
4. RESULTS
v
4. RESULTS
4.5 Machine learning
Because the differences between the data belonging to the two groups are fairly small, it is not possible to correctly classify with the data used for the statistical analysis, which used the mean. To make a good classifier, machine learning was tried in a few different ways. All code used for the machine learning can be found in appendix C: Machine learning, appendix D: Machine learning with histograms and appendix E: Comparing features.
For the statistical analysis only one value per subject was used, but with machine learning it is possible to compare the subjects for each fixel separately and build a classifier that way. This was done using the FD data from the first order mask, because this showed the best results in the statistical analyses. The only problem here was the number of subjects. There were only 27 subjects, but each subject contained values for about 7000 fixels, which means 7000 features, or dimensions, in the model. This causes a massive overfit.
It was possible to build a classifier that classifies the data with 100% accuracy using a support vector machine (SVM) when using all data to train the classifier. When splitting the data into a training and a testing set with 22 subjects in the training set and 5 subjects in the testing set, the classifier performed very bad, only getting 60% right, which can
To reduce this enormous overfit, histograms were used in another SVM. In this classifier, the fixels were not compared to each other on a spatial level. All values were sorted into a histogram for each subject and those histograms were compared to each other for classification. This classifier performed very well, even with the data split into the same training and testing groups as in the previous SVM. It even worked fairly well with a low number of buckets. Results with different numbers of buckets and different C values can be found in appendix D: Machine learning with histograms. These results show that this method could make a good classifier once data from more subjects is collected. 27 subjects are still far too few to build a reliable classifier in this case because the difference between the two groups is so low. Data with this number of subjects can only build a good classifier if the two groups are different enough. For this project more subjects are needed in the future.
Out of curiosity the different features from the machine learning with histograms were compared in a scatterplot to see if there was a visible difference and maybe find the most important features for classification. It was found that some of the features showed a more significant difference, but none were perfect. These results can be found in appendix E: Comparing features.
CONCLUSIONS AND
RECOMMENDATIONS
5.1 Conclusions
The results have proven the hypothesis that only looking at the fixel with the highest streamline density per voxel that is part of the optic radiation, will give a more significant difference between glaucoma patients and healthy subjects when looking at the fiber density. This also answers the research question ‘What methods can be used to better distinguish between the optic radiations of healthy controls and glaucoma patients, using the available dMRI data?’ SQ1, ‘Would including only the fixels with the highest streamline density per voxel be a good method to distinguish between healthy controls and glaucoma patients?’ can now be answered with yes.
This outcome became clear in chapter 4.1 where the data visualization with box-and-whisker plots and the corresponding p-values from the univariate general linear model showed a clear improvement when using the first order masks for both the left and the right optic radiation. For the right optic radiation the p-value wasn’t even significant before using the mask, so here the mask did not only prove that the using the
mask gives better results, it also proves that the fiber density is significantly affected by glaucoma in the right optic radiation.
SQ2, ‘What other methods could be used to distinguish between healthy controls and glaucoma patients, using the available dMRI data?’ was also answered chapter 4.1. As explained in chapter two, the three measures that can be taken from fixel files are FD, FDC and FC. All three of these were analyzed with the statistical methods mentioned in chapter 4.1 and it was clear that FC and FDC did not show a significant difference between the two groups. All three of these measures were analyzed with all different masks, the left and right OR seperately. The old mask that includes all fixels of the optic radiation, the first order mask that includes only the densest, the second order mask that includes only the second densest, the third and the fourth order masks.
Using all 10 masks mentioned and all three of the fixel related measures includes all relevant ways of analyzing the available data. These are the only measures that can be derived from fixels. Using data from earlier in
the pipeline would not make sense because the data is not normalized and aligned, so it would be impossible to compare subjects to each other. Other measures that would work on the aligned data such as FA and MD only include measures that average over the whole voxel, which would make the data a lot less precise and therefore less likely to show any differences between the two groups. SQ3, ‘How can machine learning help with the classification of healthy controls and glaucoma patients?’ was answered in chapter 4.5 where machine learning options were explored. From this it can be concluded that using histograms together with a larger group of subjects to train the algorithm could probably build a reliable classifier to identify if a new subject has optic radiations affected by glaucoma.
5.2 Recommendations
Something that is very important to keep in mind through this whole research is the small sample size of 27 subjects (12 glaucoma, 15 healthy). That theories are proven in these 27 subjects shows that it would probably be true for bigger groups as well, but to really prove the theories, it would be good to do the same tests on a much bigger group of subjects, this should be the next step. Having more subjects will also make the machine
learning more reliable and it could make it possible to build a reliable classifier that can be used to identify optic radiations affected by glaucoma in the future.
Another improvement would be to make it possible to run the script from the command line. Different ways to do this were already tried, but didn’t work so far. These can be found in appendix G: Simplifying the script. An improvement that could also be part of this could be to make the script in a way that it doesn’t need MatLab to work. At the moment this is not possible, since there is no MRtrix function to import MRtrix files into python. It is possible to convert the MRtrix files into NifTI files, and import those into python, but the files used for this project are too large and can’t be exported with the most recent python toolbox for importing, editing and exporting NifTI files. The problem of using the MRtrix MatLab functions when running the script from the command line was posted on the MRtrix community forum. They couldn’t figure out what the problem is, but did mention that in the future they might make a python function to read and write MRtrix files, which would be very useful for this project if it is further developed in the future.
It would also be interesting to figure out the unexpected results mentioned in chapter 4.3
about the second densest fixels in the right optic radiation being significantly different, but with the glaucoma group being denser. It would be interesting to see if this also happens in other fiber bundles and if this still occurs with a larger group of subjects.
5.3 Ethics
No one was harmed in any way by this research, all test subjects participated voluntarily and were allowed to stop participating at any moment. The data was anonymized and handled carefully. It was kept in one place to make it easy to erase if needed and it was not put on any personal laptops or computers or online.
This project has contributed to developing a better understanding of glaucoma, the leading cause of irreversible blindness, helping professionals as well as patients. If the method is developed further in the future, following the recommendations from chapter 5.2, it might be helping the millions of people who are affected by glaucoma when used in the development of treatments.
DEFINITIONS AND
ABBREVIATIONS
AD Axial Diffusivity
AUC Area Under Curve
CSD Constrained Spherical Deconvolution
CSF Cerebrospinal Fluid
DTI Diffusion Tensor Imaging
FA Fractional Anisotropy
FBA Fixel Based Analysis
FBM Fixel Based Morphometry
FD Fiber Density
FDC Fiber Density and Cross-section
FC Fiber-bundle Cross-section
Fixel A specific fiber population within a voxel FOD Fiber Orientation Distribution
GM Grey Matter
HARDI High Angular Resolution Diffusion Imaging
IOP Intraocular Pressure
LGN Lateral Geniculate Nucleus
LOR Left Optic Radiation
MD Mean Diffusivity
MRI Magnetic Resonance Imaging
dMRI diffusion MRI
NTG Normal-Tension Glaucoma
OR Optic Radiation
ROC Receiver Operating Characteristic
ROI Region Of Interest
ROR Right Optic Radiation
RQ Research Question
SVM Support Vector Machine
SQ Sub Question
Voxel Three Dimensional Pixel/Volume Element
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